Plato's Magnesia and philosophical polities in Magna Graecia

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Content PLATO’S MAGNESIA AND PHILOSOPHICAL POLITIES IN MAGNA GRAECIA by Phillip Sidney Horky A Dissertation Presented to the FACULTY OF THE GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (CLASSICAL PHILOLOGY) August 2007 Copyright 2007 Phillip Sidney Horky ii EPIGRAPH pa~sai te&xnai brotoi~sin e)k Promhqe&wj. Aeschylus, Prometheus Bound, 506. iii DEDICATION TO MY MEERMA AND BAMPA iv ACKNOWLEDGEMENTS This project began, appropriately enough, with a student, a teacher, and a book in January, 2005. It has been brought to maturity thanks to the financial support of the Department of Classics and the College of Letters, Arts, and Sciences at the University of Southern California. Research and writing were conducted in the United States (Los Angeles, CA and Claremont, CA) and in Italy (Chieti and Taranto). Principal thanks go to the libraries and institutes that have provided havens for thoughts and impressions: the Edward L.Doheny Jr. Memorial Library and the Hoose Library of Philosophy at the University of Southern California, the Claremont Colleges Libraries, the Charles E. Young Research Library at UCLA, and libraries at the Istituto per la Storia e l’Archeologia della Magna Grecia and the Sopraintendenza per i Beni Archeologici per la Puglia di Taranto. I find myself incapable of distributing appropriate justice to the many scholars and friends who have supported me in this project, and I fear that the attempt to render gratitude, like the project of creating an ideal polity, is doomed to fail from the beginning: it leaves some feeling underappreciated, others wary of excess praise. Alexander Pope, in the Temple of Fame (1711), expresses the enigma well when describing an inscribed stele that he has chanced upon: Nor was the Work impair’d by Storms alone, But felt th’Approaches of too warm a Sun; For Fame, impatient of Extreams, decays, Not more by Envy than Excess of Praise. Despite my fears, this project should in no way be considered an engraved rock, no Mesopotamian monarch’s account or Spartan tombstone: it does not, I hope, stand as v a monument of death in writing. Instead, it represents life and change, a confluence of many voices, and while this work attempts to be a symphony of sorts, I am responsible ultimately for this performance. Those who have lent me heart and courage in addition to intellectual stimulus for this project – both in conversation and in written correspondence – include: Gabor Betegh, A.J. Boyle, Walter Burkert, Bryan Burns, Jacco Dieleman, Vincent Farenga, Catherine Gilhuly, Lucas Herchenroeder, Carl Huffman, Richard Janko, Susan Lape, Beau Lindsay, G.E.R. Lloyd, Claudia Moatti, Kathryn Morgan, Josiah Ober, Grant Parker, Werner Riess, Chiara Sulprizio, and Ari Zatlin. M.S. Lane has read significant portions of this dissertation and always provides inspiration and useful advice. Special thanks go to E. Del Chrol, Robert Germany, Grant Nelsestuen, Philip Purchase, and David Wible, without whose intellectual and moral support this dissertation, indeed this career, would never have come to fruition. Several of the basic premises of this dissertation were tested out on classes taught at UCLA and Claremont McKenna College, and I thank my excellent undergraduates who lent a critical ear. Some of the ideas developed in Chapter 6 were presented in San Diego at the American Philological Association annual meeting in January, 2007 at a panel titled Words Matter: Language and Other Physical Sciences in Greco-Roman Traditions, whose participants were Brooke Holmes, Edward Schiappa, and David Timmerman. I thank them and the members of the audience for their questions and suggestions. A greater debt of thanks goes to my dissertation committee: Thomas N. Habinek, Kevin van Bladel, Ronald Hock, Christopher Bobonich, and my director vi William G. Thalmann. They are as varied and dappled as their comments: this dissertation cannot hope to imitate the choice elegance of Professors Habinek and Bobonich, nor can it sufficiently respond to the provocative challenges of Professors van Bladel and Thalmann; it cannot claim to pluck the moment as warmly and gently as Professor Hock has done. If I have failed to achieve the summits that lead beyond words to the light that lies beyond, let posterity never forget the paths that my teachers have tread for others to follow. Nobody deserves greater thanks than my own genos: my fidanzata Eliana, che ha sempre detto le cose giuste al momento giusto, my brother and sister-in-law Stan and Jaime Harper, my incomparable parents Stanley and Lucinda Horky, who have always succeeded in imparting upon me the most important element of education (love), and my grandparents Edsel and Marjorie Harper, to whom this dissertation is dedicated as a reflection of their humble and remarkable life of shared discovery. vii TABLE OF CONTENTS EPIGRAPH ii DEDICATION iii ACKNOWLEDGEMENTS iv LIST OF FIGURES ix NOTE ON CITATIONS AND ABBREVIATIONS x ABSTRACT xi INTRODUCTION: Platonopolis Founded 1 CHAPTER 1: Searching for a Third Term: The Traditions of Pythagorean Philosophy and Politics in the 5 th Century BCE Reassessed 26 The “So-Called Pythagoreans” and the Followers of Hippasus of Metapontion 55 The Third One: Philolaus of Croton and Pythagorean Participation 71 CHAPTER 2: The Mathematical Practicals: Plato’s Dialectical Revision Of Pythagorean Science in the Republic 96 CHAPTER 3: The Paradeigmatic Response: Mathematics and Dialectic in Plato’s Theaetetus, Parmenides, Sophist, and Statesman 151 Problems in Extensions: Plato’s Theaetetus and Parmenides 152 Dialectic Reassessed in the Sophist and the Statesman (Through the Myth) 169 CHAPTER 4: Mixing the Constitutions: Southern Italian Lawgivers and Plato’s Radical Cities 208 Philosophical Colonies of Magna Grecia: Theoretical Models 238 The Ideal Polities of Plato’s Timaeus-Critias 253 CHAPTER 5: The Magnesian Rock: from Radical to Mathematical City 269 Cyclical Dialectic and Political Weaving in the Statesman 271 viii Measured Pleasure or Pleasure Measured? Dialectic, Musicology, and Metaphysics in Plato’s Philebus 320 CHAPTER 6: The Tarentine Tapestry: Magnesia and Philosophical Polities in Magna Graecia 354 Plato’s Sketches for the “Second-Best” Polity and the Mixed Constitution of Magnesia 356 Archytas and Political Weaving: the Peplos of Zeus and Political Leveling in Plato’s Laws and the Archytan On Law and Justice 382 EPILOGUE: The City-State Commensurate 415 BIBLIOGRAPHY 422 ix LIST OF FIGURES Figure 1: Map of Magna Graecia and Sicily 15 Figure 2:The Soleto Map 15 Figure 3: Plan of the Ekklesiasterion II of Metapontion 223 Figure 4: 1 st (Revised) Definition of the Statesman (Pl. Plt. 258c3-276e8) 278 Figure 5: Definition of the Art of Weaving (Pl. Plt. 281d8-283a8) 288 Figure 6: Diagram of Modes Derivable from the Dorian Diatonic 340 Figure 7: Diagram of the Geometric Mean with Applied Motion 390 Figure 8: Diagram of Ideal Arithmetic Mean with Applied Motion 391 Figure 9: Circular Monumental Meeting-places in the Ancient Greek World 393 Figure 10: Tarentine Coinage Exhibiting Taras, the Eponymous Founder of the City 408 x NOTE ON CITATIONS AND ABBREVIATIONS For ancient works, I have generally employed the standard citation format of the Greek-English Lexicon of Liddell and Scott (LSJ), when possible. Not all ancient texts are featured in LSJ; so, where necessary, I have attempted to abbreviate the Latin titles of ancient works myself. Fragments are referred to by the name of the editor, e.g. Empedocles F 1 Wright = Empedocles, Fragment 1, edited by M.R. Wright. I have only abbreviated the titles of a few modern scholarly works: DK H. Diels. 1952. Die Fragmente der Vorsokratiker. 6 th Edition. Revised by W. Kranz. Berlin. IG Inscriptiones Graecae. 1873 – . Berlin. KRS Kirk, G.S.; Raven, J.E.; Schofield, M. 1983. The Presocratic Philosophers: A Critical History with a Selection of Texts. Second Edition. Cambridge. SIG Sylloge Inscriptionum Graecarum. 1915-24. Edited by Dittenberger. xi ABSTRACT Since Aristotle’s Metaphysics, scholars have recognized the influence of the Pythagoreans on Plato’s ontological theories; less well-known is the impact of the Pythagoreans’ theories of rule in the development of Plato’s political philosophy. Plato’s three visits to Magna Graecia and Sicily (ca. 388, 367, and 361 BCE) exposed the Athenian philosopher to political communities that had been established and given counsel by Pythagorean philosophers since the end of the 6 th Century BCE. This exposure catalyzed revisions to Plato’s entire philosophical program (pragmateia) in response to the political and ontological theories of the mathematical Pythagoreans, especially the heretic Hippasus of Metapontion and his followers in Southeastern Italy. Plato’s post-Republic works, including the Theaetetus, Parmenides, Sophist, Statesman, Timaeus, Critias, Philebus, Epistles VII and VIII, and Laws, demonstrate Plato’s recurring engagement with and adaptation of the philosophical principles – derived from mathematics – of the Pythagoreans Philolaus of Croton and Archytas of Taras, who led the massive Italiote League from 367-361 BCE. Indeed, the political constitutions established by Pythagoreans and other philosophers in Magna Graecia, especially those of Epizephyrian Locri, Thurii, Heracleia Italica, and Taras, provided Plato with models from which to derive his own proposed colonial polity of Magnesia in the Laws. The polity of Magnesia, a mixed constitution of the aristocratic type, finds its closest analogue in Taras, which, as a mixed constitution of the democratic type, presented a competitive political system that was influenced by the philosophy of Plato’s friend and rival Archytas. xii By evoking and modifying the philosophy of “mixture” advocated by the mathematical Pythagoreans, Plato was able to reconcile the ontological schism between Being and Becoming and its political analogues in the “first-best” ideal polity of Kallipolis in the Republic and the “second-best” imitative polity of Magnesia in the Laws, thereby providing both an answer to the problems raised against his Theory of the Forms in the Parmenides and a means to resolve the issue of incommensurability in the city-state. Thus, Plato’s entire philosophical program (pragmateia) was demonstrably affected by the ontological and political philosophy of the mathematical Pythagoreans Hippasus of Metapontion, Philolaus of Croton, and Archytas of Taras. 1 _______________________________________ INTRODUCTION: PLATONOPOLIS FOUNDED _______________________________________ )Eti&mhsan de_ to_n Plwti~non ma&lista kai_ e)se&fqhsan Galih~no&j te o( au)tokra&twr kai_ h( tou&tou gunh_ Zalwni&na. (O de_ th|~ fili&a| th|~ tou&twn kataxrw&menoj filoso&fwn tina_ po&lin kata_ th_n Kampani&an gegenh~sqai legome&nhn, a!llwj de_ kathripwme&nhn, h)ci&ou a)negei&rein kai_ th_n pe&ric xw&ran xari&sasqai oi)kisqei&sh| th|~ po&lei, No&moiv de_ xrh~sqai tou_j katoikei~n me&llontaj toi~j Pla&twnoj kai_ th_n proshgori&an au)th|~ Platwno&polin qe&sqai, e)kei~ te au)to_j meta_ tw~n e(tai&rwn a)naxwrh&sein u(pisxnei~to. Kai_ e)ge&net’ a@n to_ bou&lhma e)k tou~ r(a~|stou tw~| filoso&fw|, ei) mh& tinej tw~n suno&ntwn tw~| basilei~ fqonou~ntej h@ nemesw~ntej h@ di’ a!llhn moxqhra_n ai)ti&an e)nepo&disan. The emperor Gallienus and his wife Salonina bestowed honor and veneration in extreme measure upon Plotinus. And he, making use of their friendship, thought it a worthy exploit to revive a city of philosophers said to have been in Campania which had fallen into ruin and to bestow the arable land around it upon the city once it had been founded; and, further, that the future inhabitants should employ the Laws of Plato and name the city Platonopolis. And he himself undertook the migration of himself and his friends to that place. The philosopher would have achieved his dream easily, if some of the king’s courtiers, compelled by jealousy, spite, or some other base motive, had not prevented it. (Porphyry, On the Life of Plotinus and the Order of his Books 12.1-13) If a conventional view has pervaded the recent history of political philosophy that ancient philosophers had little interest in the actual development and sustenance of ideal city-states, it is founded upon two fundamental misinterpretations: that philosophical polities were simply ideal and that noetic philosophers always defined themselves against political actors. Such a conceit became pervasive following the 2 death of Socrates of Athens (399 BCE), and it formed a significant body of discussion among all the major schools of philosophical thought; it is what we might want to consider one of the most popular, and tangible, forms of philosophical dualism: 1 the Philosopher, whose compass was demarcated by matters that were, by nature, infinite and indivisible, was expected to keep his distance from the corrupting and potentially deceitful influence of practical politics. So goes the teaching of Socrates throughout the early-middle Platonic dialogues, from the Gorgias through the Theaetetus. 2 The philosopher’s sphere of understanding was the Intelligible, which always exists and is represented by the world of the Forms; the politician, on the other hand, was expected to live in the world of change, which is comprehended by examining sensible phenomena. This is a primary schism for Plato’s philosophy in the Republic, and the process of negotiating between Being and Becoming, i.e. between things that exist and do not change and things that are in a constant state of change, was an issue for Plato throughout his middle dialogues. Indeed, the issue of diaeresis – the process of separating out two things that are essentially different (and often oppositional) – is at the core of Plato’s dialectical method, both in terms of its place within the education of the student and in what we might understand to be the 1 The issue of binarisms is central to Plato’s philosophical thought. His interest in the problem of the Monad and the Infinite Dyad/Plurality might be considered an attempt to reconcile his own theories of physics/metaphysics with the Pythagoreans’ “Table of Opposites,” as reported by Aristotle (Metaph. 986a22) and others. See Burkert 1971: 52-3 with n. 119. 2 See Plato, Theaet. 173c6-d9. Cf. Phileb. 62a-d and Gorg. 517b2ff., where Socrates’ discussion of the usefulness of certain Athenian statesmen to the polis introduces a short monologue on the dualistic nature of pragmatics. For a reasonable discussion of the dating of Plato’s middle and late dialogues, see Bobonich 2002: 482-3 n.8. I follow Charles Kahn’s (1996) system of dating through stylometry and argumentative consistency, which posits a latest group comprised of Critias, Laws, Philebus, Sophist, Statesman, and Timaeus; a preceding group, which includes the Parmenides, Phaedrus, Republic, and Theaetetus, seems to me to have been composed before Plato’s third visit to Tarentum, in 361 BCE. 3 dominant aspects of Plato’s theories about reality, his ontology. 3 What is more, at stake in the distinction between the philosopher and the statesman is the entirety of Plato’s ethical system as adapted from the teachings of Socrates: Socrates himself was not as notable a practitioner of politics as he was a practitioner of wisdom. 4 But we cannot forget what this anachronism – this foreign element, the Socratic apolitical actor – posed to a tense and unstable Athenian democracy during that final tumultuous decade of the 5 th Century BCE. Socratic philosophy and ethics continued to live on in the writings and on the lips of his students, but Socrates the man died, and it may be said that he died as a consequence of his disdaining to integrate successfully his systems of ethics and religion with the political reality that was a democracy dominated by the power of rhetoric. Such is the picture painted by our earliest extant sources, Xenophon and Plato; such is the image we should never forget as it was imprinted in the memory of the nephew of Critias. That Plato was considerably more engaged in political theorization than his teacher Socrates can be assumed from the increased politicization of his writings as he grew older and began to look elsewhere for models of the good and happy way of life. This interest in politics went hand in hand with Plato’s revision of his entire philosophical program (pragmateia), with particular attention to the place of 3 That is to say nothing of Aristotle in Book II of the Politics, whose recurrent criticism of Socrates in the Republic and the anonymous authority behind the Laws (Aristotle refuses to call him Plato or Socrates) is presented as a lack of precision in defining terms through proper modes of dialectic. See, e.g. Pol. 1261a14-15 and 1264b27-41. Such modes of diaeresis remind us of the influence of Eleatic philosophy, located in northwestern Magna Graecia, upon Plato, especially the argumentative paradigms championed by Zeno of Elea and subsequently parodied by Plato in the Parmenides. 4 This despite the fact that Socrates declares in the Gorgias (521d6-8) that he is “one of the few, if not the only one, who makes an attempt at the political art as it is in truth and practices politics.” See Klosko 1986: 26-30 for Socrates’ political views and activities in Athens. 4 mathematics in his philosophy. In the Metaphysics, Aristotle presents a diachronic history of Plato’s philosophical career: the education into concepts derived from Cratylean and Socratic doctrine was modified by the investigation into sensibles by positing a relationship between Forms and sensibles based on the concept of “participation” (me&qecij). 5 The result, so claims Aristotle, was an intermediary class of things called “the mathematical practicals” (ta_ maqhmatika_ tw~n pragma&twn). 6 In essence, my project is an expansive and comprehensive exegesis of that statement and its relationship to Plato’s political philosophy. The idealization of the city-state and of the statesman, so central to the sketches that the major Platonic political actors (Socrates, the Eleatic Stranger, Timaeus of Epizephyrian Locri, the Athenian Stranger) give, goes hand in hand with Plato’s interest in fortifying, sustaining, and making commensurate a comprehensive and complete philosophical program, or pragmateia (pragmatei&a): this includes all the spheres of methodological application that are documented in Plato’s later dialogues. 7 Likewise, I will document how shifts in his philosophical pragmateia led to profound revisions of his political theories. At issue for Plato’s ontological and political philosophy, as well as for his student and critic Aristotle, was perhaps one of the most central dichotomies to all ancient philosophy: the difference between unity and plurality. 8 The negotiation of unity and plurality was an issue of profound interest to Plato’s post- 5 Arist. Metaph. 987b13. 6 Arist. Metaph. 987b15-16. 7 Primarily the basic “arts (texnai&)” that are responsible for the promotion of a philosophical city- state: the many forms of mathematics (or “measurement”), dialectic, Formal Theory, and especially political weaving. 8 This problem, of course, goes far back in the history of philosophy before Plato. The issue of unity versus plurality is central to Parmenides’ thesis. See Chapter 3. 5 Republic Theories of the Form, as I will demonstrate later in this project. But the terms were political as well: in the early and middle dialogues of Plato, the ideal city-state is unified, eternal, commensurate, and complete; the practical polis, on the other hand, is pluralistic, irrational, succumbs to change and requires investigation into the legitimacy both of its origin (a)rxh&, which also means “first principle,” “rule,” and “governance”) and its future goals. This fundamental set of opposite traits – here configured politically as the relationship between the ideal polity and the practical polis – also influences Aristotle when he considers the possibility of the Platonic polity – what Plotinus later calls Platonopolis 9 – in Book II of the Politics, where Aristotle summarizes and criticizes the two signficant Platonic polities: Kallipolis in the Republic and Magnesia in the Laws. An insurmountable problem for the Platonic polity, as Aristotle construes it, 10 is that its tendency towards unity presents a conflict of definition: What is more, in regard to the goal which he declares should be the undertaking of the polis, as it is said then, it is impossible; and, how one should achieve it, is never explained. I am talking about the city being fully unified as best/nobly (w(j a!riston) as possible, for Socrates takes this as his premise. And yet it is clear that, as it progresses and becomes more ‘one,’ it will not be a city at all; for a 9 With which city-state does Plotinus’ imagined polis correspond? Platonopolis, as Porphyry presents it, is too nondescript to elicit a definitive answer, but the emphasis on the arable land is more suggestive of Magnesia in the Laws: in Kallipolis, farmers form part of the lowest class of Producers, and Socrates does not emphasize their significance to the city-state at length (R .369ff.); in the Laws, however, all citizens are expected to own fields and supervise their own private slaves who farm the land (806d). See O’Meara 2003: 15-16. The actual ancient philosophical city-state in Campania to which Plotinus is referring is perhaps Elea (Velia), which Strabo (6.1.1) tells us was legislated by Parmenides and Zeno, who in Strabo’s opinion were Pythagoreans. See Sartori 1953: 105-7. 10 Despite being so critical of Plato’s and Socrates’ methods of definition and diaeresis, Aristotle tends towards conflation of terms that are considered otherwise distinct in other authors when he discusses political systems. Examples of conflations include Aristotle’s treatment of the ideal “Socratic” polity of the Republic, the “second-best” polity of the Laws (1265a1-11), and the Spartan and Cretan polities (Pol. 1269a29-34 and 1271b20-1272a14). 6 state is some number naturally, and if it becomes more ‘one,’ it will be a household from a city, and then a human being from a household, for we should declare that a household is more ‘one’ than a city and that the individual is more ‘one’ than a household; the result being that, if someone were able to do this, he must not do it, for he will destroy the polis. And not only is a polis composed of many people, but even of people differing in Form (ei!dei). For a polis cannot become so from persons alike. 11 If, on Aristotle’s view, the polis advances toward unity, then it ceases to exist as a plurality, and therefore it ceases to be a polis at all: such a criticism marks a departure from Socrates’ insistence on the categories of analogy that pervade Plato’s work, most especially the analogy between the ideal polity and the constitution of the soul. 12 Aristotle’s challenge to Plato is a general objection to the dualistic paradigm as it is formulated in Plato’s middle dialogues. What is more, Aristotle casts doubt on the notion that the unity of a polis should be a defining characteristic of the “best” (a!riston) constitution. 13 Criticisms of philosophical method aside, Aristotle’s censure of Kallipolis is also practical: his attack on the ideal city-state imagined in Plato’s Republic focuses on the insufficiency of the schema that outlines common property for the Guardians to promote unification for the polis; in a passing note, he mentions that “it seems more useful for the Farmers to hold their women and children in common than for the Guardians.” 14 It is true that Socrates is less explicit about what the social 11 Arist. Pol. 1261a13-25. 12 For a recent useful, if debatable, treatment of this subject, see Ferrari 2005. 13 Arist. Pol. 1261b16-19: “Nay, indeed, even if it is best [a!riston] for the community to be ‘one’ as much as possible, this does not seem to be clarified by the argument ‘if all (people) say mine and not mine at the same time.’” 14 Arist. Pol. 1262a39-1262b1. 7 organization of the class of Farmers/Producers will be in Kallipolis, 15 a criticism that Plato probably took seriously when composing the Laws. 16 Even so, Aristotle seems intent on showing the deficiencies of both states – Kallipolis and Magnesia – in the same “Platonic” light, as though the philosophical formulations of Plato were no different during the thirty year period between the writing of the Republic and Plato’s death: when Aristotle engages the Laws slightly later in Book II (Pol. 1264b27-1265a11), he begins by noting the similarities between the polity expressed in Plato’s last dialogue and Kallipolis in the Republic: The Republic about which Socrates spoke has these points of confusion and others not smaller than these. And nearly the same holds concerning the Laws written later, and therefore it is better to examine a few points even concerning the polity therein. For, in the Republic, Socrates defined very few things indeed – the commonwealth of women and children, how it ought to be, and property, and the structure of the polity (for the number of the inhabitants is divided into two parts, one being the farming portion, and the other those involved in defense, and a third portion derived from these that councils and governs the city-state), and the farmers and artisans, whether they have any share or not of the rule, and whether these ought to possess weapons and to serve in war with others or not – concerning these things, Socrates made nothing explicit, but he thinks that women should serve in war with others and partake in the same education as the guardians receive, and the rest of the discourse he has filled up with external arguments, especially concerning education, what form it should take for the guardians. The greatest portion of the Laws, however, happens to be laws as they exist (statutes: no&moi tugxa&nousin o!ntej), but few things have been said about the polity, and, although he wishes to make this more relative (koinote&ran) to the city-states, he brings it back around bit by bit to the other Republic. For, excepting the commonwealth of women and of possessions, he prescribes the same things for both polities: for, indeed, the education is the same, and living detached from necessary (i.e. menial: a)nagkai&wn) tasks, and similarly 15 For the continuation of Aristotle’s criticisms here, see Pol. 1264a11-b5. 16 As does Sir Thomas More, who makes every citizen of Utopia a farmer. 8 concerning public messes, except that in this polity he declares that there ought to be public messes even for women, and that he declares that, in contrast to the Republic where the number of people bearing arms was 1000, here it is 5000. Several passages here are key to the initial formulation of our project. Of primary interest is a problem that Aristotle, as well as most philosophers of the traditions of Western philosophy who wished to theorize about the best polity (including the Pythagoreans), found difficult to answer (or, for that matter, to approach): how does the philosopher reconcile the metaphysical, unchanging systems upon which ideal polities are founded with any practical polity that is susceptible to – and defined by – change/becoming? 17 The Platonic Socrates of the Republic posits a system of cyclical degeneration for Kallipolis; and so, Socrates imagines a city-state that cannot be found, a polity that might have existed “in the infinity of time that has passed on or will come” or exists “currently in some foreign land, far outside our horizon in reality,” 18 but is subject to time and therefore to the principles of division. 19 This alternative to the “first-best” city-state, to which Socrates alludes, 17 Here, a long quotation of Walter Burkert (1972:21-2) aids us in understanding the relationship between these opposites as analogous to the problem of monism-dualism: The highest principle of Platonic ontology is the One; alongside it stands the Infinite Dyad, a principle that is also described as great-and-small, many-and-few, exceeding-and-exceeded, and unequal. It is responsible for every kind of multiplicity, contrast and change in the realm of Being, and against the unity, identity, and constancy brought about by the One. The One is identical with the Good; the Infinite Dyad is the ground of all evil. It is also called Not Being (Arist. Phys. 192a7). In Aristotle’s terminology, the two principles are also related as form and matter. 18 Pl. R. 499c7-d4. Italics mine. 19 Pl. R. 545d5ff. The Platonic Socrates attempts to steer clear of terms that might confuse this kind of division of the city with proper philosophical dialectics. He refers to sustasis, phthora, and lusis, among other terms to be classed as negative; even so, it is crucial that the divisions of Kallipolis inevitably produce gene (types or classes) of humans that are alloys of the metals to which the Earth gives birth. 9 represents the initial sketch of a project that will occupy Plato’s life hereforth: the illustration of the “second-best” city-state, a community that can be achieved on earth that represents a successful imitation of the “first-best” model. As early as the Republic, Plato takes very seriously the problem of polity and polis, of ideal and practical, namely of those elements of philosophy that must, of necessity, be political and vice-versa. 20 Perhaps grudgingly, and with hesitation, Aristotle does admit that the polity described in Plato’s Laws, Magnesia, possesses something more derivative of and relative to city-states as they actually exist in the oikoumen1 at the middle of the 4 th Century BCE. Even so, Aristotle gives with one hand and takes with the other: “although [Plato] wishes to make [Magnesia] more relative [koinote&ran] to the city-states, he brings it back around bit by bit to the other Republic.” 21 In the midst of his attempts to characterize Plato’s Laws as a less formidable opponent than the Socratic Republic – I often wonder what we would think of the Laws if the text itself was not extant, and we had to conceive of it entirely from Aristotle’s and Diogenes Laertius’ summaries – Aristotle does tell us something of significance in this passage: Plato’s Laws is a dialogue that emphasizes pragmatics 20 It is possible to place these sets of dichotomies in comparison with Ferrari’s reading of the point of dissonance inherent in the Platonic Socrates’ analogy between the individual and the polis, the first of which is to be rule by necessity according to nature, and the second of which is to conduct citizens by necessity according to law (Ferrari 2005: 109-116). But even so, Ferrari, noting what seems to me a crucial point of instability in the Platonic analogy, attempts to explain away Socrates’ comment that Kallipolis will be a city-state “founded according to nature (R. 428e: kata_ fu&sin oi)kisqei~sa po&lij)” by appealing to the significance of Necessity. That Plato’s internal logic in the Republic cannot sustain consistent diaeresis between oppositional categories, a trend noted as early as Aristotle, might perhaps be instead considered as foreshadowing the development of the participatory category of form, a third term that is of utmost significance to later Platonic dialogues (see my Chapter 2). 21 Arist. Pol. 1265a1-5. 10 and attempts to locate Magnesia in common with other poleis, 22 although Aristotle does not tell us what these are. We can conclude from the implicit and explicit comparisons with other polities summarized in Book II of the Politics that Aristotle saw Plato’s two political organizations as common counterpoints to his own ideal hylomorphic polity, which he discusses in Books VII-VIII. 23 Such was the project of Glenn Morrow, whose magnificent Plato’s Cretan City (1960) undertook to articulate comprehensively the structure and administration of Magnesia by comparing it with those city-states that Aristotle had enumerated in the Politics, focusing especially on Athens and Sparta. Morrow’s study was a foundational study in the genre, culling imitators and admirers still to this day (including this author). 24 His examination of those ideal, timeless ancestral constitutions (Lycurgan Sparta, Minoan Crete, Solonian Athens, and archaic Carthage) explicitly juxtaposed with Magnesia set the stage for studies that would focus on the integration of Platonic philosophy and politics by emphasizing the historical conditions that constituted the environment in which – or against which – philosophy and political systems are developed. In this way, Plato’s Cretan City has covered much of the ground necessary to introduce readers of A.E. Taylor’s and John Burnet’s Plato to 22 I have translated the terms above without appeal to what seems to me a pun on “common,” reminding the reader (or listener) of Aristotle’s Politics of his disapproval of Plato’s communistic tendencies. 23 I borrow the term “hylomorphic,” which refers to the changing nature of the citizen body, from C.D.C. Reeve’s translation of the Politics. 24 Examples of recent secondary literature that feature a debt to Morrow’s book include Bobonich 2002 and Laks 1990, who introduces his article by stating, “Glenn Morrow, who did so much to illuminate the historical background of the Laws in his book Plato’s Cretan City, also had a sense, one quite unusual among commentators, of how the Laws really belonged to Plato’s philosophy and was needed in order to complete what might be called Plato’s general philosophical program [italics original].” 11 alternative, more systematically diaeretic and synthetic, historical investigations. Despite the immense value of Morrow’s scholarship, it has overlooked the influence of politico-philosophical city-states in the Mediterranean: it does not feature substantive comparisons between Magnesia and those practical polities that Aristotle passed over without descriptive commentary in the Politics. 25 Perhaps it is unsurprising that those polities given passing mention at the end of Book II, in particular Epizephyrian Locri and Thebes, have connections to Pythagorean political activities. 26 More surprising, perhaps, is the absence of comparison with other Pythagorean poleis whose constitutions were remarkably influential during the late 5 th and 4 th Centuries BCE, namely Croton, Taras, Metapontum, Thurii and Heraclea Italica. 27 Why would Aristotle neglect to compare these Pythagorean city-states with Plato’s Magnesia? 28 If Aristotle was willing to declare that Plato’s philosophy was essentially Socratean philosophy that had been modified, following Socrates’ death, by Pythagorean philosophy, why did he not discuss Plato’s political philosophy in reference to Pythagorean political philosophy? One possible answer is that he did, but the works are lost to us. We know, for instance, that Aristotle was influenced substantially by the philosophy of the 25 It goes without saying that Morrow’s study will be a predominant interlocutor for my project. 26 Generally, see Arist. Pol. 1274a23-b29. For Pythagorean politics at Epizephyrian Locri, see Chapters 4 and 6; for Thebes, see below in the Introduction and Chapter 1. 27 For a useful and brief overview of these city-states and their histories, see Bérard 1957: 139-185 et passim. 28 Morrow seems to follow, but also to improve upon, the points of comparison offered by Aristotle by drawing explicit comparisons between Athens, Sparta, Crete, and Carthage and Magnesia; in his defense, however, we may say that he does consider the cities of Magna Graecia and their constitutions as possible points of reference for Plato, although he always prefers to regard Plato as the source of the literary tradition regarding Pythagorean city-states. One such representative example is at p. 555, where Morrow claims, “It is more probable that Plato influenced the later tradition about Zaleucus and Charondas than that they influenced him.” 12 mathematical Pythagorean Archytas of Taras, who was both an active philosopher and statesman in Southeastern Italy during the 360s BCE. Diogenes Laertius tells us that Aristotle wrote one book On the Pythagoreans, and we know that he also wrote three books on the philosophy of Archytas of Taras and a book that summarized Plato’s Timaeus and the writings of Archytas in tandem 29 ; fragments remain of the book on the Pythagoreans, but, sadly, nothing remains of the books devoted to Archytas. 30 Even so, thanks especially to the excellent scholarship of Carl Huffman, we are able to reconstruct many of Archytas’ philosophical tenets. His monograph, Archytas of Tarentum: Pythagorean, Philosopher, and Mathematician King (2005), the first critical edition of Archytas’ fragments in English, has made the project of investigating mathematical Pythagoreanism in Plato’s works possible by improving upon the interesting, if slightly flawed, investigations into the relationships between Platonic and Archytan philosophy of the 20 th century, especially Erich Frank’s Plato und die sogenannten Pythagoreer (1923) and Walter Burkert’s Lore and Science in Ancient Pythagoreanism (1972 [1966]). Without these works, a project such as the one this dissertation attempts would never have come to fruition. Despite the debt that this project owes to the works of Huffman, Frank, and Burkert, none of these scholars ever systematically undertook the project of comparing Archytas’ and Plato’s systems of political philosophy. This project requires a comprehensive investigation into the history of city-states in Southern Italy that either were governed by Pythagoreans or for which the Pythagorean 29 D.L. 5.25. 30 Huffman 2005: 3-4. 13 brotherhoods served as an advisory board. Indeed, the discursive space circumscribed by the historical comparison between these Pythagorean poleis and Plato’s ideal and “second-best” city-states will form a significant portion of my project. The axis of my dissertation, this historical examination of Italian political and social organizations that were founded upon or related to Pythagorean philosophy during the late 5 th to mid 4 th Centuries BCE, will set in rotation these questions: if Plato’s dialectical systematization undergoes significant rearticulation in the Eleatic dialogues (Parmenides, Sophist and Statesman), can we see this revision as a response to his philosophical and political dissatisfaction in Athens? And if so, what alternatives to Athens might have appealed to the historical Plato, a studied philosopher and amateur statesman 31 whose travels – if we can trust the biographical and epistolary tradition – are credited with exposing him to a multiplicity of philosophical, political, and religious environments, most notably in Magna Graecia and Sicily? Finally, taking seriously the modifications to Plato’s dialectical system in the dialogues that postdate the Theaetetus (ca. 361 BCE), can we discover whether and, if so, how Plato’s “second best” polity of the Laws engaged in serious discursive dialogue with the administration, civic design, and 31 There is no indication that Plato’s political ideas were put into practice in any city-state during his life, although I find the argument convincing that the Academy (as a miniaturized political entity) might have been organized along lines developed in the political works of Plato. So Cornford 1964: xvi-xvii: “The Academy was, for the remaining half of his long life, the centre of Plato’s interest and his means of indirectly influencing the course of politics. It was primarily a school of philosophic statesmen, which was to attract from foreign states young men whose position and prospects were more fortunate than those of Plato’s own youth, and to train them for the exercise of the Royal Art. Some of its features, were modeled on the Pythagorean communities, which had been dispersed in the second half of the previous century, but had found a rallying-point at Taras. This city presided over a confederacy of Greek colonies in South Italy, and was itself under the personal ascendancy of the Pythagorean Archytas, who, being a noble mathematician, was a successful example of the philosophic ruler in a moderate democracy.” 14 applied politics of those city-states as well as with their concomitant ideal constitutions? The answers to these questions, I think, lie in Magna Graecia, where Plato’s lifelong engagement with the philosophy of the Italians (as Aristotle calls them) 32 concluded with a submission and assimilation to, and consequently a revision of, Pythagorean politics and philosophy. In his three visits to Sicily, Plato became acquainted with the philosophical city-state of Taras (Latin Tarentum/ modern Taranto) on the western coast of the Iapygian peninsula, where the instep of the Italian boot meets with the heel. 33 Taras, a city-state with a complex constitutional history that was famous for housing the philosophical school of the mathematical Pythagoreans, presented Plato with a model for the “second-best” mixed city-state, in that the philosophers probably had held some political authority for the preceding century. 32 Cf. Arist. Metaph. 985b32, 987a31, 989b29; Mete. 342b30, 345a14; Cael. 284b7, 293a20. Burkert 1971:29 is right to note that we are dealing here with the “Pythagoreans” as a group sometimes synonymous with, other times derivative of, the “Italians” (and, importantly, not with Pythagoras himself). On the question of Aristotle’s terminology, see Chapter 1. 33 Plato’s three visits to Syracuse occurred roughly in 388, 367, and 361 BCE. Our knowledge about Plato’s visits to Syracuse and Taras are especially derived from Plato’s famous Epistle VII, which I take to be genuine following Morrow 1962: 3-16. On Epistle VII, see Chapter 6. 15 Figure 1 (on the left): Map of Magna Graecia and Sicily. Courtesy of wikipedia.org: http://en.wikipedia.org/wiki/Magna_Graecia. Figure 2 (on the right): The Soleto Map, a piece of pottery dating to ca. 500 BCE that depicts the Iapygian peninsula, is the oldest map of the Western world. It features TARAS on the far left. Picture: Courtesy of the Archaeological Superintendency of Puglia. Taras features a tradition of philosophical statesmen, possibly starting with Archippus, a student of Pythagoras who, according to Aristoxenus, left Southwest Italy following the persecution of the Pythagoreans in Croton in the middle of the 5 th Century BCE. 34 We are told that Archippus and Lysis, two “younger” Pythagoreans, were discussing with the older Pythagoreans “political affairs” when the house of Milo, their place of deliberation, was set afire. 35 Lysis returned to Thebes, while Archippus went home to Taras. According to Aristoxenus’ account (as it is preserved in Iamblichus’ De Vita Pythagorica), the Pythagoreans ceased their charge 34 Aristoxenus F 18 Wehrli = Iambl. VP. 250. It is unclear whether or not Archippus partook in Tarentine governmental administration or not after his return to Taras. See Huffman 2005: 6-7. The Hellenistic biographer Hermippus of Smyrna tells us (D.L. 8.40) that thirty-five followers of Pythagoras were burned at the stake in Taras “for attempting to set up an oppositional government to those in power.” To what nature of government is Hermippus referring? There is some confusion here with the information related in the possibly spurious Epistle IX from Plato to Archytas, in which Archippus is said to have visited Plato in Athens and acted as messenger for Archytas. 35 Iambl. VP. 250. 16 (e)pau&santo e)pimelei&aj) over cities, in part because of the death of “hegemonic men (dia& te th_n a)pw&leian tw~n h(gemonikwta&twn a)ndrw~n).” Such terms suggest the disintegration of a Pythagorean government that had exercised political influence. 36 Regardless of the political actions of Archippus, it is clear that a remarkable diaspora of Pythagorean political ideas ensued following the Cylonian conspiracy in Croton (datable to either 509 or to the mid-5 th Century BCE) that resulted in a fundamental split of the Pythagorean brotherhoods along both political and doctrinal lines 37 ; while dating the Cylonian conspiracy is extremely challenging, we can be sure that by the late 450s BCE the schism had occurred in the Pythagorean community. Philolaus the Philosopher/Presocratic 38 and Lysis, among others, are said to have migrated to Thebes, where Lysis became the teacher of Epaminondas – who the periegete Pausanias tells us 39 was responsible, as Boeotarch in Thebes, for the decisive defeat of the Spartans at the Battle of Leuctra in 371 BCE – and Philolaus reared Simmias and Cebes, Socrates’ Pythagorean interlocutors in the 36 Guthrie 1962: 180 assumes that from the middle of the 5 th Century BCE Pythagorean societies “existed in small separate bands scattered widely over South Italy and Greece.” I will show in Chapter 1 that those communities are divided according to preference for democratic or aristocratic government. 37 Cf. Minar 1942: 52: “As early as Neanthes (third Century B.C.) the disturbances of the last years of the sixth century (ca. 509 B.C.) were being misunderstood and mixed with those of sixty years later.” Minar gestures in the direction of 453 BCE, when Sybaris was rebuilt (only to be conquered seven years later and replaced with the Athenian colony Thurii), following Kurt Von Fritz, who imagines a “great anti-Pythagorean outbreak” in Croton sometime between 450-440 BCE. For a complete treatment of the subject, see Von Fritz 1977: 68-93. For an alternative, less cynical view that prefers the earlier date, see Pugliese Carratelli 1996: 155-66. I conclude in Chapter 1 that this diaspora occurred between 473 and 453 BCE. 38 Or, perhaps, Archippus (Iambl. VP. 249; Plut. De gen. Socr. 583a-c) or Hipparchus (Olympiod. In Phaed. 9.16 Norvin). 39 Paus. 9.13-15. 17 Phaedo. 40 The importance of Epaminondas to Theban prosperity – and perhaps of others, including Simmias and Cebes – is attested by Aristotle, who is quoting Alcidamas, in the Rhetoric. 41 Philolaus probably returned to Taras or its colony Heracleia Italica, as is implied by Cebes in the Phaedo and suggested by Diodorus of Aspendus, a 4 th Century BCE follower of Pythagoras who published the acusmata. 42 This would date the return of Philolaus to after 432 BCE, when Heracleia was founded. What exactly Philolaus’ political activities might have been in Taras or Heraclea is not recorded, and as so we can only speculate about his political influence there. 43 He was certainly the teacher of Archytas, and both men undertook studies of mathematics, though at different levels of application. 44 Despite Aristoxenus’ comment that all the Pythagoreans who had moved to Rhegion 40 Pl. Phaed. 61d and scholia ad loc. 41 Arist. Rhet. 1398b18ff. Alcidamas refers to Thebes’ prosperity as occurring when philosophers became overseers (prosta&tai) of the city-state’s affairs. On the Pythagoreanism of Thebes, see Demand 1983: 70-84 and Klosko 1986: 60-1. 42 Iambl. VP. 266. See Burkert 1971: 202-4. That Socrates asks Cebes whether or not they “listened” (a)khko&ate) to Philolaus suggests that his mode of teaching adhered to the acusmata. One may contrast this mode of education, for instance, with the mathematical education (geometry, astronomy, harmony, and calculation) that Theaetetus receives from Theodorus in Plato’s Theaetetus, which is linked to the verb manqa&nw (Cf. 145c7ff.). Interestingly, Nichomachus differentiates the a)kousmatikoi& and politikoi& from the qewrhtikoi& (comparable to the maqhmatikoi& or filo&sofoi, see Burkert 1971: 192-3 with n. 5), suggesting the political enterprise of those followers of the acusmatic school. Even so, the tradition of Nichomachus is contradicted by the older, more reliable source, in Timaeus of Tauromenion. There is no difficulty in imagining, as Varro the Roman Pythagorean did (following a celebrated group of Roman statesmen who espoused Pythagorean precepts), that those who practiced philosophy were the highest group (ap. August. Ord. 2.20). 43 Philolaus is assumed to have been one of the mathematici by Burkert 1972: 198, but the evidence of Aristoxenus (F 19 Wehrli = D.L. 8.46) only lists him among the “last of the Pythagoreans.” Carl Huffman adds a significant caveat to the dispute about mathematici and acousmatici: “However, it need not be assumed that the mathematici completely abandoned the way of life followed by the acousmatici. The fact that they recognized the acousmatici as genuine Pythagoreans suggests that there was something common to the two groups and this common ground might include shared notions as to the proper way to live one’s life.” See Huffman 1993: 12. 44 Huffman 1993: 10. 18 following the middle of the 5 th Century BCE left Italy, except Archytas of Taras, 45 Diodorus of Aspendus, who seems to have had a peculiar interest in the efforts of the acousmatici (oi( a)kousmatikoi&) 46 , relates that Clinias was also in Heraclea, along with Theorides, and Eurytus and Archytas were in Taras. 47 Diodorus’ fragments are especially useful for constructing a missing piece of the puzzle: they tell us about the acousmatic, or “older,” more conservative, sect of followers of Pythagoras; they are defined against the mathematici (oi( maqhmatikoi&), a “younger” group of Pythagoreans whose interests seem to focus primarily on mathematics (both arithmetic and geometry), astronomy, and deductive proof. However, the issue of who the acousmatici and the mathematici were, and what those categories meant, is confused and contradictory in the ancient sources, and the process of distinguishing them has been attempted, nobly but without total success, by Walter Burkert, whose work on the Pythagoreans has been paradigm-shifting. 48 If we follow Burkert in assuming that the original schism between these kinds of Pythagoreans was at least known to Aristotle, then this question holds some bearing on our investigation into 45 Iambl. VP. 251. 46 See n. 42. 47 Iambl. VP. 266. Iamblichus, following Diogenes (8. 78), seems to take it for granted that all these Pythagoreans were indeed acousmatici, as the subsequent sentence refers to “Epicharmus [who] was also said to have been one of the foreign Hearers.” 48 Burkert 1972: 207n80 leaves us with what seems to me the most likely answer: “Perhaps the terms maqhmatikoi& and a)kousmatikoi& do not go back to the original schism [between followers of Pythagoras or Hippasus], but were only later applied to rival groups.” If we adopt Burkert’s assumption, that the divide is a product of Aristotle’s teachings, then we need not assume a separation according to Aristotelian diaeresis: perhaps the two groups partook in similar ways of living (which could potentially include political activism). Traditions of a tripartite system, which are later, might reflect actual developments from the 5 th to the 4 th Century systems (moving from Croton to Taras as well). 19 city-states that are both ideal and practical. For the dichotomy between ideal and pragmatic is also popularized through Aristotle’s categorizations. 49 Where Plato falls – whether at the extreme of one of these classes of Pythagorean successors, or in their midst, or without – is a matter of selecting a period of time in his career as a philosopher. Even in his later dialogues, Plato appears to prefer acousmatic Pythagoreanism at one moment, and mathematical Pythagoreanism the next. Plato does not conceptualize the term mathematicus in accordance with the schism that is well-established after Aristoxenus in the same terms whatsoever. It is clear from the Sophist, where the term mathematicus appears for the first time in Greek (219c2), that it means something closer to “one who learns” as a mode of acquisition (in contrast with the category of productive human beings who “make” things); in this way, we must assume that whether or not Plato identified differences between the two schools – and I think he did – the nomenclature had not been established by 361 BCE. Even so, the dichotomy between “learning” and “making,” which distinguishes those who are mathematici from those who are not in the Sophist, could conceivably be mapped onto the Pythagorean Table of Opposites, as reported by Aristotle in the Metaphysics, 50 and it 49 Burkert 1972: 192-7 shows that the schism traces from Aristotle. 50 Arist. Metaph. 986a23: “Others from this group [i.e. the “so-called Pythagoreans”] declare that there are ten principles, spoken of in a series of corresponding pairs: 1. Limit and Unlimited 2. Odd and Even 3. Unity and Plurality 4. Right and Left 5. Male and Female 6. Rest and Motion 7. Straight and Crooked 20 also accords with the dualistic paradigm of Form and sensible espoused by middle Platonism. 51 This represents one ancient point of view that has been assumed often by 20 th Century CE scholars. Nevertheless, the model I will propose suggests that, at least by the end of Plato’s career (in the Philebus), Plato understood well the distinction between the acousmatic and mathematical Pythagorean schools, and indeed that he proposed a reunification of the traditional and the progressive forms of Pythagoreanism in a manner that correlates with the mixture of Being and Becoming, as well as Intelligible and Sensible, all through the process of analogy. Following Plato’s death in 347 BCE, his student Aristotle would characterize Plato’s philosophy by employing an analogy that related mathematics (ta_ maqhmatika&) and applied pragmatics (ta_ pra&gmata); this is the characterization established by Aristotle in the Metaphysics, when he describes how Plato modified the Pythagoreans’ ontology by creating a “middle” term: For, the Pythagoreans claim that things exist in reality by imitation (mi&mhsei) of numbers; Plato claims by participation (me&qecei), modifying the name only. However, whatever imitation or participation might be, they left it to the rest of us to figure out. And, what is more, he states that, besides perceivable things and Forms, a middle (metacu&) term exists: the mathematical practicals (ta_ maqhmatika_ tw~n pragma&twn), which differ from perceivable things in being eternal and unmovable, and from Forms in that there 8. Light and Darkness 9. Good and Evil 10. Square and Oblong.” Indeed, Aristotle correlates these terms with the Being/Becoming dichotomy so important to Plato (965b27-29): “And since numbers are, by nature, first among these principles, and since it seemed to them appropriate to examine many analogues for things that are and that come-to-be…” 51 In the case of Sophist 219c2, Socrates defines the Sophist – here the fifth definition – within the category of acquirers. Aristotle also tells us (Metaph. 1043a22-3), in the sole reference to Archytas in his Metaphysics, that the Italian rendered definitions according to ideal and sensable. 21 are many analogous things (po&ll’ a!tta o#moia), but each Form itself is unique. 52 As this passage suggests, defining a critical relationship between the Pythagoreans and Plato requires an acute sense of Platonic dialectic and ontology; we should take Aristotle’s cue by examining exactly what Plato meant by “participation,” a term that Aristotle tells us was a revision of Pythagorean “imitation” in name only. Was Aristotle correct, and did Plato simply change the name, but not the process? In the course of our investigation into Plato’s reinscription of Pythagorean concepts, we shall have to consider both questions of terminology and process, following the diaeretic paradigms that make up all post-Pythagorean philosophy. 53 In the initial chapter of my dissertation, I examine traditions of multiple Pythagorean communities by demonstrating the existence of the dominant dichotomy of acousmatici and mathematici as attributed by Aristotle. In the process of doing so, I discuss the split in Pythagoreanism that is attributed to Hippasus of Metapontion, whose participation in the democratic revolution in Sybaris (I) is paradigmatic for political upheaval in Southern Italy. The insistence upon forms of analogical pragmatics found in Aristotle’s writings is juxtaposed with communistic – even democratic – social organizations located in Southern Italian poleis during the 52 Arist. Metaph. 987b11-18. On this difficult passage, and the contradictions it entails with later sources about Pythagorean number theory, see Ross 1924: ad loc. and Burkert 1972: 43-7. 53 This question of name and substance is crucial to our understanding of Plato’s revisions of Pythagorean metaphysics; it is at the heart of the debate as to the relationship between Kallipolis and Magnesia. Interestingly, Laks 1990: 210 follows Morrow’s thesis that there is a parallel relationship between ideal model and empirical realization for Kallipolis and Magnesia, a relationship called “projection.” But Laks’ note (n. 6) is more telling, emphasizing that “it should not be overlooked that there is some relationship between the paradigmatic city of the Republic and the Forms, as one can infer from the use of para&deigma (6.500e3).” 22 5 th Century BCE. Such information suggests that Aristotle’s criticisms of the “so- called Pythagoreans” are referring to mixed, or politically active, philosophers who traced a lineage from Hippasus. In Chapters 2 and 3, I document the shift in Plato’s thought that are evidenced in his responses to Pythagorean mathematics by showing the introduction of “third term” (tertium quid) metaphysics as a dialectical praxis into Plato’s post- 361 works (esp. Sophist and Statesman). This shift commences following the establishment of a program of mathematical and dialectical studies in the Republic derived from Archytas of Taras, then extended and criticized in the Theaetetus and Parmenides. Plato introduces this “third term” in a remarkable way: by appealing to Forms in which other Forms must partake (expounded as a criticism of ‘Socratic’ Forms in the Parmenides, and perfected as a supplement to diaeresis in the Sophist and Statesman). He then formulates this “participatory” Form as genos, a term whose semantic range is flexible enough to include socially-organized groups as well as to complicate Platonic ontology. Chapter 4 focuses on how the established Platonic “middle” or “participatory term” is applied to the organization of ideal city-states (Republic, Critias, Timaeus) and compares this structure with the Pythagorean Pseudepigrapha that can be dated to the 5 th and 4 th Centuries BCE, especially the Prooimia to the Laws of Charondas and Zaleucus and the On Polity of Hippodamus. Comparisons drawn suggest the significance of these Pythagorean Pseudepigrapha to 4 th Century BCE intellectual 23 experiments that propose how to create a happy or blessed polis. In all cases, the polities articulated refer mytho-historically to mixed constitutions of a Doric sort. In Chapter 5, I discuss modifications to Plato’s ideal political and philosophical pragmateia and its “participatory” formulation in the second half of the Statesman and in the Philebus by appealing to what I argue are the two primary elements of modification: adaption of the mathematical Pythagoreans’ metaphysical and ontological program (expressed most extensively in the Philebus) and application of Pythagorean first principles to Socratic ethics, primarily in response to the “mathematical” ethical systems of Archytas of Taras and his pupil Eudoxus of Cnidos. The result is a total revision of the dialectical and Formal theories expressed in the middle dialogues with a revised methodological emphasis on mathematics (especially astronomy) as the core element from which theories of political organization (human cosmology) can be derived. Chapter 6 concludes my dissertation by comparing the “second-best” polities of Epistles VII and VIII and the Laws with those city-states of Magna Graecia that probably influenced Plato profoundly due to their contemporary success in general ethics, education, and mathematics, as developed by Plato’s friend and contemporary Archytas of Taras. Direct comparisons between the constitutional structure of Taras, her colony Heracleia Italica, and Magnesia reveal both the influence of actual Pythagorean city-states on Plato’s political philosophy and his points of departure from those systems. Specifically, it is the issue of applying the proto-economic structure of the “discernment of Zeus” that leads to mixed constitutions for both the 24 Archytan and Platonic city-states, although the former is decidedly more “democratic,” while the latter is more “aristocratic.” Finally, I close this project with a proposition: I suggest that the problem of incommensurables, so central to the mathematical Pythagoreans’ philosophical program, is essential to understanding the “second-best” city-state of the Laws. The interweaving of irrational and rational elements of the polity is a basic premise of the later political philosophy of Plato, and it leads to a polity that can both exist perpetually and change over time without becoming corrupted: the final negotiation between Being and Becoming occurs in the Platonic colony of Magnesia. And so we will begin our study by taking seriously Aristotle’s suggestion that Plato improved upon the Pythagoreans’ dualistic scheme by mixing ideal and practical, a marked advancement in his dialectic that is echoed in the development of his scheme for the city-state that would achieve true happiness; 54 likewise, we can perhaps attempt to understand how the dichotomy between mathematici and acousmatici was understood and developed before Aristoxenus’ treatments of the subject, in the first half of the 4 th Century BCE, when Plato would have encountered 54 If we follow Burkert (1972: 196-7 and 458n.59) in attributing the information gathered at Iambl. VP. 89 (= Comm. math. s.c. p. 78) to Aristotle, then pragmateia (as Aristotle figures it for Pythagoreans) refers to the investigative activities of two groups of Pythagoreans (the mathematici and the acousmatici); first, those who have completed the appropriate tasks and are allowed to hear and see Pythagoras (the esoteric) and those who have not actually heard and seen Pythagoras but are, instead, followers of Hippasus (the exoteric). According to Simplicius, Aristotle’s works are also divided into the esoteric and exoteric (In Phys. 8. 16-20). In our attempts to understand the political administrators of the Pythagoreans found in this fragment (politikoi&, oi)konomikoi&, and nomoqetikoi&), much rests on the meaning of e)n toi~v au)toi~v. The term pragmatei&a and its correlative in pragmateu&esqai are used similarly in Fragment 4 of Archytas’ writings, from his Discourses, which Carl Huffman recently argued is genuine (2005: 225-252). For the term pragmateia in Aristoxenus F 23 Wehrli, see Chapter 1. 25 the Pythagoreans on his trips to Magna Graecia. We shall begin with the case of Hippasus of Metapontion, a name tied to both to mathematical and acousmatic social groups, whose presence at the head of the traditions of Pythagorean statesmen- philosophers provides us with a remarkable case study in the problem of Platonic, and Pythagorean, dualism. 26 _______________________________________ CHAPTER 1: SEARCHING FOR A THIRD TERM: THE TRADITIONS OF PYTHAGOREAN PHILOSOPHY AND POLITICS IN THE 5 TH CENTURY BCE REASSESSED _______________________________________ ‘Your third savior, seeing that your government was still fretting and restless, fitted it with a bridle (as it were), namely the power of the ephors, almost elected by lot. And thanks to this formula, your kingship itself, since it became a mixture of the proper things and was moderate, by its own preservation became the cause of the preservation of the rest of the state.’ – The Athenian Statesman (Plato, Laws, 692a6-b1) In Clisthène l’Athénien (1964), Pierre Lévêcque proposed a solution to a problematic contradiction involving the status of a certain Hippasus of Metapontion found in Iamblichus’ On the Pythagorean Life: When defining the opposition between acousmatics and mathematicians, Iamblichus first affirms that the former recognize the Pythagorean origin of the latter, whereas the mathematicians deny that their fellow members are authentic Pythagoreans and consider them to be disciples of Hippasus. The same Iamblichus, after having given the list of Acousmata we mentioned, declares the opposite: it is the mathematicians who recognize their rivals as Pythagoreans, heirs of the disciples of lower rank, whereas the acousmatics consider themselves to be the sole true Pythagoreans…Under these circumstances, would not the problem be resolved if one separated the two texts by relating them to two different eras? A Hippasus leader of the acousmatics, that is to say, of the “public at large” of the Pythagorean sect at the end of the sixth century, can perfectly well have in this capacity adopted democratic positions. A half century later, another Hippasus, pure mathematician, can perfectly well have 27 been victim of one of those “impiety trials” that characterize the period. 55 This argument, which occurs in the midst of Lévêcque’s attempt to make sense of the paradoxical historical evidence that describes the Pythagorean Hippasus of Metapontion, 56 hypothesizes that two men called Hippasus could have existed during the 5 th Century BCE in Southeastern Italy; this hypothesis derives from Diogenes Laertius, who, following Demetrius of Phaleron (b.ca. 350 BCE), states that “there were two men named Hippasus: one being our subject – i.e. the Pythagoric 57 who believed that the All is limited and always in motion – and the other being a man who wrote a Constitution of the Laconians in five books, who himself was a Laconian.” 58 Demetrius, for his part, as philosopher and statesman in Athens following the death of Alexander the Great, would have been interested in Hippasus as a successful philosopher-politican, and it appears that Diogenes has excerpted something from Demetrius’ writings in order to modify it. 59 The double Hippasus 55 Lévêcque 1996: 87-8. 56 Or, perhaps, Sybaris or Croton. See Thesleff 1965: 91-2. Hesychius (s.v) notes that, at Metapontion, there were a)koasth~rej, whom Sartori perceives to be “con ogni probibalità magistrate guidiziari.” See Sartori 1953: 100. 57 Importantly, Diogenes refers to Hippasus as a “Pythagoric (Puqagoriko&j);” other Pythagoreans that are called “Pythagoric” by Diogenes are Lysis, Philolaus and Archytas, all connected with Southeastern Italy. In contrast, “those who listened to Pythagoras” are Alcmaeon and Epicharmus; Empedocles’ public distribution of Pythagorean doctrine, interestingly, is responsible (according to Neanthes) for the passing of a law that outlawed poets from being Pythagorics (D.L. 8.55), suggesting that he had been one. 58 D.L. 8.84. Lévêcque also suggests (1996: 185-6 n.37) that some confusion might exist between Hippasus and Hipparchus, the Pythagorean teacher who is said by Olympiodorus (In Phd. 9.16 Norvin) to have escaped with Lysis (instead of Philolaus). Cf. Thesleff 1965: 92, who finds Hipparchus a contamination of Hippasus and Archippus. 59 Fortenbaugh and Schütrumpf, in their edition, do not include this passage among the fragments of Demetrius. If it was a description of those historians who wrote about the Spartan Constitution, it probably would have been featured in the On Lycurgus (F 113 Fortenbaugh and Schütrumpf). 28 theory adopted by Lévêcque perpetuates the distinction that had been noted by Diogenes Laertius: on the one hand, the abstruse philosopher, whose contemplative and discursive activities are separated from political activity, and on the other, the constitutional historian, whose interest in the traditions of the Doric polities reflect broader general trends in political philosophy and interest in the Lycurgan constitution from the early 4 th Century BCE through the Hellenistic era. 60 This trend presupposes that the mathematical Pythagoreans, of whom Hippasus was the progenitor 61 , assumed the Middle Platonic schism between politics and theoretical/mathematical philosophy advocated most fully by Socrates in Plato’s treatise on mathematics and epistemology, Theaetetus (composed before 361 BCE); it is therefore anachronistic to apply this distinction to Pythagoreans of the 6 th and 5 th Centuries BCE, whose combined philosophical and political activities E.L. Minar and Armand Delatte have demonstrated to be significant. 62 Indeed, the definition of a “pure mathematician,” the term Lévêcque employs to describe his proposed “earlier” historical Hippasus, is nowhere defined in his book, and we are at a loss about what Lévêcque means by the term “pure.” The lack of definition of terms presents us with an impasse, since we are not able to maneuver between the assumed distinction of political and philosophical – a Platonic (or perhaps Socratean) 60 On Spartan constitutions and their place in Greek political thought during the 4 th Century, see David 1981: 50-65. 61 See below in this chapter. 62 See Delatte 1922 and Minar 1942. 29 construction – and the information available to Demetrius that seemed to challenge the relevance of the distinction itself to Hippasus. I have begun my chapter with a lengthy quotation from Lévêcque, and with the problem of Hippasus of Metapontion, precisely to underline what seems to me a predominant trend in both modern and ancient scholarship on early Greek philosophy: the assumption that philosophy and politics were separate entities either by nature or by custom in all schools and at all times. Lévêcque is perhaps not to be excessively chastised for his anachronistic application: in a sense, modern critics of ancient political philosophy are forced to categorize ancient communities according to the terms that have been established by ancient critics, often those who were only born after the ultimate dissolution of the communities. Even if we are constrained by our material, however, there are critical alternatives which we can adopt: among them, we can challenge Lévêcque’s employment of a Socratic paradigm for Pythagorean philosophers with other ancient categorizations of philosophers and politicians. Indeed, the contraposition of multiple forms of community categorization brings to light many significant questions about how those very categories were formed by what was available to ancient philosophers, historians, and critics: in what they read, heard about from a second or third party, or even experienced themselves. The question of Pythagorean sects is a fruitful cognitive space for determining the challenges that Aristotle faced in the 4 th Century BCE and we face today, and it is one of the stimulating coincidences of history that the distinction between unity and pluralism – an issue of Pythagorean numerology – is at 30 the heart of ancient investigations into Pythagorean communities by later non- Pythagoreans. The ancient sources tend to divide the early (i.e. late 6 th and 5 th Century BCE) Pythagoreans into two groups – traditional acousmatics (a)kousmatikoi&) and progressive mathematicians (maqhmatikoi&) – and into a subsection of three groups. Armand Delatte took seriously the possibility of the tripartite organization, to which earlier and later traditions as well as the so-called Hellenistic Pythagorean writings adhere closely; 63 indeed, Delatte characterizes the political structure of the Pythagorean ideal city-state in triads. 64 Burkert, on the other hand, suggests that the triad is a sub-organization categorized according to the terms Puqagorikoi& – Puqago&reioi – Puqagoristai& corresponding to “pupils, pupils of pupils, foreign advocates” (Anon. Phot. 538b32ff; Schol. Theocr. 14.5). 65 Whether or not this triad represented a substructure of the Pythagoreans – or of which group – cannot be substantiated from the available evidence, and we may expect better success by focusing on the primary distinction between acousmatic and mathematical Pythagoreans. 63 On the later traditions of a tripartite system of grades, as he calls them, see Delatte 1922: 22-8. On the idea that certain “Apocryphal Pythagorean” writings are to be dated in the 5 th Century BCE, see Chapter 4. 64 Minar 1942: 34-5 with n. 79 criticizes Delatte 1922: 24-6 for seeing a correspondence between the three classes listed by Photius and the Scholiast to Theocritus (maqhmatikoi&, sebastikoi&, and politikoi&; see above in the Introduction) and those offices mentioned by Iamblichus at VP. 72 and 89. Minar overlooks Delatte’s care in distinguishing between, and not drawing immediate analogies among, the classes; at any rate, we take issue with Minar’s claim that “Iamblichus as usual transcribes the phrase quite mechanically in section 89 fin.” Yet again, Iamblichus is unclear whether he wishes to distinguish three classes (as he does in 89) or define one class (as he does in 74). 65 Burkert 1972: 192-3. 31 Despite the ample ancient evidence for divisions among those communities that followed the teachings of Pythagoras, it is surprising that there still remains a pervasive tradition in current scholarship that “Pythagoreanism” is a holistic, complete, and interdependent system, subject only to minor changes following the Pythagorean reinstatement of the 1 st Century BCE. Scholars are willing to admit the categorical difference between acousmatic and mathematical Pythagoreans of the 5 th Century BCE, but then they assume that certain contradictory elements within their own constructed “Pythagoreanism” are often the misinterpretation of critics like Aristotle, Aristoxenus, Dicaearchus, or Timaeus of Tauromenion, all commentators on Pythagoreanism who lived in the century following the death of Archytas, the great Tarentine philosopher and statesman (ca. 360s BCE). Several questions follow from the assumption that “Pythagoreanism” was not a unified or necessarily fluid sphere of shared communal ideas and practices: What kinds of Pythagoreans were there? What distinguished one kind of Pythagorean from another? What political structures did communal Pythagoreans exhibit? How exclusive were these political groups and how did education figure into their constitution and reconstitution? How did Pythagorean political communities theorize about their own structures and organizations? What effect did Pythagorean political organizations have on the larger development of Greek political philosophy and constitutional theory, and vice versa? And, finally, can we detect the significance of Pythagorean city-states for local (i.e. South Italian) and Mediterranean political and philosophical history? Before we can proceed with a proper interrogation of some of these issues – some of 32 them will be answered more fully in later chapters – we must reexamine with more precision the distinction between acousmatic and mathematical Pythagoreans, an issue that has at its heart the concept of pragmatics, a term that I will define in the course of this chapter. That Hippasus of Metapontion was a mathematicus (maqhmatiko&j) is well established and accepted, thanks to the work of Walter Burkert in his influential study Lore and Science in Ancient Pythagoreanism, who is nevertheless not entirely confident about what that term constitutes. 66 Burkert synthesizes the available material in order to demonstrate two significant points: first, that all followers of Pythagoras were adherents of the acusmata, also called symbola, a set of orally transmitted sayings passed down from Pythagorean teacher to students in a traditional mode; second, that what distinguished esoteric acousmatic Pythagoreans (a)kousmatikoi&) from exoteric mathematical Pythagoreans (maqhmatikoi&) was each group’s philosophical and political pragmateia: Aristotle recognizes among the Pythagoreans a twofold pragmatei&a: on the one hand, the Puqagorikoi_ mu~qoi, metempsychosis, the Pythagoras legend, and the acusmata, and on the other a philosophy of number connected with mathematics, astronomy, and music, which he never tries to trace back to Pythagoras himself and whose chronology he leaves in abeyance. 67 Burkert demonstrates that Aristotle categorized the Pythagorean acusmata according to whether or not they answered these three questions: ti& e!sti (what exists?), ti& 66 Burkert 1972: 192-201 et passim. 67 Burkert 1972: 197. 33 ma&lista (what is most?), and ti& prakte&on (what should be done?); 68 he successfully explicates the first two categories with ample supporting evidence and a critical attention to the possible spuriousness or anachronism of later information, but he neglects to discuss in detail the third category, ti& prakte&on, which refers to pragmatics and suggests political, philosophical, and religious activities; indeed, it is Burkert’s failure to discuss the third category – ti& prakte&on – in relation to the dual Pythagorean pragmatei&a that leads to his ultimate aporia when it comes to distinguishing the mathematical and the acousmatic Pythagorean groups. 69 And yet Burkert might have found an answer in the ancient source to whom he devotes so much energy. Iamblichus (b. ca. 240 CE) – just after he has referred to the schism in Pythagoreanism attributed to Hippasus of Metapontion – discusses each category in the order given: ontology 70 (VP. 82-3), ideal 71 (VP. 83-5), and pragmatic (VP. 85-7). 68 See Burkert 1972: 167-9 and Iambl. VP. 82. Burkert rightly reminds us that these “orally transmitted maxims and sayings” were also called symbola. Recently, Peter Struck has done a comprehensive study on symbolic or enigmatic communication in antiquity, although his book also fails to treat the third kind of acousma. See Struck 2004: 96-110. 69 See the Introduction. 70 Generally, the question of being refers to ontology for materialist (i.e. Ionic) philosophers, but possibly to metaphysics for immaterialist (i.e. Italian) philosophers. This distinction is owed to Iamblichus in the Protrepticus (p. 125, 6 Pistelli). For Aristotle, Being (to_ o!n) – as the subject of ontology – features many categories as figures of predication, of which the first is ti& e)sti (Metaph. 1017a25); metaphysics, on the other hand, is Being qua Being (to_ o@n h|{ o!n), and it is the study of all species of Being (Metaph. 1003a1, 1003b21-3). It is not clear that later Pythagoreans like Iamblichus, or the earlier ones whose lives they were examining, subcribed to Aristotle’s separation of ontology from metaphysics. Carl Huffman, in an email to the author (February 8, 2006), has written that “the Pythagoreans did not really stop to consider the ontological status of numbers and saw them more as an epistemological tool,” referring to his groundbreaking examination of Philolaus’ ontology and criticism of Aristotle’s summaries of Pythagorean philosophy (1993: 37-77). Despite Huffman’s careful analysis of the few genuine fragments of Philolaus that remain, I am still unconvinced that there weren’t multiple systems of Pythagorean philosophy at work in the 4 th Century BCE, as I will show later in this chapter. 71 Iamblichus, following Aristotle, mentions the distinction between “what is good” and “what is most [good]” at VP. 83. On the ti& ma&lista format for acousmata, see Burkert 1972: 169. Indeed, the first 34 Pragmatics, the third term in the Pythagorean teachings, refers to that category of human existence related to the worship of the gods and to respect for the laws, each analogous thanks to the principle of ruling and being ruled according to cosmic order; in markedly Aristotelian language, Iamblichus calls this the “first principle” (a)rxh&): All such acusmata, however, which define what is to be done or what is not to be done (peri_ tou~ pra&ttein h@ mh_ pra&ttein), are directed toward the divine, and this is the a)rxh&, and their whole way of life is arranged for following god, and this is the logos of their philosophy. 72 For human beings act ridiculously in seeking the good anywhere else than from the gods, just like someone who pays court to a subordinate governor of the citizens in a country ruled by a king, neglecting him who is the ruler of all; for just so do they think humans behave. For since there is a God, and he is Lord of all, it is agreed one ought to ask for the good from the Lord. 73 It is difficult to sift through the text, locating which portions seem to derive from Aristotle and which are later. Nevertheless, the organization of triads is crucial to the architectonics of this passage. The third term of the Pythagorean teachings, which deals with ti& prakte&on, is presented in terms of adherence to the appropriate order of rule; such a rule is presented in a tetrad, which might lead to some confusion: rule under a subordinate governor (u#parxon), king (basileu&j), a ruler of all (a!rxon pa&ntwn), and the divine lord of all (ku&rioj pa&ntwn). 74 Iamblichus’ kind of distinction for Aristotle in Book I of the Politics (1251a1-7) between kinds of communities is whether they “aim at some good (me_n a)gaqou~ tinoj stoxa&zontai)” or “at the supreme good (ma&lista de_ kai_ tou~ kuriwta&tou).” 72 Cf. Aristoxenus F 23 Wehrli: “ta_ te ga_r a!lla a)riqmo_j e!xei kai_ lo&goj e)sti_ pa&ntwn tw~n a)riqmw~n pro_j a)llh&louj...” 73 Iambl. VP. 86-7. Translation by Dillon and Hershbell (slightly modified). 74 This passage is also closely related to Philo Decal. 61, where Philo, calling to mind the organization of the Persian Empire under Darius, refers to a fourfold graded series of Maker/Father, Great King, 35 point might be that we ought to follow a generalized prescribed order of rule, but this passage takes on a richer set of meanings when it is compared with another passage of Aristotle, in which he attests to the significance of tripartite categorizations of magnitudinal division for the Pythagoreans. When defining the kinds of division that magnitude may undergo, that is to say defining the categories that may occur as a consequence of division, Aristotle tells us: Magnitude divisible in one direction is a line, in two directions a surface, and in three directions a body. There is no magnitude not included in these; for three are all, and “in three directions” is the same as “in every direction” (dia_ to_ ta_ tri&a pa&nta ei}nai kai_ to_ tri_j pa&nth|). It is just as the Pythagoreans say, the whole world and all things in it are summed up (w#ristai) in the number three; for end, middle and beginning give the number of the whole (teleuth_ ga_r kai_ me&son kai_ a)rxh_ to_n a)riqmo_n e!xei to_n tou~ panto&j), and their number is the triad. Hence it is that we have taken this number from nature, as if it were her laws (no&mouj e)kei&nhj), and we make use of it even for the worship of the gods. 75 King, Satrap; the fourfold graded series of God, daimon, hero, man is attributed to the Pythagoreans as early as Aristoxenus (F 34 Wehrli) and is common to Plato and the Pseudopythagorean Prooimia Legibus attributed to the lawgiver Zaleucus. For Zaleucus’ text, see Thesleff 1965: 225-9. Also see Chapter 4 and Burkert 1972: 73-4 with notes 131-2 for the citations. 75 Arist. Cael. 268a7-17. Translation by Guthrie (slightly modified). C. Huffman’s statement that “[Aristotle’s] evidence will still show that the one-infinite dyad opposition and the derivation sequence of point, line, surface, and solid are Platonic and not Pythagorean” (1993: 63 n.12; Cf. 362- 3) is implicitly disproved by the evidence here of a “Pythagorean” theory of magnitude based on principles of separation (which Aristotle took for granted as Pythagorean and criticizes at Metaph. 1083b15-17). Furthermore, Huffman’s point about the Timaeus cannot be definitive, in the light of the ancient assumption that Plato copied the Timaeus from Pythagorean sources (see Burkert 1972: 225-6 for the sources). What is more, Huffman’s typically acute analysis fails to consider the full import of Aristotle’s attribution of the theories of constructing nature out of numbers to “some people, such as certain Pythagoreans,” (e!nioi…w#sper tw~n Puqagorei&wn tine&j; Cael. 300a16-17) which cannot refer to Pythagoreans in general, but more likely to a sect of Pythagoreans. 36 How are we to make sense of this passage? I submit that the focus on modes of division is central to Aristotle’s description of Pythagorean magnitude. 76 If we consider that the tetraktys is the consummate system of numbers, a veritable “compendium of Pythagorean mysticism,” as Cornford called it, 77 then what is of interest to Aristotle here is not the numbers themselves (1, 2, 3, and 4), but the method of division accorded them. Magnitude cannot exist for 1, or the Monad, since it is not a number but an a)rxh_ a)riqmou~, comparable with the divine. 78 2 or Dyad, the first even number, can be divided into two portions and therefore, as a magnitude, is a line. 3, the first odd number, when divided as a magnitude, features a remainder, which Plutarch calls a “middle” (me&son) that is “generative” (go&nimon); 79 this number stands for the plane in mathematics. Finally, 4, or geometric solid 76 That magnitudes are divisible according to the same ratio is assumed by Euclid and attributed to Eudoxus, who was unquestionably a mathematicus and a student of Archytas of Taras. See Heath 1931: 224-5 and below. 77 My interpretation of this passage owes much to Cornford 1923. This article’s contents were criticized by Philip 1966, in which he argues (basically ex nihilo) that a theory of derivation would have surfaced in the Early Academy. His principle criticism of Cornford focuses on the unreliability of Sextus Empiricus’ description of Pythagorean magnitudes, but his argument fails to convince on two counts: (1) Sextus (Adv. Phys. 2. 281, Adv. Math. 4.2) speaks of “later Pythagoreans,’” who assert that “physical body is generated from the point which ‘flows’ to produce the line, line flowing to produce plane, and plane flowing to produce solid;” Philip himself concedes that this group of Pythagoreans are possibly “the Pythagoreans specializing in mathematics,” who are in all probability to be understood as the mathematici (see p. 44, n. 10, which is unconvincing); therefore, Sextus’ thesis that earlier Pythagoreans (i.e. acousmatici) posited generative numbers and that “later Pythagoreans” modified this theory by adding the element of flux (certainly available to any Southern Italian philosopher who had heard the Sophists or had knowledge of Heraclitus, as the followers of Hippasus did) corresponds to the account of De Caelo, which presupposes a theory of derivation through separation; (2) De Caelo, one of Aristotle’s earliest treatises (ca. 347-5 BCE) that is not cited by Philip in this article, represents the Pythagorean theory of magnitude as formulated through division. Philip admits implicitly that the summary given on “later Pythagoreans” could be true, even if the summary that concerns the “earlier Pythagoreans” is tainted by Stoic, Platonic, and Aristotelian theories (1966: 44). 78 Aristoxenus, F 23 Wehrli. On what a)rxh& means here, and elsewhere, see below. 79 Plut. De E ap. Delphos, 388a. 37 (sw~ma), is the number that stands for harmony and justice, being the first square number; 80 it ideally completes the tetrad, holding opposing tensions in harmony according to the law of Rhadymanthus that stipulates reciprocity. 81 In On Heaven, the significance of divisions invites us to consider how Pythagorean arithmology worked: we need to keep in mind the difference between numbers themselves and their definition through division. 82 The triad, considered so crucial to the Pythagoreans in On Heaven, refers not to the first principle 1 and the numbers 2 and 3 but, more specifically, to the division accorded to the numbers 2, 3, and 4, as magnitudes; all this number-theory is placed in context of political organization and structures of economic reciprocity both in the Aristotelian passage at Iamblichus’ On the Pythagorean Life (86-7) and in Aristotle’s Nichomachean Ethics (1132b21-a5), where Pythagorean justice is explained and criticized. These analogies need not surprise us: what we are dealing with, when we engage political organizations, are collected numbers that are divisible; the divisions themselves afford definitions of classes. 83 A fascinating fragment from Aristoxenus’ On Arithmetic (F 23 Wehrli = Stob. Ecl. I Prooem. 6) clarifies the role that division (here referred to as diaeresis) 80 See Ross 1924: 114 on dikaiosu&nh. 81 Arist. Eth.Nic. 1132b21-1133a5. I follow Cornford 1923: 4 here. 82 Of course, Aristotle tells us that the “Pythagoreans” attempted to define things too simply (Metaph. 987a20-5); he does not say that the “Pythagoreans” had no system of diaeresis, but that the system they employed confused the object of the study (to pragma) with its Being (ousia), an operation that takes place in some ill-defined way through mimesis. 83 Huffman 1993: 92 attributes the development of “a general philosophical method that applied to every area of inquiry, a method which called for an attempt to identify a minimum set of explanatory principles necessary for a given domain of phenomena” to Philolaus. On class differentiation in Pythagorean poleis of Southeastern Italy, see Chapters 4 and 6. 38 played in Pythagorean arithmology, as Aristoxenus viewed it; I will quote the fragment in Greek, since it is not commonly discussed in the secondary literature: th_n de_ peri_ tou_j a)riqmou_j pragmatei&an ma&lista pa&ntwn timh~sai dokei~ Puqago&raj kai_ proagagei~n ei)j to_ pro&sqen, a)pagagw_n a)po_ th~j tw~n e)mpo&rwn xrei&aj, pa&nta ta_ pra&gmata a)peika&zwn toi~j a)riqmoi~j. ta_ te ga_r a!lla a)riqmo_j e!xei kai_ lo&goj e)sti_ pa&ntwn tw~n a)riqmw~n pro_j a)llh&louj...[lacuna]...Ai)gu&ptioi de_ (Ermou~ fasi_n eu#rhma, o#n kalou~si Qw&q. oi$ de_ e)k tw~n qei&wn periforw~n e)pinohqh~nai. mona_j me_n ou}n e)stin a)rxh_ a)riqmou~, a)riqmo_j de_ to_ e)k tw~n mona&dwn plh~qoj sugkei&menon. tw~n de_ a)riqmw~n a!rtioi me&n ei)sin oi( ei)j i!sa diairou&menoi, perissoi_ de_ oi( ei)j a!nisa kai_ me&son e!xontej. o#utwj e)n perissai~j h(me&raij ai( kri&seij tw~n noshma&twn gi&nesqai dokou~sin kai_ ai( metabolai&, o#ti o( perisso_j kai_ a)rxh_n kai_ teleuth_n kai_ me&son e!xei, a)rxh~j kai_ a)kmh~j kai_ parakmh~j e)xo&mena. And Pythagoras seems to have honored the pragmateia concerning the subject of numbers most of all (or more than anyone) and brought it to the fore, borrowing it from mercantile practice and likening all things to numbers. For number holds the other things, and there is a logos for all numbers in relation to one another…(missing text)…But the Egyptians declare it to be the discovery of Hermes, whom they call Thoth. The others (?) say that it is comprehended through the divine circuits. So, then, the unit is the first/ruling principle/origin of number, and number is a plurality constituted from units. Even numbers are those things that are divided into equal portions, and odd numbers are those that are divided into unequal portions and have a middle/remainder. In this way, the turning points and alterations of diseases seem to happen on odd days because the odd holds the beginning and end and middle, those diseases partaking in origin and peak and decline. One is immediately struck by the similarity between this passage and the passage quoted above from Aristotle’s On Heaven. Here, in language simultaneously astrological and medical, Aristoxenus defines the numbers 1 (Monad), 2 (Even), and 3 (Odd/Triad) by means of diaeresis. Interestingly, this passage corresponds to and 39 might be the source for two much later fragments of Philolaus that Carl Huffman considers spurious, given their “clear affinities with Neoplatonism.” 84 Perhaps they are not genuinely Philolaus’, even though both Iamblichus (in Nic. Arithm. 77.8 Pistelli) and Syrianus (in Metaph. 165.33 Kroll) attribute the idea that “the One is the first principle of all things” to him. 85 But separation through triads was, for Aristotle, one of the defining characteristics of Pythagorean designation of space, and it has close affinities with Plato’s Philebus (23c1-d4), where Socrates offers up three concepts that ought to be examined through diaeresis and proposes to Protarchus a fourth sort as a natural addition to the stated Limit, Limitless, and mixed unity (to_ pe&raj, to_ a!peiron, and, remarkably, e#n ti summisgo&menon). 86 Whether or not these fragments can be traced back to Philolaus, they announce themselves as theories that Plato took for granted and wished to improve upon. They reflect, then, (at least one form of) late 5 th and/or early 4 th Century BCE Pythagoreanism. It seems likely, given the close affinities here with Aristotle’s statement in On Heaven that “end, middle, and beginning give the number of the whole,” that Aristoxenus is deriving his information here from his teacher or from the works to which his teacher had access. Understanding the relationship between Number, Being, and things is one of the greatest challenges that face both ancient and modern scholars of Pythagorean philosophy. Aristotle’s and his students’ attempts to 84 Huffman 1993: 345-7. 85 Ibid. On a)rxh& in Philolaus’ fragments, see below. 86 I will discuss this passage more comprehensively in Chapter 5. 40 analyze Pythagorean systems and synthesize them with those of the Presocratics, Plato, or the Academy reveal the tensions that result from Pythagoreans’ terminological ambiguity and confusion of categories. Walter Burkert succinctly and directly presents the problem that Aristotle and his followers could not resolve: [G]reat as the temptation has been, both for Aristotle and for modern scholars, to understand the opposition of Limit and Unlimited as identical to that of form and matter, the explicit statements that the One partakes of both Limit and Unlimited, and that number is a kind of material (u#lh), stand in the way. 87 While I completely agree here with Burkert’s statements, and with those who have followed him, 88 it does not necessarily follow that we cannot derive important and useful information from Aristotle’s summaries. Indeed, careful attention to the language that Aristotle uses in his criticisms of the Pythagoreans’ philosophy reveals precisely – in terms that were not necessarily filtered through the Aristotelian sieve – the relationship between division and imitation that leads to confusion among modern scholars. Let us recall the argument given above that the acusmata were categorized by Aristotle in three terms: 89 ontology, ideals, and pragmatics, the last being as difficult to define as the other two. Now, Aristotle sees Pythagoreans as formulating 87 Burkert 1972: 46. Cf. Philip’s (1966: 40-1) justified remark that there is confusion and contamination in Alexander Polyhistor’s (1st Century BCE) account of Pythagorean derivation of magnitude. 88 Cf. Huffman 1993: 59ff. A useful study of Aristotle’s confusions with regard to magnitude is Cherniss 1935: 37-46, although Cherniss fails to distinguish between different kinds of Pythagoreanism. 89 Unfortunately, while the triad can be distinguished, we cannot be sure by what vocabulary Aristotle categorized them. I would expect that, if we had the text of the On Pythagoreans, we would see them called mer1 (types), gen1 (kinds) or eid1 (forms). Fearing lest I presume for the Aristotelian terminology, I have imported the nondescript word “term” for these distinguished categories. 41 definitions through diaeresis from within these individual categories, as we saw above in the On Heaven, where they categorize magnitudes (he will elsewhere criticize this method as well); 90 each of these definitions would occur under the acousmatic category “ti& e!sti” and refers, therefore, to ontology. 91 But, as another fragment of Aristotle’s Metaphysics (987a13-28) testifies, Pythagoreans tend to analogize and relate the basic acusmata to one another as though they pertained to the same mode of existence: The Pythagoreans discussed the two first principles (a)rxai&) in the same way [as the Italian philosophers], but they made this addition, which is peculiar to them: they didn’t think that the Limited and Limitless were different sorts of natures, like fire and earth or another thing of this sort, but that Limitless itself and the One itself are the essence of those things of which they are predicated (tou&twn w{n kathgorou~ntai), and therefore that number is the essence of all things. And so, such is their plain speeech concerning these things, and, while they began (h!rcanto) to speak and create definitions about the “what is” (to_ ti& e)stin), their putting it into practice was too simple (li&an d’ a(plw~j e)pragmateu&qhsan). For they rendered superficial definitions, and they believed that the essence of a thing (th_n ou)si&an tou~ pra&gmatoj) is that to which the asserted definition is referred (u(pa&rceien) in the first place; for instance, if someone should think that “double” is the same as “two,” because, the first “double” refers to “two.” But perhaps to exist according to the principle of “double” is not the same thing as to exist according to the principle of “two.” Otherwise, many things will be One, which is a consequence of these things. It is well-known that Aristotle was invested in finding analogies between earlier philosophical systems and his own Four Causes: the (1) Formal, (2) Material, (3) Efficient, and (4) Final Causes, whose provenances are demarcated by, in Aristotle’s 90 At Metaph. 990a13-17, Aristotle attacks the “so-called Pythagoreans’” formulation of magnitude. Also see his summation of the “Pythagoreans’” theory of magnitude at 1080b6-33 and 1083b8-19. 91 Cf. Metaph. 1078b17-24. 42 own terms, (1) ou)si&a kai_ to_ ti& h}n ei}nai (essence and essential disposition), (2) u#lhn kai_ to_ u(pokei&menon (matter and underlyer), (3) a)rxh_ th~j kinh&sewj (origin/first principle/beginning of motion), and (4) to_ ou{ e#neka kai_ ta)gaqo&n (purpose and Good), respectively. 92 In the passage quoted above, Aristotle detects a confusion of Form and Matter, as is noted by Joseph Owens; 93 but what Owens did not notice was Aristotle’s inability to reconcile his theory of Four Causes with the stated Pythagorean acousmatic triad of ontology, ideals, and pragmatics, the third term of which Aristotle’s language suggests in the word e)pragmateu&qhsan: this word encompasses semantically the method and the object of an investigation (pragmateia), both of which are emphasized by the terms h!rcanto and its nominal form a)rxai&, the definition of which is the subject of this whole anecdotal passage. 94 And so, it is likely, contra Owens’ note, that Aristotle’s reference to this semantic range of beginnings and pragmatics reveals his attempt to coordinate the Pythagorean triad with the first three Causes of his own system (Formal, Material, and Efficient); his failure to Aristotelianize Pythagorean philosophy is admitted early 92 Arist. Metaph. 983a24-33. 93 Owens 1978: 197. 94 This passage is developed as an explanation of those thinkers who believed in two archai, of which one is Efficient (h( ki&nhsij). Aristotle sees the pragmateia of the Pythagoreans as employing superficial physics, failing to achieve metaphysics, because it concerns itself with mathematical objects alone and not with Being qua Being. For the distinction between physics and metaphysics, see Metaph. 1063a36-1064a5, where the concern for pragmatics is apparent: “Each science seeks certain first principles (a)rxa_j) and causes concerning each knowable thing under its scope, e.g. the sciences of medicine and physical performance and each of the remaining productive and mathematical sciences. For each of these, having circumscribed for itself some class, makes this the object of its study (peri_ tou~to pragmateu&etai) as something that it is predicated and exists in reality, but not qua reality (w(v u(pa&rxon kai_ o!n, ou)x h|{ de_ o!n): there is another science distinct from these that deals with this.” 43 on. 95 It lies at the heart of Aristotle’s criticism of the Pythagoreans, that they too easily confused what were distinctively defined scopes of Being, or Causes. 96 When we are discussing Aristotelian First Principles, or what Huffman designates Pythagorean Beginnings/Origins (a)rxai&), we are dealing with a terminology whose semantics encompass both the scientific and the political. Returning to the Aristotelian passage quoted by Iamblichus above, we note the two offices of subordinate governor (u#parxon) and ruler (a!rxon pa&ntwn), terms that remind us of the well-documented analogy between a beginning/origin/first principle (a)rxh&) and rule. 97 All of this is registered under the general heading of ti& prakte&on, and nowhere else in this Aristotelian passage – that is to say under the semantic category of ontology or ethics – do we find any reference to Pythagorean first principles; the correspondences between principles and rule are presumed by Iamblichus, who follows Aristotle here and is followed in turn by his student Aristoxenus later on. 98 However, we may heed Aristotle’s warning by doing our best not to analogize superficially things that are, by (Aristotelian) nature, different ontologically; so we will be critical of Minar when he argues that: The parallel [between first principles and rule] is clear. As in any object or system there is something which is naturally prior in origin, 95 At Metaph. 986aa13-15, Aristotle mentions explicitly that he aims to examine “how the first principles (a)rxa_j) [of the “so-called Pythagoreans”] coincide with our aforementioned causes (ai)ti&aj).” 96 That is not to say that Aristotle himself did not analogize these separate ousiai. See Owens 1978: 178-80. 97 On this subject in Aristoxenus’ Puqagorikai_ )Apofa&seij, see Minar 1942: 101-2. 98 The language that connects divinity to first principles is reiterated in the Aristoxenean passage at Iambl. VP. 174-5 (F 33 Wehrli). See Dillon and Hershbell’s edition of VP. p. 187 n.10. 44 in honor, and in worth, so in human society one element is naturally superior and qualified to rule over the rest – the “true ruler.” 99 Minar’s interpretation of this passage does not account for its own Aristotelian hermeneutics. More careful examination of how a)rxai& relate to rule in Pythagorean political theory is in order. Huffman’s recent editions of the fragments of Philolaus of Croton and Archytas of Taras pave the road for critical analysis of Aristotle’s language and attention to places where he – and his followers – impose their own terminology upon predecessors’ philosophical theories. 100 While I find Huffman’s studies essential to understanding late 4 th and early 3 rd century Pythagorean practitioners, I am not convinced that he has considered the relationships of a)rxai& to multiple Pythagorean communities that are demonstrable by the beginning of the mid-5 th Century BCE. In essence, it is my contention that democratic Pythagorean communities of this period defined themselves against aristocratic 101 Pythagoreans; one of the crucial grounds for self-identification for these democratic Pythagoreans was their revision of a)rxai&, which refer semantically both to first principles and to political rule. 99 Minar 1942: 102. 100 See especially Huffman 1993: 78-92 and 2005: 68-76 and 499-503. Huffman’s analyses do not doubt that what Aristotle tells us about Pythagoreans is true, but rather they focus on the difficulty of extricating Pythagorean concepts from their Aristotelian presentation. 101 The more traditional Pythagorean governmental structure may be more generally and even more favorably called “aristocratic” rather than “oligarchic,” a term which, following the calcification of these terms in Plato’s Republic (544e7-545b1) and Aristotle’s Politics (1279b5-10), is considered an inferior or deviant form of aristocracy. However, whenever cited authors (such as Iamblichus) refer to Pythagoreans as “oligarchic,” I will quote them verbatim so as to preserve the sense of the text as it stands. 45 Huffman’s rearticulation of Philolaus’ and Archytas’ principles of philosophy effectively demonstrates these Pythagoreans’ scholarly interest in the Presocratics. Despite his careful and diligent attention to the development of physical sciences and mathematics in the 5 th and 4 th Centuries BCE, he assumes too easily a monolithic, one directional – even teleological – Pythagoreanism, instead of considering, as Delatte and Guthrie did (following the traditions stemming from Aristotle), the possibilities of multiple, even contradictory forms of Pythagorean organization. 102 Before I consider the polysemy of a)rxai& in Pythagorean communities, I would like to return to the dominant dualistic paradigm that attends all post-Aristotelian views on Pythagoreanism. Whether or not we admit of three different types of Pythagoreans and consider hierarchies within each group, we must follow the ancient sources – which are uniform – in believing that there were at least two kinds of Pythagoreans, the acousmatici and mathematici. Burkert’s investigation into these philosophical groups has successfully demonstrated that the mathematici participated in the acusmata and represented, at least to later doxographers, philosophers, and commentators (both Pythagorean and non-Pythagorean), a more advanced selection of those communities that credited Pythagoras of Samos as their spiritual leader. It is generally agreed that, regardless of who came to be known as the first heretic, some 102 It should also be mentioned that it is a fallacy, though perhaps a requisite one for anyone studying ancient Greek philosophy other than Plato or Aristotle (whose works are considerably more complete), to assume consistency in any single philosopher’s life or career as a thinker. Plato’s or Aristotle’s careers, as exemplified by their writings, reveal complex imaginations that neither were at one time entirely and completely systematic nor continued without change and development (although not always with progress). For Delatte’s view, see 1922: 22-8; for Guthrie’s, see 1962: 180-1 et passim. 46 kind of split between the earlier (acousmatici) and the later (mathematici) Pythagoreans took place in the middle of the 5 th Century BCE. This split is to be associated with the democratic revolution in Taras (473 BCE) and with the fall of Croton (perhaps 453/2 BCE), both of which appear to have influenced emigrations of Pythagoreans from Southwestern Italy to the Greek city-states of Southeastern Italy and the Greek mainland. 103 At the center of this debate about the alternate doctrinal schools is Hippasus of Metapontion, whose philosophical views seem to have laid the ground for a progressivist Pythagoreanism that both subsumed acousmatic teachings and revised the method of their dissemination in Southeastern Italian Pythagorean communities. The primary source about Hippasus and the pragmatic activities of Pythagoreans in the 5 th Century BCE is testimony from Apollonius of Tyana (1 st Century CE), recorded in Iamblichus’ On the Pythagorean Life, whose account confuses the political activities of Pythagoreans between the defeat of Sybaris by Croton around 510 BCE and the destruction of Croton in the mid-5 th BCE. 104 Apollonius tells us that originally, once Sybaris fell, the Pythagoreans “administered the land, but did not divide it according to the desire of the multitude.” 105 Subsequently, we are told, “the people’s silent hatred broke out, and they formed a 103 On which, see the Introduction. 104 On the confusion of chronology in this text, see Von Fritz 1977: 54-67. Von Fritz, while he does not find reason to agree with Delatte that Apollonius derived all of his account from Timaeus of Tauromenion, still assumes (p. 65) that Apollonius preserves much that “can be attributed to Timaeus with great probability.” 105 Iambl. VP. 255-7. Translated by Dillon and Hershbell. On land redistribution in Magna Graecia during the 5 th Century BCE, see Chapter 4. 47 faction against [the Pythagorean administrators from Croton].” The leaders of this faction, whose political views were hostile to the prevailing system of Pythagorean oligarchy, 106 were “those who stood closest to the Pythagoreans in ties of kinship and friendship” (oi( tai~j suggenei&aij <kai_> tai~j oi)keio&thsin). Interestingly, this account does not tell us that they were foreigners or Italians (Lucanians, Messapians or other Iapygians), or for that matter Sybarites, but rather that they were of the same genos; 107 what we have in essence is a rift among the Pythagoreans based on division of land and inheritance laws, a recurring ground for democratic revolutions. 108 Defending the traditional Crotoniate (i.e. oligarchic) Pythagorean political institutions were the Pythagoreans Alcimachus, Deinarchus, Meton and Democides; against these, we are told, were the pro-democratic leaders from the Council of the Thousand, namely Hippasus, Diodorus, and Theages, who “spoke on behalf of all citizens having a share in the political offices and in the assembly (u(pe_r tou~ pa&ntaj koinwnei~n tw~n a)rxw~n kai_ th~j e)kklhsi&aj), and of having public officials give accounts of their conduct to those who had been elected by lot from all citizens.” 109 106 Also see Iambl. VP. 257, where those who were “educated in common were setting themselves apart.” It is impossible to gauge whether Apollonius uses the term “oligarchy” technically or just as a term denoting aristocracy. 107 Iamblichus explains that the breach occurred between those who preferred that possessions could only be shared in common among the Pythagoreans themselves, and their relatives (oi( suggenei~j), who were excluded from property inheritance. 108 This is a common issue for 5 th and 4 th Century political feuds; it is central to Aristotle’s definition of political organization. See, inter alia, Arist. Pol. 1318a4ff. 109 Iambl. VP. 257. 48 The younger oligarchic Pythagoreans who followed Democides to Plataea, Apollonius’ account continues, 110 were accused by the Sybarite citizens of planning to establish a tyranny; the citizens voted to annul the laws (oi# de_ katalu&santej tou_j no&mouj) found in the Pythagorean constitution inherited from Croton and to promise a reward of three talents to whoever might kill Democides; 111 Theages, who was responsible (along with Hippasus and Diodorus) for instituting democratic regime change in Sybaris, overcame Democides in battle and brought the fugitives to trial. Interestingly, this account mentions that the trial was placed in the hands of representatives from Taras, Metapontion and Caulonia, a fact which, we are told, is recorded in the registers of the Crotoniates (w(j e)n toi~j tw~n Krotwniatw~n u(pomnh&masin a)nage&graptai). 112 This information suggests that Sybaris underwent democratic reform and expelled the aristocratic (or oligarchic) Pythagoreans after 473 BCE, when Taras became a democracy – possibly the first 110 Iambl. VP. 261. 111 The term is pa&trion politei&an at Iambl. VP. 258. Earlier, in a speech attributed to Pythagoras (Iambl. VP. 46), he tells the Crotoniates that the fatherland (th_n patri&da) was a common deposit (koinh|~ parakataqh&khn) that ought to be handed off to their sons. According to de Vogel 1966: 108 (contra Delatte 1922: 40) this description of the state presupposes an inherited social order that “does not fit in with fourth-century democracy.” On the contrary, it resonates more clearly with oligarchic, ancestral political structures in Thebes, Rhegion, and elsewhere during the mid-5th Century BCE (See below). Aristotle (Pol. 1305b39-1306a2) tells us that oligarchic revolutions can occur when oligarchs squander their living and attempt to bring about a change in government, either putting themselves forward as tyrant or outfitting someone else for it, as Hipparinus had done with Dionysius I of Syracuse (405 BCE). 112 Iambl. VP. 262. If Iamblichus continues to use Apollonius as his source here, we have testimony that supports the suggestion that Apollonius was using very old material by historians who had access to records at Croton, e.g. Timaeus of Tauromenion. Perhaps Timaeus would have seen these registers either in Delphi (Iambl. VP. 263) or in Heraclea, which held the treasury of the Italiote league following 393 BCE (see Wuilleumier 1987: 70-1). That Metapontion had a theatre built at the end of the 5 th Century BCE, earlier used as an ekklesiasterion for popular assembly, is acknowledged by Musti 2005: 99. Cf. De Siena 2001: 32. 49 democratic polis in Southern Italy 113 – following the expulsion of her last king, Aristophilides. 114 Indeed, if we are to consider Aristotle’s praise of Tarentine democracy as referring to the mid 5 th Century BCE, we see common elements in the shift of political organization: one of two groups of administrators at Taras, we are told, is elected by lot “in order to ensure that the people may have a share (mete&xh|) in [the offices].” 115 What is especially interesting about the account preserved in the registers at Croton is the linking together of Taras, Metapontion, and Caulonia: if we imagine a league, as Polybius did, 116 constituted of newly-formed democratic 117 poleis that were unified in prosecuting and sending into exile the aristocratic Pythagoreans, then we have a geographical alliance of city-states that agreed to expel proponents of 113 It is probable that the presence of the circular building known as the ekklesiasterion in Metapontion in the 6 th Century BCE suggests a democratic regime. See my Chapters 4 and 6. 114 Hdt. 3.136. Also see Arist. Pol. 1303a8-12. Taking into account Minar’s evidence (1942: 77-8), we should then date the expulsion of the oligarchs and the juridical activity of league of Taras, Sybaris, and Caulonia to between 473 and 453 BCE. I prefer a later date for the expulsion (mid-450s) based on the expectation that it would be more likely that a judicial league could form and succeed only after democratic institutions had been in place at Metapontion and Taras. De Juliis 1996: 215 would date the expulsion after the death of Hiero in 467 BCE and before the founding of Sybaris (II) in 453 BCE. On other democratic revolutions in Southern Italy following that of Taras (most of which take place in the late 460s), see Musti 2005: 241-2. 115 Arist. Pol. 1320b10-16. The language of participation, which recalls Philolaus and Plato both (see below), is philosophical and political. 116 Plb. 2.39.6. Cf. Diod. Sic. 14.91. To be sure, Polybius does not mention the presence of any leagues between Taras and Metapontion, but we may assume that some formal alliance was in place before the attacks of the Lucanians in the early 4 th Century BCE necessitated a formal military league between the Greek city-states of the Italian peninsula. 117 We know nearly nothing about Caulonia’s constitutional structure during this period (Sartori 1953: 124), but the combination of Taras’ and Sybaris’ democratic revolts, datable to this period, with the complaint that the representatives from these groups were bribed (a typical criticism of democracies in the 5 th and 4 th Centuries BCE) suggests that all three engaged in what we might see as a democratic affiliation. On this subject, see Walbank 1957-1979 ad loc. 50 aristocratic forms of Pythagorean governance as early as the 450s BCE. 118 This suggestion would revise the hypothesis put forth by Ettore De Juliis that the federalized organization of Croton, Caulonia, and Sybaris (IV) in the 420s – which imitated the Athenian democratic league – was “il precedente e il nucleo della più ampia Lega Italiota.” 119 Hippasus, who was probably from Metapontion herself, is credited with leading the initial charge against aristocratic Pythagoreanism and supporting democratic reforms such as abolishing debts and redistributing the land. 120 Indeed, Metapontion would become one of the popular centers of Pythagoreanism in the century that was to come, to such an extent that Iamblichus’ list of Pythagoreans recounts 38 Metapontine Pythagoreans, second only to Taras with 43; 121 we can assume, with Domenico Musti, that there must have been some kind of agreement between Taras and Metapontion; it would have to have extended beyond the initial alliance against the aristocratic Pythagoreans from Croton, since no disputes are recorded between the two city-states until perhaps the advent of Alexander the Molossonian in the late 330s/early 320s BCE, when Alexander – requested to aid the Tarentines against the incurring Lucanians – established a peace 118 Similarly, at Akragas/Himeria in Sicily, Empedocles – another “Pythagorean” (D.L. 8.56, from Alcidamas’ book Fusiko&j) who was considered to have rebelled against his teacher – might have had a hand in composing laws in a democratic vein following the deposition of the tyrants (471 BCE). He is called dhmotiko&j by Timaeus of Tauromenion. On the possibility that Empedocles challenged aristocratic Pythagoreanism, see Musti 2005: 179-82. Democratic revolutions also occurred at Syracuse, Naxos, Catania, and Rhegion in 461/60. It is remarkable that Musti, in his new history of Magna Graecia, does not mention the democratic revolutions in these city-states – nor yet Hippasus – as recounted by Apollonius of Tyana and perhaps derived from Timaeus. He instead sees the revolutions among the Pythagoreans as “antipitagoriche” (p. 424) 119 De Juliis 1996: 219. Cf. Plb. 2.39.4. 120 Iambl. VP. 262. 121 Iambl. VP. 267. 51 treaty with the Metapontines, Pediculi and Romans. 122 As a city-state with democratic Pythagorean influence, Metapontion may have welcomed native Italian peoples both into its civic space and into its magistracies, at least at the end of the 5 th Century; this is when we find an inscription, written in Osco-Messapian, that celebrates a certain Aozea Kasein who held a magistracy (medikia) in Metapontine territory. 123 Certainly, there is the possibility that policy dealing with Messapians, Peucitians, and other Italic peoples from Puglia varied from Metapontion to Taras, which seems to have had a more consistently agonistic relationship with its Italian neighbors to the east throughout the 5 th Century BCE. 124 Regardless, Metapontion was only 44 kilometers from Taras, and she did not react against the establishment of Taras’ colony Heraclea Italica in 433 BCE, which effectively delimited Metapontion’s hegemony by placing it between two Tarentine city-states. 125 Archaeological evidence suggests that, during this period, Metapontion’s territory in the Sybaritide was reduced and that she was unable to reclaim it; what import of 122 See Musti 2005: 343; Justin, 12.2. Also see Delatte 1922: 258. 123 On this inscription and the terms medikia/meddiss, see Sartori 1953: 18-27 and 100. We need not assume, with Sartori, that this inscription implies “un periodo, per quanto breve, di dominio osco- messapico, durante il quale la città sarebbe stata governata con il sistema osco” in Metapontion. We must recall that the democratic revolution in Taras, which, I am suggesting, set off a series of popular revolts throughout the region, was caused by native Italians, who were made up of Iapygian peoples. Aristoxenus tells us (F 17 Wehrli) that the Messapians and Lucanians, along with the Peucitians and Romans, visited Pythagoras, presumably in order to learn about how to structure their polities, and so we may assume that there may have been a shared interest at least in the first half of the 5 th Century BCE. On the complex ethnic composition of city-states in Southern Italy, see Musti 2005: 64-5 et passim. On the other hand, as Huffman notes (2005: 9), Taras – who was probably Metapontion’s ally throughout much of the 5 th Century – allied itself with Syracuse in 415 BCE, while the Messapians were allied with Athens. The material is sparse and difficult to synthesize, to be sure. 124 Wuilleumier 1987: 65 reports a didramma from Metapontion with the legend o(monoi&a coined during this period. On o(monoi&a as a political and mathematical concept for Archytas of Taras, see Chapter 2. 125 Musti 2005: 169. 52 relations with Messapia would have had upon foreign relations with Taras is unknown. 126 The suggestion that Metapontion could have had common interests with the Messapians is justified when we consider that, in 413 BCE, Athens was allied with both Messapia and Metapontion during the Sicilian Expedition, if only in name; 127 be that as it may, no battles are recorded between Metapontion and Taras, who was allied with Syracuse in 415 BCE, and we may assume that Metapontion was simply too politically and economically debilitated to be independent of Doric Taras. I agree with Musti that Pythagoreanism was a vehicle for establishing links between Taras and Metapontion and that “questa comunità metapontina, a mio avviso, viene anticipita con la stessa logica con cui si anticipa il pitagorismo a Taranto, nonché il ruolo egemone di questa città.” 128 What Musti fails to note, however, is the presence of independent traditions deriving from Apollonius of Tyana – possibly tracing back to Timaeus of Tauromenion in the 3 rd Century BCE – that credited Hippasus as catalyst for a schism within Pythagoreanism that led to democratically-minded philosophical city-states in Metapontion, Taras, and possibly other Greek city-states of Southern Italy such as Croton and Caulonia. 129 When we 126 De Siena 2001: 35. 127 Thuc. 7.33.3-4. 128 Musti 2005: 169. 129 That the information pertaining to the agreement between Taras, Metapontion, and Caulonia was found in the registers of the Crotonians – who are not mentioned as participating – suggests that Croton wanted to highlight her democratic heritage following the establishment of the democratic league between Caulonia (which is the connecting element), Sybaris (IV) and Croton. This would date the registers to the time following Croton’s establishment as a democratic regime, not to be dated (contra De Juliis 1996: 215) before the return of the acousmatic Pythagoreans to Croton and the 53 consider that, within this tradition, Hippasus was the first mathematicus, and that the mathematici were an exoteric Pythagorean group – not identified as Pythagorean by the esoteric acousmatici – then it is no surprise that the rift assumed in tradition between them concerns, as Iamblichus describes it, the different pragmatics that each group employs: so Iamblichus, in the more reliable version of the story (Comm. Math. p. 76.19 Festa) that can be traced back to Aristotle’s list of mathematici: 130 Of these [philosophers], the acousmatici are agreed to be Pythagoreans (Puqago&reioi) by the others [the mathematici], but they do not agree that the mathematici are so, nor do they [the acousmatici] believe that the pragmateia of them [the mathematici] is derived from Pythagoras, but from Hippasus. According to this Aristotelian account, the primary difference between the acousmatici and the mathematici is pragmatic, i.e. it relates to the major elements that are bound to political organization and beginnings/origins/first principles (the a)rxai&). As such, both the fundamental principles and the politico-philosophical activities were definitive markers of each group: the acousmatics did not employ complex mathematics or phenomenological mechanics in the application of their pragmateia, while these elements were crucial in defining the mathematicians against their predecessors. 131 destruction of democratic Sybaris (II) in 448 BCE; more likely we should locate a fully-democratic regime at Croton following the defeat of the Thurians by the Tarentines and subsequent founding of Heraclea in 433 BCE but before Thurii was to undergo a revolution that converted its constitution from an aristocracy to a democracy (Arist. Pol. 1307a27ff), probably to be dated to 413 BCE. 130 See Burkert 1972: 196 and 457. 131 On which, see especially Chapters 4, 5, and 6. 54 To sum up: we have thus far examined the ways in which a tradition about which we owe our knowledge to Aristotle has postulated a breach in the Pythagorean community that existed at Croton during the late 6 th through the mid 5 th Centuries BCE. That breach occurred as a consequence of changes in the third category of Pythagorean acusmata, pragmatics, which is still a vaguely defined combination of the political and philosophical. The changes that mathematici assumed politically involved a passage from oligarchy (in Apollonius’ terminology) to democracy and a synthesis of newly-formed democratic communities into an alliance that suggests a league; I have not yet comprehensively examined the modifications to their philosophical pragmatics, but instead I have suggested that some Pythagoreans were understood to perform simple diaereseis in their attempts to arrive at definitions, both in terms of magnitudes and in terms of numbers. Indeed, the question remains whether philosophical pragmatics was responsible for developments in political organization or vice versa; it might be a chicken and egg question, but regardless we can trace the coexistence of both in the Pythagorean politico-philosophical pragmateia. Aristotle criticizes this project as it was practiced by Pythagoreans, but it seems that he refers to the acousmatici when he complains of superficial definitions that mask the conflation of categories of Being. This split in the Pythagorean unity, datable to somewhere between 473 and 453 BCE (but perhaps most likely to be dated to the end of that period), is attributed to Hippasus of Metapontion, whose modifications in the Pythagorean pragmateia characterize a new community of democratic Pythagorean philosophers who were active in politics 55 and located in Greek city-states along the Ionian Sea from the mid 5 th Century BCE into the mid-4 th Century BCE. It remains for me to define how the bifurcated definition of pragmatics, relating to philosophical and political praxis, affects and catalyzes a polysemy of the politico-philosophical term arch1. It will be possible to do so if we consider the traditions of mathematici who followed the lead of Hippasus, especially Philolaus and Archytas, and examine what relationships exist between their philosophical postulations of archai and the political concept of rule as it was inherited in this community. THE “SO-CALLED PYTHAGOREANS” AND THE FOLLOWERS OF HIPPASUS OF METAPONTION In several places (Metaph. 985b24 and 989b29, Cael. 284b7 and 293a20, Mete. 342b30, 345a14), Aristotle refers to a group of Pythagorean philosophers whose primary interests seem to be related to mathematics and astronomy; 132 these are the “so-called Pythagoreans” (oi( kalou&menoi Puqago&reioi), whose philosophical activities correlate, in some way, with those of the “Italics” (Cael. 293a20, Mete. 342b30); thus we can contextualize these citations with those 132 Few passages in Aristotle’s extant works attribute interest in astronomy to the Puqago&reioi, but all passages that deal with “oi( kalou&menoi Puqago&reioi” refer to “heaven” or other astronomical phenomena; the distinction is sustained especially in Book A of the Metaphysics. Two passages that discuss the “Pythagoreans” with a reference to mathematics (especially magnitude) and heaven (Metaph. 1080b16-21, 1090a30-1090b1) might refer to the “so-called Pythagoreans” specifically, or perhaps to Pythagoreans in general. The appearance of the “kalou&menoj ou)rano&j” as a feature of “so-called Pythagorean” astronomy at Metaph. 990a5 is rich with the same Aristotelian skepticism of the “Antichthon” denoted as a “so-called Pythagorean” proposition twice (Metaph. 986a12, Cael. 293a24). 56 additional bits that refer to “Italic” philosophy (Metaph. 987a10, 987a31, 988a26). 133 It is unclear whether, in references to “some Pythagoreans” (Cael. 300a17; cf. 303a8-9; Peri_ tw~n Puqagorei&wn F 16 Ross; perhaps Metaph. 1090b5-8), Aristotle is thinking of these “so-called Pythagoreans” or not. 134 Further, there is certainly some confusion about what passages from the later books of the Metaphysics (especially in books M and N) refer to the mathematici, and it cannot be regarded as certain that Aristotle was distinguishing between different kinds of Pythagoreans at this point in his composition. For Book A of the Metaphysics, as Maria Timpanaro Cardini has demonstrated, the kalou&menoi Puqago&reioi refer to those followers of Hippasus, the mathematici, whose political and philosophical activities seem to have been located (for the most part) in Southeastern Italy. 135 133 Domenico Musti has investigated what “Italian” could mean for pre-3 rd Century BCE historians and philosophers; his conclusions: “Nome di Italía, area achea (crotoniate), nozione di Megále Hellás, e pitagorismo, sono dunque quattro nozioni storiche che viaggiano insieme, così mostrando il progressivo estendersi delle nozioni di Italia e di Magna Grecia tra lo stretto di Messina/Reggio e la Iapigia, tra il VI e IV secolo.” See Musti 2005: 80. 134 J. Philip’s comment (following Cherniss) in 1963: 253 that “none of the several designations is to be understood as applying only to a group within the school” is a generalization that is not sustained within Book A of the text: at 986a24, Aristotle speaks of “others from [the “so-called Pythagoreans”]” who believe that ten principles (a)rxa_j) are the Table of Opposites; the “so-called Pythagoreans,” on the other hand, believe that numbers (oi( a)riqmoi&) are the first among principles (see below) and they see the Table of Opposites as subordinate, corresponding with the elements of number (stoixei~a a)riqmou~). Further, Philip’s comment (p. 253 n. 3) that “the only other school that could be called ‘Italikoi’ is the Eleatic, and it is clearly out of the question” neglects the probability that Eleatic and Pythagorean philosophies have more in common with each other than they do with Aristotle’s system of metaphysics (for which he is arguing); indeed, the short excursus on Parmenides and Melissus, couched in the middle of a longer refutation of Pythagorean philosophy (986b8-987a2), draws explicit comparisons between the “others than these” who believe that the sets of immaterial Tables of Opposites are the first principles and Parmenides who held that oppositional material forces (e.g. Hot and Cold) were the first principles! 135 See Timpanaro Cardini 1964: 3-19. She notes (pp. 9-10), in reference to political communities, that at Arist. Pol. 1290b40: “Aristotele nomina le varie categorie di abitanti, che compongono la po&lij, e comincia dai gewrgoi&, che specifica con kalou&menoi volendo indicare, in senso politico, una determinate ripartizione sociale.” 57 Let us examine the first of two longer passages from Aristotle’s Metaphysics (985b23ff. and 989b29ff.), both from Book A, which distinguish the “so-called Pythagoreans” from other Pythagoreans. We should pay attention to the rhetorical argumentation, so as to get a sense of what Aristotle implicitly sees as differences between this sect of Pythagoreans and the Puqago&reioi considered more generally: In the time of these men [sc. Leucippus and Democritus] and before them the so-called Pythagoreans first developed mathematics by applying themselves to it, and through learning it they began to believe 136 that the first principles of mathematics (a)rxa_j [tw~n maqhma&twn]) were the first principles of all things in existence (a)rxa_j tw~n o!ntwn pa&ntwn) . And since numbers are first among principles 137 by nature, it seemed to them that they could perceive many analogues (o(moiw&mata) with numbers both among things that exist and among things that are becoming, rather than with fire and earth and water. For example: this characteristic of numbers was justice, that was soul and mind, and another appropriate time, and every other one, so to speak, according to the same system. And, what is more, because they saw the characteristics and ratios of musical harmony were based on numbers – well, since other things seemed to be analogized with numbers in their whole nature and numbers seemed to be first-order of all nature, they began to assume that the elements of numbers were the elements of things that exist and that the whole of heaven was harmony and number. And however many things related to the characteristics and parts of heaven and the entire order of the cosmos they were able to analogize with numbers and harmonies (o(mologou&mena e)n te toi~j a)riqmoi~j kai_ tai~j a(rmoni&aij), they brought them together and harmonized them (e)fh&rmotton). And if anything was lacking anywhere, they hastened to apply it (prosegli&xonto) 138 in order that their entire pragmateia 136 Taking , with Tredennick, w)|h&qhsan as an inceptive aorist. Aristotle’s reference to the past here reflects his interest in creating a developmental narrative of the history of “so-called Pythagorean” philosophy. 137 This is the reading if tou&twn refers to the direct object a)rxa_j in the previous sentence, as Tredennick reads the text. However, Ross plausibly reads against the word order and suggests that tou&twn refers to maqhma&twn (Ross 1924: ad loc.). 138 This extremely uncommon word also appears at 1090b31, where Aristotle likewise complains that some Platonists (perhaps Xenocrates or Speusippus? See Annas 1976: 209-10) hasten to apply mathematics to the Forms (prosglixo&menoi tai~j i)de&aij ta_ maqhmatika_). At Cael. 293a27, 58 might be connected. For example, since the Decad is thought to be the goal and to encompass the whole nature of numbers, they assert that those things in heavenly orbit are ten, and since there are only nine that are actually visible throughout the heavens, they make the Antichthon the tenth. 139 Aristotle begins this passage on the “so-called Pythagoreans” by referring to the confused system of principles of mathematics and of reality. According to this testimony, the vehicle for confusion of these principles is the practice of analogy; instead of likening things that exist to the elements that were typical of Ionian philosophers (fire, water, earth), the “so-called Pythagoreans” likened them to numbers through homologia. 140 Throughout this passage, the emphasis on first principles and what is primary suggests Aristotle’s concern with how their a)rxai& differ from those of Leucippus and Democritus, among others recently discussed in the text. Analogy, as the operating praxis of “so-called Pythagorean” philosophy, is supplemented by “hasty addition,” which leads to a complete and connected pragmateia: the example of the Antichthon serves Aristotle by announcing the slippage that occurs between what is perceivable and what exists, a confounding of ontological elements with what is imagined. 141 The emphasis on homologia and the “so-called Pythagorean” pragmateia recalls Hippasus and the mathematici, as argued above. The difference between Aristotle accuses the “so-called Pythagoreans” of “attracting what is apparent to certain rationales and opinions of their own (pro&j tinaj lo&gouj kai_ do&caj au(tw~n ta_ faino&mena prose&lkontej).” 139 Arist. Metaph. 985b23-986a12. 140 In this way, the “so-called Pythagoreans” must be included in what Aristotle calls the “modern philosophers” who define the world according to a “common body” instead of an individual element (Metaph. 1069a24-36). 141 As Burkert shows (1972: 344), neither was the Antichthon a singularly Pythagorean concept nor was it as absurd a means to understand astronomical phenomena as Aristotle wishes it to be. 59 acusmatic and mathematic Pythagoreans lies in the various applications of their pragmatics, which involves (for Aristotle and his students) the first principles (a)rxai&) of philosophical investigation. For the “so-called Pythagoreans,” employment of mathematics is the primary activity of their pragmateia, and this suggests that this group and the mathematici are the same people. Then, within the mathematici, there is room for further division. Some mathematicians, such as Hippasus and his students Hippocrates of Chios and Theodorus of Cyrene (the teacher of the young Theaetetus in Plato’s Eleatic trilogy), seem to have involved themselves in serious experimentation dealing with astronomy, 142 mathematical proofs (including the famous “discovery” of Incommensurability attributed to Hippasus and datable to the middle of the 5 th Century BCE), and musical scales, pitch, and harmony; 143 other mathematici, like Philolaus, were not serious mathematicians, but rather they applied “basic mathematical ideas to philosophy in the same way that Plato does in the Timaeus and elsewhere.” 144 Now, it is clear that the account presented in Aristotle’s Metaphysics presents the development of “so-called Pythagorean” philosophy from an original interest in 142 In Book L of the Metaphysics (1073b3-8) Aristotle defines astronomy as an extension of arithmetic and geometry: “We must examine the plurality of circuits from that branch of mathematics most like unto philosophy, namely astronomy; for this makes the scope of its inquiry perceived and unseen Being, but the other branches of mathematics, i.e. arithmetic and geometry, do not deal with Being.” 143 The best treatment of this subject is Von Fritz 1945. But see my Chapters 5 and 6. 144 C. Huffman 1993: 10-12. Huffman’s claim that “[a] Pythagorean could become a philosopher of the Presocratic sort (a physikos), a mathematician, a physician or even a leading general” seems to apply best, in my opinion, to a mathematicus who had escaped (as Philolaus had) from Croton’s traditional, conservative, oligarchic form of Pythagoreanism to a more unrestricted form of living. On Philolaus, see below. 60 mathematics to an arithmological pragmateia that features mathematics, astronomy, and musical study alongside one another. We need to press hard upon Aristotle’s description, however: for, in the account presented in the Metaphysics, Aristotle seems to present a narrative of “so-called Pythagorean” philosophical development without Hippasus himself in mind. The evidence against Hippasus as a “so-called Pythagorean” lies in the oldest testimonium available to us about Hippasus: a single comment in the Metaphysics (984a7), in which Aristotle, operating on the assumption that Hippasus was a monist, claims that Hippasus and Heraclitus posited fire as “definitely the first principle” (ma&list’ a)rxh_n). 145 If we believe Aristotle here and follow Ross in assuming that Hippasus was a Pythagorean who “formed his system by a fusion of Pythagorean and Heraclitean elements,” 146 i.e. he analogized Number and fire, then our characterization of him as one of the exoteric or “so-called Pythagoreans” continues to convince. 147 But the ascription of fire as the first principle to Hippasus clearly contradicts what is said later about the “so-called Pythagoreans” and their principles in the second longer passage found in the Metaphysics (989b29-990a29); they, on the other hand, do not speak of fire: The “so-called Pythagoreans” use first principles (a)rxai~j) and elements (stoixei&oij) more abstrusely 148 than the physicists. The reason is that they assume that the principles and elements are not 145 Cf. Theophr. Phys. op. fr. 1 = Dox. 475. Cf. the “ancients” referred to at Metaph. 1069a26. 146 Ross 1923: ad loc. 147 Hippasus, according to Iamblichus (VP. 246; Cf. Clem. Strom. 5.58), was put to death for revealing esoteric secrets of the Pythagoreans, and was known to have published a Mystical Speech against Pythagoras (D.L. 8.7). 148 e)ktopwte&rwj following Guilielmi de Moerbeka translatio (c. 1260-1275 CE) and Asclepii commentaria. An alternative reading (e)ktopwte&roij) is possible, following Bonitz and Alexandrii commentaria. 61 from perceived things: for mathematical beings (ta_ maqhmatika_ tw~n o!ntwn), except for things related to astronomy, are lacking motion (a!neu kinh&sew&j e)stin). Nevertheless, they discuss and make the object of their investigations (pragmateu&ontai) all things that concern nature. For they generate heaven, and they observe what happens concerning the parts, characteristics, and activities of heaven, and they lavish these things with first principles and causes, as though in agreement with the physicists that Being is so much as is perceived and that “so-called heaven” (o( kalou&menoj ou)rano&j) contains it. But, as we’ve said, they declare that the causes and the first principles are able to rise up above the horizon (e)panabh~nai) 149 to the higher parts of reality; these are better fitted to the arguments that concern nature. Nevertheless, they say nothing of by what rationale there will be motion if only Limit and Limitless, Odd and Even, are premised (u(pokeime&nwn), nor (do they say) how it is possible for Becoming and destruction or the activities of things that pass along heaven to exist without motion and change (a!neu kinh&sewj kai_ metabolh~j). 150 And, what’s more, if someone were to grant to them that magnitude is composed of these things, or if this were proven by them, nevertheless according to what rationale will some bodies be light and others heavy? For, from the things which they hypothesize and say, they are talking no more about mathematical bodies than perceived bodies. And so they have said nothing whatsoever about fire or earth or any other bodies of this sort, since, in my opinion, they say nothing particular to perceived bodies. Again, how should one understand the causes of things that exist and become in heaven both from the beginning and now to be the characteristics of number and number, when no number exists other than this number of which the universe is composed? For, whenever Opinion and Opportunity are in such and such a region for them, and Injustice and Separation or Mixture 149 This translation is preferable to Tredennick’s “capable of application to the remoter class of realities,” which does not account for the technical language of astrology reported here. In a passage of the Meterologica (342b30ff.), Aristotle describes how the “some of so-called Pythagoreans” believe that Mercury is, like comets, one of the Planets which “does not rise far above the horizon (to_ mikro_n e)panabai&nein),” and therefore its appearances are invisible as it is seen in long intervals. That this word occurs here in similar contexts, and not anywhere else either in the Metaphysics or Meteorologica, suggests the possibility that Aristotle has access to a particular work on “so-called Pythagoreans” and their astronomical theories. 150 That the “so-called Pythagoreans” premised Limit and Limitless, Odd and Even, as archai does not necessarily follow from this passage. Aristotle could have used the term “u(parxo&ntwn”, as he does at 1026a32 in contrast with what exists in reality. Instead, as we discover from 986a18, the “so-called Pythagoreans” believe that Odd and Even, Limited and Limitless, were the elements (stoichea) of things. 62 are a bit higher or lower, and they declare as proof the fact that each of these is a number; furthermore, it happens that there is already a plurality of magnitudes composed [of numbers] in that place because these characteristics correspond to each of these places. So is the number which is in heaven, the one which must be understood as each of these things, the same, or something other than this? Now, it is difficult to infer what came before these lines: there is a significant lacuna in the manuscripts (169 letters by Ross’s figuration) 151 preceding this passage, which must have discussed the theories of the Monists and the Dualists. Our text preserves the criticisms of Empedocles and Anaxagoras, and we can presume – if Aristotle is in the business of repeated structural motifs – that what is missing would have explained the elemental theories of the Atomists Democritus and Leucippus, which had preceded Aristotle’s former criticism of the “so-called Pythagoreans’” pragmateia. Presumably, Aristotle saw the “so-called Pythagoreans” as a group whose first principles provided a bridge between the Presocratics and Plato, because the description of Platonic ideal theory follows directly after this section. He claims in this section that, among other things, the “so-called Pythagoreans” fail to distinguish between mathematical and perceived bodies; their failure to distinguish between number and the natural phenomena of the universe occurs as a consequence of confusing bodies of different orders, and the familiar complaint that a unified thing cannot be analogized simply with plural things is expressed here. Notably, these “so-called Pythagoreans” do not discuss how the elements, among them fire, fit 151 Ross 1924: clix. 63 into the scheme of number/cosmos. 152 Hippasus’ belief that fire is the first principle would exclude him from this criticism, and he would appear not to be one of the “so- called Pythagoreans” whose cosmology Aristotle is challenging. So where can we place Hippasus among the categories of philosophers, as Aristotle draws them up? While Hippasus is not mentioned in this section that details Aristotle’s criticisms of other philosophers’ first principles, Aristotle does refer to those who believe that fire is the most elementary body: So, in one way, someone might think that the most elementary (stoixeiwde&staton) of all things is that from which first things come to be in a composition, and this would be the rarest and finest of bodies. Therefore, however many people posit fire as the first principle (a)rxh_n) speak in a way that accords most especially with this concept. And, even among the others, each agrees that this [fire] is the element (stoixei~on) of bodies. 153 Aristotle’s summary of Heraclitus’ and Hippasus’ theory that fire is the primary element does not receive such extreme censure as the theories of those Monists who believed that earth was the primary element or first principle. At the very least, Heraclitus’ statement (preserved by Clement) that “this universe, the one composed of all things, no god or man made, but it was and is and will be ever-living fire, kindling in measures and being extinguished in measures (a(pto&menon me&tra kai_ a)posbennu&menon me&tra)” postulates a respectable kinetic force, flux embodied in 152 I will discuss this passage throughout this chapter, since its implications are far-reaching. 153 Metaph. 988b34-989a5. 64 fire; 154 interestingly, Heraclitus’ fragment also assumes the relation of fire to astronomical and mathematical figures. And so, we can assume, with Aetius (perhaps 1 st Century BCE), that the prominence of fire in Hippasus’ philosophy is in dialogue with the theories of other Presocratic philosophers who posited an elemental flux as a primary kinetic force. 155 And so, it seems that Hippasus might be best cast as a second-rate Milesian; Simplicius corrects this interpretation by discussing Hippasus’ first principle in terms not particularly Heraclitean: Hippasus of Metapontion and Heraclitus of Ephesus also [supposed that the first principle] was one and activated and limited (e$n…kai_ kinou&menon kai_ peperasme&non), but they made it fire, and they make it that the things that exist are made out of fire through condensation, and, through rarefaction, they are resolved back into fire, since this is the one premised/underlying (u(pokeime&nhj) nature. 156 According to Simplicius’ argument, Hippasus seems to have followed those who believed that the a)rxh& was one, activated, and limited. However, unlike the other Monists, Hippasus and Heraclitus believed that the first principle was fire, something that, while being one, activated, and limited, was responsible for making and 154 DK 22 B30. Aristotle’s subsequent comment (989a12-15) is: “So, according to this theory, if someone were to offer up any of these other than fire, or posit something denser than air but rarer than water, he would be wrong.” 155 Aet. 4.3.4. equates Hippasus’ theory that the soul was fire with Parmenides’ and Heraclitus’. On flux theories, and their possible application to Pythagorean theories of magnitude, see Cornford 1935: 11-12. 156 It is probable that Simplicius is quoting Theophrastus here, although he is not named explicitly in reference to this information. This theory is assumed to be Theophrastean by Cornford and Fortenbaugh. In the preceding passage, Simplicius has been quoting Aristotle and Theophrastus only. Timpanaro Cardini 1958: 95, reminds us that the phrase “fu&sewj th~j u(pokeime&nhj” is Aristotelian. Cf. Aet. 1.5.5 and D.L. 8.84, where to_ pa~n is said to be limited and always in motion. 65 dissolving things. 157 The emphasis on fire as a limited unity (e$n peperasme&non) recalls Aristotle’s comment (Metaph. 986a18) that the “so-called Pythagoreans” believed that the elements (stoixei~a) of number were the Odd and the Even, which were, respectively, “Limited and Limitless” (to_ me_n peperasme&non to_ de_ a!peiron). In this way, Simplicius (probably following Theophrastus) assumes that Hippasus saw fire as a Pythagorean first principle; his confusion of what Aristotle does not see as mutually comparable principles is understandable, given the nature of the evidence. We may contrast both these theories about a)rxai& – that of Hippasus and that of the “so-called Pythagoreans” – with the doctrine ascribed to “other [Pythagoreans] than these” who believed in the Table of Opposites, which shows a slight but determinative difference in technical terminology: “Limit and Limitless” (pe&raj a!peiron). 158 Indeed, later in Book 1, Aristotle tells us that “the Pythagoreans” spoke of two a)rxai& but with a significant addition: “they didn’t think that the Limited (to_ peperasme&non) and Limitless were different sorts of natures, like fire and earth or another thing of this sort, but that Limitless itself and the One itself are the essence of those things of which they are predicated, and therefore that number is the essence of all things.” 159 Aristotle is contrasting one theory of “Limited” (to_ peperasme&non) with another theory that simply and non-technically employs the term “One” and, as we next discover, is to be chastised for its adherence 157 If this fragment genuinely represents the ideas of Hippasus, then we may follow Cornford 1935: 23-4 in assuming that Fire rarefies and condenses in a manner comparable with Anaximenes’ Air. 158 Arist. Metaph. 986a23. 159 Arist. Metaph. 987a15-19. 66 to superficial definition. 160 The likelihood that Aristotle is referring here, in the theory that proposes Limitless and the One as the essence of predicated things, to the acousmatic branch of Pythagoreanism is supported by the earlier criticism of those Pythagoreans “other than [the so-called Pythagoreans].” Here, Aristotle complains that these Pythagoreans fail to make clear definitions because they “seem to posit elements in the form of matter.” 161 So let us sum up some of our conclusions from this investigation: the “so- called Pythagoreans” appear to adapt a modified, later version of Pythagorean doctrine. Their primary interests, like those of all mathematici, are mathematics and astronomy. The slip-shod application of mathematics (both arithmetic and basic forms of geometry, represented by Aristotle as involving theories of magnitude) to astronomy has led to the invention of a tenth body, the Antichthon, that exists in their “so-called heaven.” Aristotle criticizes these “so-called Pythagoreans” for being hasty to apply general principles of mathematics to their astronomical theories, especially the practice of homologia: such hasty application represents the “so-called Pythagoreans’” attempt to obtain a connected pragmateia by means of harmonization. 162 Their first principles (a)rxai&) are two, namely Limited and Limitless; they are, in some ill-defined way, comparable with the numbers one and 160 Slippage between the technical terms “Limited” and “One” has been the common means of explaining away the difference between what I see as alternative formulations of Pythagorean philosophy. See Ross 1924: ad loc., where he admits that even the copyist felt obliged to add an “kai_ to_ e#n” in order to resolve the problems. Cf. Huffman 1993: 206-7 and Burkert 1972: 36 n. 38. 161 Arist. Metaph. 986b4-7. 162 On this subject, see below in this chapter. 67 two. 163 In this way, the first principles of the “so-called Pythagoreans” seem to derive from the a)rxh& of Hippasus, who also subscribed to the notion that his first principle was Limited, although Aristotle does not consider Hippasus to be one of these Pythagoreans. The archai of the “so-called Pythagoreans” may be contrasted with the first principles of those “other than these [the so-called Pythagoreans],” which align with the Pythagorean Table of Opposites and include, notably, “Limit and Limitless.” 164 Aristotle criticizes these thinkers along with Alcmaeon of Croton for confusing elements (stoixei~a) with matter and for premising Being (ou)si&a) among the set of corresponding pairs that make up the Table of Opposites. Hippasus of Metapontion, who is credited as the first mathematicus, resembles a Monist of the Milesian sort more than a Pythagorean, although his theories seem to bridge the gap between Presocratic philosophy and the pragmateia of the Pythagorean mathematici. So if Aristotle’s Metaphysics (silently) disagrees with later historical sources in attributing the first schism in Pythagorean philosophy to Hippasus of Metapontion, we must ask the question: “to whom is Aristotle referring when he discusses the ‘so-called Pythagoreans?’” The answer lies partly in an understanding of how cosmological theories about the universe attributed to the “so-called Pythagoreans” developed from Hippasus and Heraclitus to those thinkers, located in Southeastern Italy, whose astronomical and mathematical philosophical propositions 163 This has confounded critics and editors alike. Huffman confuses the terms here by not attending closely to the difference between Limit, Limited, and One (1993: 179). 164 See KRS 1983: 338-9. 68 involved a fusion of earlier Pythagorean and Milesian first principles, 165 an abandonment of a single term as first principle for a dualistic paradigm based on opposition, and the subsequent development of a third term that corresponds with Aristotle’s “triad.” 166 As we have seen, later scholars of Pythagorean mathematics credited Hippasus of Metapontion with the concept that fire was the first principle of things. They further ascribed the belief that fire was divine 167 and that it constituted the soul 168 to Hippasus. Interestingly, we are also in possession of a few fragments that detail the beliefs of the “followers of Hippasus” (oi( peri_ I#ppasoj), who are confused with the acousmatici in all accounts that derive from Iamblichus. 169 If we follow Burkert’s correction of Iamblichus’ (and Syrianus’) texts, these must indeed be the mathematici referred to in On the Communal Mathematical Science. And so, we are told that these mathematici, adhering to the philosophy of their progenitor Hippasus, formulate the relationship between numbers and the heavens on the basis of paradigmatic imitation. Iamblichus (Introduction to the Arithmetic of Nichomachus 10.20), in a fragment that will be of special importance to our argument and to which we shall return often, explains: 165 Aristotle also claims that “mathematical accuracy” (th_n a_kribologi&an maqhmatikh_n) is only required for things that do not have matter; hence, he claims, mathematical proof does not deal with natural science (Metaph. 995a14-16). Hence we may venture to say that one of the distinctions between Milesian and “so-called Pythagorean” philosophy lies in the problem of matter. 166 Arist. Cael. 268a7-17. 167 Clem. Protr. 5.64. 168 Aet. 4.3.4; Tert. De anim. 5.; Cf. Claud. Mam. De anim. 2. 7. 169 See Burkert 1972: 193-4. 69 Oi( de_ peri__ I#ppason maqhmatikoi_ a)riqmo_n ei}pon para&deigma prw~ton kosmopoii&aj kai_ pa&lin kritiko_n kosmourgou~ qeou~ o!rganon. The mathematici 170 of the school of Hippasus said that number was the ‘first paradigm of the making of the cosmos’ and also ‘the discerning tool of God the cosmiourge.’ This fragment is located within a larger discourse about number and the monad; it features theories of Thales and Pythagoras in contrast with “others than these” (e#teroi tw~n), who include the followers of Hippasus along with Eudoxus the Pythagorean (from Cnidos) and Philolaus of Croton. 171 Eudoxus (perhaps 395-343 BCE), for his own part, adheres to the character traits of a mathematicus: 172 Diogenes Laertius (8. 88) tells us that he has it on the authority of Hermippus (3 rd Century BCE) from his book On the Seven Sages that Eudoxus not only wrote laws for private citizens but that he was the author of astronomical and geometrical treatises. 173 His biography is preceded by Diogenes’ lives of Archytas, Hippasus, and Philolaus, and he is the last of the “famous Pythagorics” (e)llogi&mwn Puqagorikw~n); the biography of the “sporadic” philosophers that follows begins with the life of Heraclitus. 174 That Eudoxus, as a student, learned geometry from the mathematicus Archytas of Taras is guaranteed by Diogenes as well. 175 If Hippasus 170 Replacing a)kousmatikoi& with maqhmatikoi&, following Burkert 1972 and Guthrie 1962: 191-2. 171 Iambl. In Nicom. Arithm. 10.8-24. 172 He is deemed mathematicus in many sources: Str. 14.2.15 (T 9 Lasserre) , Philargyr. Schol. In Verg. Ecl. 3.2.56 (T 10 Lasserre); Diod. Sic. 1.96.2 (T 16 Lasserre), where he is contrasted with Pythagoras; et al. The earliest source that places him among “some of the mathematicians (tine_j tw~n maqhmatikw~n) is Aristotle’s Metaphysics (1073b11-32). Generally, on Eudoxus, see Chapter 5. 173 Cf. Plut. Adv. Col. 32 (D 70 Lasserre), where he is said to have written laws for the Cnidians. 174 D.L. 8.91-9.1. 175 D.L. 8.86. 70 or another mathematicus (Archytas?) from Southeastern Italy was responsible for the discovery of Incommensurability, as is proposed by Kurt Von Fritz who was followed by W.K.C. Guthrie, then Eudoxus was responsible for the geometrical theory of proportions that answered the problem. 176 For, as Guthrie reminds us, this theory “is called ‘geometrical’ because the mean proportion in it ([2) can be precisely represented or discovered through geometrical construction, but neither arithmetically, through any rational number, nor harmonically, that is, by the string- length of a concordant note.” 177 No direct trace of the importance of fire to his cosmology or pragmatics exists; the longer excursus preserved by Aristotle and Simplicius reveals that Eudoxus applied geometry to posit a geocentric cosmos that featured a total of 27 spheres. 178 The presence of the Antichthon in “so-called Pythagorean” astronomy, however, suggests instead that another element was at the center of the universe. Hippasus, for his part, believed that fire, which was the first principle from which all things came and to which all things returned, was one, always in motion, and limited (e$n kai_... a)eiki&nhton kai_ peperasme&non). 179 Maria Timpanaro Cardini (following Wilamowitz) relates this fragment to what we know about a certain Petro of Himera, a “Dorian from Sicily,” who believed that there were 183 universes “connected element by element” (a(ptome&nouj kata_ stoixei~on) like the grades of a gnomon or 176 Von Fritz 1945: 262-4. Cf. Guthrie 1978: 448. 177 Guthrie 1978: 448 n. 3. 178 See Guthrie 1978: 450. Cf. Arist. Metaph. 1073b16-32; Simplic. In Cael. p. 492 Heiberg (124 Lasserre). 179 Aet. 1.5.5. (Timpanaro Cardini 1958: 94). 71 a series of numbers. 180 Aristotle, for his part, would have found the concept of multiple cosmoi preposterous: while he followed the mathematici Eudoxus and Callippus in positing a number of spheres, he believed that “there is only one heaven,” because a plurality of heavens would require a numerical plurality of first principles. 181 He would agree, however, with Petro’s theory that the fact of a universe can be derived from the relation of elements to one another. 182 Nevertheless, the peculiar idea that fire is the central element, around which the ever- moving cosmos rotated, corresponds with the beliefs of another Southeastern Italian whose philosophical interests included mathematics and astronomy: Philolaus of Croton. THE THIRD ONE: PHILOLAUS OF CROTON AND PYTHAGOREAN PARTICIPATION If we take seriously the idea that Hippasus of Metapontion both (1) was partially responsible for a schism within Pythagoreanism that is marked by a shift away from oligarchic political organization towards a democratic league and (2) is the figure credited by many sources with a departure from traditional acousmatic forms of Pythagorean philosophical pragmatics in favor of a revised examination of the world using mathematical proofs, deriving from a central and primordial a)rxh& 180 Plut. De def. or. 22 p. 422 B. See Timpanaro Cardini 1958: 70-3. Aristotle would not have seen the connection of elements as a necessary precondition for a graduated series (Metaph. 1069a10-11). 181 Metaph. 1074a31-8. It is also proven, on physical grounds, at Cael. 276a18-279b3. 182 Cael. 276b10-12. At Cael.287a32-b4, Aristotle argues that the spherical shape of heaven can be deduced in part from the fact of the contiguity of elements (a#ptetai de_ tou&twn). 72 (fire), then it should not be surprising that Philolaus, who settled in Southeastern Italy some time after the expulsion of the Pythagoreans from Croton, would imagine the cosmos circling about a central fire: Philolaus says that there is fire in the middle around the center which he calls the hearth of the All and the house of Zeus…and another fire above, surrounding [the All]. He says that the middle is first in nature (prw~ton fu&sei), and around this ten divine bodies dance: heaven, the planets, following which the sun, under it the moon, and under the moon the earth, under which is the Antichthon, after all of which the fire of the hearth holding the position around the center. 183 We may compare this passage with what has been said consistently about the “so- called Pythagoreans” up to this point and assume, as many critics have, that Aristotle saw Philolaus as a “so-called Pythagorean” whose astronomical and physical concepts adapted the Milesian form of monism that is represented by Hippasus and Heraclitus. A passage from Aristotle’s early treatise on astronomy On Heaven (293a17-28) reveals how Philolaus, as a mathematicus, is rightly considered a “so- called Pythagorean”: Concerning the position [of the earth], people do not all have the same opinion, but most of those who say that the whole heaven is limited say that it occupies the position at the middle, but those who live around Italy, the “so-called Pythagoreans,” say the opposite: for they declare that fire is at the middle, and that earth is one of the stars, and that it creates night and day while being borne in a circle around the middle. And, what’s more, they conceive of another earth opposite to this, which they call Antichthon, not seeking ratios and causes according to what is apparent, but attracting what is apparent to certain ratios and opinions of their own and attempting to unite the cosmos. 183 Aet. 2.7.7 = Huffman F 7. 73 That Philolaus considers fire to be the middle term is without dispute. But variations in vocabulary between “first” (prw~ton) and “first principle” (a)rxh&) make it difficult to declare conclusively that Philolaus conceived of fire as a first principle. 184 That it is primary in nature is clear from Aetius, but we must take care not to confuse terms. Let us suppose, however, that Philolaus is guilty of the crime with which Aristotle charged the “so-called Pythagoreans:” that they confuse mathematical objects (which do not have matter) with perceived objects (which are composed of matter). If this is the case, then we are prompted to think about fire as “Limited” or “Limitless,” following the terminology established by Aristotle for the “so-called Pythagoreans.” 185 This was not an issue for Aristotle, who could accept the idea that the “so-called Pythagoreans” assumed their first principles to be Limited and Limitless. On the contrary, his concern was with whether or not the Pythagoreans could assume that they had motion and were “sufficient to rise up above the horizon (e)panabh~nai) to the higher aspects of reality,” by which I assume he meant that they became cosmic entities and caused coming-to-be and destruction at a cosmic level. 186 And so Aristotle has been consistent in his criticisms of the “so-called Pythagoreans,” who did not posit a difference between the existence of first 184 Contextualizing Aristotle’s testimony here with what seems to be an Ionic version of a Doric fragment from Philolaus’ Bacchae (Stob. Ecl. 1.15.7 = Huffman F 17) suggests that fire, being in the middle, was the starting-point (h!rcato) for the cosmos that stretched forth symmetrically in all directions. If this fragment is genuine, it confirms the links between Hippasus’ cosmology (Aet. 1.1.5) and Philolaus’. 185 See above. Cf. Arist. Metaph. 989b29-990a29. 186 Ibid. 74 principles and their activities. 187 When we consider the plausibility of Aristotle’s criticisms, it presents us with a means to understand Philolaus’ fragments that describe a)rxai&. Contexualization with the other genuine fragments of Philolaus (F 6, F 7a, F 13, A 27 Huffman) that refer to the “first principles” (or “starting points,” as Huffman calls them) reiterates the criticisms Aristotle leveled against the “so- called Pythagoreans.” We shall have to attempt to correlate what he says about the pragmatic activities of a)rxai& with what examples are given as ontological a)rxai&. Let us begin, then with the most famous fragment that delineates Philolaus’ first principles: Concerning nature and harmony, this is the case: the Being of things (a( me_n e(stw_ tw~n pragma&twn), being eternal, and nature herself admit of divine and not human knowledge, except that it was not possible for anything real and known to us to have come to be without a predication of the Being of things, both Limited and Limitless, from which the cosmos is constructed (e)c w{n sune&sta o( ko&smoj). But since the a)rxai_ preexisting were neither alike (o(moi~ai) nor related, an ordering of them would have already been impossible unless harmony had come upon them in the very way in which it did. Like and related things were not lacking anything further of harmony; but for things unlike and not related and lacking the same speed, for these such things there is a need to be intermixed (sugkeklei~sqai) with harmony, if they are going to be kept in order. 188 In a sense, Philolaus’ answer to Aristotle’s criticisms – something to which Aristotle does not refer explicitly in this passage, but mentions elsewhere 189 – is that harmony 187 Indeed, in the passage cited above, he refers not only to first principles, but also to causes as though the “so-called Pythagoreans” assumed them to be the same. 188 Stob. Ecl. 1.21.7d = Huffman F 6. I adopt Huffman’s translation and text, which preserves as much of the manuscript tradition as is possible. 189 There is a vague reference at 990a8, where Aristotle claims that causes and first principles “are better fitted (a(rmottou&saj) to the arguments that concern nature.” He has earlier (985b23-986a12) claimed that the “so-called Pythagoreans” believed that the “whole of heaven was harmony and 75 was responsible for catalyzing change (i.e. from unlike to like) and establishing order for the cosmos. 190 Placing this fragment within the larger context of Presocratic thought leads Huffman to compare the origins of the Empedoclean cosmos and its structuring through harmony. He rightly concludes that Philolaus, the mathematical Presocratic, is adopting terms and formulations expounded in the previous century by Empedocles and Heraclitus; Iamblichus’ assumption that Philolaus shared in the teachings of Hippasus of Metapontion is confirmed by the fragments that refer to his followers who describe number (a)riqmo&j) as “the first paradigm of the making of the cosmos” and the “discerning tool of God the maker of the cosmos.” If we factor in the proposition that Philolaus is one of those “followers of Hippasus” mentioned by Iamblichus, we may venture some suggestions about the relationship between number and harmony that is yet incomplete in studies of Philolaus’ fragments. 191 Fragment 4 (Stob. Ecl. 1.21.7b) of Philolaus’ works claims that “all things that are known have number” (a)riqmo_n e!xonti) and that “nothing could either be known or understood without it.” It is therefore the case that number, in Philolaus’ epistemology, is something that allows the divine Being (true reality, in Plato’s terms), which we cannot attain, to be understood by human beings. That number has number.” Although harmony is the force that comes upon a)rxai& and orders them in Philolaus’ philosophy, it is never explicitly equated with “heaven.” 190 Here, again, Aristotle’s attempts to impose his own semantic terminology on Pythagoreanism reveals itself: the issue between ontology and pragmatics, for Philolaus, was an issue of the distinction between first principles and their ordering through likeness; Aristotle, in the passage cited above, complains of the lack of a description of how things become or are destroyed, assuming that motion (for a body) is the term of organization among elements of the universe. 191 Some of my argument here is informed by Huffman’s treatment of the relationship between number and ratio (1993: 70-74). 76 at least two kinds, Limited and Limitless, is guaranteed when we compare Fragment 4 with Fragment 5 (Stob. Ecl. 1.21.7c), which claims: o# ga ma_n a)riqmo_j e!xei du&o me_n i!dia ei!dh, perisso_n kai_ a!rtion, tri&ton de_ a)p’ a)mfote&rwn mixqe&ntwn a)rtiope&ritton. e(kate&rw de_ tw~ ei!deoj pollai_ morfai&, a$j e#kaston au)to_ shmai&nei. For number has two particular figures, odd and even, and a third, the even-odd, from both mixed. But many forms come from the two figures, which each [figure] itself signifies. So, in our attempts to reconstruct Philolaus’ arithmology, we see that number can be Limited (odd), Limitless (even), or a third figure that is a mixture of both (the odd- even). 192 The third term, here as elsewhere, provokes much aporia, to such an extent that Jonathan Barnes attempted to prove that Aristotle was not reading Philolaus at all while composing the Metaphysics. 193 Barnes has failed to note that Aristotle himself seems to have made use of this formulation in his own theories concerning harmony in the fragmentary On Philosophy. 194 What is more, Carl Huffman has refuted Barnes’ claim by appealing to the different relationships that number holds for Being (as a divine formulation) and what can be known by humans (which Huffman calls “phenomena,” although the term provokes the question of the relationship between “things that are known” or “understood” 195 and the more 192 For a general discussion of Limited and Limitless, and how they correspond to Odd and Even, see Cornford 1935: 3-7. For a less positivistic interpretation of the correlation of these terms, see Huffman 1993: 204-14. 193 Barnes 1982: 387-392. 194 Arist. F 47 Rose (Plu. Mor. 1138c), where Aristotle’s theories of music assume that “Both harmony and all her parts are constructed especially naturally, from their even and odd and even-odd nature” (a)rtioperi&ssou fu&sewj). 195 F 4 Huffman. 77 Aristotelian “things that are perceived” [ta_ ai)sqhta&]). 196 Huffman is right to identify Philolaus as the primary source of Aristotle’s knowledge about the Pythagoreans, as a fragment of Aristotle attests: Aristotle, in the Pythagoric [book], declares that the One partakes of (mete&xein) the nature of both [the even and the odd]: for, when it is added to an even number, it makes it odd, and when added to an odd number it makes it even, which it could not do unless it were to participate (metei~xe) in both natures; therefore, indeed, he says that the One is called the “even-odd (a)rtiope&ritton).” 197 We can be sure that even Aristotle is starting to confuse Pythagorean and Platonic in this fragment, where the third term partakes (metei~xe) of both instead of imitating them through mimesis. 198 But, as we saw in Philolaus’ Fragment 6, the a)rxai& were not originally related through likeness or imitation, but they came to be so as a consequence of the advent of harmony, which, by mixing with them, both ordered them and separated them out. It is in this way that Philolaus’ third term, which is harmonized as “even-odd” – a combination of first principles that were originally, 196 The issue is not totally resolved by Huffman’s appeal to Aristotle’s Physics 3.4 (203a4-19), where there can be no doubt that a figure (ei}doj) must possess the formal characteristics of a gnomon. If Aristotle is reading Philolaus here, as Huffman claims, then it is more probable that the presence of “figures” here reflects the original language of Philolaus rather than an importation of Aristotle’s own vocabulary. I follow Burnet 1948: 99-105 contra Huffman 1993: 184-6 in assuming that what is being referred to here is pebble arithmetic and that the forms of things are being rationalized through gnomonic figures. 197 Theo. Sm. Math. p. 21.20 Hiller (Arist. F 199 Rose). Theon goes on to say “Archytas is also in agreement with this.” For Archytas’ theories of number, see my Chapter 2. 198 Arist. Metaph. 987b11-18. The scholiast to Euclid (Schol. 7 in Euclid. Elem. 8, Heiberg 5 p. 364, 6; Timpanaro Cardini B 21d) claims that, for the Pythagoreans, the term “even-odd (a)rtiope&risson)” refers to a type of even number that “is indivisible immediately after the primary dichotomy, e.g. the number 10 into 5 and 5.” Indeed, by the time the scholiast is examining Euclidean and Pythagorean mathematics, there is a categorical difference between “even-odd (a)rtiope&risson),” the term employed by Philolaus and Aristotle, and “odd-even (perissa&rtion),” which refers to a number that can be divided into more than one dichotomy, such as the number 24. Of the “even-odd” the scholiast also tells us that it is often connected with those goddesses who “inspire virility” such as Athena, Hecate, and Artemis. 78 before the primordium, different – comes about thanks to the distinguishing and ordering instrument that is harmony, something that is comparable with Hippasus’ divine tool and is, itself, number (we shall soon see that it is also, in Philolaus’ terms, Soul). Let us recall that the followers of Hippasus saw number as both the first paradigm for the constitution of the universe and the divine tool that promotes discernment; number, then, provides not only, in Huffman’s terms, the constitution of forms, but also the means by which things are known and compared. Its primary function is epistemological. But what Philolaus adds to what we know of Hippasus’ formulation of the ordering of the cosmos is the notion that One, which is a number (see Fragment 4) in Philolaus’ arithmology, both partakes in and then consequently becomes the third term. 199 It is probable that other Italian philosophers, especially the rival school of Parmenides in Elea, were aware of Hippasus’ theories and the development of his school; if this is the case, we would expect to find criticisms of mathematic Pythagoreans as well in the writings of Parmenides. Indeed, the formulation represented by Hippasus and Fragment 5 of Philolaus’ book corresponds with the characterization of “mortal beliefs” ascribed to people who have gone astray (literally: wander) by Parmenides’ Goddess; if the notion that her criticism is leveled against Hippasus or his followers is plausible, then we may assume that Fragment 5 199 I will complete the discussion of this subject later in this chapter. 79 derives from mathematic doctrine that predates Philolaus himself. 200 The language elicits an undeniable comparison, even if we cannot be sure that night is the oppositional term to fire in the cosmological system attributed to the followers of Hippasus: do&caj d’ a)po_ tou~de brotei&aj ma&nqane ko&smon e)mw~n e)pe&wn a)pathlo_n a)kou&wn morfa_j ga_r kate&qento du&o gnw&maij 201 o)noma&zein, tw~n mi&an ou) xrew&n e)stin – e)n w{i peplanhme&noi ei)si&n – a!ntia d’ e)kri&nanto de&maj kai_ sh&mat’ e!qento xwri_j a)p’ a)llh&lwn, th~i me_n flogo_j ai)qe&rion pu~r, h!pion o!n, me&g’ e)lafro&n, e(wutw_i pa&ntose twu)to&n, tw~i d’ e(te&rwi mh_ twu)ton: a)ta_r ka)kei~no kat’ au)to& ta)nti&a nu&kt’ a)dah~, pukino_n de&maj e)mbriqe&j te. From this point, mortal beliefs Learn by listening to the deceitful order (cosmos) of my words: For they established two forms in their minds for naming, Of which one it is not right to name – wherein they wander – And they discerned opposites and posited signs Apart from one another: first, here, the aetherial flame of fire, Which is gentle, very light, everywhere the same as itself, But not the same as the other; but, there, that one too according to Itself is opposite, dark night, a dense and heavy body. 202 Here, I have put in bold-face the terms in Parmenides’ poem that recall the language of Philolaus’ Fragment 5 in conjunction with what we learn about the followers of 200 This seems to me much more likely than to assume, as Martha Nussbaum has (1979: 102), that Philolaus’ writings offer a revision of Parmenides’ epistemology by exacting an “a priori justification of our categories of thought by showing them to be necessary for thought and discourse.” In the complex back-and-forth of Southern Italian philosophy, we must attempt to reconcile the fact that Philolaus is inscribed within a tradition of revolutionary thinking and application that dates back to the time of Parmenides himself; recall that both Parmenides and Hippasus are credited with advancements in philosophy and lawgiving (Parmenides on the Tyrrhenian Sea, in Elea), and as such it is perhaps more likely that antagonisms were locally and temporally contingent. 201 Or, possibly, gnw&maj (DK and Tarán), which renders the translation (as KRS 1983 have it, p. 255): “For they made up their minds to name two forms…” Either translation preserves the same general sense. 202 Simpl. in Phys. 38.28 (Parmenides F 8 Gallop), ll. 51-9. 80 Hippasus in Iamblichus’ Introduction to the Arithmetic of Nichomachus (10.8-24). Editors of this fragment have found it difficult to understand why Parmenides’ Goddess refers to those mortals who have gone astray, 203 but the language, admittedly “deceitful” here, is adapting and playing with what appears to be the astronomical terminology characteristic of the philosophical tenets of the “so-called Pythagoreans” and Philolaus. Indeed, in Parmenides’ crafty poetic language, it is human beings – not planets or other heavenly bodies – who are doing the wandering. 204 Their going astray reveals the epistemological nature of the terms “fire” and “night,” since mortals cannot discover the objective truth in reality; on the other hand, such terms – as signs – allow mortals to make sense of what they perceive in the universe. 205 It is the discernment of opposites that marks those mortals “who know” the difference between Being and Not-Being, in contrast with those tribes of men which are “undiscerning” (a!krita fu~la). 206 The language of discernment recalls both Philolaus’ formulation of number in Fragment 5 and the tool employed by God to create distinctions between things (kritiko_n o!rganon) in the cosmology of the followers of Hippasus. The “discerning tool” of the followers of Hippasus does not seem to be simply an abstract mental function. Instead, it recalls the description of Pythagorean 203 See Gallop 1984: 10-11. 204 Cf. Simpl. in Phys. 87.27-8 (Parmenides F 6 Gallop), ll. 4-5, where Parmenides’ Goddess complains of mortals who “know nothing” and “wander two-headed.” Presumably, they are two- headed because they fail to distinguish between Being and Not-Being but instead confuse them. 205 Interestingly, the signs in Parmenides F 8 must be the words “fire”, “night”, and their corresponding adjectives and appositional terms. Earlier in F 8 (l. 2), signs function epistemologically and lead whoever goes on the “route” to understand what exists in reality. 206 Parmenides F 6 Gallop, l. 7. 81 gnomons to which Aristotle refers in the Physics (203a4-16) as shapes that, when added around either a single point or multiple points constituted of progressing odd numbers (3, 5, 7, etc.), form a square perpetually: Some, like the Pythagoreans and Plato, [have believed] that Limitless itself exists according to itself, not as being a condition incident to something else, but in reality (ou)si&an). Except that the Pythagoreans believe that [Limitless] exists in sensible things (e)n toi~j ai)sqhtoi~j) – for they do not conceive of number as separate from them – and they believe that what is outside heaven is Limitless; but Plato believes that no body exists outside, nor the forms, because they cannot be anywhere; even so, he believes that Limitless exists both in sensible things and in those things [forms]. And the Pythagoreans believe that Limitless is “even:” for they believe that when “even” has been enclosed and limited by the “odd” (u(po tou~ perittou~ peraino&menon), it provides indeterminacy to things in reality. And they believe what happens to numbers 207 is a sign of this (shmei~on d’ ei}nai tou&tou to_ sumbai~non e)pi_ tw~n a)riqmw~n): for, if the gnomons are placed around One, the figure is always the same, but without the One, the figure (to_ ei}doj) varies continually. 208 The language of signs here – and in Parmenides’ fragments – confirms Heeren’s conjecture of shmai&nei in Philolaus of Croton’s Fragment 5 for the manuscript reading dhmai&nei; it also provides some clarification for the language. The ei!dh to which Philolaus and Aristotle refer, in this case, appear to refer to the gnomonic 207 The term to_ sumbai~non plus e)pi& does not necessarily mean “property” in a technical sense, but rather generally what happens in the case of something (cf. Mete. 358b29; Cf. 352a15, where sumbainei~n plus e)pi& and peri& are distinguished). For “property,” Aristotle tends to use the perfect participle sumbebhko&j. Cornford 1935: 8 assumes that the term shmei~on refers to a “point,” but that cannot be the case for this passage or for Philolaus’ F 5, where the language reflects Sophistic theories of the sign. 208 In interpreting this extremely difficult passage, I have relied upon the translation of Wicksteed and Cornford 1935 and KRS 1983, although I have departed from them when attempting to render the language as precisely as possible. 82 figures that constitute the many forms (morfai&); 209 where harmony fits into this scheme is more difficult to assess. At the root of the problem is the definition of harmony as a kind of combination, a term that is attested in 5 th Century BCE philosophy (in the works of Heraclitus and Empedocles) and political administration in Southern Italy (at the aristocratic Pythagorean centers of Croton and Sybaris, preceding the latter’s democratic revolution), and therefore provides another example of the implication of politics and philosophy in Pythagorean poleis of Southern Italy. 210 While this lends support to our claim that the practical application of philosophical concepts to politics was a familiar feature of Southern Italian governments, it does little to help us understand specifically what harmony meant to Philolaus. We have already shown that Philolaus believed that harmony, as a mixing agent, was the instrument that allowed for correlation between the One and the odd- 209 As Cornford notes, the gnomonic language here recalls the final two oppositional terms in the Pythagorean acousmatic “Table of Opposites,” namely the Square and Oblong shapes. 210 Generally, on harmony in Empedocles’ poem, see KRS 1983: 294-313. An inscription from Southeastern Italy dating to roughly 500 BCE records a treaty between the Serdaioi and Sybaris. The text reads: )Armo&xqen oi) Subari~- tai k’ oi) su&nmaxoi k’ oi) Serdai~oi e)pi_ filo&tat- i pista~i k’ a)do&loi a)e- i&dion: pro&cenoi o) Ze- u_j k’ o)po&llon k’ o}lloi q- eoi_ kai_ po&lij Poseida- ni&a. The term a)rmo&xqen, derived from the verb a)rmo&zw, is the same word as we find in Philolaus (+ sun- in F 2 Huffman), where the cosmos is “fitted together from limiting and unlimited things” (Cf. the beginning of On Nature by Philolaus at DL 8.85 [F 1 Huffman]). It also occurs in the fragments of Pseudo-Ocellus and Pseudo-Ecphantus, perhaps to be dated to the 2 nd Century CE, and variations on the verb a)rmo&zw litter the other Hellenistic Pythagorean texts (most notably the spurious works of Archytas). Another inscription in nearby Petelia (5 th Century BCE) records the name of a certain )Armoci&damoj, who is one of the Pro&cenoi of the city of Croton. See Dubois 2002: 36-40 and 93- 156. 83 even and created likeness among things that were originally distinct; what remains is to see what further functions this third term – the harmonized – had in the cosmology of Philolaus. We may begin with another fragment from Philolaus’ book, one that makes explicit the relationship between fire and harmony: to_ pra~ton a(rmosqe&n, to_ e#n e)n tw|~ me&sw| ta~j sfai&raj, e(sti&a kalei~tai. The first thing fitted together, the One 211 at the middle of the sphere, is called the hearth. 212 Huffman is correct to note the significance of harmony to those Presocratic predecessors of Philolaus, Heraclitus and Empedocles. Harmony in Heraclitus can exist in two forms: harmony that is seen, and harmony that is unseen. Unseen harmony is “stronger,” we are told, 213 and Heraclitus’ criticism of “those who do not apprehend how, being at variance, it agrees with itself (ou) cunia~sin o#kwj diafero&menon e(wutw~| cumfe&retai) 214 recalls Empedocles’ criticisms of those who “wander” by positing oppositional terms as epistemological tools and predicts how numbers, as “figures,” aid in understanding the cosmos in Philolaus’ epistemology. Heraclitean harmony, indeed, is represented symbolically as the tension in the string of a bow or of a lyre. While harmony represents the opposite tensions that both make oppositional elements cohere and separate them out, we cannot go further with 211 I translate “to_ e#n” here as “the One,” respecting the definite article, rather than a more general “unity.” For arguments in support of the term “unity,” see Huffman 1993: 228-9. 212 Stob. Ecl. 1.21.8 = Huffman F 7. 213 Hippol. Haer. 9.9.5 = F54 DK. 214 Hippol. Haer. 9.9.1 = F51 DK; text and translation (slightly modified) by KRS 1983. 84 our speculations as to the relationship between Philolaus’ concept of harmony and Heraclitus’. For Empedocles, who was also tied to Pythagoreanism, harmony appears in one significant passage as the means by which Love and Strife, who are compared with painters (Simplicius calls this metaphor a para&deigma), are able to produce the figures that resemble all things despite – indeed, in virtue of – their oppositional force: Just as when painters dapple the temple offerings, Men well educated in their skill by wisdom, When they take in hand the many-tinted colors – Some fitted closer and others less so with harmony – From which they produce figures (ei!dea) resembling all things, They [Love and Strife] create trees and men and women, And beasts and fowl and water-nursing fish, And even long-living gods, excelling in honors. So let not deception convince your heart that the source Of mortal things, those seen and countless, lies elsewhere, But know these things clearly, as you hear the account of a god. 215 If we agree with the argument of Wright, namely that painters did not mix paints during this period but that they worked from four basic colors (black, white, red ochre, and yellow ochre), then the juxtaposition of block colors alongside one another, separated by an outline, is representative of how harmony functions both to create unity (through the alternation of complementary colors) and to separate out 215 Simpl. in Phys. 159.27 = F 15 Wright. Support for Wright’s conclusion that the basic colors were four is the notion that the basic harmonic interval for lyres was the fourth, the mathematical proportion of which was 4:3. See Burkert 1972: 394 with n. 38 and 400. 85 elements in order to establish figures (ei!dea) for all things. 216 The gods to which the activities of unity and separation are assigned are Love and Strife; the struggle between these oppositional forces establishes mortal things, i.e. things that can be seen. Thus, Empedocles establishes a familiar set of oppositional terms that perpetuate binarisms which cannot be simply extracted from one another; at the heart of conflicting forces, roots, and elements is the term harmony. All of this is fine and well if we subscribe to the notion, as many critics have, 217 that Pythagoras was the medium through which the wisdom traditions of oppositional forces – probably derived from Zoroastrianism and the cosmology of Pherecydes of Syros – developed among the Southern Italian philosophers of the 5 th Century BCE. According to this notion, the importance of harmony is due to Pythagoras’ teachings, although it is nearly impossible to substantiate this theory given the paucity of material that seems to be original with Pythagoras himself. 218 And yet, despite the evidence that Philolaus was employing a set of terms relatively common for Southern Italian philosophers of multiple schools and localities, I am not quite convinced that the concept of harmony, as it figures in the writings of Heraclitus and Empedocles, represented anything other than the environment in which any Southern Italian philosopher of Pythagorean influence would be working. 216 Wright 1981: 38-9. Empedocles’ usage here of the term eidos confirms the pre-Platonic usage found in Philolaus’ F 5 Huffman. 217 For instance, Guthrie 1962: 435-449 and KRS 1983: 232-5. 218 West 1971: 213-8. Hippolytus (Philosophumena 2.12 = F 13 Wehrli) claims that Aristoxenus and Diodorus of Eretrea establish the links between Pythagoras and Zaratas, who imparted to Pythagoras the basic dichotomy of male and female as well as the idea that the cosmos exists according to musical harmony, although strangely Hippolytus never refers to numbers in this passage. 86 While the comparisons between the writings of Parmenides and Philolaus envelop us with the complexities of number, of Limited and Limitless, the presence of harmony in the fragments of Heraclitus and Empedocles fails to evince any direct influence that could not have been channeled through Philolaus’ education among the traditional acousmatic Pythagoreans. On the other hand, if we look to the fragments of Hippasus of Metapontion, we discover closer and more direct connections between fire and harmony. One fragment of Iamblichus (Stob. Ecl. 1.49.32) describes the “simple” psychic theories of “certain Pythagoreans,” including Hippasus: a)lla_ kai_ tou~ton [to_n a)riqmo_n] a(plw~j me_n ou#twj e!nioi tw~n Puqagorei&wn th~i yuxh~i sunarmo&zousin. w(j d’ au)toki&nhton Cenokra&thj, w(j de_ lo&gouj perie&xonta Mode&ratoj o( Puqago&reioj, w(j de_ kritiko_n kosmourgou~ qeou~ o!rganon #Ipassoj o( maqhmatiko_j 219 tw~n Puqagorei&wn. But indeed certain Pythagoreans harmonize number with Soul in a simple way: for example, Xenocrates [harmonizes it] 220 so as to be self-moved, and the Pythagorean Moderatus [harmonizes it] so as to comprise ratios, and Hippasus the mathematical Pythagorean [harmonizes it] so as to be a discerning tool of God the cosmiourge. The set of philosophers here is significant because of its connections to Philolaus: first Xenocrates, who was said to have accompanied Plato on his trip to the Pythagorean center that was governed by Archytas, Taras, in 367 BCE, and to have espoused “democratic” ideals against the incursion of the Macedonians following Plato’s death. He might be best described as a Pythagoreanizing Platonist to whom 219 See above. 220 Taking the verb to be sunarmo&zousin; Dillon 1996: 350 assumes that this verb means “define,” although I do not see how that can be the case. 87 is it possible to trace the origins of Neopythagoreanism (along with Speusippus). 221 The definition of the soul as “self-moved number” indeed is first found in Aristotle’s de Anima (404b27-8) and must have been extracted from Xenocrates’ treatise of the same name. 222 As to Xenocrates’ basic principles, he famously gave the definition of the Platonic Form as “the paradigmatic cause of whatever is at any time composed according to nature.” 223 The emphasis on paradigmatic cause (ai)ti_a paradeigmatikh&) is essentially derived from Plato’s Timaeus (31a), where Timaeus argues that there must be one heaven “if indeed it will be framed according to its paradigm,” although it follows in the traditions of heavenly paradigm that ultimately leads us back to Hippasus; Xenocrates’ emphasis on “cause” bespeaks its Aristotelian heritage as well, and we are left with a definition of the Platonic Form that mixes elements of Aristotelian and Platonic philosophical formulations, in a framework that appears to have been established by Hippasus or the mathematici who carried forth his teachings. Next on the list is Moderatus of Gades, an “aggressive” Pythagorean of the 1 st Century CE who believed that number was a “system of monads, or a progression of multiplicity beginning from the monad, and a regression ending in the monad.” 224 Clearly, this language is a far cry from what we see in the genuine fragments of the Pythagoreans from the 5 th Century BCE, but he is to be grouped with Xenocrates as 221 On the life, writings, and political activity of Xenocrates, see Dillon 2003: 89-98. 222 See Dillon 2003: 121. 223 Procl. in Prm. Col. 888. See Dillon 2003: 119-121. 224 See Dillon 1996: 350-1. 88 one of the followers of the Platonic variety of Pythagoreanism. Indeed, his fragments reveal a close affinity with the theories of a)rxai& and Soul found in the fragments of Philolaus and Plato’s Parmenides: he assumes, following the establishment of the Form that participates in all other forms in Plato’s Parmenides, that there are actually three Ones, which Dillon calls “a system of hypostases.” 225 The third One, which participates in the other two (mete&xei), is called Soul; 226 it is essentially composed of number, as we saw above, in that it comprises ratios (lo&gouj periexo&nta). As a third One, Soul is essentially Platonic according to Aristotle’s clarification of the difference between Pythagoreans and Platonists in the Metaphysics: For, the Pythagoreans claim that things exist in reality by imitation (mi&mhsei) of numbers; Plato claims by participation (me&qecei), modifying the name only. However, whatever imitation or participation might be, they left it to the rest of us to figure it out. And, what is more, he states that, besides perceivable things and Forms, a middle (metacu&) term exists: the mathematical objects/practicals (ta_ maqhmatika_ tw~n pragma&twn), which differ from perceivable things in being eternal and unmovable, and from Forms in that there are many analogous things (po&ll’ a!tta o#moia), but each Form itself is unique. 227 The definition of Soul as something that comprises ratios and participates in the former two Ones is, according to Aristotle in this passage, decidedly Platonic (although we can assume that the praxis was the same for Plato and the Pythagoreans, even if the name was different). There are some problems here, since, 225 Dillon 1996: 350. I will discuss Plato’s Parmenides in Chapter 3. 226 On this term, see above with Theo. Sm. Math. p. 21.20 (Arist. F 199 Rose). 227 Arist. Metaph. 987b11-18. 89 as we saw earlier, the terminology of participation is ascribed by Aristotle to Philolaus as well. The case for Philolaus as source is strengthened by another fragment, not found among the commentary and testimonia of Philolaus in Huffman’s edition, which declares that Moderatus derives his theory of Soul as something that “comprises ratios” either from a lost work ascribed to Archytas of Taras called On the Decad or from Philolaus of Croton’s On Nature. 228 Whether or not Moderatus borrowed the theory that Soul comprises ratios from reading Archytas or Philolaus is of little import; he assumes the role of mathematicus and locates himself within the school of Hippasus. We therefore find ourselves returning to the psychic theories of Philolaus, who seems to have adopted Hippasus’ theory that fire was a first principle. Our oldest reference for Pythagorean theories of Soul is Plato’s Phaedo, where multiple theories of the yuxh& are presented. It goes without saying that Plato’s Phaedo has presented multiple problems for scholars of Philolaus and early Pythagoreanism in general; it should also be pointed out that in the Phaedo, there are no direct connections between the theory of Soul put forth by Simmias and what is said about Philolaus, who was his teacher in Thebes. On the contrary, Simmias presents his proposed theory of Soul as harmony and blending in a light that suggests it was not proffered by Philolaus at all. Instead, the theory that Soul is harmony proceeds without mathematical proof, at least as Simmias presents it, and must therefore 228 Theo Sm. p. 106 Hiller = Thesleff 1965: 21. It is impossible to conclude whether or not Archytas wrote such a book. 90 reflect simpler Pythagorean concepts of Soul than are found in whatever fragments we might attribute to Philolaus. Theon of Smyrna’s (fl. ca. 115-140 CE) comment that Philolaus, in his On Nature, described Soul as something that “comprises ratios” neither definitively supports nor contradicts the theory that Philolaus thought that Soul was harmony. 229 This simply suggests that it is harmonic or harmonized, which might represent a departure from the more traditional Pythagorean concept that Soul is harmony. Indeed, what seems to have distinguished the mathematical from the acousmatic Pythagoreans was the difference between equating abstract concepts through simple imitation – an acousmatic trait – and problematizing how those concepts functioned within the phenomenological universe, characteristic of the mathematical Pythagoreans. 230 On the contrary, while it is clear that Simmias and Cebes learned about suicide from their teacher Philolaus, we should be wary of attributing either Simmias’ theory of Soul as harmony or Cebes’ theory of Soul as proprietor of many bodies simply to Philolaus. For it is more likely, indeed, that the Pythagoreans who 229 It does, however, force us to reconsider what portions of Claudianus Mamertus 2.3 (Huffman F 22) are or are not genuinely Philolaic. The actual quotation from Claudianus does, indeed, sound post- Platonic, but his proposition that the definition of Soul in Philolaus’ book came after discussion of, at the very least, “geometry, arithmetic, and music” seems more plausible. See Guthrie 1962: 311-12. 230 In this way, Socrates’ playful remarks at Phaedo 92c-d strike a note; Tredennick and Tarrant’s translation emphasizes the puns: ‘Surely an attunement is not at all like the object of your comparison. The instrument and the strings and their untuned sounds come first; the attunement is the last of all to be constituted and the first to be destroyed. How will this account harmonize with the other?’ ‘Not at all,’ said Simmias. ‘And yet,’ said Socrates, ‘if any account ought to be harmonious, it should be an account of attunement!’ ‘Yes, it should,’ said Simmias. ‘Well,’ said Socrates, ‘this one does not harmonize with your view.’ 91 fled Croton and reached Thebes set up an acousmatic form of Pythagorean governance, extending the traditions of oligarchic Pythagoreanism that preceded the democratic revolutions of the mathematici in Sybaris and Taras during the second quarter of the 5 th Century BCE. Thebes would have afforded Lysis, an acousmatic refugee from Croton, the possibility of relatively painless reintegration into what amounted to a sympathetic land-based oligarchy. 231 Unlike Philolaus, who traveled much and returned to Southeastern Italy, either to Taras or to the Tarentine colony of Heraclea, Lysis remained in Thebes and established a rigorously conservative form of the Pythagorean life, which continued the traditions of the oligarchic Pythagoreans despite the mathematical teachings of the democratically-minded mathematici in Taras and elsewhere throughout Southeastern Italy: [Those exiled from Italy], being isolated and wholly disheartened at what had happened, scattered here and there, and absolutely could no longer bear to share conversation with any human being. Alone in solitary places, wherever they happened to be, and shut away for the most part, each took pleasure in his own company in preference to that of anyone else. And taking heed that the name of their philosophy not wholly perish among human beings and that they themselves [not] consequently be hated by the gods, for destroying completely so great a gift as theirs, they put together some works containing their teachings in summary and symbolic form. And they collected treatises of the older Pythagoreans and such sayings as they remembered (u(pomnh&mata& tina kefalaiw&dh kai_ sumbolika_ suntaca&menoi ta& te tw~n presbute&rwn suggra&mata kai_ w{n dieme&mnhnto sunali&santej). Each left these behind where he died, after strictly charging his sons, daughters, or wives to give them to no one outside of the household. They kept this charge faithfully for a 231 On the oligarchic government at Thebes, see Demand 1983: 35-40 and 70-2. 92 long time, passing on in succession the same command to their offspring. 232 This account, derived from Nichomachus (1 st – 2 nd Century CE), emphasizes the passing down of Pythagorean teachings within the family, but we need not believe that the terms “sons, daughters, wives” refer necessarily to one’s biological relations; after all, Lysis, we are told, was called “father” by his student Epaminondas. 233 Indeed, the letter of Lysis to Hipparchus (or, perhaps, Hippasus, if we assume some confusion of these names) 234 preserves the oligarchic character of Lysis’ philosophy, which refuses the public education of Pythagorean precepts, an element that would surely democratize the secret teachings of Pythagoras. 235 Indeed, Simmias’ educational program seems to have been particularly acousmatic, in that he complains that the doctrine of the theory of Soul as harmony was never presented with demonstrable proof (a!neu a)podei&cewj), but that it was taught “with some likelihood and plausibility, whence its appeal to many people.” 236 Is it possible that Lysis’ withdrawal from the public eye – even in Thebes – was a consequence of the popularization of traditional Pythagorean ideas that would have been advanced by Pythagoreans of such incomplete learning as Simmias and 232 Iambl. VP. 253. Translated by Hershbell and Dillon, with one slight change in brackets. Cf. the description of Lysis’ anger at his maltreatment at VP. 250. 233 Iambl. VP. 250. 234 On this subject, see Thesleff 1965: 92 and 111 n.14. At D.L. 8.42, the letter is said to be from Lysis to Hippasus. 235 Iambl. VP. 75-8 and Thesleff 1965: 111-5. 236 Pl. Phd. 92c11-d2. Iamblichus, in a passage that famously describes the difference between the acousmatici and the mathematici (De comm. math. sc. 76-7), claims that Pythagoras taught the mathematici “by means of demonstrable proof and mathematical learning (dia_ a)podei&cewj kai_ tw~n maqhma&twn)” in contrast with the teaching of the acousmatici, which was done simply (yilw~j). 93 Cebes? We might never know, and the issue is further compounded by the fact that Plato presents Philolaus as someone who also does not teach “clearly,” by which we must assume Simmias means employing decisive proofs; Philolaus begins to look quite like an acousmaticus in Plato’s Phaedo. 237 We are only left to speculate, but it seems probable that Philolaus’ return to Taras or Heracleia, city-states with democratic mixed constitutions in the second half of the 5 th Century BCE, marks his rejection of the aristocratic forms of Pythagorean statesmanship for something more progressive. 238 After all, we must recall that the composition of the Phaedo (ca. 380 BCE) probably preceded Plato’s total revision of his theories of dialectic and the Forms (which I locate after 367 BCE); 239 what is more, the dramatic date for the lecture(s) of Philolaus in Thebes might be located sometime after the expulsion of the oligarchic Pythagoreans from Croton, but before Philolaus had returned to Southeastern Italy; his teachings would still have concentrated on the acousmatic elements of Pythagoreanism when he was teaching Simmias, Cebes, and Echecrates. 240 In this way, it is possible to imagine that Philolaus, like Plato, modified his philosophy as he got older in the context of the philosophical communities where he located himself. 237 Pl. Phd. 62d8. Indeed, the verbs used to describe Philolaus’ teaching are always derivatives of a)kou&w (a)khko&ate, a)koh~j, a)khkow_j, h!kousa, a)kh&koa). We might recall the distinction, made explicit in Plato’s Epistle VII, between oral and written modes of education (341c4-342a1); it is not the only distinction, in that Plato also marks a difference between oral learning and mathematical learning (341c5-6). 238 On the mixed constitutions of Taras and Heracleia, see Chapter 6. 239 See Chapter 2. 240 If Philolaus went back to Heracleia, as Iamblichus suggests (VP. 266), then he would have spent a long time in Thebes (from the expulsion of the Pythagoreans from Croton, probably 460s-450s BCE, until at least 433-2 BCE, when Heracleia was founded). 94 Pythagoreanism had undergone radical changes in the century that followed the democratic and philosophical revolutions incited by Hippasus and the other mathematici in the second quarter of the 5 th Century BCE. As we have seen, mathematical Pythagoreans had endured the criticism of Parmenides that prompted them to rethink how arithmetic and the physical world could be connected. In the case of Philolaus, the redefinition of a central proposition of traditional Pythagoreanism would allow him to commingle the monistic Milesian hypotheses of Hippasus with the symbolic “Table of Opposites” that was probably original with Pythagoras himself: the praxis of harmony. For, as we have seen, the harmonized presented a third term that answered the question ti& prakte&on, being both the object of study and its principle; it was comparable – following Pythagorean analogies – with Soul, fire and the central hearth of the universe, which was number, the discerning tool of the divine figure that made the cosmos, that functioned epistemologically so that human beings could make sense of what phenomena they could perceive. The third a)rxh& – the first thing harmonized, fire, Soul, hearth, number, discerning tool – was itself not only composed of Limited and Limitless, those primary a)rxai& that could not be ordered because they were not alike without it; it had Limit and Limitless in the figures of the odd and even. To put the point another way: the third term, the even-odd which is both the triad and the combination of its terms, is both Limited and Limitless and has both odd and even. 241 Paradoxically – and this is the innovation we may attribute to Philolaus – the third 241 On the Pythagorean correlation between “being” and “having,” see Burkert 1972: 265. 95 term is itself both third and One, and thus plural and unified. 242 It represents the unification, through harmony, of the terms One, Two, and Three. 243 What is more, Aristotle’s inability to discern whether or not the third term was participatory or imitative suggests his failure to distinguish between the mathematical kind of Pythagoreanism and Platonism: we might, then, wonder whether or not Aristotle was attempting to categorize two kinds of philosophy that were much more compatible than he expected; whether or not Platonism was a form of mathematical Pythagoreanism that, following the revolutionary and “democratic” tenets of the mathematici, constantly demanded self-revision and fresh application of mathematical theories; whether or not, indeed, Plato himself became a Pythagorean mathematicus. 242 See Burkert 1972: 264 with n. 124, where he claims, “To be sure, this is unsatisfactory from a mathematical point of view, but not on that account non-Pythagorean.” 243 Is it also composed of the number 4 and thus complete the tetraktys? This is not clear from the fragments of Philolaus, but the Scholiast to Euclid conflates the “even-odd” with the number 10, which represents the summation of the numbers of the tetraktys (1+2+3+4). Perhaps we are encountering the same problem Aristotle did: if the numbers are figures, how can they create critical distinctions and thus be divisive and still be the numbers themselves? As we saw, the numbers 1-4 exist ontologically as theoretical terms, but they are separated by the activities of diaeretic numbers. How can numbers both be and function to distinguish themselves? 96 _______________________________________ CHAPTER 2: THE MATHEMATICAL PRACTICALS: PLATO’S DIALECTICAL REVISION OF PYTHAGOREAN SCIENCE IN THE REPUBLIC _______________________________________ ‘And so, these are your three kings, whether you allot them the authority of the Laconian kings or come to an agreement that their powers should be limited; install them in some such way as what I told you previously, but with the additions you shall now hear.’ – The Late Dion (Plato, Epistle VIII, 356b5-c2) We began Chapter 1 with a problem that has remained unresolved since Diogenes Laertius wrote his Lives of the Eminent Philosophers in the early 3 rd Century CE, namely the proposition that Hippasus of Metapontion was both a mathematicus involved in philosophical investigations of a Pythagorean sort and that a man named Hippasus, himself a Laconian, wrote a Constitution of the Laconians in five books. We have yet to investigate precisely how Spartan/Laconian/Doric constitutions played a significant role in the actual administration of poleis in Southern Italy, especially among the Pythagorean lawgivers (both democratic and aristocratic), or how Pythagorean mathematics and political systems are specifically analogous to one another. This subject I will undertake in Chapter 4, with appeal both to the extant Pythagorean texts of the 5 th Century BCE lawgivers Charondas, Zaleucus, and (possibly) Hippodamus, and to what we know historically and administratively about the governance of Pythagorean city-states in Southern Italy. But first we need to examine how Plato imagined the possibility that dialectic – a 97 subject we have not yet discussed explicitly – could collude with the development of his political philosophy. 244 In the following two chapters, then, I will provide an account of precisely how Plato modified his dialectical system – and consequently his theory of the Forms – in a way that would anticipate his focal shift from the ideal to the practical polis in the later works Timaeus-Critias, Epistles VII and VIII and the Laws. As I will demonstrate, the theories of dialectic detected in certain middle dialogues written before Plato’s second visit to Syracuse and Southern Italy in 367 BCE – Republic and Phaedo – give way to modifications in those later dialogues composed after Plato’s reinvigorated engagement with Italian philosophy, namely Theaetetus, Parmenides, 245 the Sophist, and the Statesman (all composed around 361/60 BCE, or slightly thereafter). Plato’s introductory engagement in the Republic with Pythagorean sciences – especially the quadrivium instituted by Archytas as the educational program of the mathematical Pythagoreans – will occupy much of Chapter 2. I will argue that the foundation of the educational system in Books VI and VII of the Republic is in dialogue with the educational program of Archytas and that elements of Plato’s ontological and phenomenological theories represent criticisms of Archytas’ propositions, despite the fact that logismos (a term that appears to mean “calculation” for Archytas and “logistic” for Plato) is the foundational activity that can be applied to the process of making definitions that 244 On how dialectic fits into 4 th Century BCE Pythagorean political philosophy, see my Chapters 5 and 6. 245 The date of composition of the Parmenides remains elusive, as I will discuss later in this chapter, but it seems to have been composed around the time of the Theaetetus (ca. 361 BCE). 98 leads to understanding both for individuals and for communities in each philosophical school. In Chapter 1, I argued that the “so-called Pythagoreans” to whom Aristotle referred in the On Heaven, Meteorologica, and in book A of the Metaphysics were the mathematici, a group of democratic Pythagoreans who had seceded from the more traditional acousmatici, who advocated a distinctly aristocratic form of political organization both before and after their dispersion from the Italian peninsula in the mid-450s BCE. The acousmatici went on to found centers of aristocratic Pythagorean education in Rhegion and Thebes, where they could continue to exercise some influence over the local political environment. On the other hand, Aristotle’s criticisms of mathematical Pythagoreans were of two kinds: first, that through homologia, the “so-called Pythagoreans” equated things that were ontologically distinct, as evidenced by their confounding of mathematical ideas and sensibles; and second, the related complaint that they imported harmony as a catalyzing force (an instrument of movement, in Aristotle’s terms) in order to make their pragmateia a comprehensive and circumscribed system. It may be said generally of Aristotle, then, that his primary criticisms of the “so-called Pythagoreans” – as well as of the acousmatic “Pythagoreans” – were issues of the confusion of praxis and actuality, of the process of coming-to-be with the things already in existence. The first criticism I mentioned – that Pythagoreans confuse material things in existence with mathematical terms – is taken up again in Aristotle’s comparison of 99 Pythagorean and Platonic pragmatics, in a passage to which we have referred in Chapter 1: For the Pythagoreans claim that things exist in reality by imitation (mi&mhsei) of numbers; Plato claims by participation (me&qecei), modifying the name only. However, whatever imitation or participation might be, they left it to the rest of us to figure it out. And, what is more, he states that, besides perceivable things and Forms, a middle (metacu&) term exists: the mathematical objects/practicals (ta_ maqhmatika_ tw~n pragma&twn), which differ from perceivable things in being eternal and unmovable, and from Forms in that there are many analogous things (po&ll’ a!tta o#moia), but each Form itself is unique. 246 By now, this passage should be more comprehensible to the reader. Aristotle’s primary claim – that things in existence are related in the Pythagorean and the Platonic philosophical systems by means of the same pragmatic (or applied) instrument which is called mi&mhsij (imitation) for the Pythagoreans and me&qecij (participation) for Plato – is supplemented by a secondary claim of utmost significance to our argument, namely that Plato’s philosophical system (Aristotle calls it a pragmateia at 987a29) is organized in triads that he calls perceivable things (ta_ ai)sqhta_), Forms (ta_ ei!dh), and the “mathematical practicals” (ta_ maqhmatika_ tw~n pragma&twn), which form a middle, intermediate, and tertiary term that represents a synthesis of sensibles with ideals; this triad, then, is an extension of Aristotle’s division of the Pythagorean acusmata, which are categorized according to 246 Arist. Metaph. 987b11-18. There is little reason to assume, with Timpanaro Cardini 1964: 97, that the mimesis given as a Pythagorean term of comparison here can be exactly accorded the same value or semantic function as the tragic form of imitation in Aristotle’s Poetics. Indeed, it is Aristotle who tells us that the only change that occurred was a change of name, not of substance. Note that Aristotle wrote that it was modified in name only (mo&non). 100 whether they answer questions of ontology (ti& e!sti), ideals (ti& ma&lista), or pragmatics (ti& prakte&on). 247 That Aristotle sees the Platonic pragmateia as an extension of Pythagoreanism is made explicit: Following the aforementioned philosophy [of the Pythagoreans], 248 Plato’s pragmateia succeeded it, adhering to it for the most part, but having, indeed, particular features contrary to the philosophy of the Italians. 249 Immediately following upon this topical shift, Aristotle embarks on a description of the history of Plato’s philosophical development. He explains that Plato, as a youth, derived his basic ontology (which Aristotle, contra the Socratic Plato, equates with observable phenomena) from Cratylus and Heraclitus, who espoused theories of flux based in the perceivable bodies of the world; 250 this corresponds directly with Aristotle’s first term in the Platonic pragmateia, which is “perceived things.” Next, he discusses the influence of Socrates in the development of the second term – the ideal – in the Platonic pragmateia, which he calls “Ideas” or “Forms”: And when Socrates made ethics the object of his study (peri_ me_n ta_ h)qika_ pragmateuome&nou) but disregarded the physical world entirely, he nevertheless sought the universal in them [ethics] and was the first to apply his thoughts to definition; in accepting this proposition, Plato assumed that this [definition] comes to be concerned not with perceived bodies but with other things (for he thought that a common definition [to_n koino_n o#ron] for any sort of perceived things was impossible, since, in fact, they were always changing). And so Plato called these sorts of things in existence Ideas 247 See Chapter 1. 248 By this point, Aristotle has retraced his steps and is now referring to the Pythagoreans as a group of philosophers unified by their propensity for superficial definition and a crude sense of predication. 249 Arist. Metaph. 987a29-31. 250 Arist. Metaph. 987a32-b1. 101 (or: these the Ideas of things in existence), and he believed that all perceived things were named after them and according to them. 251 The second part of Plato’s pragmateia, according to Aristotle’s report, both represented an extension of and problematized the first part, in that the phenomenological world disregarded by Socrates could not be defined using the ethical investigations that led to the recognition of the Forms. Therefore, the second part of the Platonic pragmateia left his philosophical system incomplete, and Plato was required to adopt a third proposition, derived from the Pythagoreans, that would provide for the existence of perceived things along with the existence of the Forms and the means by which perceived things would exist in accordance with and with the name of their Forms: kata_ me&qecin ga_r ei}nai ta_ polla_ tw~n sunwnu&mwn toi~j ei!desi. For the plurality of things which have the same name as the Forms exist in accordance with participation. 252 It may be said with some certainty, then, that Aristotle saw the developments in Plato’s education as corresponding with the completion of his philosophical pragmateia, marked by three distinct phases: (1) the identification of perceived things and their modes of change, marked by the “fluxist” philosophies of Cratylus and Heraclitus; (2) the problematization of those phenomena through the formulation of immutable Ideals achieved via ethical dialectics, learned from Socrates, which produces definitions; and (3) the means to synthesize perceived things in flux with 251 Arist. Metaph. 987b1-9. 252 Arist. Metaph. 987b9-10. Italics mine. 102 immutable Forms, a concept derived from Pythagorean pragmatics. 253 Like Philolaus, who saw the third term – the harmonized – as that which both actively mixed and was paradoxically a mixture of the preceding two terms, Plato’s participation both acts upon the preceding two categories of his pragmateia and completes the pragmateia itself by being a synthesis of perceived things and Forms. 254 But, as Aristotle goes on to remark, there are other differences between the Pythagoreans’ and the Platonists’ philosophical systems, most notably in the second category which encompasses the Forms for Plato and represents the semantic range that comprises the possible answers to the question ti& ma&lista among the Pythagoreans. It is here that Plato follows Socrates by introducing something that developed independently of the advances in philosophy that took place among the Pythagoreans, but that we can attribute to the Eleatic school of philosophy: dialectic, which is the means to a theory of the Forms. On the way to this conclusion, Aristotle enumerates Plato’s debts to Pythagorean pragmatics and locates them within his own categorical organization of types of causes: And since the Forms are the causes of other things, [Plato] believed that their elements were the elements of all things in existence. So, then, [he believed that] the Great and the Small – as principles – are matter (u#lhn to_ me&ga kai_ to_ mikro_n ei}nai a)rxa&j), and that Being is the One; for [he believed that] numbers exist from them [the Great and the Small] according to participation in the One (kata_ me&qecin tou~ e(no_j). In fact, by saying that the One is Being, and not 253 Cf. Arist. Metaph. 1078b12ff., where Aristotle is in the process of distinguishing between mathematical objects and forms and their respective developments among the philosophers. 254 On the “third term” in Philolaus’ fragments, see Chapter 1. 103 something which is called “unity,” and that numbers are likewise the causes of Being in other things, his argument comes very close to that of the Pythagoreans. 255 This passage is of utmost significance to our understanding of Platonic “first principles” since, as Plato himself admits in Epistle VII, he never wrote anything about the “first and highest things of nature” (peri_ fu&sewj a!krwn kai_ prw&twn [o!ntwn]) on the grounds that the process of dialectical education must occur between the teacher and pupil and cannot be reproduced in writing. 256 Aristotle tells us in this passage that Plato’s a)rxai& were the Great and the Small, and, perhaps, the One (although this requires an inference from the text). 257 These first principles correspond with the Formal (the One) and Material (the Great and the Small) causes. As we saw above, the “so-called Pythagoreans” assumed that their first principles (the Limited and the Limitless, which are Number) were themselves Formal, Material, and Efficient, in that they existed ontologically, were of substance, and modified things, although Aristotle is confused when attempting to reconcile his system of causes with the Pythagorean acusmata. 258 He assumes the same kind of correlation here with Plato, in that the Formal cause and the Material causes, which are circumscribed, come to be related with one another as a consequence of the third 255 Arist. Metaph. 987b18-25. 256 This specifically refers to the On Nature written by Dionysius the Younger, although Plato is distancing his own teachings from the doctrine found in Dionysius’ book because popular thought was that Dionysius’ book reproduced Plato’s teaching. Pl. Ep. VII 344d3-7. On this subject, see Morrow 1962: 60-81. 257 Aristotle (Metaph. 1012b34-1013a24) enumerates seven kinds of a)rxai&, but that the four kinds of causes (Formal, Material, Efficient, Final) which form Aristotle’s categorical system are all a)rxai& themselves suggests we should pay attention to those kinds of first principles that correspond to these causes. 258 See Chapter 1. 104 term: participation (me&qecij). We can therefore detect similarities with the Pythagorean pragmateia, in which the first two terms – ontology and the ideal – are made similar by means of mimesis 259 which somehow harmonizes them (thus representing the third, pragmatic term) just as the third “middle” term, participation, causes the ontological and the Formal terms to become intertwined in the Platonic pragmateia. In this way, Aristotle is implying – without admitting it explicitly – that Pythagorean mimesis and Platonic participation function as Efficient causes, since numbers (at least for the Platonic pragmateia) are derived from participation of the Great and the Small – principles of subjective division – in the One. 260 On Aristotle’s reading, the Pythagoreans believe that numbers, once they are both essentialized and divided, 261 can go on as the causes of existence for other entities, and thus they represent a secondary group of Formal causes (although there is 259 That this argument is circular did not escape Aristotle. Theophrastus (Metaph. 33 p. 11 a 27 Usener = Timpanaro Cardini B 14) claims that Plato and the Pythagoreans both believe that things imitate the One and the Indeterminate Dyad in being differentiated, although the text is not especially clear about how. 260 While Aristotle claims here that there are only two kinds of causes for Plato (the Formal and the Material), he later discusses the presence of something that appears to be the Efficient cause for Plato called the “eternal actuality (a)ei_ e)ne&rgeian which he says is called the a)ei_ ki&nhsin), whose origin and definition he complains are not explained (Metaph. 1071b33-37); he has said the same thing about participation. He then goes on to say (Metaph. 1071b37-1072a3): And, what is more, Plato is not even able to say what he sometimes thinks that first principle, which moves itself, is; for, as he says, Soul is both later than and contemporaneous with heaven. Aristotle believes that Plato’s Efficient cause, if it were able to be categorized, would be h( yuxh&, which, as we saw above in Chapter 1, represented the third term for Philolaus. There is some confusion between the earlier and later accounts. On the significance of Soul in Plato’s pragmateia especially in the Philebus and Timaeus, see Chapter 5. On subjective and quantitative modes of division, see below and Chapters 4 and 5. 261 While they partake of substance, they are not perceived. Here, Aristotle takes account of Plato’s theories of epistemology and perception. 105 certainly some confusion about this in Aristotle’s account). 262 That numbers exist in nature is a consequence of their derivation from the One; that they are naturally divided and distinguished is owed to their derivation from the Dyad – equivalent with the Great and the Small in Aristotle’s figuration – “as from a matrix.” 263 This theory Aristotle criticizes for being a confusion of Formal and Material causes, 264 since Platonists see the One – which is male by analogy 265 – as capable of generation only once and the Dyad – which is female – as capable of multiple generations; in reality, Aristotle says, “the female is impregnated in a single coitus, but the male can impregnate many females.” 266 Once he has established the similarities between the Platonic and the Pythagorean pragmateiai, Aristotle enumerates the differences in the passage that follows. Plato distinguishes the elements of his philosophical program from those of 262 There are problems with the suggestion that numbers are first principles for the Platonists, as Aristotle will go on to argue. At Metaph. 1081a13ff., Aristotle complains that there is too much confusion regarding the relationship between numbers and Forms, as to which is prior. He says: “But if the Forms are not numbers, they cannot exist at all. For from what first principles will the Forms be derived? Number is derived from the One and the Indeterminate Dyad, and the first principles and the elements are said to be derived from Number, and the Ideas cannot be fit into this scheme either as prior to nor posterior to numbers.” Tredennick 1973: xxii-xxiii credits Aristotle with a stubborn misunderstanding: “Unfortunately Aristotle – with what justification it is hard to say – fastens upon the term “dyad” and interprets it as a literal duality; either as a kind of 2 or as a “pair of contraries” – the Great and the Small. Many of his objections depend entirely upon this misapprehension.” 263 Arist. Metaph. 987b33-988a2. Here, the codices read “to_ de_ dua&da poih~sai th_n e(te&ran dia_ to_ tou_j a)riqmou_j e!cw tw~n prw&twn eu)fuw~j e)c au)th~j genna~sqai,” and critics have found it especially difficult to translate this passage (see Tredennick 1973: 46-7 n. a). If we see the primary things as being the One and the Dyad – those which first existed, i.e. before the other numbers (Aristotle does not say “prime numbers” but “first things”) – then this passage gives us no particular difficulty. I translate: “that the dyad renders the second nature [of numbers] is due to fact that numbers – excepting the first things [the One and the Dyad] – are readily generated from it [the Dyad].” This “second nature” is, unsurprisingly, their capacity for division. 264 Also see Arist. Metaph. 1073a18-22. 265 Here, Aristotle uses the Pythagorean term mimh&mata to refer to the analogues of the first principles, a possible slippage since he is certainly only talking about Plato’s pragmateia here. 266 Arist. Metaph. 988a1-7. 106 the Pythagoreans in three particular ways: (1) under the category of Material causes, Plato posits a “duality instead of a unified (or single) Limitless” which Aristotle says is derived from the Great and the Small; 267 (2) as to Plato’s Formal cause(s), he claims that numbers are “distinct from perceived things,” whereas the Pythagoreans believed that numbers were sensibles; and (3) that the Pythagoreans do not posit a middle (metacu_) term, which Aristotle calls the “mathematical practicals” (ta_ maqhmatika_ tou&twn [pragma&twn]). 268 Those modifications to the Pythagorean pragmateia that Aristotle cites, including the development of the Forms, are all the consequence of Plato’s investigations into logic (dia_ th_n e)n toi~j lo&goij ske&yin) which is made accessible by dialectic, of which “the earlier thinkers did not partake” (oi( ga_r pro&teroi dialektikh~j ou) metei~xon). Later in Metaphysics Book M, Aristotle returns to the historical development of the second term of the Pythagorean and Platonic pragmateiai – the ideal (ti& ma&lista) and the Ideal (ei!dh), respectively – and concludes that it was Socrates’ investigations into essence (ti& e!sti), which is primary to matter, which compelled him to disagree with the Pythagoreans; the vehicle for such investigation was dialectic, which allowed people “to have the ability to examine contraries independent of essence and whether or not opposites come under the same episteme.” 269 267 On the Great and the Small, see Chapter 5 and Sayre 2005: 84-101. 268 Taking, with Tredennick, the antecedent as ta_ pra&gmata, although it is possible that oi( a)riqmoi& is the antecedent as well. 269 Arist. Metaph. 1078b24-27. 107 And so, it is by means of comparison that Aristotle sees the Platonic pragmateia as an extension of the Pythagorean philosophical system: this comparison takes shape as a common criticism linking the assumptions of each philosophical group to the other while carefully demarcating the main differences between Plato’s and the Pythagoreans’ investigations into reality and beyond. We must recall, however, that aside from the biases that Aristotle’s account contains, it also envisions a pragmateia that does not conform with Plato’s dialogues that predate the Parmenides. 270 This should not surprise us, and we are further stimulated to consider the fact that Aristotle did not enter Plato’s academy until 367/6 BCE, after Plato had traveled to Western Greece at least twice and had engaged with Pythagorean philosophers both in Sicily and in Southern Italy. This is the period in which Plato himself establishes certain means of criticizing the Theory of Forms put forth in his Middle dialogues (especially Phaedo, Republic, and Phaedrus) and begins to retool his own philosophical pragmateia, shifting it away from its original Socratic character, which was more obviously critical of the Pythagoreans despite its insistence upon questions that were derived from the scientific projects of mathematical Pythagoreans. In the process of revision, Plato is forced to reconsider the fundamental principles, mode of communication, and technical terminology that he has employed since the middle period in the light of criticisms fostered by his further engagement with both Eleatic and Pythagorean philosophies. At the center of 270 Sayre 2005: 12-17. 108 this revision is the process of dialectic, the apex of the Platonic educational system as expounded in Books VI and VII of the Republic, to which we shall turn now. Both dialectic and mathematics receive their fullest treatments from Plato in Books VI and VII of the Republic, the famous dialogue composed around 380-370 BCE, following Plato’s first visit to Sicily and to Southern Italy in 389/388 BCE. 271 The imprint of Plato’s visit to Italy – and his subsequent (re)engagement with the mathematical philosophy of the Pythagorean Archytas of Taras – will become manifest to the reader in the course of this section of Chapter 2. As I will show, Plato composed his Republic in part as a response to the educational program advanced by the writings of Archytas of Taras, with particular attention to Archytas’ theories of the mathematical sciences known in antiquity as the quadrivium. I hope to suggest that Archytas’ fragments reveal a significant difference from Plato’s physics and metaphysics, in that Archytas believes that truth can be derived from empirical study of the natural forces of the universe as rationalized through mathematics. Plato, on the other hand, took issue with the Pythagoreans’ mathematization of the universe through mechanics and – in a Parmenidean move – believed that rationalization of phenomena did not lead one to the heights of philosophical knowledge. In the Republic, to be sure, Plato espoused a Theory of the Forms that was premised upon the notion that the Forms could only be approached 271 For Plato’s first visit to Sicily, see Morrow 1962: 146-50. Plato’s Epistle VII never says directly that Plato had visited Taras on his first trip in 388 BCE; we are simply told that he went to Sicily and Italy (326b5). But it is attested by Diogenes Laertius (3.18) and Cornelius Nepos (Dion 2) that he visited Taras around 388 BCE. 109 through a developmental understanding of mathematics corrected through dialectic, a higher mental function. Throughout the Republic, then, Plato reveals the significance of his visit to the Pythagoreans in Southern Italy and Sicily, and we are prompted to consider how Plato’s visits shaped the issues at hand in the development of his philosophical pragmateia. That Plato’s visit to Dion in Syracuse in 388 BCE was massively influential on the composition of the Republic can be deduced from the amount of similarity we detect between the vision of how to establish the ideal polis formulated by Socrates – and the challenges that lay in its wake 272 – and Plato’s own discussion of what he felt during his first trip to Sicily and Italy in Epistle VII. This theory is further strengthened by a passage in Republic Book VI that refers directly to the possibility that the ideal city-state could be achieved in reality in a dynastic succession, in words that resonate quite strongly with Dion’s favorable position for inheritance of the Sicilian throne in the 380s. 273 We are therefore reminded of the significance of the discourse of “Royalty” in the political philosophy of Plato, from its earliest minor suggestions here in the Republic to the decisive nomination of the “Kingly Art,” a euphemism for the political texnh& established by the Eleatic Stranger in the 272 See Morrow 1962: 121-2 and 217 n. 7 for citations of the Republic. 273 Socrates (Pl. R. 499b5-c2) contrasts the unlikely situation of a group of philosophers into whose hands the restructuring of the government would fall by “luck” (e)k tu&xhj) with the actual possibility that current (nu~n) dynasties and kingdoms could establish a true love for philosophy and create a philosophical polity through divine inspiration (e!k tinoj qei&aj e)pipnoi&aj). Cf. Pl. R. 502a. In Epistle VII (327b6-c6), following the death of Dionysius I, Dion hopes that Dionysius II will become one of those educated in philosophy (called the “saviors of the polity” at Pl. R. 502d1) “with the gods’ aid” (sullambano&ntwn qew~n). 110 Statesman. 274 Indeed, the famous “Philosopher-King” is never referred to per se in the Republic, an otherwise unimportant anachronism except that it has obscured an interesting comparison: in the famous passage, Socrates claims that the ideal polity will not come to light “unless the philosophers start reigning among the cities or those currently called kings and dynasts begin to philosophize nobly and sufficiently” ( )Ea_n mh&…h@ oi( filo&sofoi basileu&swsin e)n tai~j po&lesin h@ oi( basilh~j te nu~n lego&menoi kai_ duna&stai filosofh&swsi gnhsi&wj te kai_ i(kanw&j…). 275 The presence of the verb basileu&w indicates an activity – and subsequently does not simply create a new class of men – and this verb recurs in an extremely significant place at the end of Book VI, when Socrates is describing through images (he refuses to define it except through its “offspring” and “likeness”) 276 the Form of the Good: No&hson toi&nun, h}n d’e)gw&, w#sper le&gomen, du&o au)tw_ ei}nai, kai_ basileu&ein to_ me_n nohtou~ ge&nouj te kai_ to&pou, to_ d’ au} o(ratou~, i#na mh_ ou)ranou~ ei)pw_n do&cw soi sofizesqai peri_ to_ o!noma. a)ll’ ou}n e!xeij tau~ta ditta_ ei!dh, o(rato&n, nohto&n; “Conceive, then,” I said, “that the powers, as we are speaking of them, are two: [the Good], which reigns over the Intelligible kind and place; and in turn [the Sun, which reigns over] the Visible, lest – by calling it heaven – I seem to you to pun on the name. At any rate, you grasp these two forms: the Visible and the Intelligible?” 277 274 E.g. Pl. Plt. 259b1. The “political art” (politikh_ texnh&) has been referred to twice before, in the Gorgias (521d6-8) and the Protagoras (318e5-319a5). On these usages, see Rosen 1995: 4-5. 275 Pl. R. 473c11-d1. 276 He uses the terms e!kgonoj and o(moio&tatoj at Pl. R. 506e2-3. Socrates claims that he would be “laughable” (ge&lwta) if he were to reveal the true nature of the Good, the same term Plato uses when arguing that one must make use all of instruments of oral dialectical exercises rather than read from a book lest he become laughable (katage&lastoi; Pl. Ep. VII 343c8). 277 Pl. R. 509d1-4. 111 It is impossible to render the puns and verbal echoes found throughout this passage in English. Indeed, Socrates highlights for Glaucon and the others – and for the reader – the sophistic tricks he is currently employing. He worries that his argument will be dismissible for its punning on the words “o)ratou~” and “ou)ranou~,” but the initial command “No&hson” also intensifies the meaning of the nohtou~ and marks the following word for which it is a modifier: ge&nouj. What Plato is enforcing here through verbal tricks and semantic play is the distinction between the Visible and Intelligible Kinds, and the term genos here is remarkable especially for its resonance with what Socrates has said previously about the Form of the Good, which is the topic of this whole section: “So,” I said, “it was [the Sun] which I meant when I spoke of the offspring (e!kgonon) of the Good, to which the Good gave birth as its analogue (o$n ta)gaqo_n e)ge&nnhsen a)na&logon e(autw|~), the very thing which – in the visible place – is in the same relation to vision and things visible as the Good – in the Intelligible place – is to intelligence and things intelligible.” 278 One should not fail to note the presence of the term genos and words related to it in Plato’s theory of the Form of the Good in the Republic. 279 Like Number for the followers of Hippasus – the mathematical Pythagoreans – and Philolaus, the “offspring” of the Good, which is the Sun, functions epistemologically to lead the soul up to the ontological reality, which, for Plato in this period, lies in the 278 Pl. R. 508b12-c2. 279 On the significance of the term genos to the dialectical theories of the later dialogues, see Chapter 3. 112 “Intelligible place” of the Forms. 280 Indeed, Socrates uses the same astronomical terminology that Aristotle used 281 when complaining about the pragmateia of the “so-called Pythagoreans,” in which the first principles rise up to the higher aspects of reality. 282 It could be argued that Socrates’ play on the “Visible” and “heaven” – a paralogical comparison that cannot simply mark an ontological equivalency and demonstrates categorical confusion – is a criticism of mathematic Pythagoreanism and distances Plato in the Republic from what he knew of Pythagorean astronomy and cosmology at the time. There are other signs of Pythagorean influence on the “definition” of the Good in Book VI of the Republic. That the Sun is “analogue” to the Good is particularly interesting, since it establishes the links between the Pythagoreans’ “imitation” and Plato’s theory of access to the Forms. Imitations and images exist in “the Visible place” in such a way that they provide our souls with the means to conceive of the unchanging reality “in the Intelligible place.” The levels of cognition – the Visible and the Intelligible – are themselves established as analogous, in that the (1) Visible, with its subdivision into (A) images and (B) visible things, is proportionate to the (2) Intelligible, with its subdivision into (C) mathematical diagrams and postulates and (D) The Forms, including the Form of the Good. The 280 See Chapter 1. 281 Aristotle uses the terms e)panabh~nai kai_ e)pi_ ta_ a)nwte&rw tw~n o!ntwn. See Chapter 1. 282 The soul which is being educated correctly and prepared to understand the Forms, Socrates argues, must make sure not to be forced to employ hypotheses in its investigations, which would mean going away from the a)rxh& and not towards it; the soul which proceeds in this fashion is said to “rise up higher above” (a)nwte&rw e)kbai&nein; Pl. R. 511a6), a criticism conspicuously similar to what Aristotle says of the “so-called Pythagoreans.” For a more precise discussion of Plato’s dialectical criticism of the Pythagoreans, see below. 113 proportion is A + B : C + D = A : B = C : D. 283 What is of particular interest for our investigation is the description of the Intelligible place and the means to arrive at Noesis, a cognitive process that is aided by mathematical diagrams in order to achieve full knowledge. 284 It should not escape the reader that the very method Socrates is currently employing is founded upon the mathematical diagram of a line that has been divided into two main sections (1 and 2) and then subdivided into two further spaces in each section (A /B and C/D), such that the subdivisions within each primary division are proportional to one another. But what distinguishes this cognitive method from the teaching of the Pythagoreans is the notion that here, in the Republic, the mathematical diagrams, postulates, and axioms (C) are not the telos of the movement towards the top of the Intelligible place (1), as Socrates makes explicit in his implicit criticism of the Pythagoreans’ pragmateia: oi}mai ga&r se ei)de&nai o#ti peri_ ta_j gewmetri&aj te kai_ logismou_j kai_ ta_ toiau~ta pragmateuo&menoi, u(poqe&menoi to& te peritto_n kai_ to_ a!rtion kai_ ta_ sxh&mata kai_ gwniw~n tritta_ ei!dh kai_ a!lla tou&twn kaq’ e(ka&sthn me&qodon, tau~ta me_n w(j ei)do&tej, poihsa&menoi u(poqe&seij au)ta&, ou)de&na lo&gon ou!te au(toi~j ou!de a!lloi~j e!ti a)ciou~si peri_ au)tw~n dido&nai w(j panti_ fanerw~n, e)k tou&twn d’ a)rxo&menoi ta_ loipa_ h!dh diecio&ntej teleutw~sin o(mologoume&nwj e)pi_ tou~to ou{ a@n e)pi_ ske&yin o(rmh&swsi. 285 For I think you know that those who make geometry and arithmetic and those sorts of things the object of their study, by assuming the odd and the even and figures and three kinds of angles and other 283 Pl. R. 509d6-511e5. See Cornford’s translation and notes (1964: 221-3). 284 Cf. Pl. Men. 82b9-85b7. The geometric demonstration in the Meno is also said to function upon Meno’s slave “like a dream” (w#sper o!nar). For the function of this metaphor in Plato’s works, see Sayre 2006: 86-7. 285 Pl. R. 510 c2-d3. My thanks go to Greg Thalmann for advice on this passage. 114 things according to each method, on the grounds that they know these things; adopting them as assumptions, they do not even consider it worth giving any account concerning these things either to themselves or to others, since they are apparent to each person. But beginning from these things and going through what remains they end consistently at the very point they set out in their inquiry. If we compare this passage with what Aristotle says in the Metaphysics, we see the traces of Plato’s teaching upon his student: for, despite the slightly different terminology, Socrates’ principal criticisms of the Pythagoreans’ method of philosophical investigation are echoed by Aristotle in the later work. Here, Socrates censures the Pythagorean pragmateia for its adherence to mathematical applications such as figures and theorems. He claims that they are not the objects of study themselves, but that they are epistemological tools that function as imitations of the Forms, “shadows and images in the water” which lead the student in the wrong direction, not “up towards the a)rxh&,” but down and away from it. 286 Not surprisingly, as Socrates says, those who simply employ mathematical figures in order to arrive at the first principles of the universe end up where they started, confirming – through the very circuit of their argument – the very hypotheses they assumed. 287 Employment of mathematical figures, then, leads the student back to those mathematical figures that he has assumed; this sphere of activity – called “the 286 Pl. R. 510e2-3 and 511a5. 287 We may take this as a revision of the earlier views about geometric hypotheses expressed at Meno 86e3-87b2. Generally speaking, the search for the mathematical sxh~ma in the Meno (73e3-75c7 et passim) is a precursor to this theory of the Forms, in that it too employs geometrical forms in order to arrive at the unifying term. 115 geometric arts” by Glaucon 288 – cannot stand alone as a means to achieve full knowledge of the world, but at least it is propaideutic. Socrates sees mathematics as an image of the Forms; the cognitive method necessary for access to the Forms and to true knowledge is dialectic (D), as Socrates makes explicit: To_ toi&nun e#teron ma&nqane tmh~ma tou~ nohtou~ le&gonta& me tou~to ou{ au)to_j o( lo&goj a#ptetai th~| tou~ diale&gesqai duna&mei, ta_j u(poqe&seij poiou&menoj ou)k a)rxa_j a)lla_ tw~| o!nti u(poqe&seij, oi{on e)piba&seij te kai_ o(rma&j, i#na me&xri tou~ a)nupoqe&tou e)pi_ th_n tou~ panto_j a)rxh_n i)w&n, a(ya&menoj au)th~j, pa&lin au} e)xo&menoj tw~n e)kei&nhj e)xome&nwn, ou#twj e)pi_ teleuth_n katabai&nh|, ai)sqetw~| panta&pasin ou)deni_ prosxrw&menoj, a)ll’ ei!desin au)toi~j di’ au)tw~n ei)j au)ta&, kai_ teleuta~| ei)j ei!dh. 289 Now, understand that the second cut of the Intelligible is what I am calling that to which reason by itself attaches through the power of dialectic, by treating assumptions not as first principles but as hypotheses as they really are, ladders, as it were, and starting points, so as to rise up as far as that which is not an assumption, to the first principle of all. Once this [the first principle] has been attained, [the reason], since it comprehends the things that depend on it [the first principle], may go back down again to the conclusion, making use of nothing perceived in any way whatsoever, but [employing] the Forms themselves, from one to another, until finally [arriving] at the Forms. In this passage, Socrates argues that dialectic differs from the method of investigation employed by the Pythagoreans: dialectic becomes attached to logos by positing hypothetical tools – such as mathematical diagrams, axioms, etc. – not as a)rxai& themselves but as the means to ascend to that which is not hypothetical, i.e. the unassumed, namely the actual a)rxh& (note the switch from plural archai to 288 Pl. R. 511b1-2. How Philolaic are Glaucon’s ideas about mathematics here? Philolaus (F A 7a Huffman = Plutarch, Quaest. conv. 718e) believed that geometry was the “first principle and mother- city” (gewmetri&a a)rxh_ kai_ mhtro&polij) of the other sciences. 289 Pl. R. 511b3-c2. 116 singular arch1) from which all things are derived. 290 There will be no need for the student, once she has discovered the first principle, to employ phenomena, since the first principle – in this case the Good – contains all that is dependent upon it. According to the passage that started this whole digression, the Good – as the primary archon of the Intelligible place – reigns over all that is derived from it (basileu&ein to_ me_n nohtou~ ge&nouj). Again, as we saw briefly with the Pythagoreans, 291 theories of knowledge and its attainment resonate semantically with theories of political rule. That might be satisfactory for an understanding of the Socratic vision of dialectic and its place in theories of cognition in Book VI of the Republic, but Plato does something quite remarkable at this juncture: he provides the reader with a reinterpretation of Socrates’ argument through the eyes of Plato’s elder brother Glaucon: “I understand,” he said, “though not sufficiently – for you seem to me to be describing an enormous undertaking – that you intend to distinguish clearly between the examination of reality and the intelligible by means of the science of dialectic and the examination by means of the arts, as they are called (u(po_ tw~n texnw~n kaloume&nwn), which have as their first principles assumptions; people investigating these things are forced to examine them by employing thought (dianoi&a|), but not using phenomena; on the other hand, because they depart upon their examinations without ascending to the first principle, but start from assumptions, they do not seem to you really to have knowledge about things, although the objects are intelligible in reality when connected with a first principle (kai&toi 290 It is worth comparing Socrates’ criticism of Pythagorean use of first principles with his exposition of Presocratic (especially Anaxagorean) causes in the Phaedo (96a5-99d2). He claims to hypothesize the Beautiful, the Good, and the Great in response to his inquiry into Presocratic causes (100b6-8). 291 See Chapter 1. 117 nohtw~n o!ntwn meta_ a)rxh~j). And you seem to me to be calling the arrangement of geometric objects and things of this sort “thinking” (dia&noian), and not “knowledge” (nou~n), on the grounds that “thinking” is something in the middle between opinion and knowledge (w(j metacu& ti do&chj te kai_ nou~ th_n dia&noian ou}san).” 292 Here, Glaucon revises what Socrates has said and renders it in terms that he understands. What is most notable is the introduction of the “middle” (metacu&) term, which is the link that connects the separate “kinds and places” of the Visible and the Intelligible. This middle term is dianoia, and it represents the mathematical objects to which Socrates referred previously. We detect in Glaucon’s response a slight revision of Socrates’ theory of the attainment of knowledge, where Glaucon’s interests – which represent a secondary voice in the Platonic dialogues – are in the “arts” (texnai&) 293 to which Plato will turn indelibly in the later dialogues, most especially the “Royal Art” of politics to which we referred earlier in this chapter. While Book VI of the Republic ends with a theoretical discourse on how to attain knowledge of the Good, Book VII takes care to establish the practical means by which a student may proceed through dianoia into nous by employing mathematical objects and, subsequently, dialectic. It is decidedly more engaged with Pythagoreanism than Book VI, which sets the stage for but does not catalyze the direct confrontation between mathematical theories of Plato’s middle dialogues and the philosophical pragmateia of the Pythagoreans. The educational system of Kallipolis requires the mathematical sciences – here designated ta_ maqh&mata – in 292 Pl. R. 511c3-d5. 293 At Pl. R. 522b4-6, Glaucon questions Socrates’ swift dismissal of the arts as “banausic.” 118 order that the souls of the students might be “led up from Hades to the gods” on their anabasis, wherefrom they are required to return after comprehension of the Good. 294 The organization of the four mathematical sciences – astronomy, geometry, numbers, and music 295 – espoused by Archytas of Taras (ca. 430/410? – 350s BCE) and known as the quadrivium, 296 is assumed to have been previously established at the beginning of this passage. In this way, it will be of utmost profit to examine the mathematical sciences as they are presented by Socrates in relation to the fragments of Archytas that deal with those sciences. Let us begin with Fragment 1 of Archytas, so as to establish where Plato is departing from the work of his Pythagorean contemporary: kalw~j moi dokou~nti toi_ peri_ ta_ maqh&mata diagnw&men 297 kai_ ou)de_n a!topon o)rqw~j au)tou&j, oi{a& e)nti, peri_ e(ka&stou frone&n. peri_ ga_r ta~j tw~n o#lwn fu&sioj kalw~j diagno&ntej e!mellon kai_ peri_ tw~n kata_ me&roj, oi{a& e)nti, kalw~j o)yei~sqai. peri& te dh_ ta~j tw~n a!strwn taxuta~toj kai_ e)pitola~n kai_ dusi&wn pare&dwkan a(mi~n safh~ dia&gnwsin kai_ peri_ gametri&aj kai_ a)riqmw~n kai_ ou)x h#kista peri_ mwsika~j. tau~ta ga_r ta_ maqh&mata dokou~nti ei}men a)delfea&. 298 294 Pl. R. 521c1-3. Their return is required in order to teach those who are unable to depart from the cave and are constrained within the world of shadows, as the parable of the Cave tells us. 295 These are taken in the order found in Archytas F 1 Huffman. They are also given in the same order – with only the reversal of the first two terms – at Pl. Theaet. 145a6-9 (geometry, astronomy, logistic, music). 296 For one interpretation of the quadrivium, see Huffman 2005: 388-9. Interestingly, Fragment 1 does not credit Archytas with the discovery or institution of this scientific order, but the point made here (as well as in the subsequent traditions derived from Nichomachus) is that Archytas called the sciences “kin.” Archytas himself praises those who distinguished the sciences as having done well, and we may therefore assume that he has inherited this structure, perhaps from the mathematici who derived their philosophy from Hippasus of Metapontion. 297 On this form, see Huffman 2005: 149-152. 298 Porph. In Harm. 1.3. Following Huffman, I admit the final line here, but excise the line that follows in Nichomachus Ar. 1.3.3 (Huffman F 1c) which states: “peri_ ga_r a)delfea_ ta_ tou~ o!ntoj prw&tista du&o ei!dea ta_n a)nastrofa_n e!xei.” The reference to the “two forms” is an echo of Plato’s Republic (530c8), where Socrates mentions the two “forms (ei!dh)” of motion considered 119 Those who distinguish 299 the sciences seem to me to do so well, and there is nothing strange (in suggesting that) they understand individual things correctly, what sort they are. For, after they made good distinctions between the nature of wholes, they were on their way to see well concerning things, what sort they are, part by part. In fact, concerning the speed of the stars and their risings and settings, they handed down to us a clear distinction; the same goes concerning geometry and numbers and – not least (of all) – music. For these sciences seem to be akin. It should be first noted that the logic of this passage does implicitly distinguish between the operations of thought and vision, as we see that the cognitive process of distinction (diagno&ntej; cf. frone&n) is followed subsequently by seeing (e!mellon o)yei~sqai), although this is certainly not the point of emphasis here. 300 In this way, we might hesitate to conclude that “there is little in common with Plato.” 301 Indeed, apart from the set of mathematical sciences which will be adopted by Plato in the Republic, this passage too is interested in how the cognitive process of making distinctions leads to an ontological understanding of things as they are in reality, which is to say visibly. What reality means to Archytas and to Plato – and where it lies (in the visible or the intelligible) – seems to be the subject of dispute. The order of the sciences as it is presented here in Fragment 1 – which represents the beginning “counter (a)nti&strofon)” to one another, by which he means those constructed for the eyes and those for the ears. We might think that both Nichomachus and Plato were working from the same text of Archytas, except that the sentence following directly upon Nichomachus’ mention of the two forms refers to Plato’s Epinomis, suggesting that he was Platonizing the text of Archytas to which he had access. Generally speaking, I adopt Huffman’s text and admit the fragments as genuine following Huffman’s arguments (although not always). 299 For this translation of diagignw&skw, see Huffman 2005: 149-152. Cf. the echo of this verb in Pl. R. 522c6. 300 Contra Huffman 2005: 58. 301 Ibid. 120 of Archytas’ Harmonics – moves rhetorically from the visible to the audible sciences; it should not be assumed to represent a hierarchy. 302 This shift from the visible to the audible sciences is further echoed by Socrates in Republic VII (530d6- 10), when he concludes his discussion of the sciences and demonstrates the direct correlations between these texts by referring to the sciences as “kin”: “It is likely,” I said, “that the eyes have been constructed for astronomy, just as the ears are constructed for enharmonic motion (pro_j e)narmo&nion fora_n), and these sciences are some sisters of one another (a)llh&lwn a)delfai&), just as the Pythagoreans say, and we, O Glaucon, are in agreement.” That Socrates is assuming the Archytan quadrivium is apparent throughout this passage, although, as we shall see throughout this chapter, he has some revisions to offer to the Pythagorean system. Unlike the order presented in Archytas’ Fragment 1, Socrates’ educational program for the mathematical sciences in Book VII of the Republic proceeds according to a hierarchical order: logistic/arithmetic, geometry, stereometry (solid geometry), astronomy, harmonics. We shall take them subject by subject. The first science (ma&qhma) required of the educational program in the city is the one designated “common” (to_ koino&n), namely number and logistic (a)riqmo&j te kai_ logismo&j), which appear here to be the same function that deals with different subjects. 303 First, logistic allows people to advance towards the reality of the 302 Cf. Huffman 2005: 128-9. 303 Pl. R. 522c1-8. Logismos was also discussed as a mathematical process (multiplication) in the Meno (82d4). I translate the term logismos as “logistic” for Plato and “calculation” for Archytas on 121 Intelligible world (pro_j ou)si&an) when they perceive the difference between contraries of all sorts: in the example given, three fingers are compared and contrasted. The process of distinguishing (diagignw&skein) 304 between three objects, e.g. the big, small, and middle fingers, when aided by logistic (logismo&j), leads the soul to distinguish between Great and Small, since concepts that are oppositional within the realm of noesis and represent first principles among the Forms, as we saw in Aristotle’s Metaphysics. 305 The recognition of that very opposition, argues Socrates, draws the soul into that place of knowledge. We might consider, then, that logistic is here figured as the recognition of difference and consequent oppositional processes of comparison and contrast (sugkexume&na a)lla_ diwrisme&na), which are analogous with addition and subtraction in arithmetic. 306 Logistic, Socrates claims, can be useful for the Guardians – who are figured here as philosopher-soldiers – in a way explicitly contrasted with its import for merchants and shopkeepers: So it would be appropriate to legislate this science and to persuade those who intend to partake of the greatest [functions] in the city to undertake logistic and to engage in it not amateurishly, but until they advance to the sight of the nature of numbers by means of knowledge itself, practicing it not for the purposes of buying and selling like merchants and shopkeepers, but for the sake of war and the the grounds that the term “logistic” can be quantitative but also has a broader application to abstract, non-quantitative terms such as “Great” and “Small,” whereas “calculation” is solely quantitative. 304 Pl. R. 522c6. This whole passage seems to be employing the same kinds of terminology found in Fragment 1 of Archytas. Huffman 2005: 150 passes over this extremely significant instance of the use of diagignw&skw, which appears in a passage famously comparable with Archytas’ Fragment 1. 305 Pl. R. 523 b9-524d5. We shall reexamine the concepts of opposition in Plato’s dialectic in Chapters 3 and 5. 306 Pl. R. 524c7. For an examination of the problem of defining logismo&j in the works of Plato and the fragments of Archytas, see Huffman 2005: 202-6. 122 facilitating the conversion of the soul itself from Becoming to Truth and Being. 307 Logistic here is understood to function arithmetically for those engaged in trade, a pragmatic activity which belongs to the place of Becoming (gene&sewj). We are told that, for those who know about numbers, logistic and arithmetic lead the soul to employ “knowledge itself” to advance towards “truth itself” and make their practitioners quick learners of other subjects. 308 Throughout this passage, Socrates seems to echo – although with some significant modifications to the terminology – the language of a portion of Archytas’ Fragment 3 Huffman (Stobaeus 4.1.139), from his work On Sciences: sta&sin me_n e!pausen, o(mo&noian de_ au!chsen logismo_j eu(reqei&j. pleoneci&a te ga_r ou)k e!sti tou&tou genome&nou kai_ i)so&taj e!stin: tou&tw| ga_r peri_ tw~n sunallagma&twn diallasso&meqa. dia_ tou~ton ou}n oi( pe&nhtej lamba&nonti para_ tw~n duname&nwn, oi# te plou&sioi dido&nti toi~j deome&noij, pisteu&ontej a)mfo&teroi dia_ tou&tw to_ i}son e#cein. kanw_n de_ kai_ kwluth_r tw~n a)dikou&ntwn <e)w_n> tou_j me_n e)pistame&nouj logi&zesqai pri_n a)dikei~n e!pause, pei&saj o#ti ou) dunasou~ntai laqei~n, o#tan e)p’ au)to_n e!lqwnti: tou_j de_ mh_ e)pistame&nouj, e)n au)tw| dhlw&saj a)dikou~ntaj, e)kw&lusen a)dikh~sai. For, once discovered, calculation stopped discord and increased concord. For, once this has come into being, pleonexia 309 does not exist and equality does exist. For, by means of this, we reconcile concerning dealings with one another. So, through this, the poor take from the powerful, and the wealthy give to those in need, since they both believe that they will have equality through this. As it is both a standard and a hindrance to unjust people, it stopped 310 those who 307 Pl. R. 525b11-c6. 308 Pl. R. 526a6-b9. 309 Pleonexia means something like “wanting more than one’s due share.” I leave the word untranslated in order to promote clarity for the reader attempting to understand the internal logic of terms. On pleonexia in Archytas’ and Plato’s ethical philosophies, see Chapters 5 and 6. 310 Or perhaps “stops.” All these aorists may be taken as gnomic aorists. 123 know how to calculate from committing injustices, because it convinced them that they would not be able to escape unnoticed whenever they undertake it; as for those who do not know [how to calculate], it prevented them from committing injustices since it makes clear that they are doing injustices in it. Archytas’ Fragment 3, with its emphasis on calculation (logismo&j) as a tool for political organization, resonates with the political context for Books VI and VII of Plato’s Republic. A fuller treatment of this fragment, with its appeal to the doctrine of political equality, will not be attempted until Chapter 6. Suffice it to say for now, however, that Archytas’ writings form the backdrop for Plato’s consideration of these topics during the composition of the Republic and that these two philosophical thinkers are working from a common set of hypotheses. 311 Both Plato and Archytas are assuming that logismos permits people who are active in the polis to achieve their proper aims in accordance with the preservation of their community. In Fragment 3, Archytas sees calculation as something that – upon its discovery in the past – created like-mindedness (o(mo&noia) between elements in a system that had been otherwise in opposition (sta&sij). The Pythagoreanism of Archytas has been politicized, in that he seems to advance the process of calculation as something akin to the concept of Number, which we saw was the “critical tool” for the followers of Hippasus and the thing that provides understanding and knowledge to humans in Philolaus’ epistemology. 312 Likewise, for Philolaus (F 6 Huffman), Harmony was the (outside) 311 See Huffman 2005: 191. 312 See Chapter 1. What I have argued justified Huffman’s (2005: 489) comment that “Archytas like Philolaus before him seems to think that it is through numbers that we gain accurate knowledge of things.” 124 force that created likeness among things that were unlike and established order among the elements of the universe. Plato, for his part, assumes no perceivable difference between the sciences of number and logistic in the Republic. Even so, we must agree with Huffman when he claims that “Archytas, like Plato and in contrast [with, sc.] Aristotle, used the term logistikh& rather than a)riqmhtikh& to designate the entire science of numbers,” since the extant genuine fragments of Archytas do not feature the latter. 313 Plato never employs the term a)riqmhtikh& in Book VII of the Republic, but prefers to use the terms Number or numbers instead of arithmetic, following Archytas (F 1 Huffman). Socrates introduces the second mathematical science, in such a way that it is assumed both by himself and Glaucon to be geometry. 314 Glaucon assumes that the importance of geometry lies in its practical use in war, but Socrates again distinguishes between the little knowledge of geometry required for practical purposes (in this case military) and the advanced study of geometry that facilitates comprehension of the Form of the Good. 315 Socrates poses the problem: they will have to decide as to whether geometry is a suitable mathematical science based on whether or not it “forces people to see Being or Becoming” (ei) me_n ou)si&an a)nagka&zei qea&sasqai…ei) de_ ge&nesin). 316 The emphasis on vision here recalls the epistemic value of geometry, in that geometry itself is not the goal of study but 313 Manuscript S of Fragment 1 refers to a)riqmhtika~j, which probably derives from a defective text. 314 Pl. R. 526c8-10. 315 Pl. R. 526d1-e1. 316 Pl. R. 526e6-7. 125 simply a means to knowledge of the reality that lies beyond vision. This point is further emphasized when Socrates proceeds to criticize the language of those mathematicians who employ geometry in order to study the world of becoming and destruction: “So then,” I said, “no one among the number of people who are experienced even slightly in geometry will dispute that the science itself (of geometry) is entirely opposed to the arguments about it spoken by those who engage in it.” “How so?” he said. “Well, I suppose, they say things extremely silly and base; for they yammer on talking of “squaring”,“applying” and “adding” as if they were doing something and making all their arguments for the sake of praxis (w(j ga_r pra&ttonte&j te kai_ pra&cewj e#neka pa&ntaj tou_j lo&gouj poiou&menoi). But, the reality is that the purpose of the whole subject is knowledge.” “Definitely the case,” he said. “So have we come to any agreement about this?” “What’s that?” “That (the purpose of the subject of geometry) the knowledge of what is exists eternally, but not of anything that is at any time in the process of becoming or destruction?” “That will be readily agreed,” he said. “For geometry is the knowledge of what is eternally existent (tou~ ga_r a)ei_ o!ntoj h( gewmetrikh_ gnw~si&j e)stin).” 317 Socrates’ emphasis on praxis here is unusual in the Republic and significant: he is suggesting that “those who engage” in geometry use imprecise language because geometry does not deal with things in the process of Becoming (i.e. are squared, applied, or added), a set of terms he categorizes with nominal and adjectival forms of the verb prattei~n. Again, we hear a criticism of those who confuse things as they exist in reality (ontology) with the praxis employed to understand them (pragmatics). 317 Pl. R. 527a1-b8. 126 We saw the significance of this semantic field to Aristotle’s criticisms of the earlier Pythagoreans in Chapter 1. Another important fragment of Archytas of Taras extends our knowledge of the dispute over the pragmateia of the Pythagoreans: kai_ dokei~ a( logistika_ poti_ ta_n sofi&an tw~n me_n a)lla~n texnw~n kai_ polu_ diafe&rein, a)ta_r kai_ ta~j gewmetrika~j e)nargeste&rw pragmateu&esqai a$ qe&lei. kai_ a$ e)klei&pei au} a( gewmetri&a, kai_ a)podei&caj a( logistika_ e)pitelei~ kai_ o(mw~j, ei) me_n ei)de&wn tea_ pragmatei&a, kai_ ta_ peri_ toi~j ei!desin. 318 And logistic 319 indeed seems far superior to the other arts as regards wisdom, and (it seems) in particular to deal with the object of its investigations it wants more clearly than geometry. And again, in the things that geometry leaves behind, logistic completes their demonstrations and, equally, if the pragmateia deals with figures, (logistic completes the demonstrations) that deal with figures. This fragment, from a work known as the Discourses (Diatribai&) of Archytas, 320 is of utmost importance in distinguishing between Archytas’ and Plato’s views of the structure and essence of the mathematical sciences. First, it is clear from this passage that the terms of mathematical categories are considered “arts” (texnai&) here, whereas they were called “sciences” (maqh&mata) in Fragment 1. What has been confused in Archytas’ philosophy is distinguished by Glaucon and Socrates in the Republic: the technical “arts” are often considered banausic or marked by manual labor in the Republic – consequently they carry a lower class value – in contrast with the “sciences” which are pure modes of thinking that lead to the place of the 318 Archytas F 4 Huffman (Stobaeus 1. Proem 4). The translation of this passage is especially difficult. On the difficulties encountered in translation, see Huffman 2005: 225-252. 319 For the difference between logismo&j (F 3 Huffman) and logistikh& (F 4 Huffman), see Huffman 2005: 235. He concludes: “[t]he natural suggestion would then be that logistic was viewed as the science of number which underlies the practical application of mathematical calculation (logismo&j) to human life.” 320 On the title, see Huffman 2005: 228-232. 127 Intelligible. 321 Even so, as we saw earlier, in Republic VI and VII the admission of the technical arts to this system is something upon which Glaucon insists, despite Socrates’ dismissal of them as “banausic.” 322 In this way, we can conceive of Glaucon as a character in the Republic who stands in the middle – almost as a communicant – between Archytan Pythagoreanism and Socratic philosophy. The technical language of “arts” and “sciences” reveals another instance of Pythagorean terminological ambivalence, and this passage anticipates the kinds of criticisms of essence and praxis found in the later writings of Plato and Aristotle. In Archytas’ figuration, logistic is far better suited as an “art” for praxis than geometry. What are we to do with this suggestion? First of all, as Huffman has pointed out, the use of the term e)narge&steroj brings us into the Visible, which as we have seen is distinguished implicitly from the Intelligible in Fragment 1. In that fragment, Archytas’ theory of understanding supposed that the cognitive process of distinction precedes the ability to see things in their individuated parts. This is in stark contrast with the Platonic theory of knowledge proposed in the Republic, where sensible engagement with the phenomena of the world – when properly filtered through the sciences – leads one up to the world of unchanging knowledge. What is more, in Archytas’ Fragment 4, the language of “demonstrations” (a)podei&caj) is also semantically tied to the visible world. We can therefore agree with Huffman when 321 Socrates himself admits (Pl. R. 522d4-e2) that they are revising the terms of discussion and failing to adhere to a consistent terminology. 322 Pl. R. 511c3-d5, 522b4-c3. 128 he concludes that “Archytas means that logistic deals with things ‘more concretely’ and ‘more vividly,’ in a way that evokes the visible and the palpable.” 323 If this is the case, how can logistic succeed pragmatically where geometry fails? Contextualization with the passage cited above from Book VII of the Republic helps us to understand Archytas’ argument. As we saw, Socrates complains that “squaring, applying, and adding” cannot be geometric functions at all because they deal with the world of becoming and destruction, and therefore cannot relate to the unchanging world of essence to which geometry leads; these functions therefore are pragmatic and applied. Archytas’ criticism of geometry is similar here, in that he sees geometry as being deficient pragmatically, in that it does not complete the demonstrations of the objects of its investigation as well as logistic does. Thus, logistic may be understood to complete proofs because it is a pragmatic function that comes to an equation, an unsurprising theory if we assume the close connections between logistic and calculation or arithmetic. Those functions to which Socrates refers in the Republic are pragmatic, to be sure, and they would seem more effectively to fit into Archytas’ scheme for logistic than geometry, in the sense that they affect things that must be, in Socrates’ system, visible and modifiable. Interestingly, the use of the term ei!dh here echoes its semantic value in the fragments of Philolaus that we examined in Chapter 1, in that figures here are assumed to be palpable items; whether or not they are the odd, even, or even-odd gnoma of Philolaus that make up the many forms (morfai&) of the world cannot be discerned 323 Huffman 2005: 246-7. 129 from this fragment due to paucity of evidence. 324 But it is tantalizing to consider the possibility that the distinction between logistic and geometry in Archytas’ Fragment 4 coheres with the Platonic distinction between Visible and Intelligible, in that logistic – which can deal with “figures” pragmatically, if they refer to gnoma, through calculation – is a pragmatic function while geometry is entirely relegated to the Intelligible, a sphere which Archytas posits as preceding the visible world where things are experienced vividly. 325 In this way, Archytas and Plato both assume the distinction between visible and intelligible. It is apparent, however, that Plato reverses the Archytan system, which seems to prefer the visible – which is pragmatic, applicable, and leads one to an understanding of what things are ontologically – to the ancillary intelligible. 324 See Chapter 1. 325 We might reconsider, then, the place of the fragments of the Pseudo-Archytan treatise On Wisdom (Thesleff 1965: 43.25-45.4), as reported in the Exhortation to Philosophy of Iamblichus, in the corpus of Archytas’ writings. In the first fragment (Iambl. Protr. P. 16 Pistelli), Iamblichus tells us that Archytas begins his treatise: Wisdom is superior among all the human affairs (pragma&tessin) just as much as vision is superior to the senses of the body, mind to soul, and sun to the stars. For vision (o!yij) is the most far-shooting (e(kabolesta&ta) and has the most figures (polueidesta&ta) of all the other senses, and mind (no&oj) is superior in argument and thought for completing what is necessary and it is vision and the power of the most important things in existence (u(pa&rxwn). Indeed, the sun is the eye and the soul of things that have nature: for all these things are seen and come to be and are understood through it, and, once they have been rooted and generated, they are nourished and increased (a)e&cetai)and kindled (zwpurh~tai) with perception. If this passage were representative of – perhaps a forger’s imitation of – authentic Archytan philosophy, then it would be all the more convincing that Socrates in Books VI and VII of Plato’s Republic takes his point of departure from Archytas’ writings. Indeed, the theory that vision is “far- shooting,” a concrete reference to the arrow-shooter Apollo, coheres with the description of Platonic and Archytan vision by Apuleius (Apologia 15-16; Huffman A 25) which emphasizes that Archytas believed that vision occurred when rays (radii) “went forth from our eyes without any external support (oculis profecti sine ullo foris amminculo).” Even if it might be argued that the relationship between vision and figures (polueidesta&ta!) is somewhat difficult to define here, Plato’s examination of the sun in Book VI finds a counterpoint in this fragment (cf. Pl. R. 508a9-b4). On further ways in which the fragments of On Wisdom provide a possible object for criticism for Book VII of Plato’s Republic, see below. 130 This reversal of the Archytan system of visible and intelligible has further resonances in the section of Plato’s Republic VII that follows upon the discussion of geometry. Socrates introduces the third science for the optimal city-state as astronomy, following the quadrivium established by Archytas, but then criticizes this move because of its hasty neglect of the science that is underexamined and lacks disciplinary form: stereometry (solid geometry). Following the proposition that they should advance astronomy as the third science, Socrates returns to the issue of the visible and the intelligible in a passage that appears out of place in this “commentary” of sorts on the educational program and philosophy of Archytas: (Hdu_j ei}, h}n d’ e)gw&, o#ti e!oikaj dedio&ti tou_j pollou&j, mh_ dokh|~j a!xrhsta maqh&mata prosta&ttein. to_ d’ e!stin ou) pa&nu fau~lon a)lla_ xalepo_n pisteu~sai o#ti e)n tou&toij toi~j maqh&masin e(ka&stou o!rgano&n ti yuxh~j e)kkaqai&retai& te kai_ a)nazwpurei~tai a)pollu&menon kai_ tuflou&menon u(po_ tw~n a!llwn e)pithdeuma&twn, krei~tton o@n swqh~nai muri&wn o)mma&twn: mo&nw| ga_r au)tw~| a)lh&qeia o(ra~tai. oi{j me_n ou}n tau~ta sundokei~ a)mhxa&nwj w(j eu} do&ceij le&gein, o#soi de_ tou&tou mhdamh~| h|)sqhme&noi ei)si_n ei)ko&twj h(gh&sontai se le&gein ou)de&n: a!llhn ga_r a)p’ au)tw~n ou)x o(rw~sin a)ci&an lo&gou w)feli&an. 326 “It’s delightful,” I said, “how you seem to fear that the public will think you are recommending useless sciences. The fact is, it’s no trifling task at all, but actually it’s difficult to believe that a particular tool of the soul of each man – (the tool) which is more important to preserve than a thousand eyes, since Truth is seen by it alone – if it has been snuffed out or blinded by other pursuits is purified and rekindled among these sciences. So, those men who agree with these things will think that you speak well, but however many in no way have perception of this will think that you are saying nothing persuasive, since they will not see any other benefit worthy of mention from these things.” 326 Pl. R. 527d5-e6. 131 If we are willing to admit the possible genuineness of at least the doctrine represented in the first fragment of “Pseudo-Archytas’” treatise On Wisdom (Peri_ sofi&aj), 327 then Socrates’ short excursus from the subject at hand makes more sense as a refutation of Archytas. 328 Other people, Socrates is suggesting, place more emphasis on vision as a “tool” (o!rganon) for understanding the world, when they ought to realize that the “tool of the soul” which is most important – because it has access to Truth – can be “snuffed out” or “blinded” by the base pursuits to which Glaucon referred in the previous lines (farming, sailing, and military generalship). 329 In the Republic, the sciences play some part in rekindling (a)nazwpurei~) this “tool of the soul,” just as the sun – also called the “eye” and the “soul” – “increases and kindles” (a)e&cetai kai_ zwpurh~tai) things that have nature in fragment 1 of the “Pseudo-Archytan” treatise On Wisdom. All of this play on words and meanings employed by Socrates demonstrates the confusion of vision, soul, and physical entities in the fragments of “Pseudo- Archytas,” but the comparisons do not end there. The discussion of the “tool of the soul” seems implicitly intertwined with another fragment of On Wisdom. What precisely this “tool of the soul” is the reader and Glaucon are left to imagine, since Socrates is unwilling to tell us specifically (a fact emphasized by the indeterminate 327 See above. 328 The burden of proof must lie on the scholar to demonstrate spuriousness, and not on the manuscript to prove its legitimacy. Huffman’s argument (2005: 598-99) that On Wisdom demonstrates too much similarity to Aristotle’s Metaphysics is not grounds for spuriousness: that Aristotle derived many of his philosophical ideas from Archytas is assumed by Huffman throughout his edition. 329 Cf. Pl. Phd. 99e1-4. 132 ti). 330 This indeterminacy provoked Nichomachus to change, while quoting this passage of the Republic, the words “particular tool of the soul” to “eye of the soul” and “than a thousand eyes” to “than a thousand bodily eyes.” 331 If the Platonic Socrates was unwilling to designate the “tool of the soul” as its “eye” – a reasonable analogue that could be derived from earlier comparisons between the “tool in the soul” and the eye (and one that Nichomachus did import) 332 – why would he hesitate to do so here? One possible answer lies in the theory of vision ascribed to Archytas in the On Wisdom. 333 Iamblichus, who reports the fragment (Fragment 2 Thesleff p. 44.5- 15), tells us that after showing that wisdom is something of honor, “Archytas” proceeds in his exhortation to philosophy by discussing memory in this way: The human being, among all living things, has come to be the wisest by far: for he has the capacity to consider things as they are in reality and to acquire the science and knowledge of all of them. Therefore, the divine has impressed and sealed (e)nexa&race kai_ e)peshmh&nato) in the human being the system of entire reason, in which all the figures of existence (ta& te ei!dea pa&nta tw~ e)o&ntoj) are distributed, as well as the significations of nouns and verbs. For the pharynx and mouth and nostrils are assigned as the seat of articulations of voice. Just as the human being has generated a tool 330 Socrates earlier in Book VII (Pl. R. 518c4-d1) has referred to the “inherent power of each man in his soul and the tool by which each man learns” (e)nou~san e(ka&stou du&namin e)n th~| yuxh|~ kai_ to_ o!rganon w{| katamanqa&nei e#kastoj) when discussing the protrepsis of the student from the visible and changing place towards the Good. 331 See Huffman 2005: 116. 332 The comparison between the “tool” and the eye is explicit at Pl. R. 518c6: “oi{on ei) o!mma…”, and Socrates is willing to actually refer to the “eye of the soul” once he has completed his discussion of dialectic (Pl. R. 533d2), although only in poetic reference to the “barbaric boorishness” (e)n borbo&rw| barbarikw|~ tini to_ th~j yuxh~j o!mma). 333 Thesleff 1961: 112 suggests that another treatise on vision, Aristombrotos’ Peri_ o!yewj, is the work of another Italian Pythagorean from the 4 th Century BCE. For these fragments, see Thesleff 1965:53.25-54.7. 133 for voice, through which the nouns and verbs which have been impressed have meaning, so the human being has generated a tool for thinking among those things visible in reality ([ge&gonen a!nqrwpoj o!rganon] tw~n noama&twn e)n toi~j e)o&ntessin o)ptizome&noij). This seems to me to be the work of wisdom, to which the human being owes his generation and the attendant existence of his tools, and he has received his powers from God. 334 Recently, Carl Huffman has argued that the fragments of On Wisdom are too coincident with Aristotle’s treatment of wisdom (i.e. metaphysics) in the Metaphysics to be genuine. It is true that there are some interesting comparisons to be made between Metaphysics Book A and the extant fragments of the “Pseudo- Archytan” treatise, but I cannot agree that On Wisdom “is dependent on Aristotle’s account of wisdom in the Metaphysics.” 335 Indeed, his argument assumes: (1) that the five fragments preserved by Iamblichus are all from the same text of Archytas and (2) that fragments attributed to Periktione in Thesleff’s edition are from the same text. The first assumption is problematic, since Huffman provides no substantive criticism of fragments 1-3 Thesleff, which do not seem decisively Aristotelian either in terminology or in argument. Instead, all of his comparisons between the Metaphysics and On Wisdom are taken from fragments 4-5 Thesleff, which do indeed smack of Aristotelianism. About the second assumption, nothing need be argued except that we cannot consider a text attributed by Stobaeus (Thesleff p. 146.6-22 Fragment 2) to Periktione to be from the same text as On Wisdom by Archytas. 334 Iambl. Protr. P. 18 Pistelli. 335 Huffman 2005: 598-9. 134 On the other hand, this passage of On Wisdom is remarkably un-Aristotelian. While it conforms with the basic premise that humans are the wisest of all creatures because of their capacity for thought and naming, a trite conclusion (though Aristotelian as well!), 336 its insistence upon “tools” generated for the purposes of speaking and seeing bears no resemblance to Aristotle’s Metaphysics whatsoever. Indeed, the language of “imprint” that is manifest throughout this passage is markedly more Platonic or, to be more precise, even Sophistic or Orphic, which would be unsurprising for a Pythagorean in Southern Italy during the first half of the 4 th Century BCE. 337 The discourse on naming and speaking recalls Plato’s Cratylus, especially the passages where Socrates and Hermogenes discuss naming as a “tool.” 338 But what is especially interesting for our purposes is the comparison here between the “tool” of speaking and the “tool” of cognition, which is able to function “among those visible things in reality.” 339 As Francesco Romano points out, the term o)ptizome&noij is a hapax legomenon, and its coupling with the term e)o&ntessin legitimately extends the metaphor of vision to the ontological world. 340 Indeed, the “tool” of thinking, which deals explicitly with the phenomenological world and is “impressed” with the figures of existence, sounds quite like the “vision” to which 336 E.g. Arist. Metaph. 982a13-14, where a man is wiser based on his ability to understand causes precisely and to explain them to others. 337 See Horky: 2007. 338 Pl. Cratyl. 387e15-388a11. 339 Among the pseudo-Pythagorean writings collected by Thesleff, only the Epistles of Theano, wife of the Metapontine Pythagorean Brontinus (p. 197.17, 198.23) and the On Nature of “Timaeus of Locri” refer to “tools.” Theano assumes a “tool of hearing” in both her letters, while “Timaeus’” tool is decidedly Platonic and resonates with the account of the “tools” in Plato’s Timaeus (45bff.). Therefore, no pseudo-Pythagorean works refer to “tool” in the senses found here in the On Wisdom. 340 Romano 2006: 473. 135 “Pseudo-Archytas” refers in the first fragment of On Wisdom. If this is the case, it is not surprising that Socrates, in a passage that is attempting to revise and challenge Archytan physics, neglects to mention the “eye” of the soul at all, but instead leaves it indeterminate. What is more, Nichomachus’ tendency to Pythagoreanize Plato – and to Platonize the Pythagoreans – explains his glossing of Republic VII through importation of the very terms Plato aims to problematize. If, then, the theories of physical vision and knowledge of Archytas – filtered through Fragments 1 and 2 of “Pseudo-Archytas’” On Wisdom – remain a backdrop for Socrates’ discussion of the “tool of the soul” in this section, we might consider further how Archytas’ theories of physics pertain to this section on solid geometry. Socrates and Glaucon agree to move on, and Socrates proposes a median addendum to the quadrivium, claiming that they had erred in their progression: Meta_ e)pi&pedon, h}n d’ e)gw&, e)n perifora~| o@n h!dh stereo_n labo&ntej, pri_n au)to_ kaq’ au(to_ labei~n: o)rqw~j de_ e!xei e(ch~j meta_ deute&ran au!chn tri&thn lamba&nein. e!sti de& pou tou~to peri_ th_n tw~n ku&bwn au!chn kai_ to_ ba&qouj mete&xon. 341 “After plane geometry,” I said, “we hastily adopted solid geometry in circular motion (astronomy), before taking up solid geometry in itself. But it’s appropriate things in order: after second dimension, 342 third dimension. And, I suppose, that (solid geometry in circular motion) is what deals with the dimension of cubes and partakes of depth.” 341 Pl. R. 528a9-b3. 342 I have translated au!chn here as “dimension” in order to facilitate understanding of the passage for the reader, although I will challenge this translation in the text that follows. 136 This passage has been interpreted in various ways. One interesting interpretation is that of Carl Huffman in his edition of Archytas’ fragments. 343 In his discussion of a fragment of Euctocius 344 (Commentary on Archimedes’ On the Sphere and Cylinder II), which preserves Archytas’ mathematical proof of the doubling of the cube, Huffman argues that Plato cannot be referring directly to the problem of the duplication of the cube, an issue that is known famously as the Delian problem. 345 The argument that this passage is not dealing directly with the Delian problem of doubling a cube focuses specifically on the term au!ch, the definition of which is crucial to establishing or rejecting the hypothesis. Huffman is correct to note that “the immediate context” does not seem to suggest that this term can mean “increase in size,” in that the terms “second” and “third” here suggest “dimensions.” 346 But what does “dimension” mean here? We must recall that pre-Euclidean geometry does not refer to “dimensions” by this term, 347 and Pythagorean mathematics, which would have represented the greatest advances in mathematics by the 370s BCE when the Republic was composed, operated on the assumption that magnitudinal forms 343 Huffman 2005: 385-392. 344 On Eutocius and Eratosthenes, see Heath 1931: 154-5. 345 The myth of the doubling of the cube is originally assigned to Eratosthenes by Eutocius (Archytas’ A 15 Huffman; in Archim. Sphaer. et cyl. II), in which the Delians, who were requested to double an altar to Apollo in accordance with an oracle, were at a loss. Eratosthenes says that Hippocrates of Chios realized that the problem could be solved by creating a continual proportion between two mean proportions between two straight lines, of which the greater is double the lesser. But proving this geometrically was yet incomplete. Archytas “was said to have discovered them through semicylinders (dia_ tw~n h(mikuli&ndrwn), his student Eudoxus “through the so-called bent lines.” This conclusion is echoed by Vitruvius, who claims that Archytas made the discovery “by means of diagrams of cylinders (cylindrorum descriptionibus).” 346 Huffman 2005: 386. 347 The Scholiast to Euclid (in Eucl. Elem. I def. 2 = Timpanaro Cardini B 25b, 1964: 150-1) claims for Aristotle the term dia&sthma for “dimension.” Perhaps all this discussion would be clearer if Ptolemy’s Peri_ Diasta&sewj, in which he argued that only three dimensions exist, were extant. 137 were derived from the tetraktys and were composed of ascending orders of points distinguished by equal measures. 348 There is the possibility, and one not too remote if we imagine the influence of Heraclitus on the mathematical Pythagoreans who derived their philosophy from Hippasus, that Sextus Empiricus was correct in attributing the sequence of derivation – he calls it, interestingly, a sta&sij 349 – of point, line, plane, geometric solid to Pythagoreans who went further than the “older Pythagoreans.” 350 Both Timpanaro Cardini and Burkert assume that this theory of derivation can be attributed to Archytas, and I see no reason to doubt seriously the testimonia that follow from the ancient sources. 351 If it is true that the theory of derivation of magnitudes was a discovery of Archytas, how does this affect our interpretation of Socrates’ comments at Rep. 528a9-b3? If we give the term au!ch a semantic range natural to the word, meaning something like “increase” or “advancement,” as it certainly does at the other two occurrences within Book VII of the Republic, 352 what import would that have upon this passage? Archytas’ theory of the doubling of the cube, which successfully 348 Cf. [Arist.] Probl. 930b36 (Timpanaro Cardini B 16, 1964: 106-7), who asserts that “the four cubic numbers – out of which the Pythagoreans say the All is constructed – are completed in ten analogies.” See Chapter 1. 349 Cf. Archytas F 3 Huffman. 350 Sex. Adv. Math. 10.281 (Timpanaro Cardini B 25c, 1964: 150-2). The significance of “increase” to the mathematical Pythagoreans can be contextualized with the Parmenidean argument – adapted by Diotima in the Symposium – that things which exist in reality do not increase. On the import of Parmenidean thought on the Theories of the Forms espoused in Plato’s middle dialogues, see Palmer 1999: 3-5. 351 Burkert 1972: 68-9; Timpanaro Cardini 1964: 151-2. As Huffman notes (2005: 501), Nichomachus’ Introduction to Arithmetic (2.7) attributes the definition of point as the “starting point of the line” to Archytas. 352 Pl. R. 521c4, where au!ch (increase/growth) is contrasted with fqi&sij (decay) and 528c7, where it must mean “increase.” At 528d8 Socrates refers to the “increase of depth” (ba&qouj au!chj). 138 answered the Delian problem, is noteworthy for its employment of diagrams of semicylinders and cylinders, which marked it as distinctive. The proof of the doubling of the cube as it is preserved by Eutocius – who is probably quoting from Aristotle’s student Eudemus of Rhodes’ History of Geometry 353 – makes use of arithmetic and geometry throughout, but it departs from these mathematical sciences by employing rotation (periagwgh&) around a point in order to create semicylinders. 354 If we return to Socrates’ criticism, we note the emphatic placement of the term e)n perifora|~, since after all it is Socrates’ point that those who do not adopt stereometry as a median between geometry and astronomy do not do so because they neglect the difference between solid bodies without motion and solid bodies in rotation. We may thus reverse the conclusion that Archytas’ theory of the doubling of the cube is not the point of reference here in Republic VII. Indeed, it seems more plausible that the reference to solid bodies in rotation refers not simply to astronomical bodies, but also to geometrical figures that have undergone the third kind of au!ch. Immediately we are then confronted with a problem: what does the term au!ch mean after all? The “increase” of the cube, which is called the “third,” coheres with Archytas’ theory of the derivation of magnitudes in that it too represents a movement from the previous dimension to the posterior one. The first increase 353 See Huffman 2005: 346 with bibliography. 354 Archytas A 14 Huffman (Eutocius in Archim. Sphaer. et cyl. 2): “When this semicircle is rotated from D to B (to_ h(mikulindri&on periago&menon) , while the endpoint A of the diameter remains fixed, it will cut the cylindrical surface in its rotation and will describe a line on it.” Translation by Huffman. 139 (au!ch), then, would seem be the application of motion to a line, 355 leading to a magnitudinal plane; the second increase, the application of motion to a plane, creates a geometric solid; the third increase would be the addition of peripheral motion to a geometric solid, which would create a solid in motion. Such is Socrates’ logic here, and the comment that follows afterwards (marked by the return to the demonstrative pronoun tou~to in the neuter, which must grammatically refer back to e)n perifora~| o@n h!dh stereo_n) seems to describe stereometric bodies in rotation. 356 This hypothesis – it must be admitted – is not necessarily conclusive on this problematic but rich passage, but the paucity of reflection on the subject that follows does not allow for further decisive comment. We are not alone in our aporia. Socrates himself closes the discussion of stereometry with these words: “For, I passed over the study of the increase of depth, which was next, because the investigation of it is laughable, and after geometry I mentioned astronomy, which is motion of depth.” 357 “The fourth science we posited was astronomy,” Socrates continues. 358 The study of solid bodies in motion – a specifically Archytan kind of motion, namely rotation 359 – is something that would appear to lead the soul up to the things above; 355 As Huffman 2005: 502-3 argues, “[i]t is tempting to suppose that Plato was taking an Archytan position of this sort, when he maintained that points were a geometrical fiction (Arist. Metaph. 992a20).” If points did not have magnitude for Archytas, then the derivation sequence would start from the line. 356 It is entirely possible that Socrates is confused here by the terms themselves; the copyist for manuscript F (cod. Vindobonensis 55, suppl. phil. gr. 39) neglected to include the demonstrative pronoun at all, echoing the confusion about the referent. 357 Pl. R. 528d8-e1. 358 Pl. R. 528e3. 359 On “circular motion” that establishes material form in animals, see Archytas A 23a Huffman ([Arist.], Problems 915a25-32) and Chapter 5. Interestingly, the only fragment of Archytas’ works 140 this, at least, is Glaucon’s conclusion. 360 But Socrates criticizes this opinion because, as he says, astronomy as it is currently practiced tries to account for individual movements of heavenly bodies within the visible world without considering the reality of which they are an imitation: “Those dappled things in heaven, even if it was into heaven that they were embroidered, may be considered the most beautiful and most precise of these sorts of things, but they fall far short of the true things, which are real speed and real slowness (to_ o@n ta&xoj kai_ h( ou}sa braduth_j) in the true number and movements in all the true designs which are brought around to one another and carry those things involved in them, which are conceived by reason and thought, and not by the eye. Or what do you think?” “Certainly,” he said. “Accordingly,” I said, “we must employ the dappled paradigm around heaven for the sake of the science appropriate to those things, just as if someone were to happen upon the labored diagrams drawn by Daedalus or some other demiurge or artist. For, I suppose, an expert in geometry, if he were to see these things, would consider that they were the most beautiful in terms of their workmanship, but he would think it laughable to scrutinize them studiously so as to find the truth contained in their proportions, whether equal or not.” 361 Socrates’ criticism of astronomy as it is practiced fully coheres with his previous comments about geometry, and indeed the geometric element of astronomical studies is emphasized here. His appeal, however, to “true number” approaches the language of the Forms previously established for concepts like the Good and Justice. Likewise, the reference to “real speed and slowness” recalls the more basic that preserves any discussion of astronomy, Fragment 1, uses a generic periphrasis in place of astronomy: “the speed of the stars and their risings and settings (peri& te dh_ ta~j tw~n a!strwn taxuta~toj kai_ e)pitola~n kai_ dusi&wn).” In this fragment, at least, Archytas makes no particular reference to the kind of motion of the stars, although evidence from other fragments attests to the significance of circular motion in Archytas’ physics, and it seems to have been a point of contention for Plato while composing the Republic. 360 Pl. R. 528e6-529a2. 361 Pl. R. 529c7-530a1. 141 oppositional Forms of the Great and the Small, but the terms employed for astronomy involve motion. What is more, Socrates’ reference to “proportions” which are either equal or not equal (i!swn h@ diplasi&wn h@ a!llhj tino_j summetri&aj) in the diagrams of Daedalus suggests the study of proportional motion in the heavens underlying the few genuine fragments that refer to Archytas’ theories of motion. 362 These fragments testify that Archytas understood that motion was both caused and regulated by proportions, corresponding with Socrates’ account of visible astronomy in the Republic. The Pseudo-Aristotelian treatise Problems (915a25-34; Huffman F A23a) shows that Archytas believed that the proportion of equality, when it is present in things that are in motion, creates “circles and curves” (ku&klouj kai_ stroggu&la) because it “alone bends back on itself” (mo&nhn ei)j au(th_n a)naka&mptein). 363 This is apparent, Archytas tells us, because “proportion moves all things” (kinei~sqai ga_r a)na&logon pa&nta). 364 We also learn about unequal proportions from another fragment of Archytas’ works. Huffman, reading Eudemus from his Physics (4 th Century BCE), 365 claims with justification that Archytas’ physics of motion is distinguished from its Platonic counterpart because, for Archytas, “‘inequality (a!nisoj) and unevenness (a)nw&maloj) are causes (ai!tia) of 362 There is a comparable criticism of the statues of Daedalus and their inability to iterate the truth at Pl. Meno 97d6-98a8. 363 On the proportion of equality, see Huffman 2005: 520-2. I deal with proportions and their application to issues of political philosophy in Chapter 6. 364 Or “analogy changes all things.” 365 Eudemus, Physics F 60 Wehrli = Simplicius, In Arist. Phys. 3. 2 = A 23 Huffman. 142 motion’” instead of motion itself. 366 That these terms – equal and unequal proportions – are political will be explored further on, 367 but suffice it to say at this point that Socrates’ reiteration of the political significance of mathematical astronomy is not original with Plato. Indeed, lest the reader or Glaucon forget the original project, Socrates recalls their responsibilities as lawgivers before moving on to the fifth and final science that they will admit to their mathematical program: “Problems,” I said, “by making use of problems we may take up astronomy just as we did geometry, but let’s leave those other things in heaven, if, by employing real astronomy, we are intent upon making the soul’s natural intelligence something useful rather than something useless.” “Truly, you are drawing up a project much more complex than doing astronomy was a moment ago,” he said. “Definitely,” I said, “and I think we shall draw up all other things in the same way, if there is to be any benefit for us while we are establishing our laws.” 368 Socrates’ transition from astronomy to harmony is logically established by an explicit comparison of the kinds (ei!dh) of motion (fora&) that each entails. Astronomy possesses a kind of motion appropriate for the eyes, while harmony’s motion is appropriate for the ears, in accordance with the passage cited above that referred directly to Archytas’ Harmonics. Can we assume that Plato believed these kinds of motion to possess analogous physical characteristics as early as the Republic? We may recall from the discussion of astronomy Socrates’ reference to “real speed and real slowness” (to_ o@n ta&xoj kai_ h( ou}sa braduth_j) in the 366 Huffman 2005: 513-15. Eudemus is referring to Platonic physics in the Timaeus (52e, 57e-58a), and therefore we cannot assume that Plato held the same view here in the Republic. 367 See Chapter 6. 368 Pl. R. 530b6-c5. 143 Intelligible world, of which the heavenly bodies in the Visible world might only be an imitation. The terms of speed have a long history in the study of harmonics, which may go back as far as Pythagoras, although there are some doubts as to whether or not Pythagoras was responsible for empirical study of musical number. 369 On the other hand, one fragment of Theo of Smyrna attests to Hippasus of Metapontion’s active interest in musical harmony: tau&taj de_ ta_j sumfwni&aj oi( me_n a)po barw~n h)cioun lamba&nein, oi( de_ a)po_ megeqw~n, oi( de_ a)po_ kinh&sewn kai_ a)riqmw~n, oi) de_ a)po_ a)ffei&wn [kai_ megeqw~n]. La~soj de_ o( (Ermioneu&j, w#j fasi, kai_ oi( peri_ to_n Metaponti~non I#ppason Puqagoriko_n a!ndra sune&pesqai tw~n kinh&sewn ta_ ta&xh kai_ ta_j braduth~taj di’ w{n ai( sumfwni&ai <. . .> e)n a)riqmoi~j h(gou&menoj lo&gouj toiou&touj e)la&mbanen e)p’ a)ggei&wn: i!swn ga_r o!ntwn kai_ o(moi&wn pa&ntwn tw~n a)ggei&wn to_ me_n keno_n e)a&saj, to_ de_ h#misu u(grou~ <plhrw&saj> e)yo&fei e(kate&rwi, kai_ au)tw~i h( dia_ pasw~n a)pedi&doto sumfwni&a: qa&teron de_ pa&lin tw~n a)ggei&wn keno_n e)w~n ei)j qa&teron tw~n tessa&rwn merw~n to_ e$n e)ne&xee, kai_ krou&santi au)tw~i h( dia_ tessa&rwn sumfwni&a a)pedi&doto: h( de_ dia_ pe&nte, <o#te> e$n me&roj tw~n triw~n suneplh&rou ou!shj th~j kenw&sewj pro_j th_n e(te&ran e)n me_n th~i dia_ pasw~n w(j b pro_j e#n, e)n de_ tw~i dia_ pe&nte w(j g pro_j b, e)n de_ tw~i dia_ tessa&rwn w(j d pro_j g. 370 Of these consonances, some thought it best to derive them from heavy objects, others from great objects, others from movements and numbers, and others from empty objects. Lasus of Hermione, so they say, and the followers of Hippasus of Metapontion, a Pythagoric man, [thought it best?] to pursue the speeds of objects in motion and their slownesses through which consonances…(lacuna)…thinking that these sorts of ratios come from numbers, he [Hippasus? Lasus?] derived them from vases. For, using vases all equal and of like figure, he left one empty and filled another half-way full of water; he struck them together and produced consonance of an octave. And again, leaving one of the vases empty, he filled up another one-fourth of the 369 See Burkert 1972: 369-377. 370 Theon. Smyrn. p. 59.4 Hiller = Timpanaro Cardini 1958: 100-101. 144 way, and striking them together he produced consonance of a fourth. And he produced consonance of the fifth when he filled up one third of another. Thus the emptiness of the first vase was in a relation to the second of 2 : 1 in the consonance of an octave, and 3 : 2 in the consonance of a fifth, and 4 : 3 in the consonance of a fourth. While the primary subject of this passage is undoubtedly Lasus of Hermione, who was a close contemporary of Pythagoras, the reference to the followers of Hippasus suggests that the early mathematici too engaged in experiments that attempted to correlate the physical characteristics of objects with numerical ratios. 371 As Burkert notes, this testimonium echoes Aristoxenus’ account of Hippasus’ investigation of concordant intervals among pendular bronze disks – of equal diameter – whose thickness was established in proportions of 4 : 3, 3 : 2, and 2: 1. When struck together, they produced concordant intervals that reflected their ratios of weight. 372 What is especially significant for our study is the reference in Theon’s account to “speeds” and “slownesses” of objects in motion following directly after the mention of the followers of Hippasus, a subject that corresponds with Socrates’ criticism of Pythagorean studies dealing with the motion of astronomical bodies. The analogy between astronomy and harmony is continued by Socrates at Republic 531b6, where his criticisms of the Pythagoreans are specifically directed at those who seek the numbers in musical consonances: 371 The language employed here for octave (dia_ pasw~n), fourth (dia_ tessa&rwn), and fifth (dia_ pe&nte) seems to suggest that this theory can be legitimately to be ascribed to Hippasus, since it must precede Philolaus’ revision of the terms for the “Pythagoreans” reported by Theophrastus (Aelian, ap. Por. In Ptol. 96.21ff) See Huffman 1993: 145-156. I discuss this fragment at length in Chapter 5. 372 Aristox. F 90 Wehrli = Schol. Pl. Phd. 108d. See Burkert 1972: 377. Cf. Huffman 1993: 147-8. 145 I will take leave of the metaphor and tell you that I am not speaking about those [musicians who measure the intervals of notes], but of the other [Pythagoreans] whom we were just saying we would consult about harmony. For they do the same thing as what they do in astronomy: they seek numbers in these audible concords (tou_j ga_r e)n tau&taij tai~j sumfoni&aij tai~j a)koume&naij a)riqmou_j zhtou~sin), but they do not rise above into problems, to examine which numbers are concordant and which ones not, and for what reasons. It is apparent that Socrates here is criticizing the practice of Pythagoreans who seek numerical ratios in the concordances they hear, a project that corresponds directly with what is said about the followers of Hippasus and Hippasus himself. In their investigations into music, the mathematici sought to analogize their empirical observations obtained through experimentation with theories of mathematical proportion assumed beforehand, and we are yet again reminded of Socrates’ criticism of the Pythagoreans’ pragmateia in Book VI of the Republic. Even so, the vagueness of technical terminology and language employed by Socrates does not permit us to see any direct links between the discussion of harmony in Book VII of the Republic and the fragments of the mathematician Archytas of Taras. It is even difficult to see any specific interaction between Socrates’ criticisms and the philosophy of music ascribed to Philolaus. 373 We may conclude only that at this stage of Plato’s career he was not yet especially interested in the technical 373 Cf. Burkert 1972: 400. But see Huffman’s revisions of Burkert’s account in 1993: 146-156. 146 examination of motion in sound to the same extent as his contemporary in Southern Italy. 374 On the other hand, the general tenor of this passage and its vocabulary does direct the reader and Glaucon towards what will be a significant addition to the preludic quadrivium of mathematical sciences attributed to Archytas of Taras: dialectic. What is notable about Socrates’ vocabulary here is that it reflects the conceptual inheritance of terms derived from his exposition on mathematics wedded to a political terminology: Oi}mai de& ge, h{n d’ e)gw&, kai_ h( tou&twn pa&ntwn w{n dielhlu&qamen me&qodoj e)a_n me_n e)pi_ th_n a)llh&lwn koinwni&an a)fikhtai kai_ sugge&neian, kai_ sullogisqh|~ tau~ta h|{ e)sti_n a)llh&loij oi)kei~a, fe&rein ti au)tw~n ei)j a$ boulo&meqa th_n pragmatei&an kai_ ou)k a)no&nhta ponei~sqai, ei_ de_ mh&, a)no&nhta. 375 “Further,” I said, “the course of study of all these things which we took up will, in my opinion, be of some import upon the pragmateia of the things as we desire them to be and will not be labor wasted, if it achieves the community and mutual relations of the sciences and calculates those things that are appropriate to each with one another.” In the transition from the mathematical sciences to dialectic, Socrates builds upon the conceptual space of “concords” (su&mfwnoi) previously established for the study of harmony to a category of thought that synthesizes (sullogisqh|~) particularities of each science into a single cognitive process. 376 What is especially interesting about this logical development in Socrates’ argument is how – in its modification of the 374 Plato would develop a much more systematic treatment of harmony several decades later in the Timaeus, which I will discuss in Chapter 5. On Archytas’ contributions to harmonic theory, see Huffman 2005: 129-148. 375 Pl. R. 531c9-d4. 376 Brumbaugh 1942: 22-26 sees this section on harmony as explicitly introducing analogy as a methodological device for the mathematician. 147 pragmateia of harmony – it returns to and extends the metaphor of logistic (logismo&j), which, as we recall, was the form of learning “common” (koino&n) to all. 377 For Socrates speaks of the “community” (koinwni&a) and “mutual kinship” (sugge&neia) of the sciences, which, as political terms, demonstrate the combined effort to establish a unified political community in Kallipolis in tandem with his dialectical theory. 378 Later on, Socrates will further extend the Archytan metaphor by intensifying the metaphorical element of vision, calling dialectic “synoptic” (sunoptiko_j). 379 Socrates’ program of mathematical study is seen in even more explicitly political terms in the passage that follows. Indeed, it is remarkable that Socrates calls this program in the advanced sciences (the quadrivium), which students will undertake from the ages of 20 to 30, 380 a “prelude” – a term that lends a musical and constitutional color to the terms 381 – to the real education (“law”) in dialectic, with which the student will be occupied from the ages of 30 to 35: 382 377 Pl. R. 522c1. In this way, Plato’s derivation of dialectic principally from logistic echoes Archytas’ belief that logistic was superior to geometry in pragmatics (Archytas F 4 Huffman). Plato, then, should be seen embracing Archytas’ criticism of Philolaus (A 7a Huffman), who believed that geometry was the “source and mother-city” of the mathematical sciences. 378 There are two notable differences between dialectic as it is presented here in the Republic (and later in the Sophist, see below) and the process as described in the Phaedrus: first, here the analogistic/synthetic method is only applied after logistic’s diaeretic process, whereas in the Phaedrus (255d2-266b1) it precedes diaeresis; second, there is no trace of explicit political import in the Phaedrus. Whether or not the Phaedrus – and its attendant Theories of the Form – was composed around the time of the Republic or just before the Theaetetus (as Hackforth held), I am not convinced by Runciman’s conviction that the Phaedrus postdates the Parmenides. See Runciman 1962: 2-3. 379 Pl. R. 537c7. 380 Pl. R. 537b8-d3. 381 On preludes, see Chapter 6. 382 Pl. R. 537d3-8. 148 “So I suspect,” he said. “But you’re talking about an enormous task, Socrates.” “Are you talking about our prelude, or something else?” I said. “Don’t we know that all these things are preludes to this law which must be learned (pa&nta tau~ta prooi&mia& e)stin au)tou~ tou~ no&mou o$n dei~ maqei~n)? Surely you would not think that people who are experts in the sciences are masters of dialectic.” 383 Once Socrates has arrived at the “law/theme itself (au)to_j o( no&moj)” of their discussion, how one may advance beyond the Visible to the Intelligible place through dialectic, he ceases to describe it any further and reiterates many of the elements to which he had referred in Book VI before establishing a program of mathematical sciences. The entire pragmateia of mathematics (pa~sa au#th h( pragmatei&a tw~n texnw~n) cannot lead the prisoner directly up from the cave to the sun, but it functions as a “liberation from the chains and a turning from the shadows to the images and light.” 384 But of dialectic, we hear nothing more than a general description. What few hints we possess deal with the qualities of the dialectician: one who is proficient in dialectic, we are told, should possess a reasonable account for each thing in reality (to_n lo&gon e(ka&stou lamba&nonta th~j ou)si&aj), and he must be able to distinguish (diori&sasqai) and isolate the essential Form of the Good from all others, a process that suggests the project of diaeresis yet to be defined as such in this dialogue. 385 The question remains: why does Socrates refuse to explain dialectic further? 383 Pl. R. 531d5-e1. On preludes to the laws, see Chapters 4 and 6. 384 Pl. R. 532b6-7. 385 Pl. R. 534b3-c1. 149 The reason echoes Socrates’ justification in Book VI and in Epistle VII for not defining the Good in writing, for Glaucon, we are told, cannot follow his teacher towards the Good; his life has already passed without the education they have just described. 386 We can only hope, Socrates suggests, that Glaucon’s children will advance beyond the point of being “irrational lines, so to speak, when – as archons in the city – they are in charge of the highest responsibilities” (a)lo&gouj o!ntaj w#sper gramma&j, a!rxontaj e)n th~| po&lei kuri&ouj tw~n megi&stwn ei}nai). 387 Such is the ideal. But the final admission that Glaucon is beyond the age to partake in this educational program leaves the reader with a sense of the impending collapse of this project, a sense that recalls Socrates’ failure to nurture Alcibiades into a successful political actor as paradigmatically represented in the Gorgias and lamented in the Symposium and First Alcibiades. 388 By the time we move on to Book VIII of the Republic, we have been prepared for the discourse on the failure of the ideal city- state to perpetuate itself and its manifold forms of corruption. To conclude: a critical examination of the descriptions of the philosophical pragmateia of the Pythagoreans in Aristotle’s Metaphysics reveals affinities with the criticisms made by Socrates when referring to the Pythagoreans in Books VI and VII of the Republic. Even so, Plato’s figuration of the Good in Book VI and of the foundational educational system in Book VII recalls the fragments of Archytas, both those considered genuine by scholars and the Archytan On Wisdom, which appears 386 Pl. R. 533a1-2. 387 Pl. R. 534d5-6. 388 Cf. the description of the haughty youth at Pl. R. 494c4-d2. 150 to preserve independent traditions to which Plato was responding in the image of the Divided Line. Plato’s educational program for the Republic – both in its underlying theoretical framework and in its curriculum – represents an adoption and criticism of the quadrivium of sciences attributed to the mathematical Pythagorean Archytas of Taras. Plato’s improvement upon the Archytan educational program is most expressly demonstrated in the addition of a fifth subject for study, dialectic, which is described in fundamentally mathematical terms (in that it incorporates logistic, geometry, solid geometry, and astronomy into its method) that are also, intriguingly but unsurprisingly for a dialogue entitled the Republic, political. But before Plato was to modify his political philosophy, he felt inclined to revisit the mathematical substructure of his Theory of the Forms, a project undertaken especially in the Theaetetus and Parmenides that resulted in a substantial overhaul of his earlier ideas about metaphysics, method, and ontology. 151 _______________________________________ CHAPTER 3: THE PARADEIGMATIC RESPONSE: MATHEMATICS AND DIALECTIC IN PLATO’S THEAETETUS, PARMENIDES, SOPHIST, AND STATESMAN _______________________________________ As we argued in Chapter 2, Plato in the Republic established his philosophical pragmateia by considering the theories of education and sciences of the Archytan quadrivium. The consequence was the proposition of a program of education based on the four Pythagorean sciences (logistic, geometry, astronomy, harmonics) with the significant addition of dialectic, a kind of philosophical method that involved definition primarily through distinction (although Socrates is not explicit about how this happens). If a student were to achieve all of these sciences, she would be able to rise up beyond understanding of mere sensibles to the comprehension of the Good in the Intelligible place; the Theory of the Forms espoused by the Republic and the Phaedo assumes that the Visible place is related to the Intelligible place through imitation, a theory that Plato will continue to revise, as we will see in Chapter 3, in tandem with his reconsideration of mathematics in the dialogues that were subsequent to the Republic and functioned essentially as sequels to portions of that major work: the Parmenides and the Theaetetus. As I will demonstrate, Plato tends to propose advances to his Theory of the Forms as he reconsiders the method of dialectic in these works, but extending the pragmateia of the Republic reveals certain problems especially in Plato’s ontological system and epistemology. We will examine these in the first half of this chapter. Then, in the 152 second half of this chapter, we will demonstrate how the Eleatic Stranger in the Sophist and the Statesman enacts a revision of the Middle Theory of the Forms by proposing fundamental innovations in dialectical method, including the introduction of paradeigmata and consideration of the possibilities of Forms “mixed” through participation. All of these revisions of Plato’s dialectical and formal theories apply to Plato’s blossoming political philosophy, and they serve no less a purpose than to provide the student of philosophy a means to understand the best way to navigate the city-state through the “political art.” PROBLEMS IN EXTENSIONS: PLATO’S THEAETETUS AND PARMENIDES It is difficult to say definitively whether or not Plato composed and finished the Theaetetus or the Parmenides first 389 ; they are to be located in the period after 367 BCE, when Plato had visited Taras and Syracuse a second time, and I think – for reasons I will discuss later in this chapter – that composition was at least initiated before Plato’s return to Western Greece around 360 BCE; they must have been completed before he began the Sophist and Statesman, which demonstrate extensions of the problems raised especially in the Parmenides. We shall not concern ourselves with the issue of which dialogue was composed first at this time, but instead we shall proceed with an examination of how Plato began to extend and therefore challenge the philosophical pragmateia put forth in the Republic in these two enigmatic and 389 Generally, it is well-accepted that they both belong to Group II along with the Republic and Phaedrus. On the problems of chronology, see Kahn 1996: 42-8. 153 fascinating dialogues. As I hope to demonstrate, the Theaetetus presupposes a Participatory (or Middle) 390 Theory of the Forms that was expressed in Plato’s Republic, Phaedo, and Phaedrus in its attempts to polish and expand the mathematical foundation of dialectical theory as practiced between Socrates and the young mathematician Theaetetus; but the Parmenides presents challenges to the Participatory Theory of the Forms by problematizing the concepts that underlie the language employed for the Theory. Each of these texts, then, extends and problematizes the primary mode of investigation of the Forms, dialectic, in its pursuit of knowledge. From a thematic point of view, the Theaetetus follows more closely on the heels of Republic Books VI and VII, in that the beginning of the dialogue deals specifically with the application of mathematics to dialectic. It also reiterates the close of Republic VII, in that we discover that the geometer Theodorus of Cyrene – despite his status as teacher and fame as a mathematician – cannot partake of the highest element of the educational program outlined in the Republic: SOCRATES: Who among us will be first to speak [about what knowledge is]? If he misses the mark – and this applies to anyone who misses the mark at any time – he will “be the ass,” as children say when playing ball. But whoever rises to the challenge and doesn’t make any mistake will rule over us and structure the discussion just as he wishes (basileu&sei h(mw~n kai_ e)pita&cei o#ti a$n bou&lhtai a)pokri&nesqai). Why all silent? Surely, Theodorus, I’m not stepping on anyone’s feet with my fondness for talk, being so passionate to get us to discuss things (diale&gesqai) and to establish a friendly rapport with one another? 390 Such is the term employed by Sayre 2005. 154 THEODORUS: Not at all, Socrates, this wouldn’t be considered rude, but direct your question-and-answer at the young men, since I am unaccustomed to this sort of dialectic (a)h&qhj th~j diale&ktou), and I’m too old to form the habit now (kai_ ou)d’ au} suneqi&zesqai h(liki&an e!xw). 391 Like Glaucon, Theodorus is incapable of – and unwilling to – participate in the highest portion of the Socratic educational system, namely dialectic. Plato’s play with the terms diale&gesqai and dia&lektoj is explicit: what Socrates puts forth as a friendly conversation is immediately and correctly identified by his contemporary Theodorus as a ruse to implicate the mathematical sciences which Theodorus teaches and subsume them under the ethical science of dialectic. 392 Theodorus refuses to engage in this method, giving as an excuse the exact same reason as Socrates had for why Glaucon could advance no further towards the Good. The resonances with Republic VI and VII do not end there: “whoever doesn’t err in his definition of knowledge” will “rule over” (basileu&sei) those who partake in the discussion, just as the ideal city-state could not be achieved in the Republic without philosophers ruling in imitation of the sun, which rules over the Visible place. 393 The hope, of course, is that the young Theaetetus of Athens (ca. 415 – 369 BCE), who is described by his teacher Theodorus 394 as possessing the essential qualities of a philosopher that Socrates had listed in Republic VI, 395 will inherit the reins and “put into order” (e)pita&cei) the philosophical discussion, an echo of Socrates’ unfulfilled 391 Pl. Theaet. 146a1-b4. 392 The same ambiguity is assumed during Socrates’ discussion of dialectic at Pl. Meno 75c8-e5. 393 See Chapter 2. 394 Pl. Theaet. 144a1-b6. 395 Pl. R. 503c2-7. 155 wish to find a “director” (e)pista&thj) of stereometric studies in Republic VII. 396 For the Theaetetus, inasmuch as it is a dialogue that explores multiple definitions of knowledge (e)pisth&mh) and the failure of each and every one, 397 remains a painful eulogy for the mathematician who was responsible for discovering the fourth and fifth geometric solids (octahedron and the icosohedron) 398 and, as Eudemus tells us, for systematizing irrational lines according to the different mathematical means (geometric, arithmetic, harmonic). 399 That Theaetetus’ death (369 BCE) falls between the compositions of the Republic and the Theaetetus secures the connection, and we may consider the Theaetetus as a sequel of sorts to the Republic. This shift in the object of the Platonic eulogy – no longer composed for Socrates but instead for Plato’s contemporary mathematician Theaetetus – marks a significant departure for Plato’s writing that will be reiterated again and again in the later dialogues with the characters of Parmenides, the Eleatic Stranger (?), Timaeus of Locri (Eudoxus? Perhaps Archytas?), and the Athenian Stranger (Plato himself?). Following the mathematical program established in Book VII of the Republic, the argument of the Theaetetus proceeds from mathematical sciences to dialectic. Socrates asks Theaetetus about the kinds of mathematical “sciences” 396 Pl. R. 528b7ff. That the Theaetetus is a lament for the unfulfilled transfer of the Academy to Plato’s younger contemporary is further suggested by the ending of the dialogue (Pl. Theaet. 210b11- d4), where Socrates recalls these passages about philosophical “rule” when he tells Theaetetus and Theodorus that he needs to go to the “stoa of the king (ei)j th_n tou~ basile&wj stoa&n) to face the charge against him written by Meletus, the charge which will culminate in his own forced suicide. 397 Pl. Theaet. 210a7-b2. Should we take the text at its word? See Waterfield 1987: 154-163. 398 See Huffman 2005: 389-90. 399 See Burkert 1972: 440-1 n. 82. On the possible significance of this organization to systems of political organization, see Chapter 6. 156 (e)pisth~mai) taught by Theodorus (which correlate with the Archytan quadrivium); likewise, the banausic “arts of the other technicians” (ai( tw~n a!llwn dhmiourgw~n te&xnai) like cobbling and carpentry are admitted, at least operatively, as “sciences,” a remarkable departure from the Republic that sets the tone for revision of the previous work. 400 But Socrates will not let Theaetetus divert the subject of the discussion: they cannot discover what knowledge “is” by enumerating (a)riqmh~sai) its permutations, that is, by telling how many or what sorts of science there could be (ti&nwn h( e)pisth&mh, ou)de_ o(po&sai tine&j). 401 Instead, Socrates says, they are looking for a simple answer about the essential composition of knowledge, just as “clay” is “earth mixed with water.” 402 Theaetetus’ response effectively provides an example of dialectical mathematics and extends the syllogistic model of dialectic offered in Republic VII to geometry: THEAETETUS: Theodorus here was drawing a diagram for us about irrational square roots, showing us that, for squares whose areas are three and five square feet respectively, the length of the sides is incommensurable with one foot (ou) su&mmetroi th~| podiai&a|), and he proceeded according to each length until the square of seventeen square feet, where he, for some reason, stopped. So it occurred to us that, since the number of irrational square roots appeared to be infinite, we should attempt to bring them all together into one (peiraqh~nai sullabei~n ei)j e#n), which we might call “all the irrational square roots (pa&saj ta_j duna&meij). SOCRATES: And did you discover what sort of thing this was? THEAETETUS: Well, I think we did. But tell me what you think. SOCRATES: Explain it. 400 Pl. Theaet. 146c7-d3. 401 Pl. Theaet. 146e7-8. 402 Pl. Theaet. 146e7-10. Cf. ontology as represented earlier in the Meno (77a5-b1), where Socrates asks Meno to define virtue “speaking generally about [it], what it is (kata_ o#lou ei)pw_n a)reth~j pe&ri o#ti e)sti&n)” and to “stop making many things from one (pau~sai polla_ poiw~n e)k tou~ e(no&j).” 157 THEAETETUS: We distinguished all things into two groups of Number: what has the capacity to be the product of a number multiplied by itself we called a “square” and “equal-sided,” analogizing it with the figure of the square (tw~| tetragw&nw| to_ sxh~ma a)peika&santej). SOCRATES: Fine. THEAETETUS: Then, for the class of Number intermediate of this (to_n metacu_ tou&tou), e.g. three and five and every number which does not have the capacity to be the product of a number multiplied by itself, but which is instead the product of a greater number multiplied by a smaller one or vice versa and always has sides of greater or lesser length, we called it the oblong number, analogizing it, in turn, with the oblong figure (tw~| promh&kei a)peika&santej au} sxh&mati). SOCRATES: Excellent! What happened next? THEAETETUS: Whatever lines formed a square plane equal-sided in number, we defined as “rational length” (mh~koj w(risa&meqa), but whatever lines formed a plane of other-than-equal sides (e(teromh&kh), we defined as “irrational lengths” (duna&meij), on the grounds that they are incommensurable with the former lines in length, but their squares have the capacity to be commensurable with the former lines (toi~j d’ e)pipe&doij a$ du&nantai). The same distinction exists for solid geometrical figures. 403 This long passage, which occurs near the beginning of the Theaetetus, presents us with an application of dialectical synthesis, in that Theaetetus and Socrates the Younger, who move beyond their teacher Theodorus, employ geometrical figures and axioms to arrive at the proper categorization of kinds of lines. They move from “many” – literally an “infinite” number – to “one” by “bringing together” (sullabei~n) those lines not commensurable with rational roots. The process of defining them and giving them a name – so significant in the Platonic philosophical pragmateia – coheres with Socrates’ method of comparison through images (a)peika&santej) as exemplified in the Republic, with one particular difference here: 403 Pl. Theaet. 147d4-148b3. 158 the use of the geometrical figure (to_ sxh~ma) is explicit. Theaetetus posits that “irrational numbers” could be defined under a single term “powers” (duna&meij), a word that has obvious semantic connections with the political and religious spheres. Theaetetus’ process of diaeresis and synthesis is not simply mathematical: it proceeds along lines of definition as well, in that the name “irrationals” (duna&meij) reflects the potential of the squares (toi~j d’ e)pipe&doij a$ du&nantai) of these lines to be commensurable with rational numbers. The mathematical formula expressed here is: FOR EVERY POSITIVE INTEGER n: n is irrational IF AND ONLY IF: THERE IS NO POSITIVE INTEGER m SUCH THAT n = m x m. 404 What is more, Theaetetus says, the same formula applies to those “solid geometrical figures” that plagued Socrates and Glaucon in the Republic and that would eventually make Theaetetus famous as a stereometer. But what is especially interesting for the development of Plato’s dialectic is the reference to the class of irrational integers as what is “in the middle (to_n metacu_ tou&tou)” of the class of rational integers (3, 5, etc.). Do these refer to what will become the third “middle” term, the mathematical practicals (ta_ maqhmatika_ tw~n pragma&twn as Aristotle called them)? 405 A fuller examination of the relationship between rationals and irrationals – and the application of this relationship to political organizations – will 404 Cf. Burnyeat 1978: 494. 405 See Chapter 2. In Book V of Plato’s Republic (479c7ff.), Socrates refers to the “middle between Being and Not-Being” which is the dream-world of doxa. This intermediate world is subject to relativity and change, and therefore corresponds with impure reason or “irrationality.” 159 be attempted later on, 406 but for now we can only highlight the reference to this term that will become so important to later Platonic thought and its analogy with the class of number that is irrational (duna&meij). That this classification of number is representative of Platonic dialectic in this period is demonstrated in Socrates’ response to Theaetetus’ description of how he and Socrates the Younger had proceeded beyond their teacher’s mathematical diagrams: SW. I!qi dh& - kalw~j ga_r a!rti u(fhgh&sw – peirw~ mimou&menoj th_n peri_ tw~n duna&mewn a)po&krisin, w#sper tau&taj polla_j ou!saj e(ni_ ei!dei perie&labej, ou#tw kai_ ta_j polla_j e)pisth&maj e(ni_ lo&gw| proseipei~n. 407 SOCRATES: Come on, then – for you showed the way well just now – by imitating your answer concerning the irrational roots, try to advance a single account (logos) of all sciences, just as you collected all these powers, which are many, in a single Form. Socrates’ response effectively represents the dialectical process and its assumption of irrational elements. Just as Theaetetus had earlier deduced a Form for all irrational numbers, so dialectic rationalizes (e(ni_ lo&gw|) all the sciences. The language is both ethical and mathematical, a consequence of the analogical reasoning being employed throughout this passage. The topic also refers to the problem of negotiating plurality and unity, a recurrent problem for Plato’s ontological and political philosophy. 408 This discussion of the categorization of numbers, then, is employed by Socrates as a paradigm (mimou&menoj) for the process of dialectic, and vice versa; it is employed by 406 In the Epilogue. 407 Pl. Theaet. 148d4-7. 408 On which, see Chapter 6. 160 Plato as a means to extend and exemplify the educational process delineated in the Republic. But in the course of the Theaetetus, it is a prelude to Socrates’ famous comparison of his activity with that of midwives. Socrates’ appeal to Artemis, who he says – in language with an acousmatic Pythagorean flavor – was “the cause” (ai)ti&a) of the law that midwives aid in birth only when they themselves are barren, emphasizes the significance of the mixed in the scheme of dialectic: if we are to believe the Scholiast to Euclid, Artemis was the goddess represented by the “even- odd” (a)rtiope&ritton) number, 409 which, Aristotle tells us, was the combination of the One and the Dyad in the philosophy of Philolaus of Croton: The One partakes of (mete&xein) the nature of both [the even and the odd]: for, when it is added to an even number, it makes it odd, and when added to an odd number it makes it even, which it could not do unless it were to participate (metei~xe) in both natures; therefore, indeed, he says that the One is called the “even-odd (a)rtiope&ritton).” 410 Socrates, indeed, assumes an arithmology comparable with that of Philolaus (and perhaps Archytas). 411 Artemis, who is “childless but in charge of childbirth” (a!loxoj ou}sa th_n loxei&an ei!lhxe) is a paradoxical mixture of the male and female, the rational and irrational elements, that participate in one another. 412 Socrates realizes the significance of “pairing men and women (sunagwgh_n a)ndro_j 409 Schol. 7 in Euclid. Elem. 7, Heiberg 5 p. 364, 6 = Timpanaro Cardini B 21d (1964: 125-9). 410 Theo. Sm. Math. p. 21.20 Hiller (Arist. F 199 Rose). 411 Ibid. 412 Interestingly, Socrates soon claims that his god, who we may assume is Apollo from the Apology, forces him to attend to the labor of others but prohibits him from giving birth (Pl. Theaet. 150c7-8). Apollo was readily arithmologized as the One in Pythagorean philosophy (Iambl. in Nichom. Arith. 13.10 Pistelli). 161 kai_ gunaiko&j)” in the labor of the midwife, a project that will assume a central part of the ideal politikos’ responsibilities in the Statesman. 413 Here it is but a passing remark, to be subsumed soon by Socrates’ claim that his responsibilities to the souls of those who will give birth to ideas are of greater import than the efforts of midwives, who only preserve the body. 414 It will require the introduction of a new authoritative voice, the Eleatic Stranger, for Plato to initiate the revision of the political and dialectical theories originally proposed in the Republic and extended in the Theaetetus. But, in our study, the Eleatic Stranger may not precede his teacher and “father” Parmenides, who is featured in the Platonic dialogue that features his name. Dialectic and mathematical ratios figure only briefly in the Parmenides, a dialogue that emphasizes what ought to be hermeneutic difficulties encountered whenever reading any of Plato’s works. 415 In the first section (126a-135c4), the subject and dramatic date are defined: Socrates and some friends, who are still in their youth, have come to see Zeno of Elea deliver his famous speech on the non- existence of the Many at the Grand Panathenaic Festival at Athens in June, 449 BCE. Zeno’s teacher, the Eleatic philosopher Parmenides, is in attendance, and it is to Parmenides that Socrates addresses his questions. But the roles have been reversed – 413 See below in this chapter. 414 Pl. Theaet. 150a8-b4. 415 This interpretation of the Parmenides owes much to the “Introduction” and “Notes” sections of the Laterza Edition of Plato’s Parmenides, edited by Francesco Fronterotta (1998). Fronterotta’s ancillary texts aid the reader significantly in understanding this extremely difficult dialogue. Kenneth Sayre (2005: 49-62) has argued for the Pythagoreanizing elements in the second part of the Parmenides, and, given the constraints of time and space, I refer the reader to his study of the second portion of the Parmenides. 162 a topos that echoes the mysterious presence of Socrates’ namesake (Socrates the Younger) and the young Theaetetus, who resembles Socrates physically, 416 in the Theaetetus – and Parmenides proceeds to engage Socrates in elenchus. Thus, the work seems tied to two distinct phases of philosophical investigation, and we are hard pressed to distinguish between the historical representation of the characters in this dialogue – in the mid-5 th Century BCE – and the place of the Parmenides in the development of Plato’s pragmateia roughly about 360 BCE. For example, the form of elenchus is derivative of what we have seen throughout Plato’s whole career, and it takes the form of a Socratic dialectic encountered in the Republic. Interestingly, Parmenides suggests that the diaeretic aspect of his philosophical program is appropriately Socratic when he posits his first question about the Theory of Ideas: And Parmenides said, “O Socrates, how worthy you are for the passion which you apply to the discussion. And tell me, have you practiced division in the way you are saying (au)to_j su_ ou#tw dih|&rhsai w(j le&geij), some Forms themselves separate and some which, in turn, participate in them? 417 By referring to the method of diaeresis “as Socrates” does it, Parmenides emphasizes the Socratic component of Plato’s dialectic, which, as we saw, applied ethics to Pythagorean forms of definition (i.e. they are dealing with intellectual concepts, not just numbers or mathematical entities). Indeed, it is a Theory of Ideas bereft of any particularly detectable mathematical Pythagorean influence that is under examination in this passage. What is new and emphasized here is the Participatory Theory of 416 Pl. Theaet. 143e8-9. 417 Pl. Parm. 130a8-b3. 163 Ideas presented in Phaedo with its marked emphasis on Participation (me&qecij), a quality perhaps derived from Philolaus of Croton’s or Archytas of Taras’ physics. 418 If so, it is anachronistic to understand the application of Participation as derived from a Theory of Ideas from Socrates’ youth, before Philolaus could have been old enough to develop this hypothesis. It appears that certain aspects of Pythagorean influence have been excised, while others have been added. This theory, which is here boiled down to its main postulates, proceeds along these lines: 1. For each quality of things, e.g. likeness or unlikeness or unity or multiplicity, a particular Form exists in itself according to itself (au)ta_ kaq’ au(ta_): the Form of Likeness, of Unlikeness, etc. The Form of Likeness, for instance, has an opposite (a!llo ti e)nanti&on), namely the Form of Unlikeness. 419 2. By means of Participation (me&qecij), empirical things (things that may be perceived) partake of the attributes and characteristics of the Forms; e.g. the things which partake of Likeness become (note the emphasis on the Visible place of “becoming”) alike (ta_ me_n th~j o(moio&thtoj metalamba&nonta o#moia gi&gnesqai). 420 3. Empirical things participate in both plurality and in unity; because Socrates a man is among seven men, he participates in plurality; but because he himself is one man, he participates in unity (mete&xwn kai_ tou~ e(no&j). 421 There is no sense that this applies to the Forms. 418 The Phaedo makes suggestions in the direction of a Participatory Theory of Forms (e.g. 101b10- 102a1), most notably when Socrates discusses how things partake (metalamba&nonta) of their namesakes (Phd. 102a11ff). 419 Pl. Parm. 128e5-129a2. Cf. Pl. Phd. 74a2-76e7, where knowledge of the Forms is assumed to be inborn – and from a previous incarnation – and we are challenged to “remember” what we have forgotten. 420 Pl. Parm. 129a2-b6. 421 Pl. Parm 129c4-d2. 164 4. Examination of the Forms will lead to their separation and combination in the mind of the examiner. I will quote directly, since this passage is of utmost significance to later Platonic dialectic: e)a_n de& tij w{n nundh_ e)gw_ e!legon prw~ton me_n diairh~tai xwri_j au)ta_ kaq’ au(ta_ ta_ ei!dh, oi{on o(moio&thta& te kai_ a)nomoio&thta kai_ plh~qoj kai_ to_ e$n kai_ sta&sin kai_ ki&nhsin kai_ pa&nta ta_ toiau~ta, ei}ta e)n e(autoi~j tau~ta duna&mena sugkera&nnusqai kai_ diakri&nesqai a)pofai&nh|, a)gai&mhn a@n e!gwg’, e!fh, qaumastw~j, w} Zh&nwn. 422 “If someone among those people I was just discussing in the first place were to distinguish separately the Forms themselves according to themselves, e.g. likeness and unlikeness and multiplicity and unity and stillness and motion and all such things, and then to show that those things among themselves have the capacity to be combined and to be separated, I would be extraordinarily pleased, O Zeno,” he said. 5. The difficulty in understanding the Forms dialectically is implicated in the Forms (th_n a)pori&an e)n au)toi~j toi~j ei!desi pantodapw~j plekome&nhn) for those who receive them using logistic (en) toi~j logismw~| lambanome&noij). 423 Socrates’ five arguments, which appear to represent the middle dialogues’ Participatory Theory of Ideas, are notable for their emphasis on non-mathematical axioms. 424 The ethical characteristics of this form of dialectic do not retain any traces of Pythagorean mathematics as it was understood by the Plato who wrote the Meno, Republic, and Theaetetus. Instead, mathematical Pythagorean influence – 422 Pl. Parm. 129d6-e4. 423 Pl. Parm. 129e5-130a2. 424 On participation and the Forms, see Natorp 2004: 167-70. 165 reference to geometric figures, numbers both rational and irrational, proportions – is notably lacking in this abstract hyperlogic. 425 Parmenides aims his criticism at the ontological and epistemological value of Forms and the means of communication between these “separate” kinds in four primary postulates: 1. The existence of noble or intellectual Forms may be defended, but what about Forms of things that exist in nature, such as “Man” or “Water” or “Fire?” Or, for that matter, what about base or ignoble things such as “Hair” or “Nails,” or “Dirt?” Socrates’ Theory of Forms cannot be extended to empirical things nor to things of relative insignificance. 426 2. If empirical things participate in their particular Forms, and therefore the Forms participate in those same empirical things, then will every Form be present in those empirical things in their totality or differently in different portions? This presents a problem if empirical things receive their names from the Ideas of whose characteristics they partake. 427 3. If a Form – being unified – can be divided by us, it can no longer be unified, since it has been separated. It is absurd to assume that, e.g., when Greatness has been divided, each of the many things that partake of Greatness will be great in virtue of the portion of Greatness which is smaller than Greatness itself. This, Parmenides claims, would appear “irrational” (a!logon). 428 4. The “Third Man” Criticism: If a Form “Greatness in itself” exists and certain empirical things possess the quality of “Greatness” as a consequence of their participation in that Form, then the Form “Greatness” and those empirical things that are “Great” will form a unified entity (e#n ti). This unified entity will require another Form 425 Indeed, Parmenides is interested in the possibilities of ontological confusion among the terms “One” and “limitless multitude” in Socrates’ Theory of the Forms. On the importance of this to the development of Plato’s later ontology, see Sayre 2005: 29 and 118-22. 426 Pl. Parm. 130b7-e4. 427 Pl. Parm. 130e4-131b6. 428 Pl. Parm. 131b7-d2. 166 (“Greatness 1 ”) which “comes to be in addition to Greatness itself and [in addition to] the things that participate in it [Greatness] (par’ au)to& te to_ me&geqoj gegono_j kai_ ta_ mete&xonta au)tou~).” Then, another will be born by this, etc., ad infinitum. Therefore, as Parmenides declares, “And, indeed, there will no longer be a single particular form for you, but a limitless multitude!” (kai_ ou)ke&ti dh_ e$n e#kasto&n soi tw~n ei(dw~n e!stai, a)lla_ a!peira to_ plh~qoj). 429 What is astonishing about the Parmenides is its focus on Participation as an intermediary between the Forms and empirical things, a concept only highlighted in the Phaedo (among pre-Parmenides dialogues) and the immediate criticism of this emphasis by a representative of Eleatic thought. In this way, Parmenides – like the Eleatic Stranger of the Sophist and Statesman – is represented “not as a monist but as a representative of precise reasoning.” 430 Parmenides’ criticisms here are valid in that they demonstrate the challenges of extending the logical postulates of this theory of the Forms and steering clear of irrationality or absurdity. 431 The most significant of these criticisms, the “Third Man” argument, rests upon the two terms that will mark shifts in Platonic dialectic from this point forward: gegono_j and mete&xonta. 432 As we saw in Republic VI, the Sun is the “offspring” of the Good, but Socrates willfully neglects to define precisely how this term bridges the gap 429 Pl. Parm. 132a1-b2. Aristotle (Metaph. 990b15-17; Cf. 1079a11-13) refers to those who adhere to the “Third Man” argument as distinct from the Idealists who deny that a separate genos of Forms exists “according to itself (au(to_ ge&noj).” 430 Ross 1976: 91-2. 431 We must recall, with Ross, that the “Third Man” argument is “not fatal to the theory” of Ideas but “to the language in which Plato has formulated it.” The focus here on terminology and the relation between names and things as they exist in reality becomes more central to Plato’s philosophy. See Ross 1976: 87-9. 432 It is interesting to note that derivatives of these words appear in the second portion of the dialogue, which features something akin to “Eleatic” dialectic. Despite the refutation of this new Theory of Forms, Parmenides employs the new terms and axioms as though they were his own. See Fronterotta 1998: xxii-xxxv. It is unfortunate that even Ross, in his classic Plato’s Theory of Ideas, does not engage seriously with the shifts in Platonic vocabulary. 167 between the Intelligible and the Visible places. Here, the argument shifts: Forms are capable of existing in addition to and partaking in other Forms, i.e., other entities in the Intelligible world that are not supposed to be able to be created or destroyed, a postulate that Socrates might have wished to contradict. But Socrates’ failure to dispute this point marks what we might consider the final separation of Platonic dialectic from its parent Socratic dialectic. 433 Indeed, as we shall see with the Sophist and the Statesman, the definition of and investigation into genos – and the consequent emphasis on generation – becomes crucial to Platonic dialectic, in that it becomes known as the “third term” which represents participation among Forms. 434 Despite his criticisms, Parmenides recognizes the necessity of the Forms as an abstract concept that must exist in order for the philosopher to be able to practice philosophy. They represent a point of reference for philosophers, a place “whither to turn one’s thought” (o#poi tre&yei th_n dia&noian). 435 In this way, the Forms are comparable with geometric figures as they were employed propaedeutically in the Republic and Theaetetus: they have become protreptic tools that allow the student to turn his gaze in the right direction. But there is no sense that, as we saw in the Republic, the Forms are themselves reality in the Parmenides. 436 Instead, Parmenides closes this section of the dialogue by appealing to the practical function 433 Socrates attempts to shift the discourse on the Forms and assign to those empirical forms a paradigmatic function in the soul (Pl. Parm. 132d1-4). But Parmenides’ response, which constitutes a “second Third Man” criticism, refutes Socrates (Pl. Parm. 132d5-133a3). 434 See below in this chapter. 435 Pl. Parm. 135b8. 436 Socrates’ attempt to make them correlative with thoughts and paradeigmata fails. See Sayre 2005: 30-33. 168 of the Forms, without which “someone will destroy the power of practicing dialectic in every way” (th_n tou~ diale&gesqai du&namin panta&pasi diafqerei~). 437 At the close of the decade, Plato has begun to overhaul radically the Theory of the Forms and the praxis of dialectic in the Parmenides and the Theaetetus as a consequence of his reexamination of the basic tenets of Socratic philosophy. Generally speaking, we may suggest that it was Plato’s serious reevaluation of Socratic Form Theory and Pythagorean geometry through the lenses of Eleatic dialectic that led him to a total revision of his philosophical pragmateia: but there remains some confusion about the precise role that Eleatic philosophy played in the noted shifts and developments in Platonic metaphysics and dialectic. 438 And what successes may be gained from the Parmenides’ immediate criticism of the Participatory Theory of Forms and Plato’s subsequent adoption of its hypotheses? 439 This question has plagued critics of Platonic philosophy since antiquity. Whatever the answers may be, an examination of the sequels to these great works of scholarly investigation, the Sophist and the Statesman, exposes remarkable reflections upon this very subject. 437 Pl. Parm. 135c1-2. 438 For a more recent examination of the “Eleaticism” of the Eleatic Stranger, see Palmer 1999. 439 One interesting investigation into this question is Sayre 2006. 169 DIALECTIC REASSESSED IN THE SOPHIST AND THE STATESMAN (THROUGH THE MYTH) Parmenides’ closing criticism of Socrates’ Participatory Theory of the Forms raises a significant and potentially insurmountable criticism based on the analogy with the knowledge that masters and slaves possess: if Forms exist according to themselves in the divine world, and the knowledge that the gods possess is separate from the human kinds of knowledge, then the gods cannot know about human affairs either: So, if the highest mastery (h( a)kribesta&th despotei&a) and the highest science itself are the provenance of God (para_ tw~| qew~|), neither would their mastery ever dominate us nor would their knowledge know us or any of the things in our provenance. Rather, in the same way that (o(moi&wj) we do not rule (ou)k a!rxomen) over them with rule in our provenance (th~| par’ h(mi~n a)rxh|~) nor do we know anything of the divine by means of our science, so, in turn, according to the same logic, neither are they masters of us nor do they know about human affairs, despite being gods. 440 This passage recalls previous criticisms about hypotheses, principles, and epistemology discussed in the Republic – and adopted by Aristotle in the Metaphysics 441 – and provides a prelude for the first and perhaps most important subject discussed in the Sophist, which, if it is the narrative sequel to the Theaetetus, 442 is no less the philosophical sequel to the Parmenides. In the Republic, we noted Socrates’ criticisms of the Pythagoreans’ employment of hypotheses; beginning from hypotheses and axioms assumed to be true, the Pythagoreans 440 Pl. Parm. 134d9-e6. 441 See Chapter 2. 442 Cf. Pl. Soph. 216a1-2. 170 proceeded to prove those very axioms by applying them to the higher elements of the universe (i.e. the heavens, etc.). Again, here, Parmenides does not allow for the reversal of imperfect and divine: the human a)rxh&, which should be understood both as political “rule” and philosophical “first principle,” cannot “rule over” the Gods. It would be absurd, Parmenides is suggesting, to assume that the Gods are subject to human principles or human epistemology. Thus, the problem of the proper distinction between divine and human pervades the solemn conclusion of the first portion of the Parmenides. Deducing the difference between gen1 becomes a central feature of Platonic dialectic in the two dialogues that follow upon the criticisms advanced by Parmenides in the eponymous dialogue written by Plato; in the Sophist, as Plato introduces a new authoritative speaker known only as the Eleatic Stranger, the issue of defining genos becomes crucial to the project of revising Plato’s philosophy. In many ways, we may see the function of the Eleatic Stranger in the development of Plato’s pragmateia as the complication of Socratic Theories of the Form and dialectical procedures with Eleatic types of philosophical investigation, though with an eye to the ways in which all these modes of philosophical inquiry relate to Pythagoreanism more generally considered. This complication includes a concerted and intense scrutinizing of two innovations in Platonic dialectic, namely diaeresis into Kinds (gen1) and Parts (mer1). At the beginning of the Sophist, we note that the narrative frame found in the Theaetetus – Euclid and Terpsion discussing what happened many years ago – has been cut out, and the dramatis personae are simply those characters who will engage 171 in the dialogue. 443 We are introduced to what Campbell called the “more remote” 444 subject of the dialogue, i.e. what exactly genos means, in the first lines, which are especially significant for extending the philosophical questions encountered in the Parmenides: THEODORUS: Following our agreement yesterday, Socrates, we ourselves have come in fine form (kosmi&wj) and we’ve brought this foreigner, who is in respect to Kind from Elea (to_ me_n ge&noj e)c )Ele&aj), and who is an associate (e(tai~ron) of the school of Parmenides and Zeno, truly a man who loves wisdom (ma&la de_ a!ndra filo&sofon). 445 Theodorus introduces the Stranger from Elea by first telling us that his genos is from Elea, suggesting initially that his family is Eleatic, but then he shifts the semantic meaning of genos with the two following explanatory phrases: he is an associate of the Eleatic school, and he’s a true “man who loves wisdom.” 446 Theodorus is using the term genos to refer to the community whence his philosophical views are derived, just as genos refers to Pythagorean philosophical schools, as we saw in Chapter 1. But Theodorus has not been careful enough to distinguish between the categories of man and philosopher, and Socrates responds by drawing an analogy with the human and the divine: SW. }Ar’ ou}n, w} Qeo&dwre, ou) ce&non a)lla& tina qeo_n a!gwn kata_ to_n (Omh&rou lo&gon le&lhqaj; o#v fhsin a!llouj te qeou_j toi~j 443 On the absence of a narrative frame here and its significance for establishing a “common reading” of the Sophist and Statesman, see Lane 1998: 7. Despite the will to a common reading that systemizes the modes of diaeresis and synthesis, we should not assume that the Statesman simply extends the Sophist’s propositions. Indeed, it might be argued that the Statesman perpetuates a continual revision of Plato’s dialectical methods. 444 Campbell 1988: 6. 445 Pl. Soph. 216a1-4. 446 Palmer 1999: 118-121 argues convincingly for the term “associate.” 172 a)nqrw&poij o(po&soi mete&xousin ai)dou~j dikai&aj, kai_ dh_ kai_ to_n ce&nion ou)x h#kista qeo_n sunopado_n gigno&menon u#breij te kai_ eu)nomi&aj tw~n a)nqrw&pwn kaqora~n. ta&x’ ou}n a@n kai_ soi& tij ou{toj tw~n kreitto&nwn sune&poito, fau&louj h(ma~j o!ntaj e)n toi~j lo&goij e)poyo&meno&j te kai_ e)le&gcwn, qeo_j w!n tij e)legktiko&j. 447 SOCRATES: Perhaps, Theodorus, by bringing not a visitor but some god, you’ve given us the slip; it’s Homer who says that the other gods attend to men who partake of just decisions, especially the god of strangers, who becomes a supporter and scrutinizes the hubristic and well-lawed affairs of humans. Perhaps he may be one of the higher powers and attend even to you as a god of elenchus, in order that he may survey and scrutinize us, the poor creatures we are, in arguments. Socrates raises the doubt that the character who will become his authoritative replacement in the dialogues of Plato is human at all, but rather he compares the Stranger (Xenos) with Zeus Xenios, the “god of strangers” (to_n ce&nion qeo&n) who watches over both the “hubristic and well-lawed affairs” of humans. He also might be one of the “higher powers” who watch over human affairs to which Plato later refers in Epistle VII and the Laws. 448 The Stranger’s divinity draws comparisons with Eros as represented in Diotima’s speech in the Symposium: the “hermeneutic” god, considered “daemonic” (daimo&nion) or “in the middle of god and mortal” (metacu& e)sti qeou~ te kai_ qnhtou~), is also said to be a “philosopher in the middle of wisdom and ignorance” (filo&sofon de_ o!nta metacu_ ei}nai sofou~ kai_ a)maqou~j). 449 There is a hint that Plato is fashioning the Eleatic Stranger as the divine representative of philosophy, the “really quite amazing” (qaumastote&rou) man of the Parmenides who both “will discover” (eu(rh&sontoj) the genos of each 447 Pl. Soph. 216a5-b6. 448 Pl. Ep. VII. 326e2. Cf. Pl. Leg. 718a5. 449 Pl. Symp. 202d11-e7 and 204b4-5. 173 thing and its Being and “will be able to teach all these things” (dunhsome&nou dida&cai tau~ta pa&nta) to others. 450 The Eleatic Stranger’s advocacy of didacticism is inscribed within what we might want to see as a criticism of the second half of Plato’s own Parmenides: in this way, he both suggests the parodic nature of the Zenonian argumentation in the Parmenides and distances himself from Eleatic philosophy as it was more traditionally practiced and from his philosophical “father” Parmenides. 451 Such a characterization echoes Plato’s greater interest in the popularization of philosophy as evidenced in the post-360 works. 452 Likewise, the Eleatic Stranger is compared with the Zeus Xenios, to which Plato refers in Epistle VII, the god to whom Plato “discharged his obligations” and “cleared [him]self of reproach from Philosophy” when he returned to Syracuse in an attempt to reform the tyrannical regime of Dionysius II in Syracuse (367 BCE). 453 The blend of politics and philosophy in practice therefore assumes the form of a divine responsibility to Zeus Xenios, a communicative god who moderates foreign relations, and thus the 450 Pl. Parm. 135a7-b2. 451 Pl. Soph. 241d5-7 and 243a7-b1. Palmer 1999: 145-6 offers an intriguing and fresh interpretation of this passage, in which he suggests that it is the appropriation of Parmenides’ logos by the sophists that is under scrutiny (a term I prefer to Palmer’s “examination” for e)legxqe&ntwn). 452 Christopher Bobonich locates the shift towards didacticism in the Statesman, but we might suggest that it is noted slightly earlier in the Sophist. For a fuller account of the significance of transferal of philosophical ethics to hoi polloi, see Bobonich 2002: 412-17. 453 Pl. Ep. VII. 329b3-5. Translation by Morrow. It does not follow, as Scodel 1987: 16 has suggested, that “a more likely hypothesis on a priori grounds…is that the Stranger does not speak voce Platonis.” We might instead suggest that all characters in the Platonic dialogues are themselves dramatic manifestations of a complicated Platonic voice composed of multiple voices (vocibus Platonis) according to a synthetic model itself tested earlier and appropriated throughout the later dialogues. What is more, we cannot simply dismiss the whole corpus of Epistles without justification (as Scodel does). 174 Eleatic Stranger is introduced as a divine figure whose specific provenance is political philosophy. Nevertheless, Theodorus immediately corrects Socrates’ final comment – that the Stranger is a god of elenchus – by suggesting that the man from Elea is not to be confused with those followers of Parmenides who are serious about eristic discourse (by which we may assume he means Zeno, Melissus, and other Eleatics): 454 THEODORUS: No, Socrates, that’s not the way of the Stranger; he is more measured (metriw&teroj) than those who study eristics. And he seems to me to be no god-man (qeo_j me_n a)nh_r) 455 at all, but divine (qei~oj mh&n): for I apply the name of philosopher to all these sorts of people. 456 Theodorus’ correction of Socrates – that the Stranger is not a “god-man” but a “divine man” (qei~oj a)nh_r) – establishes an intermediate (but not a mixed) category between the divine and the human realms that were considered to be distinct in the propositions of the Parmenides: the “true” philosopher. 457 Here, Theodorus’ comments echo, indeed, what Socrates had previously said in Republic VI: “In fact, the philosopher himself, being the companion of the divine and the cosmic order, becomes both ordered and divine (ko&smio&j te kai_ qei~oj) as far as a human can.” 458 But Theodorus the Geometer mathematicizes the Stranger, referring to him in terms (metriw&teroj) that suggest the Stranger’s possible interest in those topics that 454 See Miller 1979: 11-14. 455 Following the manuscripts bTW. Bekker introduces an unnecessary correction of a(nh_r. See Campbell 1988: 5. 456 Pl. Soph. 216b7-c1. 457 Is this an attempt by Theodorus to demonstrate that the Eleatic Stranger is not to be confused with those practitioners of wisdom who, like Empedocles, claimed to be gods? 458 Pl. R. 500c9-d1. 175 Theodorus himself teaches. Socrates continues to debate with Theodorus about the genos of the philosopher and the ways in which it is distinct from the god’s: SW. kai_ kalw~j ge, w} fi&le. tou~to me&ntoi kinduneu&ei to_ ge&noj ou) polu& ti r(a~|on w(j e!poj ei)pei~n ei}nai diakri&nein h@ to_ tou~ qeou~: pa&nu ga_r a{ndrej ou{toi “p a n t o i~ o i” fantazo&menoi dia_ th_n tw~n allw~n a!gnoian “e) p i s t r w f w~ s i p o& l h a j,” oi( mh_ plastw~j a)ll’ o!ntwj filo&sofoi, kaqorw~ntej u(yo&qen to_n tw~n ka&tw bi&on, kai_ toi~j me_n dokou~sin ei}nai tou~ mhdeno_j ti&mioi, toi~j d’ a!cioi tou~ panto&j: kai_ tote_ me_n politikoi_ fanta&zontai, tote_ de_ sofistai&, tote_ d’ e!stin oi{j do&can para&sxoint’ a@n w(j panta&pasin e!xontej manikw~j. 459 SOCRATES: Well said, friend. Yet, there is the probability that it is not so very easy, so to say, to distinguish this Kind or that of the god; for certainly these men – the ones who are not phony but real philosophers, scrutinizing from above the life below – appear as “multi-faceted city-travelers” because of the ignorance of the rest; and to some, they seem to be worth nothing; to others, they are worth everything; now they appear as statesmen, now as sophists, now they give to some [grounds to] believe that they are total maniacs. Socrates continues to develop the argument about the genos of the Stranger: in contrast with ignorant people, this philosophical “Kind” watches the life from above (although it is notable that they do not descend to congregate with those below, as was required of the philosophers in the Republic) and is imagined (fanta&zontai) as statesman, sophist, and religious leader. What is more, Socrates’ response guarantees a frame of reference, as well as a set of terms, that will structure the debate about subsequent topics of Sophist and Statesman. The terms of discussion will involve perception, fantasy, and opinion, all of which Socrates has discussed with Theaetetus on the previous day, and all of which factor into the investigation of 459 Pl. Soph. 216c2-d2. 176 epistemology. 460 Socrates determines the subject for the discussion today: they should distinguish between the Sophist, the Statesman, and the Philosopher, responding first by establishing what “people in that place (i.e. Elea) think about these things.” 461 This subject is iterated in the terms that had come under criticism in the Parmenides: po&teron e$n pa&nta tau~ta e)no&mizon h@ du&o, h@ kaqa&per ta_ o)no&mata tri&a, tri&a kai_ ge&nh diairou&menoi kaq’ e$n o!noma ge&noj e(ka&stw| prosh~pton; 462 Did they consider all these things one or two, or, in accordance with there being three names, if they distinguished three Kinds, indeed, did they attach a Kind to each according to one name? Socrates’ mode of diaeresis and model for the Forms present us with some difficulties. He questions whether or not these categories can be considered unified, split, or “three” according to the fact that there are three names for these Kinds. The discourse about names and their relation to the Forms had been brought up and challenged in the Parmenides, where Socrates had claimed that the names of things imitated the Form whence they were derived. 463 But what is even more striking than Socrates’ insistence upon the possible import of names for distinguishing gen1 is the Eleatic Stranger’s response to Socrates’ proposition: 460 On the problem of epistemology and opinion in the Sophist, see Palmer 1999: 141-5. 461 Pl. Soph. 217a1 ff. Note the abundance of verbs that involve “distinction through” (dia-) in the next few lines (diaporhqei_j; dienoh&qhj; diairou&menoi; dielqei~n; diori&sasqai; dierwtw~ntej; diakhkoe&nai). 462 Pl. Soph. 217a7-9. 463 A fuller account of the problem of naming and its relation to things in reality – while crucial to understanding the shifts in Plato’s philosophy – is unfortunately beyond the scope of this dissertation. 177 CE. Ou#twj, w} Qeo&dwre. fqo&noj me_n ga_r ou)dei_j ou)de_ xalepo_n ei)pei~n o#ti ge tri’ h(gou~nto: kaq’ e#kaston mh_n diori&sasqai safw~j ti& pot’ e!stin, ou) smikro_n ou)de_ r(a&|dion e!rgon. 464 STRANGER: That’s right, Theodorus, I have no scruples against it, nor is it difficult to say that they are considered three (Kinds). But to distinguish them each according to itself clearly, what in the world it is, is neither a trivial nor an easy task. The Stranger, who has been listening carefully to Theodorus and Socrates, accepts both the subject of the discourse and the terms by which to discuss it. Nevertheless, he modifies Socrates’ employment of genos by removing the necessary connection between name and kind proposed by Socrates here and in the Parmenides. 465 Instead, he wishes to distinguish each according to each (kaq’ e#kaston). The Stranger, however, is faced with a difficult task of moderation: the revision of the former Platonic Theory of Forms without totally throwing everything out the window. As Aristotle went on to characterize him in the Metaphysics, Plato, through the Eleatic Stranger, advises the Philosopher to navigate the middle course 466 between all-encompassing Eleatic Monism, whose proponents held that Being was unchanging (lit. “not moving”), the Pluralism of the “Friends of the Forms,” 467 whose proponents believed in many Forms as unchanging, and the 464 Pl. Soph. 217b1-4. 465 Cf. Pl. Soph. 218b6-d6, where the Stranger proposes that they consider the ergon of the Sophist and not his name. On the “Janus-faced” account of names developed by the Eleatic Stranger, see Lane 1998: 31-3. 466 Pl. Soph. 251a1-3, retaining the manuscript readings (bTW) of diwso&meqa ou#twj a)mfoi~n a#ma. 467 I follow Proclus (in Parm. 5a2), Burnet, and Taylor in assuming that this refers to the Pythagoreans, but I would suggest that this probably is specifically directed against the acousmatic branch, who did not engage in mathematical proofs (like Archytas) that involved motion. Nevertheless, it seems to refer also to Plato’s earlier Theory of the Forms (Soph. 248a4-b8), and in this way we can see the influence of the mathematical school upon Plato’s theories. Cf. Gill 1996: 178 relativists who believed that everything is always moving (e.g. Heraclitus, Hippasus of Metapontion, and Empedocles): CE. Tw|~ dh_ filoso&fw| kai_ tau~ta ma&lista timw~nti pa~sa, w(j e!oiken, a)na&gkh dia_ tau~ta mh&te tw~n e$n h@ kai_ ta_ polla_ ei!dh lego&ntwn to_ pa_n e(sthko_j a)pode&xesqai, tw~n te au} pantaxh|~ to_ o@n kinou&ntwn mhde_ to_ para&pan a)kou&ein, a)lla_ kata_ th_n tw~n pai&dwn eu)xh&n, o#sa a)ki&nhta kai_ kekinhme&na, to_ o!n te kai_ to_ pa_n sunamfo&tera le&gein. 468 STRANGER: It seems that the philosopher who especially honors all these things is required to refuse the notion that the All is at rest, to which the supporters of the One and the Many ascribe. In turn, he must turn a deaf ear to those who make the entirety in existence moving everywhere. But, in a manner that accords with the begging of the children (for “both”), he is required to declare that Existence and the All are both at once, however many things are not moved and are moved. Having properly distinguished between different kinds of philosophy, the Stranger enacts dialectic as established in the Theaetetus by reintegrating them together to create a mixed Form. The emphasis on “having both,” indeed, extends the “mixing” metaphors that we have seen employed by earlier Pythagoreans and, as we shall see, 469 by Empedocles. Indeed, it is a political term, koinwni&a, that the Eleatic Stranger employs to define the Form of this combination of opposing terms (stasis and kinesis), and this term recalls the democratic political influence that the 300-1. Guthrie 1978: 141 emphasizes the relationship between this passage and the Phaedo and Theaetetus, and concludes rightly that “[f]aced with this…I do not see how anyone can doubt that Plato is preparing the reader for a modification of his own metaphysics.” For an examination of the problems involved in interpreting this passage, see Ross 1951: 104-8. More recently, Palmer 1999: 179-80 has demonstrated the inherent Parmenideanism of the doctrine ascribed to the “friends of the forms,” and it would thus be unsurprising if Proclus saw the “friends of the forms” as Pythagoreans, since Parmenides’ philosophy was considered by Proclus (quoting Nichomachus) to be derivative of “Pythagoric learning” (DK A 4 = in Parm. Cousin 619). 468 Pl. Soph. 249c10-d4. 469 See below in this chapter. 179 mathematicus Hippasus of Metapontion (the other “Ionian” muse?) and Empedocles exercised in their home city-states. 470 Here, the use of the term “community” is selected to vary the applications of political terminology in later Platonic dialectic; it also reflects changes in Plato’s theories of ontology: STRANGER: Fine, then, did you not say that motion and stasis were opposites of one another? THEAETETUS: How could they not be? STRANGER: And, indeed, in like manner did you declare that they – severally and both – exist? THEAETETUS: Surely I did. STRANGER: When you allow that they exist, are you saying that they are moved (kinei~sqai) severally and both? THEAETETUS: Not at all. STRANGER: But by saying that they both are (ei}nai), do you mean that they are at rest (e(sta&nai)? 471 THEAETETUS: How could I? STRANGER: Are you positing that Being in the soul is some third thing (tri&ton ti) distinct from these (motion and rest), just as motion and stasis are encompassed by it (Being); and did you advance the notion that they both exist with an eye to their common participation in Being (pro_j th_n th~j ou)si&aj koinwni&an)? 472 Being, then, is hypothesized as a “third thing” in which motion and stasis share in communion. Nevertheless, it is considered possible that Being is distinct from motion and stasis because it “encompasses” (periexome&nhn) them. The Stranger and Theaetetus conclude, however, that Being cannot be “outside” (e)kto&j) of both motion and stasis, and the interlocutors arrive at a point of confusion: they have come to believe that they know as little about Being as about Not-Being. Thus, as 470 See Chapter 1. 471 As Guthrie 1978: 143 noted, the “confusion between the abstract nouns ‘motion’ and ‘rest’ (ki&nhsij and sta&sij) and the verbs ‘to be moved’ or ‘at rest’ (kinei~sqai and e(sta&nai) with their participles, seems complete.” 472 Pl. Soph. 250a8-b11. 180 we are in the midst of a revision of Platonic dialectic, we are also cast into a reexamination of Platonic ontology. 473 A partial answer to the problems raised here lies in the Stranger’s adherence to the revised principles of dialectic. 474 He refuses to leave behind the metaphorical language of mixture and commonality, eschewing the ad nauseam Eleatic reversals for something less based than they are upon categorical opposition. The emphasis on diaeresis and synthesis mentioned before, which is practiced by the “Ionian and Sicilian Muses,” could not exist without the presence of mixture (su&mmeicij), a concept that has its roots in Empedoclean and Heraclitean cosmology. 475 The Eleatic Stranger concludes by declaring true the third postulate that “some things want to be mixed together, and others do not.” 476 Indeed, the name given to those “things” which can be mixed or not mixed is gen1: CE. Ti& d’; e)peidh_ kai_ ta_ ge&nh pro_j a!llhla kata_ tau)ta_ mei&cewj e!xein w(mologh&kamen, a}r’ ou) met’ e)pisth&mhj tino_j a)nagkai~on dia_ tw~n lo&gwn poreu&esqai to_n o)rqw~j me&llonta dei&cein poi~a poi&oij sumfwnei~ tw~n genw~n kai_ poi~a a!llhla ou) de&xetai; kai_ dh_ kai_ dia_ pa&ntwn ei) sune&xont’ a!tt’ au!t’ 473 To be sure, we must generally agree with Guthrie 1978: 142 that “Plato’s language here is bewilderingly loose, even for him.” But the looseness of the language permits the Stranger to expose the arbitrariness of meaning that leads to aporia, a key element of his dialectical program. 474 See Guthrie 1978: 147-50. For a useful collection of the main passages of Plato’s dialogues that express the changes to Plato’s dialectical program (from the Sophist through the Timaeus), see De Vogel 1963: 246-271. 475 Pl. Soph. 252b1-6. Cf. the use of suggenh~ (Soph. 221d8-e3) to describe the angler and the sophist, who are both a kind of hunter, on which see Lane 1998: 28-9. At 242d7ff., the Eleatic Stranger describes the Ionian/Sicilian dialectical process (note the sun- words): The Ionian Muses, and later the Sicilian ones, comprehended (suneno&hsan) that it was safest to interweave (sumple&kein) both and to say that Being is many and unified, and that it is held together (sune&xetai) by hate and love. For, as the more severe of the Muses says, “For, by being borne apart, it is always brought together (diafero&menon ga_r a)ei_ sumfe&retai).” 476 Pl. Soph. 252e17. 181 e)stin, w#ste summei&gnusqai dunata_ ei}nai, kai_ pa&lin e)n tai~j diaire&sesin, ei) di’ o#lwn e#tera th~j diaire&sewj ai!tia; 477 ELEATIC STRANGER: What then? Since we agreed that Kinds relate to one another through mixture 478 in accordance with the same things, won’t a man need a particular science to advance correctly through arguments if he intends to show what sorts of kinds are concordant with what and what sorts do not admit of one another? More especially, if some are consistent through all, so that they are able to be mixed together? And again, in divisions, if others are causes of division through wholes? As the Eleatic Stranger argues, the goal of dialectic as it is being taught to Theaetetus is to demonstrate the categories (gen1) of things that can bind with others to create a mixture and the things that cause division. In this way, the new Kind (genos) that is being introduced here is particularly directed towards the relationships between things, with especial attention to things that can be mixed and things that do not mix. It represents the systemization of intergenous Forms and a significant advance over earlier theories which assumed all Forms to be separate from each other and from the phenomenological world. 479 477 Pl. Soph. 253b9-c3. 478 Greg Thalmann has offered a very interesting suggestion that e!xein stands for me&texein, which renders a translation of “share in mixture with each other in the same way.” But I agree with Campbell, who has argued that mei&cewj should be taken as a genitive of respect. See Campbell 1988: 144. 479 As Natorp 2004: 294-5 points out, the Philebus extends this complication of Being and Becoming further as mathematical concepts: “Coming into being must rather be represented in terms of the introduction of determinacy into what is indeterminate. Thus in the present passage (26d) the ‘third thing that arises out of both,’ that is, the ‘offspring’ of the indeterminate and determination, is defined as becoming unto being (ge&nesij ei)j ou)sia&n), and it is made possible through the determinations of measure (e)k tw~n meta_ tou~ pe&ratoj a)peirgasme&nwn me&trwn) that are fashioned in accordance with the principle of determinacy (pe&raj).” Cf. Runciman 1962: 22, who shows that the disjunction between Becoming and Being is not absolute. Cf. Sayre 2005: 49 an 174-5. On Being, Becoming, and the Philebus, see Chapter 5. 182 Further interrogation of the term genos reveals its place at the center of the new Platonic dialectic. As Charles Kahn has noted, genos is seamlessly incorporated into the familiar vocabulary of the middle dialogues (ei}doj and i)de&a) for the units to be collected and divided in diaeresis. 480 This follows from the Parmenides, where, in a prelude to our current discussion, we saw that genos was employed as if synonymous with the other terms for Form. 481 If it is Theodorus who introduces the term genos at the beginning, and if Socrates plays off of the term by disputing the genos of this visitor, then the Stranger modifies the application of the term significantly throughout the Sophist. If we keep in mind the set of terms laid out by Theodorus and Socrates at the beginning as well as the previous criticisms of the Participatory Theory of Forms that we encountered in the Parmenides, we detect the agonistic tone – marked by a revision of the meaning of important terms established at the beginning of the dialogue – that the Eleatic Stranger employs while revising Socratic dialectic: CE. Ti&n’ ou}n au} nu~n proserou~men, w} Qeai&thte, tau&thn; h@ pro_j Dio_j e)la&qomen ei)j th_n tw~n e)leuqe&rwn e)mpeso&ntej e)pisth&mhn, kai_ kinduneu&omen zhtou~ntej to_n sofisth_n pro&teron a)nhurhke&nai to_n filo&sofon; QEAI. Pw~j le&geiv; CE. To_ kata_ ge&nh diairei~sqai kai_ mh&te tau)to_n ei}doj e#teron h(gh&sasqai mh&te e#teron o@n tau)to_n mw~n ou) th~v dialektikh~j fh&somen e)pisth&mhj ei}nai; QEAI. Nai&, fh&somen. CE. Ou)kou~n o# ge tou~to dunato_j dra~n mi&an i)de&an dia_ pollw~n, e(no_j e(ka&stou keime&nou xwri&j, pa&nth| diatetame&nhn i(kanw~j 480 Kahn 1995: 55-6. Kahn follows Guthrie 1978: 129 n.4. 481 There is even the notable confusion of genos with Being (ou)si&a) in Parmenides’ comments (Parm. 135a8). 183 diaisqa&netai, kai_ polla_j e(te&raj a)llh&lwn u(po_ mia~j e!cwqen periexome&naj, kai_ mi&an au} di’ o#lwn pollw~n e)n e(ni_ sunhmme&nhn, kai_ polla_j xwri_j pa&nth| diwrisme&naj: tou~to d’ e!stin, h{| te koinwnei~n e#kasta du&natai kai_ o#ph| mh&, diakri&nein kata_ ge&noj e)pi&stasqai. 482 ELEATIC STRANGER: What name shall we attach to this (science)? Or, by Zeus, have we slipped and fallen upon the science of free men? Is it probable that we, in our search for the sophist, have discovered the philosopher first? THEATETUS: What do you mean? ELEATIC STRANGER: To divide things according to genos and not to consider the same form as different, nor what is different as the same; won’t we say that this is the business of the science of dialectic? THEATETUS: Sure, we will say this. ELEATIC STRANGER: So, then, the one who is able to do this: to perceive a single Form ubiquitously diffused among many things, of which each one remains singular, and to perceive many different Forms comprehended from without within one Form, and again a single Form mixed through many whole things within a unity, and many other things separated apart everywhere; this is to know how to judge by distinction according to genos, how each has, or does not have, the power to communicate with others. The Stranger’s language here employs the same terms established by Theodorus and Socrates at the beginning of the dialogue. 483 The concern for naming (proserou~men), slipping into (e)la&qomen) knowledge, proper judgment according to distinction (diakri&nein) 484 through segregation (diwrisme&naj), all recall the 482 Pl. Soph. 253c6-e1. 483 Taylor suggests that “[t]he point of this passage will thus be that it enlarges the conception of dialectic presented e.g. in the Phaedrus, as ability to divide things correctly by genus and species; it adds the task of studying the all-pervasive “categorical characters.” See Taylor 1961: 157. Socrates in Phaedrus distinguishes between eidos and idea, but leaves out genos entirely (Phaedr. 238a3). I presume by “categorical characters” Taylor is referring to ge&nh, which is the term that the Stranger applies to “the same” (i.e. identity), “the different” (i.e. otherness), “motion”, “rest”, and “being” (Pl. Soph. 254d4-255a2). The term “Not-being” is, of course, a mixture of “the different” and “being,” according to the Stranger (259a3-b1). 484 That diacritic diaeresis functions as a metaphysical tool in Plato’s corpus is most elegantly exposed in Aristophanes’ speech in the Symposium, where, after performing the primordial diaeresis, Apollo 184 comments made before the Eleatic Stranger even spoke and expose his project of modifying – but not totally excising – the meaning of the terms established at the beginning of the dialogue. The words that carry with them connotations of “distinction through” are balanced by terms of mixture and unity (though not outright harmony, which would be too Pythagorean for an Eleatic). This combination extends the system that had been proposed in the Republic and the Theaetetus, but it revises the monological search for the Forms in the Intelligible Place. The development of a dialectical system based on initial synthesis, then diaeresis, followed by revised synthesis is prelude to the Eleatic Stranger’s proposition that some Forms – called the “Greatest Kinds” (me&gista ge&nh), which are Motion, Stasis, Being, Not-Being, and Difference 485 – can be understood to pervade all other things and act either as “bonds enabling others to combine or conversely in some cases responsible for keeping them apart.” 486 But the mode of participation as it figures into dialectic here is expressed using political terminology (and not the other way around, as is the case in the Republic) of communion: 487 uses “some sort of tool (ti toiou~ton o!rganon) as the cobblers use about the shoemaker’s best for smoothing out the wrinkles (Pl. Symp. 190e9-191a3).” Here the tool is employed not simply diacritically, but in order to create an undifferentiated unity from what has been sundered into two. 485 On this subject see Guthrie 1978: 151-4 and Cornford 1935: 273-85. For a good historical narrative of the changes afforded by the Sophist to the Theory of the “Greatest” Forms, see Natorp 2004: 274-9. 486 See Guthrie 1978: 151 and Runciman 1962: 62-3, who is correct to note that after the Phaedrus “[d]ialectic…involves the ascertaining of the nature of the Forms not by the method of hypothesis but by ascertaining their relations to one another.” 487 Cf. Natorp 2004: 277-8. 185 ELEATIC STRANGER: We agree, then, that some Kinds are willing to communicate (koinwnei~n) with one another, and some aren’t; some do it in fewer cases (ta_ me_n e)p’ o)li&gon), and others in more cases (ta_ d’ e)pi_ polla&), and even some all-pervasive do not prevent any from being communicated with all (the rest). So, granted this, we must examine and follow up this argument, not selecting all Forms, lest we be confused in the multitude, but instead those designated the greatest (tw~n megi&stwn legome&nwn [ei)dw~n]), 488 noting first what sort each of them is, and then how far they are capable of communication with one another, in order that – even if we are not able to grasp Being and Not-Being with all clarity – we may not become indigent of an argument concerning them (according as the course admits of the current examination) to see whether it is allowed for us to come off unscathed in declaring that Not-Being as it exists really is a non-entity. 489 The project established at the beginning of the Sophist has taken on new dimensions: the questioning of the Eleatic Stranger’s genos, which is the primary issue of the dialogue 490 and an underlying current throughout the Statesman – as we shall see – is part of a more comprehensive revision of the language for a Participatory Theory of 488 The referent for legome&nwn is not explicitly expressed. It can only refer logically to the Forms listed earlier (ei)dw~n), but the Eleatic Stranger slyly leaves the referent out. This is crucial, since the next time any reference to the Greatest Forms occurs, the Eleatic calls them “me&gista tw~n genw~n” (Pl. Soph. 254d4-5), successfully marking the logical and terminological synthesis of eid1 and gen1. We should not consider, with Cornford 1935: 276, that there is an indifferent usage of these terms (Cf. Pl. Soph. 267d4-32). Rather, this shift in terminology is further reflective of the synthesis between the worlds of Being and Becoming in Plato’s ontology. Cornford 1935: 268-9 assumes, incorrectly, I think, that Plato’s ontological system remained fundamentally the same throughout his career. 489 Pl. Soph. 254b8-d2. 490 Interestingly, the Eleatic Stranger closes the Sophist by declaring that he and Theaetetus have been successful in identifying the “lineage and blood (th~j genea~j te kai_ ai$matoj)” of the true Sophist (he is quoting Iliad Z 211), which is in contradistinction with the genos of the Stranger himself, being the true Philosopher. The irony of the Sophist is that the declaration at the beginning of the dialogue that they need to discover the natures of the Sophist, Statesman, and Philosopher is complicated throughout this dialogue: in this dialogue they investigate the Sophist and discover the Philosopher as well as the Sophist; the Statesman must wait for the sequel. We might question the usual assumption that the Philosopher was a dialogue never intended to be completed by Plato while he was writing the Sophist, since the definition of the Philosopher is implicit throughout the dialogue. Cf. Frede 1996: 149-51. Nevertheless, the introduction of the Statesman (257a1-258b5) suggests that, by the time he began revising even the philosophical theories put forth in the Sophist, he may have reconsidered composing a dialogue about the Philosopher. 186 the Forms explicitly put forth in the Phaedo and criticized in the Parmenides. With this category of genos, we detect what will become part of the apparatus for Aristotelian dialectic, a process adopted and refined from Aristotle’s education in the Academy itself. But what Aristotle and other students of Plato did not apply to their own systems of dialectic is the paradoxical synthesis of political language and philosophical investigation, a trend noted in Pythagorean and Eleatic philosophy before Plato’s birth. It is perhaps surprising, then, that the adoption of genos as the term denoting the sphere of Form Participation (whether positive or negative) does not seem to be derived from Parmenidean thought. Given the influence of Parmenideanism on Plato’s Formal Theory, the innovation of Formal Participation is remarkable. As Guthrie notes, this section of the Sophist successfully refutes Parmenides’ statement that Being is unified and that “to be” (ei}nai) can have only one meaning, since, “[b]y noting the all-pervading nature of Difference Plato has been able to maintain against Parmenides that what is not really is.” 491 The plurality of essences that change, then, marks a significant shift away from the dualism of the Republic. Likewise, the term genos and those words associated with it in Plato’s dialectical schemes show no connection with the extant fragments of Parmenides’ On Nature, where the term genos does not occur and other terms derivative of the gen- root (ge&nesij or ge&nna) show no affiliation whatsoever with the Eleatic Stranger’s use of genos. Evidently, the gen-words in Parmenides’ poem are used more often in concert with notions of 491 Guthrie 1978: 154. Italics original. 187 Becoming and are likened to words relating to death and perishing, but there is little sense of implicit categorical “Being” and no sense that there is even the consideration of whether or not things that are becoming are. 492 To what other Presocratic philosophers might we look to detect etchings of what will become the ontology of Plato in his later dialogues? If we look to the fragments of Empedocles, the mixed philosopher and “Sicilian Muse” who is adopted by Pythagoreans and Eleatics and thought himself both divine and human, we see the traces of genos and the dialectical theory it symbolizes as it appears in Plato’s Sophist and Statesman. In On Nature, Empedocles describes the two complementary forces of Nature: Neikos, who separates things, and Aphrodite, who unifies them: di&pl’ e)re&w: tote_ me_n ga_r e$n hu)ch&qh mo&non ei}nai e)k pleo&nwn, tote_ d’ au} di&efu ple&on’ e)c e(noj ei}nai. doih_ de_ qnhtw~n ge&nesij, doih_ d’ a)poleiyij: th_n me_n ga_r pa&ntwn su&nodoj ti&ktei t’ o)le&kei te, h( de_ pa&lin diafuome&nwn †qrufqei~sa drepth&†. kai_ tau~t’ a)lla&ssonta diampere_j ou)dama_ lh&gei, a!llote me_n filo&thti sunerxo&men’ ei)j e$n a#panta, a!llote d’ au} di&x’ e#kasta foreu&mena nei&koj e!xqei. I’ll speak double: at one time it grew to be one only from many, And at another again it divided to be many from one. There is a double birth for mortal things, and a double departure; For the uniting of all things brings one generation into being And destroys it, and the other is reared and scattered As they are again being divided. All these things never cease their Continual exchange of position, at one time all coming together into 492 For genesis and genna in Parmenides’ poem, see Fragments 8.6, 8.21, and 8.27, in Gallop 1984: 42-3. 188 One through love, at another again being borne away from each other By strife’s repulsion. 493 While the mathematical and dialectical terms are not exact analogues, we must recall that Simplicius quotes these lines in order to demonstrate how Empedocles espoused a system of philosophical distinction and collection. 494 If the point isn’t quite clear, Empedocles reminds us of the unhappy genos of mortals, which, when compared with the genesis of mortals here, suggests stronger ties between categorical essences and Becoming in Empedocles’ physics than in the extant fragments of Parmenides. 495 It may be suggested, then, that Plato’s Empedoclean leanings in a dialogue ostensibly about a “true philosopher” of the “Eleatic Kind” focus on the comparable terms of gen- words which suggest the “place” of Becoming so central to the metaphysics and cosmology of Plato’s dialogues since the Republic. If the search for the genos of the Eleatic Stranger – an investigation into the possibility that things that are become 496 – forms the subtext throughout the Sophist, it can be said with some certainty (as has been emphasized by Christopher Gill) that the Statesman too encompasses an investigation into one particular concept in the 493 Empedocles F 8 Wright = Simplicius in Phys. 157.25. Cf. F 25 Wright ll. 6-10, in which two “types” are distinguished (ge&nnh| te krh&sei te kai_ ei!desin neikeogenne&sthsin). Also see fragments a(ii) 23-30 of the Strasbourg Empedocles. Translation by Wright, modified. 494 Simplicius in Phys. 157.25: “o( de_ )Empedoklh~j to_ e$n kai_ ta_ polla_ ta_ peperasme&na kai_ th_n kata_ peri&odon a)pokata&stasin kai_ th_n kata_ su&gkrisin kai_ dia&krisin ge&nesin kai_ fqora_n ou#twj e)n tw~| prw&tw| tw~n Fusikw~n parade&dwsi.” 495 Empedocles F 114 Wright. 496 This move towards appreciation of the “place of Becoming” might best be analogized with the project of Platonic philosophy, as Gill 1992: 162-3 and 1993 passim argue, which becomes self- consciously revisionist and proceeds as an “expression of a continuing argument” (Gill 1995: 304 n.59). This tendency in Plato’s later dialogues develops most obviously from the Parmenides, where the second half of the dialogue proceeds according to constant revision through dialectic. Whether or not we believe its historical validity, Plato characterizes this rhetorical and philosophical strategy as Eleatic. 189 search for the “political art,” namely “error” (a(ma&rthma). 497 Indeed, as I will suggest, the “error” which becomes the subtextual point of investigation in the Statesman is directly linked to the method of dialectic espoused by the middle dialogues, and the Stranger will offer a revision of dialectic through the thematic consideration of the issue of “error.” 498 The subject is introduced at the beginning of the dialogue, once again, by Theodorus of Cyrene, and it is immediately given a mathematical value, as we have seen for the previous discourses on dialectical method in the Meno, Republic and Theaetetus: SOCRATES: Much is the debt of gratitude (pollh_n xa&rin) I owe you, O Theodorus, for the introduction of Theaetetus and also to the visitor. THEODORUS: It’s likely, Socrates, that you’ll triple the debt you owe once they will have worked over the statesman and philosopher for you. SOCRATES: Yes. But, dear Theodorus, shall we say that we heard this from a master of arithmetic and geometry? THEODORUS: Why not, Socrates? SOCRATES: You set each of the men at equal worth, when, in terms of honor, they differ too much from one another for the proportioning of your art (kata_ th_n a)nalogi&an th_n th~j u(mete&raj te&xnhj). THEODORUS: Well done, by our god Ammon, O Socrates, and justly! How sharp of memory you are, when you reproach me for my error in logistic (peri_ tou_j logismou_j a(ma&rthma)! However, I’ll wait my turn to avenge myself in return. But, Stranger, don’t ever grow tired of indulging us, but continue: whether you select the political man or the philosopher first, once you’ve made your choice explain him to us. 499 497 Gill 1995: 297-301. 498 The issue of “error” will further permeate the political philosophy and constitutionalism expressed in the Statesman, and I will treat this subject at length in Chapter 5. 499 Pl. Plt. 257a3-c2. 190 Theodorus’ mistake, as expressed here, is a preference for geometric proportion over basic logistics: he assumes a ratio of value for the (A) Sophist, (B) Statesman, and (C) Philosopher as A : B : C, when, as Socrates reminds him, one of these is worth more than the others in honor. Theodorus has made the mistake of assuming a quantitatively equal proportion between the Sophist, Statesman, and Philosopher, when their relationship is qualitatively unequal and therefore belongs to the sphere of logistic, which, as we saw in Republic Book VI, distinguishes between the sizes of three fingers which are individual due to their distinguishing characteristics but unified by being part of the body. 500 Once, however, the discourse is turned over to the Stranger again, we note again how his dialectical mode is constituted of a studious investigation into the terms that his interlocutors have been employing. 501 He exploits the terms as well as the philosophical concepts taken for granted by his joking friends in order to propose radical changes to the systems that they employ. In this case, the Eleatic Stranger proposes the definition of the Statesman as the subject for discussion and modifies the tone of the conversation by changing his partner from Theaetetus to Socrates the Younger, who is yet untried in the narrative 500 See Chapter 2. Interestingly, Socrates emphasizes this point in the portion of the Statesman that follows when he appeals to the Participatory Theory of the Forms (Pl. Plt. 257d1-258a6) by demonstrating the formal connections between himself and the younger men: “On the one hand, then, you say that this one (i.e. Theaetetus) resembles me in the nature of his face, but as to the other (Socrates the Younger) the nomenclature which is homonymous and the calling offer some likeness for you as well.” Socrates thereby maintains his position as the paradigm for a Form whence some other empirical elements can take their names (i.e. Socrates the Younger) and others may derive their figures (i.e. Theaetetus). 501 In this way, we can agree with Scodel 1987: 15 that Socrates indeed “is not entirely silent,” since his terms and propositions form the theoretical and terminological apparatus that the Stranger will carefully undermine. On most other counts, I am not convinced by Scodel’s interpretation of the Statesman. 191 of the Platonic dialogues but, as we recall from the Theaetetus, participated in the formal categorization of irrational numbers with Theaetetus. 502 He begins the diaeresis of the Statesman by suggesting that they begin with a division of the sciences, with particular interest in the “political art” (politikh_ te&xnh) – which is analogized with the “political science” (politikh_ e)pisth&mh) 503 – following a model encountered before in Plato’s dialogues. As in the Sophist, the Eleatic Stranger begins his simple diaeresis through a familiar mode: cut and combine. They first divide the sciences according to their practical or non-practical function, a “subjective” or categorical division. 504 This division establishes two lines from which the complete diaeresis of the Statesman’s episteme can be defined: all sciences may be divided into the applied and the theoretical. 505 According to this scheme, the Statesman’s science is theoretical and not applied; this distinction maintains the division we have seen for some time. On the other hand, the cognitive sciences, which include arithmetic and “the other arts that are akin to it” (a)riqmhtikh_ me_n kai& tinej e#terai tau&th| suggenei~j te&xnai), are claimed as the sciences of the Statesman. In an argumentative move that will 502 Later on in the dialogue (Pl. Plt. 266a1-b7), the Stranger jokes with Socrates the Younger about the theory of incommensurables that he and Theaetetus are said to have discovered in the Theaetetus (see above). Here, the squaring of “feet” distinguishes human beings from pigs, in that the squaring of the diagonal of a 1 X 1 X 2 triangle will equal the number of feet for a human (2), whereas a pig is represented by the squaring of the squaring of the diagonal, or 4 feet. This may be seen as a jab at those Pythagoreans who thought that all things were constituted of peculiar numbers. 503 On the politikh_ e)pisth&mh, see Gill 1995 and Gould 1955: 205-6. 504 Taylor 1962: 262 explains: “Plato’s object is to distinguish what are called in the scholastic terminology subjective from what are called quantitative parts. Subjective parts are the constituent sub-classes, or species, each with its characteristic differentia, which constitute a genus; the quantitative parts of an aggregate are the units, or lesser aggregates, from which it can be made up by addition.” Italics original. 505 Pl. Plt. 258e4-7. 192 foreshadow the final confirmation of the Statesman’s knowledge, he is required to know those gen1 that formed Archytas’ of Taras’ educational program as well as how they are related. 506 The Stranger then moves to analogy and synthesis: ELEATIC STRANGER: So, shall we posit the Statesman and the King and the Master and even the Household Manager by calling all these things one, or shall we say that there are as many arts as there are names for them? 507 Worried that this might be too fast for Socrates the Younger, the Eleatic Stranger advances on this issue from another angle: if someone were a private individual skilled in giving counsel to the King, he would possess the Kingly science regardless of whether he was a ruler (a!rxwn) or not. 508 The response that follows is critical to understanding the Eleatic’s initial criticisms of Socrates’ dialectic: ELEATIC STRANGER: So, then, concerning what we were just considering, it’s clear that a single science exists for all these things: but whether someone calls the art kingly or political or of household management, we shall not dispute with him at all. 509 The combination and interchangeability of these particular names for a single episteme, a point that Aristotle vehemently criticized in the Politics, underlies this initial diaeresis of the Statesman. 510 It is remarkable that Aristotle would assume that this point represents Platonic doctrine, since the Stranger concludes that this 506 See Chapter 2. 507 Pl. Plt. 258e8-11. 508 Pl. Plt. 259a6-b5. 509 Pl. Plt. 259c1-4. 510 Aristotle actually begins his Politics with this criticism of Plato. See Arist. Pol. 1252a7-24. Aristotle himself assumes that a mistake has occurred in the dialectical method (Pol. 1252a19-23): “Just as in all other circumstances it is necessary to distinguish the composite as far as its uncompounded things (for these are the smallest parts of the whole), so too with the city-state; by examining the things of which it is mixed together, we will see better concerning these things in how they differ from one another…” Cf. Pol. 1274b39ff. 193 diaeresis has been conducted in error. 511 Whether Aristotle thought it was Plato’s or Socrates’, or someone else’s philosophical doctrine, his criticism is directed against the dialectical method employed, precisely what the Stranger aims to exemplify in the process of this primary diaeresis. Indeed, just as we saw in the Parmenides before, the authoritative interlocutor – in this case, the Eleatic Stranger – expresses a new or underemphasized aspect of dialectical theory only in order to raise objections to it. From the diaeresis of the Statesman’s science in the first portion of the dialogue, Plato advances his dialectical theory by exposing two different Forms 512 of cutting, introducing a new term in me&roj: SOCRATES THE YOUNGER: So then what are you saying we did incorrectly in our recent division? ELEATIC STRANGER: This: if someone should attempt to divide the human type in two, he would make the division just as the many of those who live here do. They distinguish the Greek Kind (ge&noj) as one apart from the others, but as for all the other Kinds together, while they are inexperienced and unmixed and discordant with one another (a)pei&roij ou}si kai_ a)mei&ktoij kai_ a)sumfw&noij), they call this (Kind) with a single term (mia~| klh&sei): Barbaric. Because there is one term and Kind, they assume that it [the Barbaric] is unified. Or: if someone, in turn, were to think that he was dividing Number according to two Forms (ei!dh) because he had cut 10,000 from all numbers, set it apart as a single Form, and then posited one name for all that remained, again he would approve of the notion that – since there was one term – what was different and separate from the 10,000 had become a unified Kind (ge&noj e)kei&nou xwri&j e#teron e$n gi&gnesqai). Surely, it would be better and more in accordance with the Forms (ma~llon kat’ ei!dh) if someone were to divide in two by cutting Number into Even and Odd, and in turn cutting the Kind of 511 It may be possible that Aristotle did not assume these ideas to be specifically Plato’s, and this notion casts some doubt on the hypothesis that Plato was communicating doctrine taught at the Academy here. Indeed, Aristotle never names Plato in his criticism of the Eleatic Stranger’s ideas. 512 Interestingly, he calls the categories of numerical division ei!dh but analogizes them with the ge&nh of ethnic types. 194 human beings into male and female. Someone should separate out (a)posxi&zoi) Lydians or Phrygians or some others by drawing them up in contradistinction with all the rest only whenever he is at a loss (a)poroi~) to discover each of the separate groups both in terms of Kind and Part (ge&noj a#ma kai_ me&roj). 513 When introducing a new subordinate term – the Part (me&roj) – the Eleatic Stranger complains that the mistake he and Socrates the Younger have been committing has to do with a failure to distinguish between two kinds of division: the first kind of diaeresis through kind, which should lead to the discovery of gen1, fails to attend to whether or not its constituents mix with one another or not, as in the case of Barbaric peoples; 514 the other type of diaeresis through numbers, which leads to eid1, is mistaken for its neglect of proper measure and fails to objectify size. They propose to investigate how to employ both types of diaeresis in the passages that follow. The first type of diaeresis – in which the term Barbaric is used as a blanket term for all non-Greeks – does not account for distinction within the Barbaric genos and assumes that all non-Greeks are a unified and mixed Kind, while it is apparent that some mix and others do not intragenously. The Stranger locates the error in diaeresis with Socrates the Younger’s positing of two Kinds of herding, namely the herding of humans and the herding of “all the others together,” which he designated 513 Pl. Plt. 262c8-263a1. 514 Kevin van Bladel, in comments written on this passage, raises a significant challenge to my interpretation: “The criticism is not about mixing – it has to do with the ‘order’ or ‘level’ at which one may make philosophically meaningful distinctions.” I disagree with Professor van Bladel primarily because this passage demonstrates an interest in the application of dialectic to political communities, and vice versa. The problems here involve the application of dialectical method (that is philosophically meaningful) to understanding the differences between Greeks and Barbarians, and Plato does not demonstrate as comprehensive or systematic a sense of how to make these applications – the Sophist and Statesman, after all, are primarily experimental dialogues – function as logically as his successor Aristotle, who owed much to Plato’s innovations, did. 195 as a unified Kind called “wild.” This error of division occurs as a consequence of a misapplication of categorical divides, since they defined according to genos instead of meros and consequently confused the registers of formal concept and particular attribute: for mer1, inasmuch as they are subdivisions of gen1, should not be distinguished according to their capacity for participation or communion with one another. 515 This kind of error in diaeresis, explains the Stranger, causes them to move “more slowly” despite its haste, as the proverb goes. 516 What they should do, he suggests implicitly, is to deal with cuts at the subdivided level. Indeed, the analysis of division according to gen1 is almost silently dropped in favor of the analysis of division according to mer1. 517 The other error in division, which is equally significant for division according to Part, is notable for its lack of attention to measure. But a proper kind of division through Part, explains the Stranger, will feature a synthesis through alternation of diaeresis through subjective and quantitative sub-categories: ELEATIC STRANGER: As to the art of rearing herds that go on foot, we must bring it to light by cutting it in two, just like an even number (a!rtion a)riqmo&n). SOCRATES THE YOUNGER: That’s clear. ELEATIC STRANGER: But actually, the Part which our argument has brought up (e)f’ o# ge me&roj w#rmhken h(mi~n o( lo&goj) is the very thing for which two certain routes drawn up for us to examine have appeared: [1] the faster route, which distinguishes a small part from a great one (pro_j me&ga me&roj smikro_n diairoume&nhn), and [2] the other one, which conforms more closely to the rule of which we were 515 Pl. Plt. 263c3-d1 and e7-10. 516 Pl. Plt. 264a8-b5. 517 The Eleatic Stranger and Socrates the Younger attempt to distinguish (and mark out the rules of distinction) by mer1 – and not by gen1 – from 264d5-265d4. 196 just speaking, namely that we must divide along the middle as much as possible (o#ti dei~ mesotomei~n w(j ma&lista), although it is a longer route. So it is possible to advance along whichever of the two we want. SOCRATES THE YOUNGER: But why? Can’t we use both? ELEATIC STRANGER: My dear boy, both! Indeed, it is clear that we can do them in order (e)n me&rei)! SOCRATES THE YOUNGER: Well, then, I choose doing both in order. ELEATIC STRANGER: It will be easy, since not much is left to the present discussion. But your injunction would have been difficult from the beginning or the half-way point of our journey (kat’ a)rxa_j mh_n kai_ mesou~sin a#ma th~j porei&aj). As it is, however, since it seems appropriate to proceed in this way, let’s go first on the longer route. For we shall proceed more easily due to our fresh strength, but pay attention to the division. 518 The first kind of subdivision [1] – by means of measure (i.e. through the Great and the Small) – corresponds with logistic as it has been defined since the Republic; it is thus a subjective investigation that relies upon the relative size of things in comparison with one another, and it perhaps finds its roots in Archytas. 519 The second kind [2] – in quantitative halves cut down the middle of the even – is an explicitly Pythagorean praxis that is assumed among both the acousmatic and mathematical schools as well: it is quantitative in the sense that a standard may be applied to measure it in regulated parts. 520 We may recall yet again Aristotle’s 518 Pl. Plt. 264e12-265b6. 519 We might, then, feel less worried about the place of logistic in Plato’s dialectical theory at the head of his Archytan educational system than Sayre 2006: 168-70 is. Logistic in the Republic is a basic and primary mathema, as it is in Archytas Fragment 3 Huffman; indeed, the correlation between the Great and the Small and Limitless (to_ a!peiron) found in Plato’s post-Statesman dialectical theory might be best understood as a revision on Plato’s part of the place of Pythagoreanism in his philosophical pragmateia. See Chapter 5. 520 Brumbaugh 1942: 13 describes these two kinds of subdivision as “normative” [1] and “descriptive” [2] measure: “Descriptive measure [2] compares contrary qualities with each other, but provides no norms; thus a metric artist may decide that one body is “light” or “heavy” relative to another, but never that it is “too light” or “too heavy.” A productive artist, however, must compare his products to 197 declaration of the correspondences between Plato’s and the Pythagoreans’ philosophical pragmateia in Book A of the Metaphysics, in a passage that I mentioned at the beginning of Chapter 2: And since the Forms are the causes of other things, [Plato] believed that their elements were the elements of all things in existence. So, then, [he believed that] the Great and the Small – as first principles – are matter (u#lhn to_ me&ga kai_ to_ mikro_n ei}nai a)rxa&j), just as the One is Being; for [he believed that] numbers exist from them [the Great and the Small] according to participation in the One (kata_ me&qecin tou~ e(no_j). In fact, by saying that the One is Being, and not something which is called “unity,” and that numbers are likewise the causes of Being in other things, his argument comes very close to that of the Pythagoreans. 521 The Eleatic Stranger’s own emphasis on the problem of diaeresis over time is highlighted in the preceding passage of the Statesman. He suggests that they were unable to proceed along these dialectical lines at the beginning or at the middle of their investigations, when they undertook what became argument at hand on this day which is Plato’s survey of his own theories of dialectic. But whereas Aristotle believed that the first principles for Plato were the Great and the Small, and that numbers were derived from those first principles, it seems that Aristotle has reversed the order produced by the Eleatic Stranger, who suggests that they begin with quantitative distinctions (corresponding with objective, geometrical measure) before proceeding in order (e)n me&rei) to the subjective analysis structured according to the relative principles of the Great and the Small, which seems to refer in Plato’s some normative standard [2], and must think of them as wholes composed of parts related to a proper function and total structure. The use of norms separates measure in the productive and metric arts, but descriptive and normative measure are not mutually exclusive.” Cf. Brumbaugh 1942: 36-42. 521 Arist. Metaph. 987b18-25. 198 philosophy to logistic. Why would Aristotle reverse the course of dialectical investigation advanced by the Eleatic Stranger and Socrates the Younger? The answer, I think, lies in the now-familiar character of Plato’s dialogues that propose revised theories of dialectic. The Eleatic does proceed to perform diaereseis according to quantitative measures first, then to subjective comparisons that accord to the Great and the Small, 522 but he concludes – despite introducing a new order of dialectical process that places logistic ordinally after geometry 523 – that they have failed again in their attempts to distinguish well in their comprehensive definition of the “political science”: ELEATIC STRANGER: Well, Socrates, is it just as you say that we’ve dealt with the affair (pepragme&non) simply? SOCRATES THE YOUNGER: What do you mean? ELEATIC STRANGER: That we’ve spoken sufficiently in every way about what we set out to investigate? Or has our investigation neglected – and in a significant way – the argument (lo&gon) which, though it has been advanced somehow, has nevertheless in no way come to its final completion (ou) mh_n panta&pasi& ge tele&wj a)peirga&sqai)? 524 The emphasis on completion reveals the failure of division as a means to the rational investigation in the philosophical pragmateia (note the emphasis on pepragme&non), since it does not complete the definition sufficiently. 525 Despite the multiple kinds of 522 Quantitative measurement through bifurcation: Pl. Plt. 265b7-266d11; subjective division through relative comparison: Pl. Plt. 266d12-267a7. 523 In this way, the argument of Lane 1998, which contends that the Statesman’s mastery of kairos directly influences his capacity as a philosopher and a statesman, corresponds with my conclusions about the importance of temporality in the conceptualization of things according to order (e)n me&rei). On timing and opportunity in Plato’s later dialectical theories, see Chapter 5. 524 Pl. Plt. 267c5-d2. I translate logos here as “argument,” but it could easily also mean “ratio.” 525 Lane 1998: 47 adeptly draws up a comparison between the prescriptive passages of the Sophist and Statesman that declare how examples can aid in defining a subject. She draws up a remarkable table 199 division – categorically through eid1, gen1, and mer1, and pragmatically through quantitative and subjective means – the philosopher’s task remains incomplete. The Eleatic Stranger tells Socrates that they have not yet distinguished between the Statesman and his rivals, who claim to share the herding of people along with him (e.g. doctors, farmers). 526 In order to complete the argument at hand, the Eleatic Stranger proposes that they import a paradeigma (example) in the form of a mythos (story). But before they undertake the “actual” division of the political episteme, the Eleatic Stranger revises the dialectical mode that they had used before but in an erroneous fashion in this “prescriptive” passage: 527 ELEATIC STRANGER: Well then, we must set out again from another beginning (e)c a!llhj a)rxh~j) along some other road. SOCRATES THE YOUNGER: Which one? ELEATIC STRANGER: Basically by mixing in play (Sxedo_n that lays out some of the crucial extensions of the Sophist’s diaeretic mode and requirements for exempla: “Each dialogue enjoins that the example chosen must be: Sophist (218e2-3) Statesman (279a7-b1) (a) minor (smikron) (a) minor (smikrotaton) (b) familiar (eugnCston) (b) ready-to-hand (prokheiron) (c) have logos (c) [take part (meros) of it] (d) share kinship (be suggen1) (d) share activity (pragmateian) with telos of inquiry (221d9) with telos of inquiry (279a7-8)” The most notable differences here are in (c), where the application of examples is required to have logos in the Sophist and the meaning must be contextualized with its mathematical context (he literally says “having a logos no less than any of the greater things”), and in (d), where examples are expected in the Statesman to move beyond mere kinship relations and achieve a conclusive teleological pragmateia. It is important to remember, though that logos often meant mathematical ratio during the 4 th Century BCE . 526 Pl. Plt. 268c5-11. The metaphor, as we saw in the Republic: they will divide in order to advance upward to the “pinnacle” (e)p’ a!kron) through division, a notion that extends the Republic’s diaeretic teleology and recalls both Plato’s and Aristotle’s criticisms of the Pythagoreans. 527 Lane 1998: 14 clarifies the difference between “actual” divisions and “prescriptive” passages: “The ‘actual divisions’ are strictly confined to forms of expertise (technai or epist1mai), the persons who exercise them of the objects on which they do so…None of the prescriptive passages from the Stranger’s dialogues or Socrates’ say anything about example.” 200 paidia_n e)gkerasame&nouj). We must apply a long part of a great story (suxnw|~ ga_r me&rei dei~ mega&lou mu&qou prosxrh&sasqai), and what remains thereby, just as we did before, we must divide part by part until we reach the pinnacle of our investigation. 528 Here, the Eleatic Stranger suggests that division must be preceded by mixing in (note the verbal echo of the Empedoclean kera&nnumi) 529 a part of a very long mythos. So they revise their approach to defining the Statesman by introducing the story of the Myths of the Rule of Kronos, the Reversal of the Cosmos, and the Rule of Zeus, which is subsumed under a single title “On the Unwinding of the Universe.” 530 As I will show, this paradeigmatic story acts as a tertium quid that allows for the establishment of similarities and differences between the quantitative and subjective modes of division. Furthermore, it functions both to highlight the significance of time to dialectical procedure and to problematize the teleological conclusion that they have announced is lacking in their pragmateia. 531 The mythos produces a cycle of ages, within which the human genos grows old until the end of the axis of the cosmos is reached under the Rule of Kronos, and then they grow younger to die once Kronos has removed his guiding hand from the system. According to the Stranger, the god accompanied the movement of the 528 Pl. Plt. 268d5-e2. 529 See Empedocles F 47 Wright. Cf. e)ke&krato at Pl. Plt. 272a6-7 and e)pegkerannu&menoj at Pl. Plt. 273d2-3. 530 This seems to be the title allotted by the Stranger himself to this myth (Pl. Plt. 286b9). See Ferrari 1995. Generally, for an interpretation of this myth that comes to different conclusions that are not incommensurable with my own, see Lane 1998: 99-136. For these three periods of rule, see Brisson 1995: 358-60. 531 Lane 1998: 85-6, following Cherniss 1962, sees example as what “fills the vacuum of likeness” when likeness is considered as a ubiquitous and slippery line. Morgan 2000: 253-61 also considers the Statesman’s mythos as primarily methodological, although she does not expand beyond an interpretation of the story that subjectively interrogates the Greatness and Smallness of the story. 201 universe at one time, turning the circuits until the appointed measure of time, and then he let go, whereupon the circuits of the cosmos (which are synchronized with the circuits of time) unwound in the other direction of their own volition in the second motion of the universe. 532 These circuits of time and space resemble the “whirl” of Empedoclean cosmology, a metaphor that Empedocles applies both to things under the influence of Neikos (or division) and of Aphrodite (or mixing). 533 Timing and sequence are crucial in Empedocles’ account of the cosmology of the universe: first, as it seems, things are held together without motion (a)kinhsi&an) 534 in the Sphere, which is “equal to itself (i}soj e)stin au(tw~|),” 535 by “the close obscurity of Harmony (a(rmoni&hj pukinw~| krufw~|). 536 Then, Strife motivates (ki&nhsij) the limbs of elements within the Sphere again (pa&lin), 537 and, once the elements of the universe enter the “middle whirl” of Aphrodite, Empedocles claims that “in her then all these unite to be only One.” 538 Empedocles distinguishes here between those who enter into the whirl of Aphrodite and those whom “Strife still restrain[s] above, 532 Pl. Plt. 269c4-d3. 533 See Dillon 1996: 365 with n. 4 and 373, who asks the pointed question: “Did [the cyclical process] begin a Kronian cycle or a Zeusian cycle? Or did it begin at all?” Italics mine. 534 At least according to Eudemus. See Empedocles F 21 Wright = Simplicius in Phys. 1183.24. 535 So Empedocles F 22 Wright = Hippolytus Ref. VII. 29. 13. 536 Empedocles F 21 Wright = Simplicius in Phys. 1183.24. 537 According to Simplicius in Phys. 1184.2 = Empedocles F 24 Wright. The presence of the word “again” signals the cyclical motion of the spherical cosmos in Empedocles’ cosmology. 538 Empedocles F 47 Wright = Simplicius in Cael. 52.8.30. The text is: …e)pei_ nei~koj me_n e)ne&rtaton i#keto be&nqoj di&nhj, e)n de_ me&sh| filo&thj strofa&liggi ge&nhtai, e)n th|~ dh_ ta&de pa&nta sune&rxetai e$n mo&non ei}nai… One may note the semantic motion from Becoming (ge&nhtai) to Collection (sune&rxetai) and finally Being (ei}nai). 202 staying unmixed, alternating with those which [are] combining.” 539 The result, we are told, is that: ai}ya de_ qnh&t’ e)fu&onto, ta_ pri_n ma&qon a)qanat’ ei}nai, zwra& te pri_n ke&krhto, dialla&canta keleu&qouj. tw~n de& te misgome&nwn xei~t’ e!qnea muri&a qnhtw~n, pantoi&aij i)de&h|sin a)rhro&ta, qau~ma i)de&sqai. 540 Immediately, what had learned previously to be immortal Grew mortal, and what had formerly been unmixed were mixed, Alternating their paths. When they were mixed, thousands of Tribes of mortals poured forth, fitted with figures 541 of all sorts, A marvel to see. The Eleatic Stranger exposes the Empedocleanism of his mythos by appealing to the reversals of the cosmos in accordance with the mortality or immortality of things, corresponding respectively with the unmixed and the mixed. Indeed, his argument turns particularly “Sicilian” when he mentions the “condition of ancient disjunction” (to_ th~j palaia~j a)narmosti&aj pa&qoj) which “prevails even more and more until, when time has reached its end, the world produces little that is good, mixing up many combinations of contraries (pollh_n de_ th_n tw~n kra~sin e)pegkerannu&menoj), and so comes into the danger of its own perishing with all its contents.” 542 Then, God, who had previously abandoned the cosmos after it had reached the end of its first cycle, returns to the helm and “puts it into order and completes it as immortal 539 It is clear that Aphrodite possess the center of the eddy, but the metaphor is also applied to the spin-offs (puknh~isin di&nhsin) that Neikos causes. See the Strasbourg Empedocles, ll. a(ii) 1-7 and 18-22. 540 Empedocles F 47 Wright = Simplicius in Cael. 52.8.30. 541 On this use of the term “figure” in Empedocles’ and Philolaus’ cosmologies, see Chapter 1. 542 Pl. Plt. 273c7-d3. 203 and unaging” (kosmei~ te kai_ e)panorqw~n a)qa&naton au)to_n kai_ a)gh&rwn a)perga&zetai). 543 Such a cycle, as explained here and in reference to the Eleatic Stranger’s dissatisfaction with his pragmateia and its condition of being incomplete, reflects the methodological praxis that dialectic entails. Indeed, following the story’s telling, the Eleatic Stranger and Socrates the Younger return to quantitative division in their attempts to fashion a new definition – given the paradeigmatic function of the story as a tertium quid – of the political art. 544 The appeal to Empedocles’ cosmology, in which Strife quickens and divides, then Aphrodite unites, and then Strife again divides, impresses the reader with the cyclicality of dialectic and acknowledges the challenge to attain any origin whence and whither the investigation can apply itself. 545 The goal, of course, is total comprehension of the pragmateia by means of comparison with the paradeigmatic tertium quid. 546 Cyclicality is therefore reflected in the continued methodological shifting from synthesis to diaeresis as the Stranger and Socrates the Younger attempt to perfect the practice of dialectic. Here we may see the error, which is not so much an error, in Aristotle’s presentation of Platonic 543 Pl. Plt. 273e3-4. Note the repetition of the verb a)perga&zomai here and also at 273a4. 544 Pl. Plt. 274e4-277a2. On paradeigmata and their place in Plato’s corpus, see Sayre 2006: 73-91. I agree generally with his interpretation of the shifting signification of paradeigma, but with two reservations: (1) I am not convinced that paradigms replace combination (or, as I deem it in this Empedoclean context, synthesis), and (2) I regret that Sayre has not considered fully the place of paradeigmata in response to the Third Man Argument in Plato’s Parmenides. At any rate, this topic could occupy a whole dissertation in itself. 545 The Statesman (273a1-4) is explicit about the confusion of the beginning and end (a)rxh~j te kai_ teleuth~j e)nanti&an o(rmh_n o(rmhqei&j) at the points of temporal juncture in the cosmos, an echo (as Skemp 1952: 151 reminds us) of Heraclitus’ (F 103 Diels) belief that “beginning and limit come together at the circumference of a circle (cuno_n ga_r a)rxh_ kai_ pe&raj e)pi_ ku&klou periferei&aj).” 546 Pl. Plt. 279a. We should note the Pythagoreanizing tendancy on Plato’s part here, wherein the third term deals with pragmatics (on which, see Chapter 1). 204 diaeretic method: the original point of departure in an argument, whether it be division or synthesis, is difficult to know, and we can only proceed in dialectic through the alternation (e)n me&rei) of separation and combination, and vice versa. But just as they think that they have succeeded in composing a logos of the political art with the aid of the story – and thus in communicating the sheer cyclicality of the dialectical method – the Eleatic Stranger criticizes their conclusions yet again. He complains that they have been mistaken in their application of the story because of their zeal to embellish things against propriety by adding too many things and losing control of the size of the embellishment. 547 He complains that they were mistaken when they: ...tw|~ basilei~ nomi&santej pre&pein mega&la paradei&gmata poiei~sqai, qaumasto_n o!gkon a)ra&menoi tou~ mu&qou, mei&zoni tou~ de&ontoj h)nagaka&sqhmen au)tou~ me&rei prosxrh&sasqai: dio_ makrote&ran th_n a)po&deicin pepoih&kamen kai_ pa&ntwj tw|~ mu&qw| te&loj ou)k e)pe&qemen, a)ll’ a)texnw~j o( lo&goj h(mi~n w#sper zw~|on th_n e!cwqen me_n perigrafh_n e!oiken i(kanw~j e!xein, th_n de_ oi{on toi~j farma&koij kai_ th|~ sugkra&sei tw~n xrwma&twn e)na&rgeian ou)k a)peilhfe&nai pw. grafh~j de_ kai_ sumpa&shj xeirourgi&aj le&cei kai_ lo&gw| dhlou~n pa~n zw|~on ma~llon pre&pei toi~j duname&noij e#pesqai: toi~j d’ a!lloij dia_ xeirourgiw~n. 548 …considered that the application of great examples to the King was appropriate, and by raising up an astounding mass of a story, we forced ourselves to make use of a greater Part than was necessary. Therefore, the demonstration we made was longer and we have in every way failed to achieve a completion to the story, but – speaking simply - our logos, just like a portrait, seems to be sufficient in terms of the outside line, but it has not yet achieved clarity in its “paints” and the “mixture of colors,” as it were. But it is more appropriate to demonstrate the whole portrait in word and logos than through any 547 Pl. Plt. 277a6-b1. 548 Pl. Plt. 277b3-c6. 205 hand-sketched drawing, that is, for those who are capable of following it. But for those who are not capable it is appropriate through hand-sketched things. Despite the difficulty in making sense of this passage (which occurs because of the ambiguity of zw~|on, which means both “living thing” and “portrait” here), it is apparent that the Eleatic is criticizing their use of the story because of its combination of being disproportionately great and incapable of completing the picture: to follow the metaphor, the story fails to convince as a living paradeigma of its object of imitation because it lacks the “paints” and the “mixture of colors.” It has succeeded, in a sense, in fulfilling its purpose with a view to distinguishing the Statesman from others (the distinguishing line, which marks the barrier between self and other, is sufficient), but it has not convincingly provided the clear synthesis (sugkra&sei) that is necessary for a successful example. They have failed in some way to create a suitable tertium quid. Socrates the Younger is confused: he asks why their mythos has failed. The Eleatic Stranger responds with a comment that extends the problematics of the Third Man argument proposed in the Parmenides. The problem with the too-great paradeigma of the story, he claims, can only be illustrated through a smaller paradeigma to be taken from the Eleatic Stranger’s linguistic theories. 549 Specifically, he suggests that children can learn syllables by positing a third syllable – here metaphorized as a paradeigma 550 – that establishes similarity and difference 549 Also see Sayre 2006: 81-85. 550 Pl. Plt. 278b4-5: “paradei&gmata ou#tw gigno&mena…” 206 for the syllable under examination. The paradigm in this case marks the difference between previously-learned syllables in terms of a particular element. Through the breakdown of the individual elements of the syllables, resulting from that process of comparison and contrast, the child can learn the difference between the elements of words and, microcosmically speaking, the elements of the universe. 551 Methodologically, the application of another tertium quid to the previous tertium quid in order to establish difference and similarity results in a remarkable paradox: things can be compared to one another through the consequent paradeigma, but each new comparison and contrast between two elements – possible only through an exemplary norm – begets another tertium quid, and we are left with a resultant perpetuation of the cycle of dialectic, and the argument cannot achieve its proper telos. Indeed, it will take the introduction of a new term – the measured (to_ me&trion) – to establish the boundaries and facilitate the proper coloring of the tertium quid. But we shall have to wait to examine this methodological proposition, and its Pythagorean links, until Chapter 5. In conclusion, Plato’s Parmenides, Theaetetus, Sophist and Statesman reveal that theories of dialectic and the Forms went hand in hand in the development of Plato’s philosophy, and as he made modifications and extensions to his dialectical scheme in the Theaetetus and Parmenides, so too the composition of the Forms underwent metamorphoses. Such shifts prompted Plato to problematize the sharp distinctions between Being and Becoming, as espoused by the Republic, in those 551 Pl. Plt. 277e2-278e2. 207 works that followed his second visit to Taras in 367 BCE. Left with more questions than answers at the close of the Parmenides, Plato in his subsequent dialogues – the Sophist and the Statesman – revised the theoretical and functional models for dialectic by investigating the possibility of shared connections (in gen1) and diaeretic distinction (by means of mer1) in the philosophical investigation of the Forms. Finally, the emphasis on diaeresis and synthesis underwent a critical reexamination in the first two-thirds of the Statesman, where the Eleatic Stranger problematized the very foundations of scientific investigation by challenging the archaeology of dialectic, inviting the reader and Socrates the Younger to posit cyclicality as the state of the universe and challenging the assumption of first principles in the paradeigmatic Myth of the Unwinding of the Universe. It remains to see how Plato was able to resolve this programmatic aporia placed at the peak of his career, a subject we will resume in Chapter 5 with the close of the Statesman and the return of Socrates in the Philebus. 208 _______________________________________ CHAPTER 4: MIXING THE CONSTITUTIONS: SOUTHERN ITALIAN LAWGIVERS AND PLATO’S RADICAL CITIES _______________________________________ ‘There are, as it were, two mother-constitutions, from which someone, if he were to say so, would say correctly that the others are derived: one is rightly called monarchy, and the other, in turn, is democracy. The former Kind is represented in the extreme by the Persians, and the latter by us [the Athenians]. Nearly all the others, as I have said, are varieties of these. It is especially necessary that one partake of both of these if freedom and friendship are to be combined with intelligence.’ – The Athenian Stranger (Plato, Laws, 693d2-e1) As we discovered in Chapter 1, the progenitor of the mathematical school of Pythagoreanism, Hippasus of Metapontion, appears both to have espoused philosophical propositions that fused traditional Pythagorean and Milesian first principles, demarcating a space for sciences – including political science – that were particularly “mathematical,” and to have composed a Constitution of the Laconians in five books. The nature of “mathematical” sciences and its relation to Laconian or Spartan constitutionalism as it had been developed by the mid- 5 th Century BCE has yet to be determined, and it will occupy the first half of Chapter 4 and portions of Chapter 6. I will juxtapose what we can construct of the civic legislation, administration and design of those Pythagorean city-states that were politically significant in Southern Italy from the mid-5 th Century BCE until the Peloponnesian War (Rhegion, Epizephyrian Locri, Croton, Sybaris, Thurii, Heraclea Lucania, and Metapontion) with three politico-philosophical treatises that can be historically located within this period, namely the Prooimion to the Laws of Zaleucus, the 209 Prooimion to the Laws of Charondas, and the On Polity of Hippodamus, all of which proffer various forms of mixed constitutions that point to the joint influence of Doric political ideals and Pythagorean political structures. This marriage of Spartan and Pythagorean is extremely important for understanding the various forms that Pythagorean politics could have taken for Plato in the following century, when the archaic Italian mixed constitution provided Plato with paradigms for his political philosophy. Once I have established the peculiar historical nature of the design and administration of Pythagorean city-states (those governed according to both acousmatic and mathematical philosophical precepts) in the first half of this chapter, I will compare the ideal and applied formulation of these polities with the ideal political structures described in Plato’s Republic, Timaeus, and Critias, each of which provides proleptic paradigms for Plato’s second-best polity as expressed in the Epistles and Laws. These late texts, and their respective political systems, will be discussed in Chapter 6, following a concluding investigation into the elements of the Platonic “political art” as defined in tandem with late dialectic in Chapter 5. Pythagorean political philosophy, naturally, begins with Pythagoras himself. Both Iamblichus and Diogenes Laertius preserve a story about Pythagoras in which, following his political self-exile from the tyrant Polycrates in Samos, 552 he arrived on the shores near Croton and, after a few days, began to educate the youth of the city: A few days later, [Pythagoras] entered the gymnasium. When the youths crowded about him, it is related that he gave them talks in which he encouraged them to have esteem for their elders. He 552 Aristoxenus F 16 Wehrli = Porphyry De vita Pythag. 9. 210 demonstrated that in the cosmos and in life, cities and nature, what precedes in time is more honorable than what follows: for example, the sun’s rising is more honorable than its setting, the dawn more than the evening, the beginning more than the end, birth more than death. Similarly, natives are more to be honored than foreigners, and in like manner, founders of cities and leaders of colonies. And universally, the gods are more honorable than daimones, and the latter more than demigods, and heroes more than humans. 553 Iamblichus’ story about the first teachings of Pythagoras sows the seeds for what would become an insurmountable stumbling block for political theorists who would follow in his footsteps. Pythagoras praises the beginning (a)rxh&) as being “more honorable” than the “end” (teleuth&) and “birth” (or more precisely, “coming into existence,” ge&nesij) than “death” (fqora&). That the beginning or first principle of something is “more honorable” (ma~llon timw&menon), which is to say superior in a hierarchical sense, than its end – especially when analogized with terms of life and death – is apparently not problematic for any humanistic doctrine, despite the possible threat to personal autonomy imbued in the polyseme a)rxh&, which means both “beginning” and “rule.” And it is to the issue of “rule” that Pythagoras – if we are willing to grant these exempla as legitimately derived from speeches of Pythagoras 554 and preserved perhaps by the Crotonians themselves 555 – directs his 553 Iambl. VP. 37. Translation by Dillon and Hershbell. If we compare D.L. 8. 22-3, it becomes apparent that both Iamblichus and Diogenes derive the story from the same source, although that source is probably neither Hieronymous nor Aristippus (note the change to le&getai at D.L. 8. 22). 554 On the legitimacy of Pythagoras’ speeches in Iamblichus’ De Vita Pythagorica, see De Vogel 1966. 555 Alexander (Polyhistor), to whom Diogenes Laertius refers in the passage that directly succeeds this discussion in his Life of Pythagoras (D.L. 8. 24) , is known to have consulted the Pythagorean Registers (e_n Puqagorikoi~j u(pomnh&masin) in trying to compile the doctrines of Pythagoras. In Chapter 1, we discussed Timaeus of Tauromenion, who also (Iambl. VP. 262) seems to have learned 211 speech, as he establishes a basic hierarchy anchored by the terms “elders” (tou_j presbute&rouj) and “what precedes in time” (to_ prohgou&menon tw~| xro&nw|). This passage illustrates the process of analogy wherein correlations are established between ontology and politics: Pythagoras draws an analogy between those things that lead and those that follow – imagine the rising of the sun as a precedent for its setting – with natives (au)to&xqonaj) and immigrants (e)phlu&dwn) as the foremost elements in the community, followed by founders of cities and initiators of colonies. 556 It is apparently the case, then, that Pythagoras exhorts the Crotonian youth to compare a)rxai& with the original human elements of a community, a proposition that would come to be charged with undertones of aristocratic ideals by Plato. 557 Politically speaking, Pythagoras, who himself was not a Crotoniate, was distancing himself from the project of political rule that he would subsequently undertake in the city of Croton. Since he was not tied to the Italian soil by nature, Pythagoras was able to mitigate the fact that his appearance in Croton would drastically change the system of laws in the city – as well as the political atmosphere in Southern Italy – by about early Pythagorean history in the registers of the Crotoniates. Are these “registers” one and the same? 556 Compare Pl. Mex. 237b2 ff., where Socrates claims: “As concerns their nobility of birth (eu)genei&a), it is first supposed by them that the origin (ge&nesij) of their ancestors was not immigrant (e)phlu&j), nor did the origin reveal them as children who were visitors in this land from another group of people come there, but natives who, in reality, live and dwell in their fatherland, not reared by a stepmother as others, but by the mother-land in which they lived…” 557 Pl. Mex. 238d1. Socrates calls autochthonous Athens an “aristocracy backed by popular approval” (met’ eu)doci&aj plh&qouj a)ristkrati&a) in contrast with other polities (oligarchies and tyrranies) which are “heterogeneous” (a)nw&maloi) because of their anomalous compositions of disparate peoples. 212 appearing in the guise of a traveling foreign practitioner of wisdom. The ideological structure of the government he proposes to the Crotonians, ostensibly aristocratic, is marked by the absence of Pythagoras as a ruler or governor of any sort, and instead he acts as an external force – nearly a deus ex machina – whose presence establishes new laws and institutions for a community lacking motivation for aristocratic ethics. 558 Pythagoras himself was allowed to give advice to the Thousand, the council of male citizens at Croton, but the city also extended him the right to summon the young men in assembly at the Temple of Pythian Apollo and women at the Temple of Hera. 559 From there, so Iamblichus’ source continues, he freed the poleis that were “enslaved to one another,” namely Croton, Sybaris, Catania, Rhegion, Himera, Acragas, Tauromenion, “and some others.” 560 What these “others” were cannot be established for certain, but we cannot assume that he was referring to Locri, Metapontion, or Taras, which do not show signs of welcoming Pythagoras’ influence over Southern Italy near the last decade of the 6 th Century or the first decade of the 5 th Century BCE. Of utmost significance, however, is the fact that students of Pythagoras go on to influence the communities of their upbringing or those nearby in Italy. Tradition preserves several philosophical practitioners who would come to influence Magna 558 For the general political environment of Magna Graecia in the final quarter of the 6 th Century BCE, see Musti 2005: 103-5. If the chronology is correct, Pythagoras’ revision of Crotonian laws – with its emphasis on order and harmonization – may have directly or indirectly influenced the military tactics that led to Croton’s humiliation of Sybaris around 510 BCE. 559 Iambl. VP. 50. 560 Iambl. VP. 33. Dillon and Hershbell 1991: 59 n.1 assume here that Iamblichus is deriving this portion of his history from Nichomachus. Cf. Iambl. VP. 133, where Iamblichus compares the freeing of these cities with the “overthrow of tyrants.” 213 Graecia in ways that cannot be easily comprehended: the lawmakers Zaleucus of Locri and Charondas of Catana, the city-planner and political theorist Hippodamus of Miletus, the doctor and attempted usurper Democedes of Croton, the mystic lawgiver Empedocles of Acragas, and the philosopher-statesman Parmenides of Elea. We have already discussed Hippasus of Metapontion who, in light of the predominance of aristocratic forms of Pythagorean governance established in Southwestern Italy, supported democratic revolutions in the east with an eye to revising entirely the educational curriculum in the school of his own mathematical Pythagoreans. But the question remains: if democracy represented a radical shift of political organization, from what kinds of aristocratic governance did it revolt? Indeed, what cities featured predominantly acousmatic and traditional constitutions that were buttressed – and even later adopted – by the Pythagorean way of life? On this issue, we have some guidance thanks to the combination of historical texts and pseudepigraphical treatises from the mid-4 th Century BCE that, as I shall argue, preserve the constitutional forms of traditional “Pythagorean” poleis which were attempting to legitimate their constitutional structures in response to the string of democratic revolutions that were exploding like firecrackers throughout Southeastern Italy. 561 561 It should be noted that the important Dorian colony of Cyrene, which had also been governed monarchically by the Battiads, encountered subsequent shifts in its constitutional structure around 550 and 450 BCE: in the mid-6 th Century BCE, a democratic constitution was introduced to separate out the people into three tribes, and then around 456 BCE the monarchy ended entirely and the so-called “Ten-Thousand” took power. See Sartori 1996: 215. 214 In order to respond to the questions I have posed, we might examine first the history of the founding of those cities affected by Pythagoras’ arrival in Southern Italy insofar as we can understand them. It may be generally agreed that Spartan colonization of the 8 th Century BCE was responsible for the development of many city-states in Magna Graecia that would later adopt Pythagorean governance. According to Pausanias, both of the aristocratic centers of Southern Italy in the 6 th Century BCE – Epizephyrian Locri and Croton – were founded by Lacedaimonians around the time of the First Messenian War (ca. 710 BCE). 562 This may be true, but it is more likely that – regardless of who actually founded Croton – those who had access to the production of ideology in Croton were attempting to link themselves politically to Sparta with appeal to heritage. Irad Malkin sees the pro- Lacedaimonian nationalism and its emphasis in the 540s as part and parcel of the “world of Sparta” and its “mythological historicizations and connections,” the proof of which was the “narrative” of Menelaos’ travels and founding of cities in time immemorial. 563 Indeed, Menelaos is represented as having visited Taras first on his travels to Western Greece, then Siris, Cape Lacinion, Croton, and finally western Sicily. Taras, founded in 706 BCE as a Spartan colony, does not seem to have adopted a Spartanate government in any traceable form before the mid-5 th Century 562 Paus. 3.3.1. Croton was also said to have been founded by Achaians. On the issues involved in this subject, see Berard 1957: 154-8 and Malkin 1994: 61-4. 563 Malkin 1994: 64. 215 BCE. 564 We are left with the assumption that the founder of Taras, a certain Phalanthus, was the first in a line of kings that concluded with the democratic revolution against Aristophilides in 473 BCE, but it is equally possible that Aristophilides was simply a tyrant who commandeered power in the late 6 th Century BCE. 565 Either way, there is no trace of the Spartan diarchy. The presence of an ephorate at Taras, previously only demonstrable at its colony Heracleia, has recently been confirmed by a titulus pictus found in Taranto with the inscription ora // e)fo&rou )Aristoda&mou. 566 But even there, the inscription dates to the early 3 rd Century BCE, and it cannot be said with certainty to demonstrate three centuries of the presence of an ephorate system in Taras; more likely, as I shall argue in Chapter 6, the Tarantine ephorate is developed out of an innovative “mixed constitution” in the second half of the 5 th Century BCE. Croton, on the other hand, and the Lacinian Cape (today called the Capo Colonna), feature notable Spartan connections as well, although ancient historians dispute the identity of the first settlers. Antiochus (mid-5 th Century BCE) and Herodotus agree that the Crotonians were originally emigrants from Achaea, although closer investigation of these sources may expose the tenuous links between 564 Brauer 1986: 11-17; De Juliis 2000: 19-21; Malkin 1994: 57-61. On the expedition to Taras, see Wuilleumier 1987: 45-7. For the mixed constitution at Taras, also see Chapter 6. 565 De Juliis 2000: 20-1. Herodotus (3.138) tells us that the Tarentines were on good standing with the Cnidians, who we discover from Aristotle (Pol. 1035b8-18) had originally been an oligarchic government that had been overthrown internally by the people, who replaced them with a “champion” (prosta&thn) from among them. Herodotus (1.174; cf. 2.178) claims that the Cnidians too were originally Lacedaimonian emigrants. 566 De Juliis 2000: 21. 216 Crotonians and their mother-country during the Persian wars. 567 As Herodotus tells us, in preparation for the Battle of Salamis in 480 BCE, the Achaeans appealed to other Greek states for support against the invading Persian fleet. Persia’s relations with Southern Italy, if we are to believe Herodotus, had only been established a generation before, when Democedes, the troublesome Crotonian who became the personal physician of Darius following self-imposed exile from Croton, returned home. 568 According to the story, Democedes returned from Persia with fifteen Persians (planning to “observe” Greece) and stopped in Taras, where he appealed to the king Aristophilides to protect him from the Persian envoy. Democedes, who would later attempt to establish a tyranny in Plataea, found a friend in Aristophilides, who seized the Persians’ rudders and allowed Democedes to return to Croton unhindered. The Persians pursued Democedes to Croton, where the Crotonians – at a loss about whether to hand him over or not – were threatened by the Persians with enslavement. If, at this time, they were willing to defend Democedes against the Persians, they became tired of Democedes’ antics when he, much older, attempted to establish a tyranny with support of the young men of Croton. This story – if it is to be believed – represents a corruption of Pythagoras’ arrival at the Capo Colonna, in which Democedes stimulates the youth (probably in the Pythagorean assembly of the youth at the gymnasium) against their parents in order to establish a new form of government. Depending on how we read the text of Iamblichus, it seems that 567 Antiochus F 1 Jacoby apud Strabo 6.1.11. 568 On Democedes, see Chapter 1. The political activity of Democedes can be reconstructed by combining the stories of Herodotus (3.125-37) and Apollonius of Tyana (apud Iambl. VP. 256-62). 217 Theages the Crotonian defeated and killed Democedes in battle; the youth were sent into exile. 569 It is apparent, then, Croton had its own problems to deal with in the early part of the 5 th Century BCE. And so, although Croton – in its wealth and luxury – was the only Southern Italian city to aid Athens in preparations for the Battle of Salamis in 480 BCE, it only sent one trireme. 570 What could be the reason for this? Had Achaean settlers in Southern Italy adopted a pro-Persian stance in the time since their settlement, or were they more concerned with the local political issues including revolutions, inter-generational conflicts, and threats from native peoples? Were they debilitated by wars, or was something else at issue for the Crotonians? The likely answer to these questions is Croton’s failure to resolve itself into a democratic regime of the Athenian sort, possibly owing to the enormous size and grandeur of its empire. It seems that Croton, within ten or twenty years of the expulsion of the youths who supported Democedes, had become a formidable Mediterranean metropolis. 571 As Franco Sartori notes, the Achaean colonies of Magna Graecia that had been either founded by or put into a relationship of dependence on Croton around 460 BCE (Crimisa, Petelia, Terina, Scylacium, and Caulonia) featured a common magistrate, namely the damiourge/demiourge, 569 If Democedes’ travel took place around 500 BCE, there is little issue with the possibility that the democratic split among the Pythagoreans in Southeastern Italy took place in the 470s or 460s BCE. The difficulty here lies in two words of Herodotus’: he claims that the Persians who went to Taras and Croton with Democedes were the “first from Asia to come into Greece,” and that this all took place before Darius seized Samos (ca. 520 BCE) from Polycrates. 570 Hdt. 8.47. 571 The Crotonians are said (Timaeus 566 F 44 Jacoby) to have taken on the luxury of the Sybarites, whose city (I) they had sacked in 510 BCE. 218 although it is difficult to assess what his role was in each city. 572 The damiourge/demiourge may have been comparable with the pre-Cleisthenean (Solonian?) Athenian office, 573 or with the demiourgic magistracy within the federalist Athenian League of the 3 rd Century BCE, 574 and as such it reflects aristocratic aspects of Croton’s “democratic” constitution. Damiourgoi have been located at Archaic Argos and the Heraion nearby (first half of the 6 th Century BCE), 575 at Crete (late 7 th Century BCE), 576 and, among the Dorians, so claims Hesychius, the title “damiourge” stood for “archon,” a suggestion that we shall soon exhibit as coincident with the testimony of Hellenistic historians. 577 The function of damiourges may have been to compose laws, as Aristotle suggests in the Politics, without establishing an actual constitution. 578 They may have been responsible for policing citizenship, as in Larisa in the second half of the 5 th Century BCE. 579 In all cases, several damiourges are employed as administrators, sometimes ten. 572 See Sartori 1953: 115-126. Cf. Sartori 1996: 217-18. 573 See Arist. AP (F 385 and 386 Rose). Cleisthenes’ reforms may have modified the office of demiourgos and replaced it nominally with the term archon, but this can only be conjectured. See Levecque 1996: 50. 574 Von Fritz 1975: 4 discusses the presence of the demiourge in the Athenian League known to Polybius in these terms: “The executive or administrative branch of the government was headed by the strategos, who was at the same time the actual, not merely nominal, commander-in-chief of the federal military forces and the president of the League. In addition to this president there was a college of ten damiurgs, who seem to have had a position similar to that of the Athenian archons.” 575 Hall 1995: 610. See Jeffrey 1976: 140. 576 Jeffrey 1976: 189-90. 577 Hesych. s.v. Cf. Sartori 1953: 118. We may assume that the source in Athenaeus (the oi( de&) for the information pertaining to the “archon” of Croton was contemporaneous with Timaeus of Tauromenion and Clearchus of Soli (both quoted in proximity), roughly fl. 250 BCE. See below. 578 Arist. Pol. 1273b32-5. 579 Arist. Pol. 1275b29. The suggestion of date assumes that Gorgias of Leontini’s joke at the Larisaeans’ expense would have been pertinent at the time of Gorgias’ life and visits to Achaea (ca. 430 BCE). 219 In Terina, a Crotonian colony further inland from the Ionian Sea, an extant small bronze lamella features the damiourge and prytanis, and the conjecture of Sartori that the prytanis and damiourge were complementary offices in Crotonian governance is possible. 580 Further reflection on this suggests that the Crotonian damiourge was probably an inferior magistracy to the prytanis. Athenaeus discusses an “archon” of the Crotonians – in terms that suggest its correlation with the damiourgos – by appealing to a story that features (unsurprisingly) Democedes as a central figure. Following their incursion into and subsequent destruction of Sybaris (I) around 510 BCE, Timaeus mentions an “archon of [the Crotonians, who] went around the city dressed in a purple robe and garlanded with a golden crown, his feet shod with white boots.” 581 Others, so claims Athenaeus, say that the Persianizing of an “archon” of the Crotonians took place not as a consequence of contagion from Sybarite luxury, but as a consequence of Democedes’ return from Persia. According to this version of the story, which abbreviates the same excursion of Democedes into Persia as recounted by Herodotus in the Histories, 582 the “archon” to whom Timaeus of Tauromenion refers wears the clothing of a Persian king in defiance of the threats that the fifteen Persians had leveled against the Crotonians once Democedes had returned home: [Democedes] wanted to remain there [in Croton], but a Persian, who apprehended him, claimed him as the King’s slave. The Crotonians, however, took him back [from the Persian] and, after 580 SEG IV.73. Cf. Sartori 1953: 117-18. 581 Athen. 12.22 (522a) = Timaeus 566 F 44 Jacoby. 582 Hdt. 3.136-8. 220 stripping the Persian of his clothing, they put the clothes on the subordinate to the prytanis. From that time, then, [the subordinate to the prytanis], wearing the Persian garb, goes about the altars on the seventh day with the prytanis, neither for luxury or hubris, but doing this to spite the Persians. 583 While this story does not make clear what duties were allotted to each of these offices, it features the administrative posts in such a way as to make them prominent and highlight their Persian origin. 584 We may then, with some certainty, suggest that Croton featured, as a part of its aristocratic governance at the turn of the 5 th Century BCE, a superior governor called a prytanis and a subordinate archon called a damiourgos. 585 Croton, then, underwent a period of vast expansion and development during the first half of the 5 th Century BCE, only once threatened early on by a tyrannical uprising (that of Clinias, perhaps around 494 BCE) 586 and in relative security for the following forty years. During this time, it seems to have attempted to abolish the Olympic festival by establishing games at the same time with “silver prizes.” 587 In Athenaeus’ account of the vices of the Italian peoples, this event is quickly followed 583 Athen. 12.22 (522b-c). 584 It may be possible that the terms are originally derived from Asia Minor. The anthroponym *brundF is attested in Lydia, and the Etruscans – whose inheritance of Phoenician culture is still woefully underexamined – featured a magistrate variously termed purq, purqne, epiqni, and puruqn. See Chantraine 1968: ad loc. 585 We may compare the movement from prytany to tyranny in Miletus as reported by Aristotle (Pol. 1305a15-17), where he tells us that “tyrannies used to come into existence in former times more than now on account of the fact that the great offices were entrusted to certain men, just as in Miletus, where [a tyranny came into being] from a prytany, for the prytanis was in control of many great offices.” Prytanies of this sort are also reported in and around Asia Minor at Rhodes (Plu. 2.813d), Halicarnassus (SIG 1015.2), and Mytilene (IG 12[2] 68). These kinds of prytanies are markedly distinct from those of Athens (which are collective) or Plato’s second-best city-state in the Laws. See Morrow 1960: 172-3. 586 Dion. Hal. Ant. Rom. 20.7. On this, see the clear discussion by Minar 1942: 71-5. 587 Athen. 12.22 (522c) = Timaeus 566 F 45 Jacoby. 221 by a description of the development of Tarentine luxury, a consequence of the acquisition of power during the same period. Croton’s expansion is borne out in the historical record (both by literary sources and coinage) as well, since, following the destruction of Sybaris (I) and the subsequent acquisition of her territory, Croton seems to have advanced far to the north along the Ionian Sea, perhaps nearing the area where Siris had once been controlled by the Metapontines. 588 We should not underestimate the extent of Croton’s influence during this period: covering a region that reached to Laos and Metapontion to the north and Locri to the south, extending all the way to the Tyrrhenian Sea, its empire was four times the size of Attica. 589 It may have been problems with a hastily-organized empire, compounded by intense economic development, that contributed to the internal instability of Croton. Nevertheless, following the expulsion of the aristocratic Pythagoreans in the 450s, Croton seems to have continued in its democratic governance at least for part of the 5 th Century BCE, although probably a democratic form of governance alternative to that of Athens. 590 She remained hostile to those aristocratic Sybarites who proposed the refoundation of Sybaris (II) and destroyed the city again around 448 BCE. 591 588 See De Juliis 1996: 213-15. 589 See Minar 1942: 36-7. 590 It is entirely probable that many of the so-called “democratic” constitutions of these cities, especially those that featured assemblies of a “thousand,” would be better described as “mild aristocracies,” as Minar nominates them (1942: 44). Heracleides of Pontus, Plato’s student and head of the Academy while Plato was traveling to Italy, described the constitution of Charondas – a “student” of Pythagoras – as “aristocratic” in that “one thousand, selected from the honorable men, take care of all business” (pa&nta dioikou~sin). See 219 Jacoby. 591 Diod. 11.90.4, 12.10.2. On the date, see Ehrenberg 1948: 150. 222 Those same Sybarites, in a fascinating passage found in Diodorus Siculus, appealed to Athens and the Lacedaimonians for support against the Crotonians: The Sybarites who were driven from their fatherland a second time sent ambassadors into Greece, before the Lacedaimonians and the Athenians, requesting their participation in their return and sharing in the settlement (a)ciou~ntej sunepilabe&sqai th~j kaqo&dou kai_ koinwnh~sai th~j a)poiki&aj). The Lacedaimonians paid no attention to them, but the Athenians announced that they would aid in the enterprise. 592 The city that these Sybarites would go on to found, a comprehensive effort on the part of the Athenians and others, was a panellenic colony called Thurii. Interestingly, the Lacedaimonians had no interest in this project, and the presence of Athens led to an initially “democratic” form of rule, which was challenged soon thereafter by the aristocratic tendencies of the original Sybarites. 593 I will discuss the founding of Thurii – and its constitutional structure – later in this chapter. To the north on the Ionian coast, Metapontion, perhaps led by the Pythagorean Brontinus (who may have been the teacher – along with Hippasus of Metapontion – of the democratically-inclined Empedocles) 594 , did little to protect Pythagoras when he fled from Croton in the first decade or so of the 5 th Century BCE 592 Diod. 12.10.3-4. 593 Sparta and Athens had just concluded the Thirty Years’ Peace in 445 BCE, and Sparta seemed concerned to preserve rather than expand its League. See Cartledge 1979: 229-34. 594 D.L. 8.55. On Empedocles as a “democratic” Pythagorean, see Chapter 1. According to Diogenes Laertius, the historian Neanthes (3 rd BCE) claims that until the time of Philolaus and Empedocles (mid 5 th BCE) “all Pythagorics partook (e)koinw&noun) of the discussions, but when [Empedocles] publicized (e)dhmosi&wsin) them in his poem, they made a law that these should never be given to a poet. They say that Plato suffered the same thing, for he too was excommunicated (kwluqh~nai).” The trend is notable: Empedocles, Hippasus, and Plato are all excommunicated or punished for their publication of acousmatic Pythagorean secrets. That Empedocles was democratic was assumed by Aristotle as well as Timaeus. See D.L. 8.63-4. 223 and, as Minar reminds us, he probably died of starvation at the “Temple of the Muses;” as an exile, he was being besieged by enemies and could not leave sacrosanct ground. 595 This same Metapontion, as I showed in Chapter 1, was the axis for the democratic league of Pythagorean city-states (along with Taras and Caulonia, which had previously been part of the aristocratic Crotonian governance) and represented the new democratic face of Magna Graecia that threatened Crotonian and Locrian aristocratic governance in 470-50 BCE: its ekklesiasterion, pictured below in a reconstruction by Dieter Mertens, was rebuilt and expanded to fit 7500- 8000 people at the beginning of the 5 th Century BCE: Figure 3: Ekklesiasterion II of Metapontum (Early 5 th Century BCE), 1:500, from Mertens 2006: 335. 595 Minar 1942: 39-40, 72-3. 224 The ekklesiasterion represents an attempt by the citizens of Metapontion to reflect the democratic structure of their political constitution by means of a circular topographical design. Although it was a civic building, its religious significance has been emphasized by the discovery of an altar along the western wall of the ekklesiasterion and an inscription in a stone bearing the writing “DIOS AGORA.” 596 We may follow De Siena in assuming that this stone, and its placement near the ekklesiasterion, mark the presence of the worship of Zeus Agoraios. 597 Little is known about the altar to Zeus Agoraios in Athens except that, as the scholiast to Aristophanes tells us, it “[was] located in the agora and in the e)kklhsi&a|.” 598 Is it possible that the ekklesiasterion of Metapontion, known to the inhabitants of Magna Graecia as one of the democratic city-states that promoted Pythagorean education and ethics, was itself the centralized location where the “league” of Tarentines, Caulonians, and Metapontines met to adjudicate the fate of those followers of the would-be tyrant Democedes in the first half of the 5 th Century BCE? While this hypothesis cannot be proven definitively, it is supported by the later development of a league in Magna Graecia around 420 BCE involving Croton, Sybaris (IV) on the Traeis, and Caulonia in the war of these states against Thurii. This league – in 596 De Siena 2001: 32. 597 De Siena 2001: 35. Another stela found nearby features the words “Zeus Aglaos,” an epithet echoed by the discovery of another stone stela near the Temple to Artemis in nearby San Biagio alla Venella at Bernalda. This stela was located in a rectangular “fountain” shrine that featured a basin which collected water from the nearby spring. We may thus assume that the epithet “aglaos” here, which means “luminous,” may have referred to the shrine’s significance as a fountain. See Cerchiai et al. 2002: 140-2. 598 Schol. Ar. Equit. 410. Another shrine to Zeus Agoraios was set in Marathon. See Wycherley 1955: 118 n.16. 225 imitation of the Achaean League – was dedicated to Zeus Homarios, near Aegium (at least by the middle of the 3 rd Century BCE). 599 Power and alliances shifted along the coast of the Ionian Sea, and with these the contingent forms of constitution in a location that can be said, with some certainty, to have been a testing-ground for inter- and intrapolitical structures. The circular structure of the ekklesiasterion is unusual in Western Greece, and its meaning is extremely hard to pin down; indeed, the circle – as a form that carried with it concepts of topographical and cosmological unity, immortality, and divine form – could be employed to reflect the ideologies of democratic, aristocratic, and monarchical governance. 600 The point of distinction, in proper Pythagorean style, is magnitude or, more precisely, proportion. In Metapontion, a relatively small city-state whose constitution seems to have either changed from an aristocracy to a democracy or simply to have been a democracy from the mid-6 th Century BCE (the latter seems unlikely), the size of the ekklesiasterion suggests a comprehensive and inclusive ekklesia. Indeed, it is far larger than the circular monuments found at Poseidonia and Acragas. The circular meeting place at Poseidonia is more likely a bouleuterion, as Musti suggests, because this monument could seat only 500-600 people in what was a massive city by 5 th Century standards. 601 Acragas, which had 599 Plb. 2.39.6. See Walbank’s commentary on this point. 600 Mantinea, which was democratic certainly before 421 (and probably in the 470s-60s; see Cartledge 1979: 215), was constructed as a circular synoikos. As we shall see later in this chapter, the circle becomes used as a metaphorical plan for some Platonic ideal city-states. Generally, see Lévêcque 1996: 85-97 and Chapter 6. 601 Musti 2005: 99-100. 226 been “liberated” by Pythagoras 602 and defended with arms by the Pythagoreans, 603 had been called “democratic” by Timaeus (who speaks of the “Gathering of the Thousand” [to_ tw~n xili&wn a!qroisma]), at least during the time of Empedocles’ political and philosophical influence (ca. 471-469 BCE). 604 Its circular ekklesiasterion, a cavea built out of the side of a hill that could seat about 3000 people, was larger than was needed to accomondate the “democratic” group known as the “Thousand,” and this numerical inconsistency suggests that, whether or not Empedocles’ actual administrative modifications remained, the principle of democratizing remained in Acragas for a short time during the 5 th Century BCE. 605 In both cases involving “democratic” rule and circular ekklesiasteria (Acragas and Metapontion), we note the presence of exoteric Pythagoreans who envisioned a body politic constituted through mathematical means. The presence of these circular structures enforces and illuminates the mathematical Pythagoreans’ perpetual 602 Iambl. VP. 33. 603 If we are to believe Hermippus, who claims that Pythagoras died in the war against Syracuse. See D.L. 8.40. 604 Timaeus 566 F 2 Jacoby = D.L. 8.66. What “democratic” means here is difficult to assess. What is more, the term a!qroisma is particularly vexing. It is used loosely by Euripides (Or. 874, cf. Hec. 1139) to refer to the collocation of things, animals, or people. Aristotle never uses this particular term, although he refers to the gathering of a party (Pol. 1304b33) using the term a)qroisqe&ntej. More likely, I might conjecture, the “Gathering” to which Timaeus refers represents one of the innovations that Empedocles introduced as a “democratizing” factor in Acragas, as he is then said to have broken it up three years after its establishment. The source is late, but an anonymous Christian author of the Prolegomena Artis Rhetoricae (Prol. Syll. 25) claims that Corax, the famous co-inventor of rhetoric with Empedocles (see Hinks 1940: 61-2), went into the Syracusan ekklesia “in which the entire demos was gathered” (sunhqroi&sqh). Acragas and Syracuse, who both underwent “democratic” revolutions in the 460s, may have adopted similar constitutional structures. Generally speaking, the term a!qroisma is philosophical and relates to Empedocles’ physics. As attested by Aetius (De Placitis Reliquiae F44) and Plutarch (Stromat. ap. Eus. P.E. 1.8-10), Empedocles believed that the origin of the motion (a)rxh_n th~j kinh&sewj) of the two hemispheres (day and night, the first entirely comprised of fire, and the other a mixture of fire and air) occurred when fire was weighed down as a consequence of its “concentration” (kata_ to_n a)qroismo_n). 605 On the ekklesiasterion of Acragas, see Cerchiai et al. 2002: 251-2 and Mertens 2006: 318-20. 227 curiosity about the problems of politicizing mathematics and, in particular, geometry. As Lévêcque reminds us, the problem of squaring the circle here, as elsewhere, is manifested physically in the city-plan, where circular monuments are fit in among quadrate zones and in concert with rectangular or square temple monuments. 606 Nevertheless, as soon as democracy had set a foot on the Italian and Sicilian shores, it was consumed and radically combined with traditional forms of aristocratic governance, either through attempts to mollify internal strife or thanks to external threat from the native Italian peoples. Acragas, as we discover from Timaeus of Tauromenion and Xanthus, offered Empedocles the kingship (basilei&a), which he turned down. 607 His fears that the a!qroisma of the Thousand had exceeded their democratic function compelled him to disband it, because, as we hear, he was among those who favored the “popular cause” (ta_ dhmotika&). 608 He left Acragas for the Peloponnese, perhaps – if we take the manuscript readings as legitimate – due to his displeasure with what the government of Acragas had become in those three years; 609 when those supporters of democratic ideals requested his return (possibly in 461 BCE), he was kept away by the children of his personal enemies. 610 If this anecdote preserves the sense of authority held by aristocrats in Acragas during this period, it 606 Lévêcque 1996: 87. 607 D.L. 8. 66. 608 D.L. 8. 65. 609 Construing the text (fhsi_n e)nanti&an e)sxhke&nai gnw&mhn au)to_n th~| politei&a| fai&nesqai) to mean “that he seems to have come to hold an opposite opinion to the polity.” Diels emends the text unnecessarily. See Tucker 1931: 50-1. 610 In 461 BCE, as Diodorus Siculus tells us (11.76.4), those who had been expelled (e)kpeptwko&tej) from Acragas, Gela, and Himera during the reign of Hieron of Syracuse were allowed to return to their poleis. 228 may be assumed that democracy only survived there in a dominant form for fifteen years. In Metapontion, however, it was the development of new poleis that restricted the possibility of expansion along the Ionian Sea; instead, the city-state’s influence pushed inwards to the countryside. Metapontion appears to have cultivated a complex of ethnic and political identities – both Italian and Greek – and its multiethnic status might explain its relative security as a “Greek” polis with coeval rural Italians to the north. 611 Indeed, as Joseph Carter has shown, the settlement of the chora increased during this period and resident families came to occupy all land. 612 The small sanctuaries outside the city were frequented, but the temples in the city were neglected. Although the water table seems to have risen as much as a meter, a rise that led to swampy conditions that hastened the deterioration of monuments and presented challenges to farmers, Metapontion maintained a comfortable relationship with its inland inhabitants. 613 On the other hand, the Tarentines were faced with frequent alliances with and wars against native peoples of the Iapygean peninsula and the land to the north. 614 Metapontion, which probably continued its (loose?) alliance with Taras following the democratic revolutions of the 470s-60s, may have successfully faced down the threat of Crotonian expansion, but 611 On the presence of the Osco-Etruscan meddiss at Metapontion, see Chapter 1 and Sartori 1953: 17- 27. Recent studies (Carter 2004, Hall 2004) have demonstrated the integration of ethnic communities in Metapontion and generally throughout Southern Italy. 612 Carter 1998, Vol. 1: 13. 613 Ibid. 614 We may follow Wuilleumier (1987: 57-8) in assuming that the ex-voto at Delphi, dedicated by the Tarentines, refers to a victory over the king of the Iapygeans around 460 BCE. 229 the destruction of Sybaris (II) and the refounding of the city, a panhellenic enterprise led by Athens, under the name Thurii, certainly limited the possibilities for Metapontine expansion. 615 Metapontion found itself in the midst of an expanding competition that featured several ideological disputes: Tarantine versus Thurian, democratic versus aristocratic, and (implicitly) Athenian versus Spartan. 616 Sicilian poleis, too, began to take note of the possibilities afforded them by establishing alliances with or conquering Italian city-states along the Ionian Sea. As early as 477 BCE, the Sicilian tyrant Hiero offered support to Sybaris (II) in its attempt to secede from the Crotonian empire, an about-face from his earlier policy regarding Croton – which he saw as a possible ally against competitor Rhegion – that highlights the threat Croton presented to Syracuse in the first quarter of the 5 th Century BCE. 617 Nevertheless, following his death, the failed succession of Thrasybalous in Syracuse led to a revolution there (ca. 466 BCE), perhaps coordinate with the political situations in Taras and along the rest of the Ionian coast, and the establishment of a “democratic” government that lasted until the accession of Dionysius I in 406 BCE. 618 We cannot assume that this revolution was instigated by Pythagoreans. Iamblichus’ list of Pythagoreans at the end of the De Vita Pythagorica names three Syracusan Pythagoreans (Leptines, Phintias, and Damon), none of whom seems to have been historical figures active until the mid-4 th Century 615 On Thurii, see below. 616 The so-called “First Peloponnesian War” was largely ideological and promulgated away from mainland Greece. We may also recall that Taras was the sole Spartan colony established in Southern Italy during the 8 th Century BCE. 617 On the difficult chronology, see Minar 1942: 42-3 and Ciaceri 1928, Vol. 2: 314. 618 Diod. 11.67.1 ff. 230 BCE. 619 The nature of this Syracusan “democracy” also deserves special scrutiny, since, as Aristotle suggested, this form of political organization, which seems to have lasted from 466 until 412 BCE, was better identified with a mixed constitution (politei&a) than a proper democracy (dhmokrati&a). 620 The death of Hieron and subsequent adoption of a democratic mixed constitution – perhaps the best term – is inextricably tied with the development of rhetoric in Sicily. 621 The two historical “rivals” for the title of “progenitor of rhetoric,” Corax and Empedocles, might better be seen as engaging in a collective exercise in establishing an applied “democratic” language and form of discourse for newly-fashioned mixed constitutions in Syracuse and Acragas. 622 Indeed, Hinks’ attempts to distinguish early rhetoricians as “theorists not in the political but in the forensic field” assumes anachronistic subdivisions of discursive genres, as though Corax, Tisias, and Empedocles as citizens of Sicilian poleis felt a difference between political and legal activities! 623 619 Phintias and Damon lived during the second and third quarters of the 4 th Century BCE (see Iambl. VP. 234-6, on authority of Aristoxenus). Leptines is far more difficult to identify; due to the collocation here with Phintias and Damon, we might consider this Leptines identifiable with the Syracusan Leptines who joined with Callippus in expelling Dionysius the Younger to Corinth and freeing Rhegion in 351 BCE (Diod. 16.45.9) or, perhaps, the Leptines who composed the Ars Eudoxi (e.g. Eudoxus Fragments 128 and 137 Lasserre). Indeed, they may well have been the same person: the Ars Eudoxi refers to Callippus as a follower of Eudoxus who divided the year into unequal seasons. 620 Arist. Pol. 1304a27-29. He claims that, following the Syracusan expedition, “Syracuse changed from a politeia to a demokratia” owing to the fact that the “people” (dh~moj) were the cause of the victory over Athens. 621 For further investigation into the problem of the Syracusan constitution before the advent of Dionysius I, see Chapter 6. 622 Thus we may leave behind the dispute – originating with Aristotle himself – over whether Corax (Arist. F 137 Rose = Cic. Brut. 46) or Empedocles (Arist. F 48 Rose = D.L. 8.57) was the originator of the rhetorical art. Thanks to Lucas Herchenroeder, who pointed out to me the significance of Corax and Tisias to Syracusan politics. 623 Hicks 1940:62. 231 More likely the attempts to formulate a set of standards for the allocation of land and rights to property were themselves coincidental with the destabilization of tyrannical regimes and the subsequent shifting of populations in Sicily. 624 Syracuse’s constitutional structure (as a politeia with democratic leanings) may have exercised some influence upon the design of city-state constitutions throughout the region, especially because Syracuse and Acragas continued to thrive economically. By the time Alcibiades advocated the Athenian invasion of Sicily, the democratic mixed constitution had provided for enough destabilization of aristocratic citizenship rights and inclusion that its citizens could be described as “mixed-up mobs of all kinds of people” (o!xloij te ga_r cummei&ktoij poluandrou~sin) and its city-states could be said to make it easy for people to change and admit themselves as citizens. 625 Athenian democracy, with its autochthonous citizenship rights, assumed economic as well as ethical superiority over Syracuse with its democratic mixed constitution. 626 Indeed, the question of the superiority of Athenian over Syracusan (and hence Dorian) 627 political structure is best exemplified in the case of the founding of Thurii on the Ionian Coast in 443 BCE. On the authority of Diodorus Siculus, we 624 See Finley 1979: 61-2. 625 Thuc. 6.17.2. Thucydides might be referring to Syracuse as an ochlocracy, the degenerate form of democracy, although the term itself does not appear in extant Greek literature until Polybius. The sixfold division of the three legitimate forms of governance (monarchy, aristocracy, good democracy) and the contingent degenerate forms (tyranny, oligarchy, and bad democracy) is essentially stated at Pl. Plt. 291d ff. 626 Nevertheless, we might ask whether or not this is a case of narcissism of minor differences: as Finley 1979: 61-2 notes, Athenian and Syracusan governance and administration were closely comparable. 627 See Finley 1979: 65-6, who recalls that both Acragas and Syracuse, who were at odds in the 440s, were of Dorian origin. 232 learn that relations between two of the richest city-states in Greece, Acragas and Syracuse, had deteriorated and a war had broken out in 445 BCE. 628 Following the defeat of Acragas at the Battle of the River Himera, the Acragantines sued for peace; other cities of Sicily, then, followed one another in conceding leading status (h(gemoni&a) to Syracuse. 629 In Italy, after the destruction of Sybaris (II), the appeal by the former Sybarites to create a new panhellenic city-state were ignored by the “Lacedaimonians” and the list of phylae given in Diodorus does not include any specific indication that other Sicilians or Southern Italians wanted anything to do with the founding of this colony. 630 The aristocrats who had formerly exercised rule in Sybaris – instigated by their wives, according to Diodorus 631 – were assigning the highest offices to themselves and relegating lower magistracies to the foreign colonists. What is more, they were assigning the land nearest to the center to themselves while distributing land farther away from the center to the newcomers. The assumption here, then, is that the land had already been reparceled and that the city had already been laid out according to the design that Hippodamus of Miletus had established. 632 If this is the case, then we might want to examine the civic design and plots as they were designed by Hippodamus. A native of Miletus, he had come to fame in 628 Diod. 12.8.1-4 629 Diod. 12.26.3. 630 Diod. 12.11.3. 631 Aristotle ascribes this as a weakness to primarily oligarchic constitutions. On women as the cause of political dissolution in Sparta, see Arist. Pol. 1268b15-1270b6. 632 The redesign of the city and its chora was understood to be a marker of the democratic phase of a polity’s development by Plato. See Chapter 6. 233 antiquity for the innovations in civic design he seems to have introduced in the mid- 5 th Century BCE throughout western Asia Minor, mainland Greece, and Italy. 633 He was also famous, so claims Aristotle, for having been the “first among those not engaged in politics to attempt to say something concerning the best constitution” (prw~toj tw~n mh_ politeuome&nwn e)nexei&rhse& ti peri_ politei&aj ei)pei~n th~j a)ri&sthj). 634 It is probable, then, that Hippodamean civic design is essentially connected to his theory of the “best constitution,” a subject we shall take up in the second half of this chapter. In regard to the civic plans attributed to him, Castagnoli has persuasively shown that orthogonal civic design existed in Miletus before Hippodamus designed the Athenian Piraeus, but that he was responsible for innovations that led to the development of a uniform and regular grid pattern for city-states. 635 We may assume, then, that his activity in Thurii occurred during or slightly after the design of the Piraeus in the time of Pericles’ generalship in Athens (before 445 BCE). 636 If the plots in the colony were being distributed unfairly by the aristocratic former inhabitants of Sybaris (III), it is probable that Hippodamus set out a civic design at the inception of the colony, 446/5 BCE. That the civic design at Thurii illustrated and enforced the structure of what Aristotle called the “best constitution” of Hippodamus is a matter of point of view: like the circle, which could be adapted to either aristocratic or democratic ideological systems, the orthogonal 633 Generally, on Hippodamus, see Castagnoli 1971: 66-72. 634 Arist. Pol. 1267b29-31. 635 Castagnoli 1971: 66-72. 636 Arist. Pol. 1267b22. 234 plan could be exploited both by aristocrats or democrats. The history of Thurii in the years following its founding suggests that it was: according to Diodorus, strife ensued when the new immigrants, who were added to the colony after the aristocratic Sybarites (oi( prosgrafe&ntej), were superior in strength and number, and they killed nearly all of the original Sybarites who were in charge and took over the colonization of the city. Interestingly, Diodorus claims that directly following the extermination of the ruling Sybarites and the subsequent takeover of the polis, the chora was redistributed in equal shares (dienei&manto th_n po&lin kai_ th_n xw&ran e)p’ i!shj e!nemon). We may thus designate the colony founded in 445 BCE, before the democratic revolution, as Sybaris (III), and the resultant city-state that came to adopt a democratic constitutional system was Thurii. Just as had occurred following the revolution in Croton, the distribution of land in equal parcels to a multitude demonstrates the “democratic” structure for the newly-established Thurii: Diodorus secures this interpretation, because he claims that Thurii became very wealthy quickly and forged a relationship of fili&a with “democratic” Croton. What is more, the Tarentines seem to have had some effect on the shift from an aristocratic to a democratic form of government as well, as a passage from Aristotle’s Politics (1307a26-34) suggests: And the change mentioned [from an aristocracy to democracy] happened at Thurii, for because the property-qualification for offices (ta_j a)rxa&j) was too high, the constitution was changed to a lower property-qualification and to a larger number of offices. Nevertheless, since the notables had bought up illegally the whole of the land (for the constitution was too oligarchic, so much that they 235 were able to indulge in their wealth)…. 637 the people, who had been trained in the war, became stronger than the guard, until those who had more land (than was lawful) gave up their hold. Commentators have often assumed that the “war” to which Aristotle refers was a civil war in Thurii, but there is no account of this attested anywhere else. 638 Instead, given the corresponding information from Diodorus that illustrates the battles between aristocratic Sybarites and democratic colonists from all around the Greek world, it may be better to assume that the “war” to which Aristotle refers was inter- political, pitting “democratic” Taras against the aristocratic former Sybarites living in the “new” Sybaris (III). In this case, democratic Tarentines (who still may have been particularly radical in this period) could be seen as defending their regional control, which extended as far south along the Ionian Sea as the chora of Metapontion. What is a mystery, however, is why Taras and Thurii continued to fight against one another over the Siritide for the subsequent decade. Antiochus, for one, claims that the battle was over the land that had previously been Siris, and that a compromise was reached by which the Thurians and Tarentines could jointly live in the new colony; nonetheless, the colony, Heracleia, was considered Taras’. 639 At any rate, the war was not particularly intense during the initial stages: it was composed of light battles and skirmishes. 640 637 There is a lacuna here. We should not assume that something like “civil war ensued” occurs here. 638 The later colonists are said to have “put to death” the Sybarites, but there is no mention of an actual war or battles. 639 Ap. Strabo 6.1.14. 640 Diod. 12.23.2. 236 Following the democratic revolution in Thurii, it seems that the sophist Protagoras was brought in to modify the existing constitution of the new colony – a constitution based on the laws of the “Pythagorean” Charondas – presumably in a way that reflected Athens’ ideological interests. 641 The result, so claims Diodorus, was the establishment of a democratic form of governance (poli&teuma dhmokratiko&n). Thurii continued to cultivate its relationship with democratic Athens, but Taras’ interests in extending its influence in Magna Grecia, especially in the Siritide, continued to plague Thurii for the next ten years. Relations with Croton seem to have deteriorated as well, and when Thurii invaded Crotonian land sometime in the late 440s or early 430s, the former Pythagorean exiles from Croton (about 60 of them, according to Iamblichus) who had been welcomed back into the city marched out to defend their polis, many dying in the common cause (met’ a)llh&lwn). 642 The war with Thurii continued until 433/2 BCE, when, following the defeat of the Thurians by the Tarentines (attested in an inscription on a lance dedicated to Zeus Olympios at Delphi), Taras established Heracleia Italica on what was perhaps the former acropolis of Siris, which had been destroyed nearly a century before. 643 Thurii’s influence was now limited by Sybaris (IV) on the Traeis to the 641 Diod. 12.11.3 and Heraclid. Pont. F 150 Wehrli = D.L. 9.50. On the constitution of Charondas, see below in this chapter. 642 Iambl. VP. 264. 643 For the lance dedicated at Delphi, see De Juliis 1996: 208 and 224 n.33. 237 south, which was allied with Croton and Caulonia, 644 and Heracleia to the north, which protected Metapontion and Taras from incursions by Thurians on land. In its inability – or unwillingness – to get along with the other “democratic” city-states of Southern Italy, Thurii represents an especially interesting case as the first attempt to create an “ideal” polity – both in terms of civic design and lawgiving – from the “best” constitutions available. 645 Although the original lawcode employed for the city was “Pythagorean,” in the sense that it was derived from that of Charondas, the new settlers seem to have requested an immediate revision of it by Protagoras. The suggestion that Thurii failed to be a “philosophical” polity (in a strictly Pythagorean sense, as at Croton, Metapontion, Acragas, and Taras) is further strengthened by the notable absence of any Pythagoreans from Thurii in Iamblichus’ list. Although he lists Pythagoreans from Croton, Metapontion, Elea, Taras, Sybaris, Locri, Poseidonia, Rhegion, Caulonia, even Etruria and Lucania – among settlements in Italy – Iamblichus preserves no record of Thurian Pythagoreans. Nevertheless, Thurii, as an experiment in colonial design, was to have a profound effect on the development of city-states designed according to ideal systems of civic order, even in Heracleia, which, as a doppelgänger of Thurii, represented Taras’ best attempt to formulate a new philosophical city-state. Once peace was established between Thurii and Taras, they jointly applied themselves to building a new colony that featured a Hippodamean city-plan and came to be the ideological face of the 644 In the 420s. See Plb. 2.39.6. 645 Diod. 12.23.4. 238 Tarentine League. Both Thurii and Heracleia – as models of colonial design – would influence Plato’s political philosophy in ways that have been under-examined by scholars. In this first half of this chapter, I have attempted to provide a history of the democratic revolutions in Southern Italy and Sicily that challenged the traditional constitutional formats, the result of which was experimentation in laws and lawgiving as well as in city-design in order to attain the “best” polity. In the second half of this chapter, we shall explore the surviving fragments and descriptions of the Hippodamean and Charondan constitutions in an attempt to understand the origins of a discourse that would come to dominate the debate about the best constitution in the writings of Plato and Aristotle. PHILOSOPHICAL COLONIES OF MAGNA GRECIA: THEORETICAL MODELS Despite Aristotle’s comment that Hippodamus was the first person who did not practice politics to “attempt to say something about the best constitution,” the testimony of Herodotus suggests that Persians undertook discussions of the best constitution as early as 522/1 BCE – following the usurpation of the Persian throne by the Median Magi – led by the mysterious figure Otanes. 646 Indeed, the links between Southern Italy and Asia Minor are significant during the first half of the 5 th Century BCE: as we have already seen, the Persian force that was sent by Darius in 646 Hdt. 3.80-83. Herodotus, indeed, acknowledges the dispute among (what we must assume are) Greeks (of Athens or Thurii?) as to whether this debate took place (3.80). If we believe Herodotus, the distinction between monarchy, oligarchy, and democracy is again expressed by Pindar in his ode to Hieron (Pyth. 2.85ff.), perhaps composed around 470 BCE. Otanes, as Lateiner (1991: 272 n.12) points out, may have been the focal figure in the “unofficial” Persian source whence Herodotus received this tale. 239 search of Democedes landed both at Taras and at Croton, and the Medizing of the clothing of the of the prytanis in Croton was later thought to be in response to this episode. Likewise, Ionian philosophy from the western coast of Asia Minor was migrating from Miletos and Samos already in the late 6 th Century BCE, and the relocation of Hippodamus to the panhellenic colony of Thurii appears to have had serious repercussions throughout Western Greece: the Hippodamean city-plan was adopted in Thurii, Poseidonia, Neapolis, Metapontion, Heracleia, and in the redesign of Taras. 647 In addition, we have reason to believe that Herodotus relocated from Halicarnassos to Thurii as a new colonist during this period: the oldest extant citation of the famous beginning of Herodotus’ Histories, in Aristotle’s Rhetoric (Rh. 3.9.2), testifies that Herodotus was from Thurii. 648 Hippodamus, too, was credited with being from Thurii. 649 The consensus is that both men immigrated to Magna Graecia in response to the political upheaval in Miletos and Halicarnassos. 650 These links between Western Greece and Asia Minor are significant because they appear to justify the “orientalizing” of political philosophy that may be detected in Herodotus’ Histories, although we cannot be sure that the Persians themselves were responsible for debates concerning the best kind of government. 647 Mertens 2006: 362-70. 648 Aristotle cites the beginning of the Histories in order to demonstrate continuous style: “the continuous style is the ancient one: ‘This is the exposition of the investigation of Herodotus of Thurii’ ( (Hrodo&tou Qouri&ou h#d’ i(stori&hj a)po&deicij).” 649 Hippodamus, De Felic. 1 Thesleff = Stob. 4.49.26; Suid.s.v. Qeanw&. 650 For Hippodamus, see Castagnoli 1971: 66-71; for Herodotus, see the useful biographical study of Smith 1967: 431-2. Incidentally Pliny (HN 12.4.8) claims that Herodotus composed his Histories in Thurii. 240 If, as I have suggested, the original (ca. 445 BCE) plan of Sybaris (III) was designed by Hippodamus of Miletus, we should consider what we can reconstruct of his “best city” from two sources that seem to derive from the 5 th Century BCE: the Doric fragments of Hippodamus’ Peri_ Politei&aj as preserved by Stobaeus and Aristotle’s summary of Hippodamus’ political theory as recorded in the Politics. 651 In all cases, the dominant characteristic is division into triads. Both testimonia and fragments imagine a polity that is to be divided among three classes, all of whom have the capacity to participate politically (koinwnou~si th~j politei&aj) 652 by taking office 653 or voting 654 : the council (bouleutiko&n), the auxiliary (e)pi&kouron), and the mechanic (ba&nauson), which correspond optimally (dei~) with those who rule (a!rxen), those who rule and are ruled (a!rxen kai_ a!rxesqai) and those who are ruled (a!rxesqai). 655 I submit that these classes generally correspond, though not perfectly, with the three kinds of governance to which both Herodotus (in the voice of Darius) and Pindar had made reference: monarchs (or the ruling element), 651 On the dating and general characteristics of these fragments, see Delatte 1922: 125-160. Thesleff (1961: 115 et passim) thought them later (early 3 rd Century BCE), although he assumes without justification that the fragments of group II are all interrelated. 652 Arist. Pol. 1268a18-19. Some discrepancies exist between the summary of Aristotle and the Stobaean fragments: for instance, Aristotle ascribes three classes, namely the artisans (texni&taj), farmers (gewrgou&j), and the military (to_ propolemou~n kai_ ta_ o{pla e!xon). The Stobaean fragments subsume the artisans and farmers into the third “mechanic” (ba&nauson) class, while preserving the “military” (e)pi&kouron) class. The difference, then, lies in the first class in the Stobaean fragments, the council, who are rather poorly described in Stob. 4.1.94 p. 29 He = Thesleff 1965: 98. I shall discuss this first class a bit later in this chapter. 653 Aristotle (Pol. 1268a15-21) complains that inevitably the farmers and mechanics will forfeit all offices since the military class has arms and land. 654 So Aristotle (Pol. 1268b12-14): “The archons were all to be chosen by the people, and the people he made the tripartite division of the city” (tou_j d’ a!rxontaj ai(retou_j u(po_ tou~ dh&mou ei}nai pa&ntaj, dh~mon d’ e)poi&ei ta_ tri&a me&rh th~j po&lewj). 655 Stob. 4.1.93 p. 28 He. = Thesleff 1965: 98.18-20. 241 oligarchy (or the element that rules and is ruled), and democracy (or the element that is ruled). 656 A fascinating fragment of the On Polity as preserved by Stobaeus anticipates the constitutional theory of Plato’s Republic: The laws, then, are responsible to import safety, if the constitution is integrated (su&nqetoj) and drawn up (suntetagme&na) from all others, but I’m not talking about those that are contrary to nature, but the ones that are in accordance with nature. For there is no need for a tyrant in cities, unless, for a short time, there is need for an oligarchy. Therefore, first a monarchy (basilei&a) should be drawn up, and second an aristocracy (a)ristokrati&an). For a monarchy is a thing that imitates God (qeomi&maton pra~gma), and it is hard to keep preserved (dusfu&lakton) by the human soul; for it is changed quickly by luxury and hubris. Hence we should not employ a monarchy universally (kata_ pa~n), but only as far as it may be potent and useful to the constitution. An aristocracy should be interwoven (e)mple&ken) 657 even more, since there are many rulers and they are arranged competitively (filozh&lwj) against one another, and they often exchange rule with one another alternatively. And it is necessary (a)nagkai~on) that democracy be pervasive 658 (damokrati&an…ei}men pa&ntwj), for the citizen, as a subordinate part of the entire constitution, should receive some reward from it. But democracy must be sufficiently restrained, for the masses are brash and headlong. 659 This section of Hippodamus’ treatise expands upon an earlier point he had made in the distribution of the “political commonwealth” (politika_ koinwni&a), a term that the author uses to refer to the entire constitution in its synthetic form. 660 This 656 Hdt. 3.82. Pind. Pyth. 2.85. 657 Note the correspondence here with Plato’s famous interweaving of opposites in the Statesman. On interweaving the polity in Plato, see Chapter 5. 658 Or, possibly, as Greg Thalmann has suggested to me, “that it is altogether necessary that there be democracy.” But we should note the use of pa~n with reference to monarchy two sentences before. 659 Stob. 4.1.95 p. 33 He. = Thesleff 1965: 102.6-20. 660 Stob. 4.1.94 p. 30 He. = Thesleff 1965 99.16-18. Aristotle (Pol. 1252a7 ff.) uses the term to refer to the h( koinwni&a h( politikh& as “the most supreme of all that encompasses all the others (pa&saj perie&xousa ta_j a!llaj).” Nevertheless, he imagines this to be a “middle” and not necessarily a “mixed” constitution, as Hippodamus seems to have believed (although Aristotle does praise the 242 political commonwealth, which resembles a lyre inasmuch as it “requires apparatus, mutual adjustment, and, in sum, some handling and requisite musicianship,” is “fit together (sunarmo&zesqai) with these three elements: logoi, pursuits of habits, and laws.” 661 The function of the laws, so claims Hippodamus, is to preserve the political constitution (as well as the internal constitutions of its citizens) by instilling fear, causing people to abstain from detrimental behaviors, and by exhorting to happiness, a beneficent consequence of honors and gifts. 662 Laws, then, are responsible for safeguarding and perpetuating what is a constitution in the “mixed” sense 663 : while monarchy, aristocracy, and democracy are each part of the political commonwealth, there is a prevailing hierarchy that is analogous to the other hierarchical organizations laid out hitherto. Despite the hierarchy – monarchy, aristocracy, democracy – within the constitution, the quantitative extent to which each governmental form can be present is staggered in the opposite direction: permanence of “mixed” constitutions at Pol. 1297a6-8). There is no reason to assume that when Photius and others called this kind of mixed constitution “Dicaearchic (Dikaiarxiko&n)” (Dicaearchus F88 Fortenbaugh and Schütrumpf), it originated in Dicaearchus’ Tripoliticus: as Fortenbaugh and Schütrumpf point out, the term “Dicaearchic” probably refers only to “just rule” (dikaia arch1). Also see White 2001: 226-7. 661 Stob. 4.1.94 pp. 30-1 He. = Thesleff 1965: 99.18-24. Logoi seem more likely to refer to verbal arguments rather than mathematical ratios of the Pythagorean sort: they are said to “teach and implant desires by turning men towards virtue.” Pursuits of habits, in a highly sophistic way, imprint the youth like wax. On imprints of the soul from the second half of the 5 th Century BCE forward, see Horky 2007 passim. 662 Cf. Arist. Pol. 1268a6-7 and 1268b23-4. 663 Nevertheless, the author of Hippodamus’ On Polity does not use the term “mixed” anywhere, and this notable absence suggests that he had not, at least, read Plato yet. Instead, terms such as sunarmo&zesqai elicit comparisons with Philolaus (F 2 and F 7 Huffman) and Southern Italian inscriptions from Sybaris and Petelia (on which see Chapter 1). 243 democracy is to be totally interwoven within the community, followed by aristocracy (to a lesser extent) and monarchy (inasmuch as it is useful, and no further). 664 Such is the political theory of Hippodamus. Nevertheless, we do not hear that Thurii received its laws according to Hippodamus’ political theory: the colony was only laid out according to the Hippodamean city plan. On the kinds of land and its distribution, the fragments preserved by Stobaeus are silent. But other evidence suggests that Thurii was constituted according to Hippodamean political theory. To substantiate this, we are required to count on the summary of Aristotle, who claims that Hippodamus divided the chora into three parts: the sacred, public, and the private (th_n me_n i(era_n th_n de_ dhmosi&an th_n d’ i)di&an). 665 Aristotle complains that, given the structure of the citizen body, the land-tenure system is too obscure to be practicable: Next, consider the public land, which is to feed the defenders. If they themselves farm it, the fighting part will not be different from the farming one, as the legislator intends. And if there are going to be some others to do so, different from those who farm privately and from the warriors, they will constitute a fourth part in the city-state that participates in nothing and is hostile to the constitution. Yet if one makes those who farm the private land and those who farm the public land the same, the quantity of produce from each one’s farming will be inadequate for two households. Why will they not at once feed themselves and the soldiers from the same land and the same allotments? There is a lot of confusion in all of this. 666 664 It is in this way that we can make sense of Aristotle’s claim that the “people” elected the archons of the city: since democracy was fully interwoven, all the “people” were allowed to vote. 665 Arist. Pol. 1267b34-35. 666 Arist. Pol. 1268a35-b4. Translated by C.D.C. Reeve. 244 Confusion, indeed, mars both the consequences of Hippodamus’ land-tenure policy and Aristotle’s criticisms. What actually happened in Sybaris (III) following its foundation suggests that the military class (or Guard) – who, according to the Stobaean fragments, was meant to mediate between the consular and the mechanic classes 667 – was overpowered (tw~n frourw~n e)ge&neto krei&ttwn) by the people (by which he must mean the lowest contingent) because they had been trained in the war against the Tarentines. 668 It is apparent, then, that the confusion of classes – a consequence of foreign wars – resulted in the failure of the Hippodamean system to sustain the proper internal class structure in Thurii. Aristotle considers this kind of revolution a movement from an aristocracy to a democracy, as I mentioned above. It is in the context of this historical situation that we may consider the Hippodamean political commonwealth a mixed constitution that favors the aristocracy (who are understood as the auxiliary or military class) too heavily, to such an extent that Aristotle dubbed the Thurian constitution “rather oligarchic” (o)ligarxikwte&ra). 669 While the Hippodamean mixed constitution seems to have formed the ideological context for the land organization in Sybaris (III), the laws initially adopted were probably those of Charondas of Catana, to whom later authors laid claim as a “Pythagorean.” 670 Indeed, the ideological program of the Hippodamean constitution reverberates with what we can reconstruct of Charondas’ laws from 667 Stob. 4.1.93 p. 29 He = Thesleff 1965: 98.18-19. 668 On which, see above. 669 Arist. Pol. 1307a32. 670 Iambl. VP. 267, 104. 245 summaries and the Stobaean fragments that preserve the Prooimion to his Laws. 671 Aristotle, who preserves our earliest testimony on Charondas, claims that he was responsible for law-codes in Catana and the other Chalcidic colonies in Southern Italy and Sicily, by which Aristotle meant perhaps Rhegion, Naxos, Leontini, Zancle, Kallipolis, Himera and Tauromenion. 672 Aristoxenus gives us a more selected set of cities – with a few additions – whose laws were crafted according to the law-codes set out by Zaleucus of Locri and Charondas: Croton, Sybaris (I), Catana, Rhegion, Himera, Acragas, Tauromenion, and “some others.” 673 It is the precision of his laws (a)kribei&a| tw~n no&mwn), so claims Aristotle, that establishes Charondas as “more exact” (glafurw&teroj) than the other lawgivers. 674 According to Heracleides Lembus, whose source was Aristotle, the constitution of Charondas established in Rhegion was “aristocratic” (a)ristokratikh_n) because “the Thousand, selected from among the honored, took care of everything.” 675 In this way, Rhegion was constitutionally structured with a boul1 of a similar size to those of aristocratic Croton and Acragas (despite the fact that the “Gathering” of Acragas was established to democratize the government). Further evidence of the aristocratic nature of the Charondan constitution derives from the Stobaean fragments, datable to the 5 th Century BCE, that legislate an 671 On these texts and their dating, see Delatte 1922: 178-202. The texts are probably older than their koine form; see Thesleff 1961: 111-13. 672 Generally, on Chalcidian colonies, see Berard 1957: 68-107. This list corresponds with that given by Ps.-Scym. 283-290. 673 Aristox. F 17 Wehrli. 674 Arist. Pol. 1274b7-8. 675 Heraclides Lembus F 55 Delts. 246 undying loyalty to the “fatherland” (patri&j). The Prooimia to the Laws claim that he who “informs [against someone who is unjust] should be considered pious, even if he reports against one of his own, because nothing is more one’s own (oi)keio&teron) than his patris.” The hierarchy is aristocratic, the language religious: one should honor first the gods, then parents, archons, and laws. 676 The author of the Charondan Prooimia establishes an analogical relationship between obedience owed to archons and that owed to fathers: Men should preserve their good disposition also towards the archons (kai_ pro_j tou_j a!rxontaj eu!noian diafula&ttein), obeying them and honoring them like fathers: to the extent that one lacks sense, so greatly will he pay the penalty (ti&sei di&khn) to the daimones who are the guardians (dai&mosin e(stiou&xoij) for his poor counsel. For the archons guard over (e(stiouxou~si) the city and the safety of the citizens. 677 The Prooimion to the Laws of Charondas, then, equates the archons with daimones in the sense that they “guard” the city. This feature of the constitution, which conflates magistrates with religious figures, is reflective of more widespread religious traditions throughout Magna Graecia in the 5 th and 4 th Centuries BCE. In the ‘Orphic’ gold tablets – many of which were discovered throughout Southern Italy and Sicily (especially in Thurii, Petelia, and Entella) – we hear of the “guardians” (fu&lakej) who request of the initiate that (s)he declare a symbolon in order to be accepted among the heroes, bacchants and mystics who go on the holy journey in the 676 Stob. 4.2.24 p. 153 He = Thesleff 1965: 61.36-62.4. 677 Stob. 4.2.24 p. 152 He. = Thesleff 1965: 61.16-19. 247 underworld. 678 In both the political philosophy of Charondas and the ‘Orphic’ Gold Tablets, “guardians” are responsible for determining who has allowance to participate in a given community, whether religious or political. Indeed, the religious language of initiation is politicized in the Charondan ideal city-state: But it is the character of an upright man (a)ndragaqi&an) to befriend men previously judged to be good (prokekrime&nouj a!ndraj a)gaqou_j) and to associate with them and to be initiated into the greatest and most perfect mysteries (telei~sqai te th_n megi&sthn kai_ teleiota&thn teleth&n) by imitating them in truth and achieving virtue; for no man is complete (te&leioj)without her [virtue]. 679 In this constitution, where education by means of example is central, the youth are expected to follow in the footsteps of men who, in the course of their lives, have proven themselves virtuous. 680 Daimones, who may be either presiding magistrates or avenging chthonic deities in the archaic communities of Southern Italy, both have juridical and punitive functions in the lives – and afterlives – of citizens of these city- states. The elision is not total, but the religious and civic lives of citizens are under examination by these figures. Comparison with a passage from the Prooimia to the Laws of Zaleucus, whose laws were considered to have had the same characteristics as those of Charondas, 681 further demonstrates the common function of the living magistrate and immortal daimon: 678 See Bernabé 474-476 F. We need not, then, consider the political or religious office of “Guardian” original to Plato’s Republic. 679 Stob. 4.2.24 p. 150 He. = Thesleff 1965: 60.22-25. 680 Compare Xen. Const. Lac. 4.2, where the Spartan youth may attain a)ndragaqi&a by means of organized competitions. 681 Ar. Pol. 1274a23-31. Cf. Diod. 12.19.3. Ephorus (ap. Strabo 6.1.8) claims that Zaleucus’ laws were derived from the Cretan, Laconian, and Areopagite laws. His lawcode thus is also mixed. 248 Those who are not impelled to this [justice], especially those who have a soul bent on injustice, let them be advised, as we are, they who are these sorts of citizens and fellow-residents (poli&taij kai_ sunoi&koij): be mindful of the gods, that they exist (memnh~sqai qew~n w(j o!ntwn), and that they let loose judgments on the unjust (di&kaj e)pipempo&ntwn toi~v a)di&koij), and put before their eyes this opportune moment (kairo_n), in which the final point of release from life occurs for every man. For repentance comes upon all who are about to die, when they recall (memnhme&noij) the injustices they committed, and they wish they had done things justly. Therefore, each person, in each thing he has done, should always dwell with (sunoikeiou~n) the opportune moment as if it were indeed present. This is mindful of the good and just. But if some daimon comes upon him turning him towards unjustice, he should spend time in the temples and altars and sacred groves, fleeing injustice like an impious and most difficult mistress, supplicating the gods to aid him in turning her away. He should go before men who have a mind to good virtue (do&can e!xontaj e)p’ a)ndragaqi&a|) and hear about the happy life and the punishments for bad men, in order to be turned away (a)potre&phtai) from unjust deeds, fearing avenging daimones. And they should honor all the gods according to the ways of the inhabitants of the city and according the other paternal laws; the fatherland (pa&tria) is the most beautiful. 682 That the system of justice here reflects Orphic concepts involving the krisis of the afterlife and the payment for unjust deeds is confirmed by the text of the Derveni Papyrus, a fragmentary poem from the late 5 th Century BCE from Thessaloniki that preserves a telestic interpretation of the Poem of Orpheus. 683 In it we hear of Justice (Di&kh) who “punishes pernicious men through each of the Erinyes” and “daimones in the underworld” who “never sleep” 684 and require libations and sacrifices in order 682 Stob. 4.2.19 pp. 124-6 He. = Thesleff 1965: 227.5-22. 683 Generally, see Betegh 2004 and Kouremenos et al. 2006. 684 Taking the object of t]hrou~si as u#pnon or something of the sort. See Kouremenos et al. 2006: 147. 249 to pay the penalty for injustices. 685 Likewise, the Prooimion to the Laws of Charondas preserves a clause in which the citizens of the polis are expected to honor the dead – who may be equated with the chthonian daimones, as they are in the Derveni Papyrus 686 – with beneficent sacrifices: Let us honor each of the dead (tw~n teleutw&ntwn) not with tears or lamentations, but with good memory (mnh&mh| a)gaqh~|) and with an oblation of annual fruits, for grief becomes immoderate (u(per to_ me&tron) when there is ingratitude towards the chthonian daimones. 687 It is worth noting the blend of Orphic and Pythagorean language employed here. The language of initiation and death corresponds specifically with the few comments we hear in Plato’s Republic about Orphics, 688 and the emphasis on “moderation” coupled with memory recalls Pythagorean education 689 and the Orphic Gold Tablets. 690 The Prooimia to the Laws of Charondas and Zaleucus, then, preserve a unique sense of how it was possible to conflate Orphic cult activities and the ideological structures that constituted them, Pythagorean wisdom traditions, and traditional political organizations of Pythagorean polities in Southeastern Italy. It is thanks in part to the publication of the Derveni Papyrus and the Orphic Gold Tablets that scholars can now dispense with Thesleff’s assumption that there is nothing 685 Kouremenos et al. 2006: Columns III and VI. Cf. the ‘Orphic’ Gold Tablet from Thurii (Bernabé 490 F) and Pind. F 133 Sn.-Maehl. and O. 2.58. Also see Hes. WD. 122-23 and 141. 686 Kouremenos et al. 2006: Column VI. Here, too, the magi perform sacrifices to appease the daimones. 687 Stob. 4.2.24 p. 153 He. = Thesleff 1965: 62.8-11. 688 Pl. R. 364b-e. 689 On anamnesis among the Pythagoreans and Plato, see Burkert 1972: 213-15. 690 The Orphic Tablets (e.g. Bernabé 476 F, from Petelia) tell the initiate to pass by the stream of Lethe and proceed forward to the Lake of Memory (ta~j Mnamosu&naj li&mnaj), a concept that is also found in Pythagorean eschatology. See Burkert 1972: 213-15. 250 “particulary Pythagorean” or Orphic about the Stobaean extracts from the Prooimia to the Laws of Charondas. 691 Thus, the Charondan and Zaleucan constitutions appear to be the representatives of the “paternal polity” that is identified with acousmatic Pythagoreans by Iamblichus, against which the democratic Pythagoreans revolted in the mid-5 th Century BCE. 692 Following the democratic revolt in Thurii and the execution of the Sybaritic refugees, the laws of Thurii were probably revised by Protagoras, and it is here that we might see the increased influence of Athens over the Thurian constitution. 693 Little can be said about the laws themselves: Ephorus claims that the character of the Thurian laws was more exact and featured extensive punishments for false accusers, although he criticized these laws for being too complex; 694 we may see this as testimony – coincident with Aristotle’s – for the difference between Charondas’ and Zaleucus’ codes, as Aristotle claims that the legislation of Charondas was remarkable and distinctive precisely for its legislation on false witnesses. 695 Unfortunately, we are left without a clear sense of Protagoras’ involvement in drawing up the Thurian constitution. 691 Thesleff 1965: 63. 692 On which, see Chapter 1. 693 Strabo (6.1.13) confirms this chronology: “Later on, the few survivors [of the destruction of Sybaris (II)] came together and founded it [again], but in time they were destroyed by the Athenians and other Greeks who, although they came to live in tandem with them (sunoikh&sontej), contemned them (katafronh&santej) to such an extent that they both slew them and moved the city to another location, and they named it Thurii after the spring of the same name.” 694 F 139 Jacoby = Strabo 6.1.8. 695 Arist. Pol. 1274b6-7. This contra Ehrenberg 1948: 169, who suggests that the difference here was between Zaleucus’ and Protagoras’ laws. 251 The only extant information about Thurii’s democratic constitution that may perhaps derive from Protagoras’ reforms is the law forbidding consecutive generalships within five years of abdication of office. 696 Our informant is Aristotle, and this passage comes quickly on the heels of the previous discussion of the revolt in Thurii that was responsible for the constitutional change from an aristocracy to a democracy; we should therefore be suspicious of its attribution to Protagoras. Here, the elements are ostensibly the same, but the consequences are radically different. 697 We hear that some young men, who, “having become warlike” (geno&menoi …polemikoi_) earned the admiration of the Guard (or military class), “despised” (katafronh&santej) 698 the men involved in political affairs. They thought that they could gain control easily and tried to repeal the law that prohibited consecutive generalships, on the grounds that “the people would vote for them enthusiastically” (dh~mon au)tou_j xeirotonh&sonta proqu&mwj). The magistrates whose responsibility was to oversee the preservation of the laws, called “councilors” (su&mbouloi), originally opposed the measure, but, as we are told, they “were convinced since they assumed that after the repeal of this law the rest of the constitution would be left alone.” The consequences, so claims Aristotle, were long- lasting: one by one laws continued to be repealed until the whole constitution itself was changed “into a power monopoly” (ei)j dunastei&an) composed of the men who 696 Arist. Pol. 1307b7-8. 697 The account in preserved in Arist. Pol. 1307b4-19. 698 The recurrence of this word suggests either that Strabo (6.1.13) took his version of this story from Aristotle or, more likely, that they both derived their accounts from a single source, probably Ephorus. 252 had initiated the changes. We may therefore understand three consequent shifts in the Thurian constitution: (1) the “people” – having been taught military skills in the war against Taras – rose up and executed the aristocratic Sybarites and redistributed the land, forming a democracy (ca. 445 BCE); (2) Protagoras reformed the Charondan laws and the city was then called Thurii, but the “young men” who had been involved in the wars against Taras began to repeal the laws one by one (with the support of the d1mos), starting with the law that forbade consecutive generalships before four years had passed (ca. 443 BCE); (3) “later on,” so claims Aristotle, the Thurian constitution was changed from a democracy with aristocratic leanings to a dynasteia (perhaps in the 430s). While this chronology of Thurii can be understood within these bounds, we are still unable to confirm whether the law concerning generalships in Thurii is to be ascribed to Charondas’ or Protagoras’ lawcode. Either way, Thurii stands as a significant example of the instability of a polity founded on “philosophical” principles. By the end of the 5 th Century BCE, Thurii’s influence had been reduced and it had been weakened in the war against the Tarentines. And so, when the ever-democratic Lucanians invaded and enslaved Thurii sometime in the early 4 th Century BCE, the revenge of democracy made itself explicit. 699 699 Strabo 6.1.13. On the Lucanians as democratic except in times of war (when they chose a king), see Strabo 6.1.3. 253 THE IDEAL POLITIES OF PLATO’S TIMAEUS-CRITIAS When the Timaeus-Critias was composed, Plato was very clear about the shift away from a Socratic political philosophy of the Republic to the new ideals that he was forging (as experiments in composing “better-governed” 700 and “best- governed” 701 states) in these later dialogues. Socrates himself – in a gesture that recalls the transferal of authority to the Eleatic Stranger in the Sophist – takes leave of the “best” (a)ri&sth) 702 polity they had described in the Republic by relegating it to a Formal status: So, following this, listen now to what I shall explain concerning the Constitution, how I feel about it. My feelings may be compared (prose&oike) with this: if, suppose, after seeing beautiful creatures – whether compositions of painting or actually alive, but at rest – someone would come to the desire to gaze upon them in motion and actively engaged in some exercise appropriate to their bodies. That is how I feel about the city we’ve described. 703 Before this passage, Socrates has been summarizing some of the main points (e)n kefalai&oij) of the Republic, at least as they are applicable to the Timaeus, Critias, and the unwritten Hermocrates. 704 The selection of main points here is worth 700 This term (e!ti ma~llon eu)nomou&menoi) is applied to Athens before the most recent deluge at Pl. Tim. 24d4. Note that it does not refer to Sparta. 701 On this term (eu)nomwta&thj), see below in this chapter. 702 So Pl. Tim. 17c1-3. 703 Pl. Tim. 19b3-c2. 704 At Pl. Crit. 108a5-b7, Socrates tells that Hermocrates will be speaking after Critias, but the Critias itself ends abruptly and without comment. Scholars have assumed that the trilogy would have been structured diachronically: (1) the myth of creation that ends with the birth of humans (Timaeus); (2) the story of primitive Athens and its defeat of the invaders from Atlantis (Critias); (3) a study of the laws of historical Greek polities, up to the setting of the dialogue in the 2 nd Peloponnesian War (Hermocrates). That Hermocrates was the Syracusan general who defeated the Athenian expedition and who, according to Thucydides (4.58), delivered a speech among the Sicilian confederacy in 424 BCE that advised them to unite in fear of an Athenian incursion, cannot be insignificant to the 254 considering carefully: never do we hear about the analogy between the soul and the city or the Myth of Er, which would become so significant to later interpreters of the Republic. What we have instead is circumscribed within the semantic scope of constitutional and legal design: the establishment of a banausic class of farmers and craftsmen who could not bear weapons 705 ; the separation of the Guardian class (fu&lakaj th~j po&lewj) – who were to defend the city externally by arms and internally through litigation – from those lower classes 706 ; the training of the Guardians (both musical and gymnastic) 707 ; the economic commonwealth between the members of the (lower) 708 Guardian class – also called the “auxiliaries” (w(j e)pikou&rouj) – that derives from an ethics of temperance 709 ; the equal status and responsibilities of women for the polity 710 ; and, finally, the common ownership of all children. 711 The constitutional structure of the Republic, as it is summarized completely for the coming discussion, echoes the constitutional structure ascribed to the On Polity of Hippodamus: it features a three-tiered class organization, with a consular class at the top, an auxiliary military class in the middle, and a mechanic class at the bottom. The names of the classes, however, are particularly interesting in Plato’s dialogue or to the history of Plato’s attempts to reform the Sicilian constitutional structure. See Cornford 1959: xviii and xxiii-xxvi. 705 Pl. Tim. 17c6-8. Cf. R. 369e ff. and 374e ff. 706 Pl. Tim. 17c10-18a2. Cf. R. 375b ff. 707 Pl. Tim. 18a9-10. Cf. R. 376d ff. 708 This is not made clear in the Timaeus, but see below. 709 Pl. Tim. 18b1-7. Cf. R. 416d ff. 710 Pl. Tim. 18c1-4. Cf. R. 451c ff. 711 Pl. Tim. 18c6-d5. Cf. R. 457ff. 255 account. Plato initially sees the Guardians as a mixture of the first two classes, separate from the lower “technical” class (374d8-e2) – in the sense that both may carry weapons – but later on (at 412b8 ff.) he distinguishes the Guardians into two further classes: the rulers and the ruled (oi#tinej a!rcousi& te kai_ a!rcontai). The rulers will be called the “Complete Guardians” (fu&lakaj pantelei~j) and the ruled (among the Guardian classes) will be called the “Auxiliaries” (e)pikou&rouj). 712 The plan of Plato’s polity in the Republic, thus, is more complex than that of Hippodamus and appears to modify the basic structure of the Hippodamean ideal city-state: whereas Hippodamus’ constitution features a separate council – a remnant of political structures of the 5 th Century BCE – Plato’s council is integrated with the auxiliary class by means of a common program of education. It is also not apparent that the consular class in the Hippodamean state is capable of bearing weapons: they are related to the auxiliary class in the sense that both have a “free livelihood” (e)leuqe&ran biota_n) and form a “private group” (oi)kh|~a), 713 but the former are expected to “navigate the commonwealth through virtue” (tw~n a)reta~| kubernw&ntwn ta_ koina&) ; the latter, on the other hand, do so “through physical power” (tw~n duna&mei). 714 Of the mechanic class (ba&nauson), there is no sense that the Platonic and Aristotelian concept that one who participates in governance must 712 Pl. R. 414b1-6. 713 Stob. 4.1.93 p. 29 He. = Thesleff 1965: 98.16-17. 714 Stob. 4.1.93 p. 28 He. = Thesleff 1965: 98.13-14. 256 be a “craftsman of virtue” (th~j a)reth~j dhmiourgo&n), 715 which Aristotle states cannot be achieved by the mechanic class, 716 was even within the semantic range for the Hippodamean constitution. Instead, the On Polity of Hippodamus – as we have it – makes no larger claims to a metaphysics of the city or to a paradigm of the lawgiver. We hear simply that the mechanic class is constituted by the portion that works the land (gewpo&non), the craftsmen (texnatiko&n), and the trading (metablatiko_n) and bartering (e)mporiko&n) subgroup. 717 It is in this way that the Hippodamean constitution operates much more pragmatically – and without any attempt to constitute a complex and integrated philosophical pragmateia – than the “best” constitutions expressed in Plato’s Republic or Aristotle’s Politics. The constitution of the Hippodamean On Polity is thus congruent with Aristotle’s description of the primitive constitution of Hippodamus, the first person to discuss the best polity while maintaining distance from political practice. Likewise, in the Timaeus, Socrates summarizes the main points of the Republic in order to distill the main elements of the ideal polity into a format that will be significant for the trilogy to come. In doing so, he highlights those basic and skeletal elements of his earlier constitution. Essentially, what Socrates had never lived to see was the far-reaching consequences of a return from the “mixed” 715 Arist. Pol. 1329a20-2. Aristotle quotes Socrates here (Pl. R. 500d4-8). But the title damiourge, as we discussed earlier in this chapter, was an official magistracy in Croton, Argos, the Heraion, among the “Dorians,” and – of particular importance for Plato – in Solonian Athens and archaic Crete. 716 Arist. Pol. 1228b39-1239a3. 717 Stob. 4.1.94 p. 30 He. = Thesleff 1965: 99.10-15. 257 constitution instituted in 411 BCE to a democratic constitution in Athens. 718 While ethics could lead the philosopher out of the cave and into the world above – where he might come as close as possible to divinity – he was responsible for returning whence he came, back to the world of illusion and imitation, and therefore back to the world of pragmatic politics. What made Plato’s ideal constitution in the Republic so particular – and perhaps something Plato later wished to downplay – was its total pragmateia that was unified along ethical lines. Travels to Sicily and Southern Italy had revealed for Plato the impossibility of the Socratic constitution, and measures to modify it needed to be taken. It is as if Plato’s carefully-constructed revision of his philosophical pragmateia, which I discussed in Chapter 2, had led him back to a pre- Socratic and therefore pre-ethical state of philosophical inquiry. But Plato was still Plato, and that meant rebuilding from the first principles forward: hence the myth of origins presented in the voice of Timaeus, an obscure fiction “from Locri in Italy, indeed, a best-lawed city (eu)nomwta&thj).” 719 Like other Pythagoreans and philosophers from Magna Graecia, he is also drawn up as a statesman: ou)si&a| kai_ ge&nei ou)deno_j u#steroj w@n tw~n e)kei~, ta_j megi&staj me_n a)rxa&j te kai_ tima_j tw~n e)n th|~ po&lei metakexei&ristai, filosofi&aj d’ au} kat’ e)mh_n do&can e)p’ a!kron a(pa&shj e)lh&luqe: 720 718 Interestingly, Thucydides (8. 97) claims that the constitution established following the oligarchy of 411 “became a mixture, a median between the few and the masses (me&tria ga_r h# te e)j tou_j o)li&gouj kai_ tou_j pollou_j cu&gkrasij e)ge&neto)” and that Athens “for the first time in my life appeared to be well-governed (eu} politeu&santej).” I will discuss this passage further in Chapter 6. On the combination of “middle” and “mixed” constitution here, see Von Fritz 1975: 417 n.43. 719 Pl. Tim. 20a2. 720 Pl. Tim. 20a2-5. 258 [He is] inferior neither in property nor in kind to any of the people there, and he has both achieved the highest offices and honors in the city and attained, in my opinion, the summit of philosophy. This is all we know of Timaeus of Locri. The term applied to his polis, eu)nomwta&thj, is particularly interesting because of its scarcity in the Greco-Roman world. A survey conducted using the Thesaurus Graecae Linguae demonstrates that outside of the traditions linked specifically to Plato, this term is only applied to Lycurgan Sparta in cases which are explicitly or implicitly philosophical. 721 As Maximus of Tyre, the 2 nd Century CE sophist claims, Sparta under Lycurgus was “best-lawed” and this in contrast with the Laconian, Attic, Cretan and Persian constitutions. 722 He was partaking in a constitutional history that traces back to the Hellenistic period – indeed, maybe even to the mid-5 th Century BCE, when disputes about the “best” constitution as attributed to mytho-historical “lawgivers” like Zaleucus, Charondas, Solon, Hippodamus, Minos, et al. were popular – that saw Lycurgus as the first lawgiver to find fault with the simple constitutional forms and propose a “mixed” form of governance (specifically the combining of the triad of monarchical, aristocratic, and democratic forms). 723 But the presentation of the constitution of Epizephyrian Locri by Socrates as “best-lawed,” which probably refers to the constitution drawn up by Zaleucus that was, according to Aristotle, 721 This is not the case for Strabo, who uses the term in a non-technical way. 722 Maximus of Tyre, Dialexeis 23.2.c2. Greg Thalmann has reminded me of the eu)nomi&a of the Spartan poet Tyrtaeus (late 8 th Century BCE), which contained praise of Sparta. None of the extant fragments deal with constitutional thought, though, and it is possible that Lycurgus himself never appeared in the poem. Regardless, Herodotus (1.66) claims that under the Lycurgan system, the Spartans “were well-lawed” (eu)nomh&qhsan). 723 This thanks to Polybius (6.3). On the Hellenistic or earlier origins of this concept, see Von Fritz 1975: 83-95. 259 essentially the same as that of Charondas, establishes a subtext to the Timaeus that continues the investigation into and modification of the best constitution in Plato’s works. In fact, the term “best-lawed” (eu)nomwta&th) only occurs in two other places in Plato’s entire corpus: one (Tim. 23c6) immediately follows the introduction of the speaker Timaeus, when Critias tells a story he heard from another Critias (the grandfather of the eponymous oligarch himself) 724 that responds to Socrates’ description of Locri as “best-lawed” by positing the only other “best-lawed” polis he knows of: antediluvian Athens. The second appearance is in the Laws (638b2), once again in reference to Epizephyrian Locri. Contrary to expectation, Sparta is never called “well-lawed” nor is there any specific reference to its eu)nomi&a among the works of Plato; this absence suggests that the influence of Sparta over Plato’s theories of lawgiving – and, consequently, Plato’s political thought – is less marked than that of Epizephyrian Locri. Thus, Epizephyrian Locri appears to provide the best model for Plato’s ancestral lawcode. 725 The mythos of antediluvian Athens is set up in signature Platonic style: Hermocrates responds to Socrates’ request to discuss the “continuation” (to_n e(ch~j lo&gon) of the argument that they had undertaken yesterday in the Republic by recalling what they (i.e. Hermocrates and Critias) had also been discussing yesterday 724 There is no reason, however, to assume that the Critias, who participated in the revolt of the Thirty Tyrants, is not implicitly suggested here. Plato’s great-grandfather and Critias’ grandfather, Critias the Elder, provided Plato with the perfect character to call upon the memory of primitive Athens without unnecessarily offending his democratic Athenian reader. In the meantime, Plato is able to preserve some semblance of historicity in this manner. 725 On this subject, see especially Chapter 6. 260 in lieu of the Socratic discussion that became the Republic. 726 Plato, then, is setting up an alternative narrative to that of his Republic and marking a new turn in his own philosophical pragmateia, but he does so in such a way as to combine the mythoi of political histories of Socrates, Hermocrates and Critias, and Timaeus. Hermocrates appeals to Critias to recite again the story that he had told yesterday, and through this rhetorical move Plato both establishes the alternative political history of Athens of which we will soon learn and provides – at least initially – the impetus for revision of even that model that will be proposed by Critias; after all, as Critias later acknowledges, the antediluvian Athenian state he had heard about from his grandfather is similar to the ideal constitution of the Republic. 727 Today’s discussion, however, is founded on the astronomy and cosmology of Timaeus of Locri, a representative of Pythagorean philosophy, and the goal of the trilogy seems to be to leave the past to the past. Critias begins by setting up the narrative structure of the story, another set of Russian dolls that involve multiple levels of authorial distance: Critias’ grandfather heard from Solon when he was a young boy an “untold” (ou) lego&menon) story – yet unrecorded because of Solon’s concerns about “factions” (dia_ ta_j sta&seij) upon his return to Athens – that recounted Solon’s experiences in Egypt when he was visiting the priests of Sais. A nameless Egyptian priest, whose anonymity recalls the Eleatic Stranger from the Sophist and the Statesman, chides Solon for inquiring 726 Pl. Tim. 20c4-d3. 727 Pl. Tim. 25e2-5. 261 about the most ancient stories available to him (e.g. Deucalion and Pyrrha surviving the flood): “You Greeks are always children; there is no such thing as a Greek elder…You’re all young in your souls, because you have no belief system of old in them that goes back to the original tradition nor any learning hoary with time.” 728 Indeed, the anonymous priest claims, the Greeks and others like them cannot preserve their memories because they are often destroyed by natural calamities, especially fire and deluge, whereas the Egyptians’ records survive because of the Nile, which represents a cycle of stability. If records had survived these calamities in Athens, the Athenians would have known that they once possessed the “best- lawed” city: h}n ga_r dh& pote, w} So&lwn, u(pe_r th_n megi&sthn fqora_n u#dasin h( nu~n )Aqhnai&wn ou}sa po&lij a)ri&sth pro&j te to_n po&lemon kai_ kata_ pa&nta eu)nomwta&th diafero&ntwj: h|{ ka&llista e!rga kai_ politei~ai gene&sqai le&gontai ka&llistai pasw~n o(po&swn u(po_ to_n ou)rano_n h(mei~j a)koh_n paredeca&meqa. 729 Once, Solon, before supreme destruction by floods, the city that is currently Athens was best in regard to war and outstandingly best- lawed in regard to all things: for her deeds and her governances (constitutions?) were said to have become the most noble of all those under heaven handed down by tradition. The traditional constitutional structure of antediluvian Athens, which, according to the Egyptian priest, dates to 9000 years before the time of Solon, resembles that of Egypt during this time: there is a separation of antediluvian Athenian society into what appear to be three classes, each distinct from the other: priestly, military, and 728 Pl. Tim. 44b4-8. 729 Pl. Tim. 23c3-d1. 262 the “mixed” demiourgic or banausic. 730 In the expanded version of this story, recorded in the incomplete sequel to the Timaeus, Critias tells us very little about the priestly class: the only thing we learn – and only if we adopt Hermann’s unconvincing emendation 731 – is that it lived in common with the military class on a segregated area of the old acropolis that was fenced in by a single enclosure that effected a “single house” (mia~j oi)ki&aj). 732 The enclosure at the topmost part of the acropolis featured two temples – one to Athena and one to Hephaestus – that reflect the ideology of the constitutional division into classes (i.e. intelligence, military strength, and the banausic arts). 733 It seems that the priests and the military class – who are compared with the Guardians despite some slight differences of emphasis 734 and called a “single genos” 735 – shared their “polity” (th|~ koinh|~ politei&a|) and received nothing from the lowest class except sufficient sustenance. 736 If the priestly class was included among this group, then the commonwealth among the higher two classes of the Republic is concordant with the sketch of antediluvian Athens, and vice versa. 737 If not, we learn little explicit about the priestly class except that they 730 Pl. Tim. 24a3-b3. 731 Pl. Crit. 112c1. Hermann adopts i(ere&wn, while the manuscripts preserve i(erw~n. The temples of Athena and Hephaestus have been mentioned in the previous sentence, but we have not heard anything about the priests since the introduction to the Timaeus. 732 Pl. Crit. 112b4-5. 733 Pl. Crit. 112b4-5. 734 Pl. Crit. 110d4. On differences, see below. 735 Pl. Crit. 112b3. Indeed, the text itself (au)to kaq’ au(to_ mo&non ge&noj) suggests that Critias is only referring to the military class (and not a mixed Kind), which is distinct from that of the priestly class. 736 Pl. Crit. 110c7-d2 and 112b7-c1. I say “seems” because there is a dispute in the manuscript tradition regarding the term. 737 Let us not forget, as Critias emphasizes ad nauseam at the beginning of the Critias (106b8-108a4), that this is only an “obscure sketch” (skiagrafi&a| a)safei~) and imitation of the true constitution of antediluvian Athens. 263 dwell apart and (perhaps) that they are responsible for the initial social organization of the city-state. 738 What immediately strikes the reader is the difference between the highest classes of antediluvian Athens and the politeia of the Republic: in the Republic, the Guardians were not expected to partake of religious responsibilities, the latter being reserved for the priests at Delphi. 739 Things divine, so claims Socrates in the Republic, cannot be understood by Socrates and the citizens of the polity they are inventing. As for antediluvian Athens, the priestly class was expected to reflect Athena’s proclivity for intelligence, being responsible – it is implied – for the care of the cosmos/order (e)pime&leian…peri& te to_n ko&smon), by which the Egyptian priest means what is “derived from divine things as applied to human affairs: divination, medicine – with a view to health – and all other sciences (maqh&mata) acquired that are attached thereto.” 740 Plato gives no reason for the lack of a governing and separate Guardian class and the inclusion of a priestly class, but the absence of the centralized panhellenic authority at Delphi in antediluvian Athens is revealing: the Guardians of antediluvian Athens, who lived near a “spring” that once nourished the Athenian acropolis, governed the “rest of the Greeks” (tw~n de_ a!llwn (Ellh&nwn 738 Pl. Tim. 24a4-5. At Crit. 110c5-6, we hear that the military class was “separated off at the beginning by the divine men” (u(p’ a)ndrw~n qei&wn kat’ a)rxa_j a)forisqe&n). It is unclear whether these “divine men” are priests or lawgivers, or perhaps both. Nevertheless, the term “in the beginning” occurs in similar conditions (prw~ton) at Tim. 24a, where Critias separates out the “class of Priests” (to_ tw~n i(ere&wn ge&noj). 739 Pl. R. 427b1-c4. 740 Pl. Tim. 24b7-c3. 264 h(gemo&nej e(ko&ntwn) who agreed to be ruled by their own consent. 741 Like the Nile that moderated the land in the Egyptian Delta and the spring from which the panhellenic colony Thurii received its name (thanks to the Dephic oracle), this spring in antediluvian Athens was “tempered both in winter and in summer” (eu)kra_j ou}sa pro_j xeimw~na& te kai_ qe&roj). 742 Antediluvian Athens is presented, then, as a state slightly modified from the Socratic politeia of the Republic: it features a “separate” priestly class that went unmentioned in the Republic and an ill-defined military class that does not seem to be split into a ruling and a ruled element, and it appears to have been the leader of a federated group of Greeks. While it is possible (though improbable) that this city- state existed 9000 years before the time of Solon or even in Egypt during Solon’s lifetime, its constitutional structure reflects polities that existed in Magna Graecia during the mid-5 th Century BCE whose laws were originally laid down according to the lawcodes of the “Pythagoreans” (as they were understood popularly during the mid-4 th Century BCE) Zaleucus and Charondas. Even the new emphasis on starting from divine principles and moving towards the human – expressed pragmatically by the introduction of a new “priestly” class in the account of “best-lawed” antediluvian Athens – reflects the ethics and legislative structure of the Prooimion to the Laws of 741 Pl. Crit. 112c8-d5. 742 Pl. Crit. 112d3. 265 Zaleucus, who was traditionally understood to have given laws to “best-lawed” Epizephyrian Locri. 743 As of 352 BCE, Epizephyrian Locri probably represented the most stable lawcode in the Greek world, having not changed its laws in 200 years (presumably since they were established by Zaleucus) except once. 744 The term “best-lawed,” then, also connoted a system of laws that, ideally, was stable enough to perpetuate itself ad infinitum, or at least until a natural calamity befell the citizens of that polis. The constitution of Epizephyrian Locri featured an assembly of the Thousand, like Rhegion, Croton, and Acragas in the mid-5 th Century, who exercised control over the other archons. 745 The presiding magistrate, who was assigned supreme jurisdiction but who had to answer to appeals made by the Thousand, was called the kosmo&polij, whose other responsibilities and powers are unknown. 746 His duty to preserve the kosmos, however, corresponds to the terms in which the priestly class in Critias’ account of antediluvian Athens was described (e)pime&leian…peri& te to_n ko&smon). 747 Likewise, of the archons, we hear that there are “Guardians of the Laws” (tw~n no&mwn fu&lakej) whose responsibilities echo those of Plato’s 743 Locri was said to have had fostered ten Pythagoreans (Iambl. VP. 267). 744 Demosthenes, In Timocr. 24.140. As Sartori (1953: 130) reminds us, the period in which Dionysius II ruled over Epizephyrian Locri (352-346 BCE) saw massive constitutional changes. How ironic it is that the former student of Plato would be responsible for upheaval in the most stable constitution in the Greek world. See Chapter 6. 745 Plb. 12.16.10-11. 746 Plb. 12.16.6 and 13. On this term, see Sartori 1953: 130 with n.8. 747 Pl. Tim. 24b7-c3. Cf. Stob. 4.2.19 pp. 123-4 He. = Thesleff 1965: 226.24-6: Tou_j katoikou~ntaj th_n po&lin kai_ th_n xw&ran pa&ntaj prw~ton pepei~sqai xrh_ kai_ nomi&zein qeou_j ei}nai a)nable&pontaj e)j ou)rano_n kai_ to_n ko&smon kai_ th_n e)n au)toi~j diako&smhsin kai_ ta&cin. We also hear of kosmoi in Crete, on which see Sartori 1953: 131. 266 Guardians both in the Republic and the Critias and predict the nomophylakes of the Laws: Let the guardians of the laws (oi( tw~n no&mwn fu&lakej) take as their responsibility (e)pimelei&sqwsan) offenders, first by warning them, and if they don’t obey, by punishing them. If someone thinks that the laws as they stand are not good, let him change them for the better. But for those that remain, let all obey their order. While it is neither good nor beneficial for the laws to be degraded by men, it is good and beneficial for a degraded man to be ruled over by a better law. But transgressors of these things should be punished for setting up a rule by the most evil (men) in the city: anarchy. The archons should not be arrogant, nor judge insultingly, nor be mindful of friendship nor hate, but of justice. Thus they will render most just judgments and be worthy of rule. 748 While we may conclude with Morrow that the text of Zaleucus’ Prooimion to the Laws as preserved by Stobaeus features many elements in common with Plato’s texts, we need not assume that the text of Zaleucus derived its terms from Plato’s works. 749 If, as I am suggesting, the Prooimia to the Laws of Charondas and Zaleucus and the On Polity of Hippodamus reflect attempts by acousmatic Pythagoreans to legitimate their own position as central to the traditions of developing “best” constitutions that establish a tripartite class system, there is no reason to assume that the whole composition of these Stobaean texts must have been derived from Plato, and this theory does not respond to the evidence found in traditions not bound to Platonic philosophy and epigraphy. It is more likely, given the evidence above, that Plato found himself competing against and assimilating 748 Stob. 4.2.19 pp. 126-7 He. = Thesleff 1965: 228.2-13. Generally, on the Stobaean fragments of the Prooimion to the Laws of Zaleucus, see Delatte 1922: 177-195. 749 On the term “Guardian” or “Guard” in the late 5 th Century BCE ‘Orphic’ Gold Tablets, see above. 267 traditions of Pythagorean governance and constitutional design throughout his career in much the same way he was responding to the tenets of both acousmatic and mathematical Pythagoreanism throughout the entirety of his philosophical pragmateia. The failure of Athens to perpetuate a “best” system of governance led Plato first to compose an ideal Socratic polity in the Republic, then to modify that ideal polity slightly in his representation of antediluvian Athens in the Timaeus and Critias. Had he finished the Hermocrates, we might perhaps have heard much more about Epizephyrian Locri and the other historical “Pythagorean” city-states of Southern Italy in the 5 th Century BCE that provided Plato with a context from which to derive his constitutional ideals, but even the Critias preserves what would become for Plato an obsession to which I have gestured: the battle between Athenian and Persian constitutional systems (democracy and monarchy, respectively), those “mother-constitutions” of all others that would become central to Plato’s understanding of the history of governments as he began to lose confidence that any ideal polity could be established in his world. The war between antediluvian Athens and Atlantis in the Critias would come to mirror the negotiation of democratic and monarchical elements in the “second-best” constitution of the Laws, 750 and Magna Graecia occupied the middle – indeed, the mixing – ground between those extreme poles: 750 I cannot go into detail here about the reflections of Ecbatana and the the Median empire that preceded Darius’ reign in Critias’ presentation of Atlantis. See Chapter 6 and Friedländer 1958: 314- 322. 268 There are, as it were, two mother-constitutions, from which someone, if he were to say so, would say correctly that the others are derived: one is rightly called monarchy, and the other, in turn, is democracy. The former Kind is represented in the extreme by the Persians, and the latter by us [the Athenians]. Nearly all the others, as I have said, are varieties of these. It is especially necessary that one partake of (metalabei~n) both of these if freedom and friendship are to be combined with intelligence. 751 The missing term in Magnesia, then, is Magna Graecia. For, if we are to believe Herodotus, Magna Graecia had been the first place that the Persians had “encountered” the Greeks in the early 5 th Century BCE before the Persian Wars, and as such it was the original conduit for Persianizing elements in the Greek world (at least according to tradition). Thus Pythagoras had emigrated from Samos to Croton, becoming a vessel for transmission of eastern elements of science, ethics, and rule to the West. In Chapter 6, I will go on to explore the “mixed” constitution of the Epistles and Laws in reference to another influence on the later political philosophy of Plato: the constitutional theory of the mathematical Pythagoreans, as reconstructed from the fragments of the philosopher-politician Archytas of Taras. But before attempting this difficult subject, I hope to contextualize the later political philosophy of Plato by constructing a narrative of the changes that occurred in Plato’s entire philosophical pragmateia as a consequence of innovations made in mathematics by Archytas and his pupil Eudoxus of Cnidos. 751 Pl. Lg. 693d2-e1. 269 _______________________________________ CHAPTER 5: THE MAGNESIAN ROCK: FROM RADICAL TO MATHEMATICAL CITY _______________________________________ “You see, good Philebus, the Goddess, when she saw the hubris and all the wickedness of all people – that there was no limit to their pleasures nor to their indulgences – established law and order as limits.” – Socrates, Plato’s Philebus (26b7-10) In Chapters 3 and 4, I argued that shifts in Plato’s theories of dialectic and of Form went hand in hand with his attempts to substantiate mathematics fully as a foundational element of his philosophical pragmateia. A consequence of this complication of mathematics with Socratic ethical systems as proposed in the pre- 367 BCE dialogues was the problematization of the doctrine of separate but participatory Forms established especially in the Phaedo and Republic; as Plato’s dialectical theory – and, consequently, his ontology – underwent radical shifts, he began to reconsider the place of logistic (i.e. the negotiation of the Great and the Small) in his diaeretic and synthetic systems. Plato also began to reconsider the teleological element of dialectic, and the Myth of the Unwinding of the Universe functioned in the Statesman as a paradigm for understanding the place of dialectical cyclicality within the process of attaining knowledge (through alternations of division and combination). The introduction of cyclical dialectic creates new problems, however, for the Eleatic Stranger’s definition of the political or kingly art and, by extension, of the Statesman himself. Cyclical dialectic perpetuates the 270 investigation into a selected topic while it fails to be conclusive, and the Stranger proposes alternate avenues for attaining a complete and measured definition of the Statesman. These methodological procedures, as we will discover in this chapter, are further elaborated in the highly complex Philebus, where Socrates’ last gasp in the Platonic corpus proposes an ethics based on principles derived from the mathematical Pythagoreans that implicitly engages the ethical systems of Philolaus of Croton, Archytas of Taras, and his pupil Eudoxus of Cnidos. The new dialectical method proposed in the Philebus expands upon the doctrine of mixture – first attested in the fragments of Philolaus – in combination with the cyclical temporal procedure expressed at the fulcrum of the Statesman, and the resulting dialectical theory (also a theory of ontology) reflects further modifications in Plato’s Theory of the Forms. As I will also demonstrate, these advances in dialectical theory are expressed in political terms, and the Statesman’s activity is finally defined in paradeigmatic analogy with weaving, a practice that leads to communion and harmony according to Pythagorean principles (indeed, in concert with the political theory of the Pythagoreans at Taras). Plato’s defense of participation in the Philebus, in response to the criticisms that he expounded in the Parmenides, focuses not only on the systematic adoption of the Pythagorean Limit and Limitless as principles and Number as an intermediary, but also the introduction of a Fourth Kind that provides Plato with a means to regulate the infinite regress of the Third Man argument. 271 CYCLICAL DIALECTIC AND POLITICAL WEAVING IN THE STATESMAN In the Statesman, the Myth of the Unwinding of the Universe is a paradeigma that functions to highlight the presence of cyclical argumentation as an improvement over the simple dichotomies expressed in their earlier form of “right- hand” definition in the Sophist. 752 Without attention to the reversals, combinations of opposites, and structural reorganization of the universe – that is to say, without a nuanced appreciation of and reflection upon cosmic motion and time – the student cannot arrive at knowledge about a subject. 753 Technically speaking, the methodological “way” (o#doj) becomes circuitous (peri&odoj). It is here, in the Myth, that the Eleatic Stranger begins to extend the experiments in eristic of the second half of the Parmenides that dealt specifically with the Pythagorean (indeed, Philolaic and Archytan) application of first principles involving Limited and Limitless. 754 But the movement towards a Pythagoreanized dialectical theory is only partially complete: indeed, the Myth itself can only stand as a point of convergence that allows for comparison between the older dialectical theories of the Middle Period and the future of dialectical procedure, to be completely explained later in the Philebus. As a paradeigma, however, the Myth provides Socrates the Younger and 752 See Kenneth Sayre’s excellent discussion of different kinds of diaeresis in Sayre 2006: 52-72. 753 It is in this sense that Melissa Lane (1998) appreciates the Statesman’s necessary skill of kairos (opportunity). Nevertheless, she has not applied the kairotic skill to music and mathematics, a topic I shall undertake later in this chapter when discussing the “Promethean” gift in the Philebus. 754 See Sayre 2006: 162-168, building upon Sayre 2005: 18-49. 272 the reader glimpses of what will be a revised dialectical procedure by employing the concepts behind Limited and Limitless without explicit appeal to the familiar formula from the Pythagorean Table of Opposites. Let us begin by examining, once again, the Myth of the Unwinding of the Universe which divides the Statesman into two thematic halves. 755 Once Kronos, here called the Pilot of the All (tou~ panto_j o( kubernh&thj), has let go of the rudder and retired to his tower, “fate and its fellow-grown desire” cause a reversal in the turning of the universe, a sign that the daimones interpret as marking the time to “relinquish the Parts of the cosmos from their care” (a)fi&esan au} ta_ me&rh tou~ ko&smou th~j au(tw~n e)pimelei&aj). 756 The reversal is significant here and, as we will see, anticipates the divine dialectical theory of the Philebus: “the cosmos was incited with an opposite impulse, regarding beginning and end” (a)rxh~j te kai_ teleuth~j e)nanti&an o(rmh_n o(rmhqei&j). 757 After a sufficient amount of time, chaos and confusion are given pause (pauo&menoj) – another concept that will be crucial in Plato’s later dialectics – and the universe rights itself under its own care and power (e)pime&leian kai_ kra&toj e!xwn) according to its recollection of the teachings of the demiurge/father. As a consequence of its somatic element, which causes forgetting, however, the universe gradually begins to spin out of control again, and the 755 Although it does not correspond as a mean division, as it falls roughly 1/3 of the way into the dialogue. As a “cut” in the dialogue, then, it functions to limit the dialogue subjectively. 756 Pl. Plt. 272e3-273a1. Cyclicality and weaving are correlated later in the lusus Troiae of the Aeneid and may be more generally related in archaic Roman culture. See Scheid and Svenbro 1996: 35-49 and Habinek 2005: 19-21 and 114-21. 757 Pl. Plt. 273a2-3. For translation of this passage, see Campbell 1988: ad loc. and Taylor 1961: 280. 273 helmsman takes control in turn. As we saw in Chapter 3, this process of shifting back and forth between oppositional forces of confusion and order is modeled on the alternations in Empedoclean metaphysics, which is substantially related to Pythagoreanism of a democratic sort. 758 Indeed, the short summary of this process offered by the Eleatic Stranger that concludes the Myth suggests the Pythagorean first principles of Limited and Limitless: dio_ dh_ kai_ to&t’ h!dh qeo_j o( kosmh&saj au)to&n, kaqorw~n e)n a)pori&aij o!nta, khdo&menoj i#na mh_ xeimasqei_j u(po_ taraxh~j dialuqei_j ei)j to_n th~j a)nomoio&thtoj a!peiron o!nta po&nton du&h|, pa&lin e!fedroj au)tou~ tw~n phdali&wn gigno&menoj, ta_ nosh&santa kai_ luqe&nta e)n th|~ kaq’ e(auto_n prote&ra| perio&dw| stre&yaj, kosmei~ te kai_ e)panorqw~n a)qa&naton au)to_n kai_ a)gh&rwn a)perga&zetai. 759 And so, there comes a time when God, who had put it into order, when he gazes down upon it in these confusions, concerned lest it be stormed by disorder and so founder in the limitless sea of unlikeness, once again becomes helmsman of the tiller; he turns back the things that had become ill or dissolute in the previous cycle of self- sufficiency, gives it order, and, by realigning it, completes it as immortal and unaging. While the term “Limit” never appears in this passage, it is clear that the principle of the “Limitless sea” (a!peiron po&nton) is exposed here as the threat to the universe that would cause its destruction if it weren’t for the imposition of order (kosmei~) that completes the universe by making it immortal and unaging (that is, no longer in a 758 Indeed, all accounts (Empedocles, Philolaus, Plato) might be derived structurally from the cosmology of Parmenides. Fragment 306 KRS (= Simplicius in Phys. 39.14 and 31.13) shows that the goddess Justice or Necessity (cf. Fragment 307 KRS = Aetius 2.7.1) is in the midst (e)n me&sw|) of the inner (central) fire and the outer (perimeter) fire and “governs all things” (pa&nta kuberna~|). This scheme is also adapted by Plato in the Myth of Er (Republic 617-18). 759 Pl. Plt. 273d4-e4. 274 state of Becoming). Plato does not adopt simply the Limit and Limitless of the Pythagoreans as principles or constituents of the universe, but he has begun to apply basic Pythagorean oppositions to his own cosmology. The Eleatic Stranger here embraces the second half of the Pythagorean opposition, while almost explicitly calling to mind Philolaus of Croton’s Fragment 1, the beginning of On Nature: tou~to&n fhsi Dhmh&trioj e)n (Omwnu&moij prw~ton tw~n Puqagorikw~n Peri_ fu&sewj, w{n a)rxh_ h!de: a( fu&sij d’ e)n ko&smw| a(rmo&xqh e)c a)pei&rwn te kai_ periano&ntwn kai_ o#loj <o(> ko&smoj kai_ ta_ e)n au)tw|~ pa&nta. Demetrius, in People of the Same Name, says that he [Philolaus] was the first of the Pythagorics to publish an On Nature, of which this is the beginning: “Nature in the cosmos was fitted together both out of Limitless things and Limited things, both the cosmos as a whole entity and all the things in it.” Philolaus’ method of understanding the cosmos as a Limitless entity that has been given boundaries by Limited constituents is now well-established thanks to the work of Carl Huffman. 760 Furthermore, a fragment of doubtful authenticity preserved by Johannes Lydus (F 20a Huffman) colors our understanding of the possible Philolaic reference in the Myth of the Unwinding of the Universe. Lydus claims that “Philolaus is correct when he claims that the Dyad is the consort of Kronos (th_n dua&da Kro&nou su&neunon), whom one could obviously call Chronos. It is to time as the cause of destruction that the Dyad is joined. It [the Dyad] is the mother of 760 Huffman 1993: 37-53. Huffman overlooks this passage of the Statesman in reference to Platonic parallels with Philolaus. 275 flowing being (mh&thr…th~j r(eusth~j ou)si&aj).” 761 The marriage of Kronos and Rhea was traditional as recorded in Hesiod’s Theogony, 762 and it is also attested in the Orphic Hymns as preserved by the author of the Derveni Papyrus, whose testimony that Rhea was the “mother of the many dappled things” is punctuated by the explanation of her name: (Re&a d’ o#ti polla_ kai_ po[i]k[i&la] zw~ia e!fu [e)kreu&santa] e)c auth~j... 763 (She is called) Rhea because she gives birth To many dappled living things and they flow forth from her…. Huffman is hesitant to attribute this fragment to Philolaus, believing that the notion that Rhea was equated with “flowing” could not predate Xenocrates and was primarily academic. But Plato had no issue with attributing to the onomatology of Rhea a sense of “flowing” in a passage that deals very much with Heraclitean and Orphic kinds of signification: Socrates assumes that Heraclitus and Orpheus both named the gods according to their attributes and actions within the cosmos. 764 The Derveni Papyrus substantiates Plato’s claim and suggests that the engagement of Rhea, the flowing goddess, with Kronos is central to cosmogonic stories ascribed to 761 Lydus, de Mensibus 4.64 (114.20 Wünsch) = F 20a Huffman. Translation by Huffman (with slight changes). Cf. F 20 Huffman, in which Lydus explicitly compares Philolaic and Orphic numerology. Philolaus seems to have been interested in using the term “mother” metaphorically and in connection with politics and mathematics, as T A7a Huffman (= Plutarch Quaest. Conv. 718e) attests: “Geometry being, as Philolaus says, the source and the mother-city (a)rxh_ kai_ mhtro&polij) of the rest (of the mathematical sciences)…”. So too Xenocrates, on whom see Burkert 1971: 249n.53. 762 Hes. Th. 446ff. 763 Col. XXII.14-15. I am adopting Tsantsanoglou and Parássoglou’s emendation of the text (assumed by Burkert as well), which follows the logic of the passage in which names are being defended for their function in the Derveni author’s system of interpretation. Also see Betegh 2004: 189-90. 764 Pl. Cratyl. 400c ff. 276 Orpheus. Now Orphism and Pythagoreanism were correlated as early as Herodotus and Ion of Chios, 765 and so we are not compromised in assuming that some aspect of Philolaus’ genuine philosophy might be at least responsive to Orphic ideas. 766 Plato also employs Orphic ideas, especially in the myths that involve life cycles and death; like Philolaus, he adapts Orphic traditions to fit into his philosophical program. This is achieved by appropriating Orphic language and imagery into a new context of philosophy, involving ethics (as in the Myth of the Judgment in the Gorgias), astronomy (as in the Myth of Er in Republic X) and mathematics, as in the Statesman. Indeed, the Myth of the Unwinding of the Universe assumes a relationship between Kronos, whose sure hand guides the Universe away from dissolution, and the “Limitless sea” (a!peiron po&nton) that threatens the ordered cosmos. The Eleatic Stranger’s Myth here assumes a Pythagorean/Orphic cosmology based on the limiting factor associated with Kronos and the flowing sea, the consort of Kronos (in Philolaus’ terms). 767 Further reflection on the Myth reveals the characteristic Pythagorean/Orphic obsession over memory and recollection, and the contrary forces of memory and forgetting that fuel Orphic eschatology as encountered in the Orphic Gold Tablets correspond with the 765 Hdt. 2.81.2 = Bernabé 650 T and D.L. 8.8 = Bernabé 506 T. 766 Certainly Clement (Stromata 3.17 = F 14 Huffman) had no problems connecting Philolaus to the Orphics through the Cratylus passage referred to above. Huffman (1993: 402-4) himself is at a loss about whether to attribute the famous sw~ma/sh~ma paralogy to Philolaus. 767 Archytas of Taras, possibly Philolaus’ student (A 5c2 Huffman = Cicero, de Oratore 3.34.138-9), also understood the sea (qa&latta) as a limitless factor within ratios of limited to limitless terms. See A22 Huffman = Arist. Metaph. 1043a14-26 and the accompanying discussion, especially pp. 498-9. I discuss this fragment in Chapter 6. 277 forces of order and disorder exposed in the Myth. 768 Nevertheless, as Plato’s paradeigmatic myths often do, the Orphic mysticism is suppressed behind vague references and nearly insurmountable enigmatic language. 769 For Plato’s later dialectical theory, as we will see in the Epilogue, myths provide one half of the dialectical equation, namely the “irrational” or “incommensurable” element that must be made commensurable with commensurables. Following the Myth, the Eleatic Stranger and Socrates the Younger return to the implicit discursive topic of the afternoon: error. They revive the earlier discussion about “caretaking” (e)pime&leia) and reassess their conclusions by noting the manner of rule, whether it is divine or human; 770 for, as we noted in Chapter 3, one of the significant undercurrents in the Sophist and the Statesman is the apparent dichotomy between divine and human, and the possibility of a mixed Kind that participates in both. Now, the Eleatic Stranger wants to be clear about the nature of the two chronological circuits of the universe: one is essentially marked as immortal, the other mortal. 771 The Myth functioned as a paradeigma, but the Stranger warns Socrates the Younger that they need to be clear about what compares with what; again, the emphasis on timing is crucial. Having distinguished between human and divine caretaking, they finalize the definition of the Statesman begun way back at 768 Among Tablets of Southern Italian or Sicilian provenance, see Bernabé 474 F (from Hipponion), 475 F (from Sicily), 476 F (from Petelia). For bibiliography on the exhaustive studies that deal with memory in the Orphic Gold Tablets and in other 5 th and 4 th Century BCE writings, see Bernabé 2005: 17. A useful recent comparison between Orphics and Pythagoreans is Bremmer 1997. 769 See, for instance, Horky 2007. Also see Edmonds 2004: 159-219 and 227-8. 770 Pl. Plt. 274d9-276d6. For a useful summary of this passage and of its import upon the shifting dialectical method, see Sayre 2006: 25-28. 771 Pl. Plt. 274e9-275a3. 278 Plt. 258c3, using only what Kenneth Sayre, following the terms laid out in the Sophist, calls “right-hand” division, illustrated here in this diagram: Figure 4: 1 st (Revised) Definition of the Statesman (Plt. 258c3-276e8), from Sayre 2006: 27. As Sayre has shown, the Eleatic Stranger and Socrates the Younger have adhered to “Right-hand” division since concluding their discussion of Not-Being at Soph. 264d10, following the Stranger’s command to “keep dividing in Parts to the right” (kata_ tou)pi_ deci_a a)ei_ me&roj tou~ tmhqe&ntoj) in all subsequent diaereseis. 772 This method must be considered in tandem with the paradeigmatic Myth, which is employed to provide a comparison from the non-technical world; indeed, while 772 Sayre 2006: 109. 279 paradigms will continue to be useful as a partial response to the criticisms raised in the first part of the Parmenides, “right-hand” selection is immediately replaced by a more comprehensive and synthetic kind of diaeresis that involves both right- and left-handed division. 773 But before returning to paradigms and divisions in both directions, I want to conclude the discussion of the errors encountered in the first definition of the Statesman, which was subsequently revised following the Myth of the Unwinding of the Universe. Once the participants have concluded the right-hand diaeresis, Socrates the Younger assumes that they have finally arrived at the definition of the Statesman. Nevertheless, the Eleatic Stranger complains that they have erred once again in their definition: Actually, in my opinion, our king does not yet appear to have his sketch complete, but just as sculptors, who from time to time are inopportune in their zeal and embellish each thing in their work more or less than is necessary (para_ kairo_n e)ni&ote speu&dontej plei&w kai_ mei&zw tou~ de&ontoj), slow everything down, so we, for the sake of demonstrating quickly and with immediacy the error in the progression we made earlier, considered it appropriate to make up large-scale paradigms for the king; by raising up a remarkable mass of myth, we were forced to apply a greater Part of the myth than is necessary. Thus we made a demonstration too long and did not achieve its total completion, but our logos was simple, just like a picture that seems sufficient in its outline but has not been distinguished in any way by colors and composition of the tones, so to say (oi{on toi~j farma&koij kai_ th~| sugkra&sei tw~n xrwma&twn e)na&rgeian ou)k a)peilhfe&nai pw). 774 773 On “mixed” kinds of division, see below. 774 Pl. Plt. 277a4-c3. On the meaning of e)na&rgeia here, see Campbell 1988: ad loc. 280 This passage demonstrates the heightened presence of oppositional forces which come to dominate the later dialectical theory of the Philebus that Aristotle, in the Metaphysics, understood as based on the principles of the “Great and the Small.” 775 Sayre overlooks the mixing of oppositional dialectics here, especially in reference to the process of combining right- and left-handed diaereseis in order to produce a comprehensive and complete definition (logos) of the Statesman: for, as he has convincingly shown elsewhere, the process of defining weaving that will take up most of the second half of the dialogue as well as the method applied to defining the Statesman in his final presentation both involve dichotomous (i.e. “right-hand”) and poly-tomous (i.e. “left-handed”) division. 776 Synthetic diaeresis, then, which leads to a definition, involves a mixing of opposites (specifically, Pythagorean opposites) in a methodological sense: the mixing involves combining right- and left-handed division, or dichotomous and poly-tomous division. Dichotomous division is a simple bifurcation that establishes a binary pair; poly-tomous division, however, breaks down a genus into individuated species by cutting “limb-by-limb” (kata_ me&lh), like cutting a sacrificial victim. 777 Even with the mythic paradigm, the Eleatic Stranger is claiming, they have not been able to create a division that is complete with its full mixture of oppositional forces: the Great and the Small, Quickness and Slowness, Right and Left, Subjective and Quantitative. They have not yet arrived at a sophisticated application of the principles of Limit and Limitless that are 775 On which, see most recently Sayre 2006: 154-70. 776 Sayre 2006: 26, 122, and 127. 777 Sayre 2006: 124-5. 281 fundamental to the philosophical system of Philolaus and (probably) Archytas, although the interest in outline and fill in the added paradigm of the sculptors anticipates what is to come. Nevertheless, the language that speaks here of mixing and colors recalls Empedocles’ conceptualization of a harmony of four tones, a subject I explored in reference to the writings of Hippasus and Philolaus in Chapter 1. 778 What is to be the factor that produces a well-mixed definition that employs dichotomous and poly-tomous diaereseis? As Lane has shown, the element of timing (kairos) is important here as elsewhere in the Statesman for establishing a temporal mean that functions to establish a well-made paradigm: The passage criticizing the story (277a-c) serves as a fulcrum for the introduction not only of paradeigma but also of measurement. Each of the points of criticism assesses the story against an explicit or implicit standard. Recall the simile of the hasty sculptors who ‘hurry when it is not appropriate (para kairon) to do so and actually lose time by making additions and increasing the size of the various parts of their work beyond what is necessary (tou deontos)’ (277a6-b1). Their actions are measured against the kairos, the right opportunity for action, and found wanting. The additions are measured against the deon, the necessary, and found excessive both in number and in scale. 779 Lane’s focus on the temporal element is a bit misapplied here, although it will be more significant in the musical dialectical theory proposed by the Philebus. 780 778 As, indeed, I discussed Empedoclean ontology and division in Chapter 3. Taylor 1961: 287 went so far as to translate th~| sugkra&sei tw~n xrwma&twn as “harmony of the tones.” 779 Lane 1998: 125. She is right to locate this passage as the fulcrum of the whole dialogue and to criticize those scholars who have ignored or dismissed this passage as something “virtually severed from the rest of the dialogue” (1998: 100). 780 On which, see later in this chapter. While Lane is right to detect the significance of the kairos here, her treatment focuses too extensively on its temporal (i.e. Sophistic) quality. Part of the problem 282 Nevertheless, we can adapt Lane’s reading of this passage by exposing its inherent mathematicization: proper timing (kairos) functions as a standard that mediates between oppositions and catalyzes the proper mixture between binary forces that make up a subjective measurement. We can therefore understand this passage within the discourse of logistic which, as I claimed in Chapter 2 when discussing the sciences of the Republic, facilitates a subjective measurement of things by localizing them with a tertium quid that sets a standard by which to allow for designations of “greater” or “smaller” in comparative terms. Thus the whole discourse about paradeigmata that follows upon and criticizes the Myth of the Unwinding of the Universe successfully explores the possibilities for application of logistic to definitions. 781 If we are confused about these relationships and the method by which the Eleatic Stranger has expressed them, we are not alone: Socrates the Younger asks for more clarification. The Eleatic Stranger responds by invoking the teaching of language to children, with a particular emphasis on the use of paradeigmatic sounds in order to instill memory of individual letters. Once again, the paradeigma of teaching letters functions as a tertium quid that illustrates, through comparison, the method of logistic to which the Eleatic Stranger has just referred in 277a-b: it is, in with interpreting the kairos in these passages, I think, is Plato’s unwillingness to reverse totally the criticisms he has made of Gorgianic rhetoric and its focus on kairotics in the Gorgias. 781 Cf. Archytas F 3 Huffman, where logistic is said to reconcile opposite elements of the society, including the powerful and the poor, the wealthy and the needy. See Chapter 6. 283 the words of the Eleatic Stranger, a “paradeigma of paradeigma.” 782 The learning of letters follows the new methodological program involving forward and reverse motion – as demonstrated in the Myth of the Unwinding of the Universe – while emphasizing the significance of comparison by means of interweaving (sumplokh&), a word that functions to introduce the subject of weaving that will occupy what remains of the dialogue: ELEATIC STRANGER: So isn’t it easiest and best to lead them [children] up to what they don’t know – SOCRATES THE YOUNGER: Yes? ELEATIC STRANGER: – by first leading them back to those syllables of which they made a correct interpretation as being the same? Once they’ve been led back, [it’s best] to place those things next to the ones they don’t yet know and, once they’re side-by-side, to demonstrate that the same likeness and nature exists in both interweavings (th_n au)th_n o(moio&thta kai_ fu&sin e)n a)mfote&raij ou}san tai~j sumplokai~j), until those placed next to all the ones they don’t know have been demonstrated as identified truly, and once demonstrated, they become paradeigmata as such. 783 This form of logistic, what we might call paradeigmatic logistic, allows children to identify elements within compositions (i.e. letters within syllables) by means of comparison and contrast with other syllables. This constitutes a relative or subjective kind of comparison. The main objective, so claims the Eleatic Stranger, is to be able to understand sameness and difference, so as to be able to formulate a true opinion. Nevertheless, the Eleatic continues, this form of comparison requires an original standard that is truly judged and known, and not just anything can function 782 Pl. Plt. 277d9-10. Cf. Soph. 252e9-253e2, where learning letters is analogous to dialectical praxis. 783 Pl. Plt. 278a5-b5. On weaving in the Statesman and its relationship with Athenian politics, see also the excellent treatment of Scheid and Svenbro 1996: 9-34, although their treatment neglects the Pythagorean echoes. 284 as a paradeigma and tertium quid by which to posit comparative relationships between two different combinations. One must seek a standard that can be known in truth and whose elements interweave with other elements in order to create combinations. In this sense, this second reference 784 to weaving in the Statesman functions as an incomplete answer to the challenges that the Third Man argument of the Parmenides posed: the third combination that provides a point of comparison and contrast – the standard – must be known according to true belief in the first place. When the Eleatic Stranger and Socrates the Younger undertake the final paradeigma of the dialogue – the definition of weaving – they do so without having first agreed what this “standard,” by which points of comparison and constrast can be rendered, must be. Once again, motion back and forth from first principles and elementals to complex combinations is the rule of the game: in this way, the Eleatic Stranger’s dialectical method echoes the back-and-forth circuitry of the Myth of the Unwinding of the Universe and establishes itself in contradistinction to other Pythagorean and Presocratic traditions such as what is preserved in the On Nature of 784 The first reference, at 267b6, is used in the “right-handed” form of definition without any explicit application to dialectical process. It is used, however, to refer to the process of combining elements to create a “triple” name. Terms rooted in “sumplek/-ok” are featured throughout the Sophist (240c2, 242e1, 259e6, 262c6, 262d4). Of these, the occurrences at 242e1 and in 262 are remarkable: the former is used in reference to the “interweaving” that the Sicilian and Ionian Muses practice (on which, see Chapter 3), and the latter is also employed to discuss the process of creating language. Other pre-Statesman occurrences of sumplek/-ok terms are worth mentioning: Theaet. 292b5 also refers to the understanding of interwoven letters in words (a passage that Sayre: 77 has failed to note also features a recurrence of dreams in reference to paradeigmatic language-dialectic theories), and at Symp. 191a-c, Aristophanes paints the initial diaereseis and reintegration of the sundered humans after the fall. I have earlier discussed the significance of Apollo’s diacritic tool (in Chapter 3), although a total comparison between the myth of Aristophanes’ speech and Plato’s theories of dialectic is beyond the scope of this project. This usage is reflected in the spurious Platonic Epistle 6 (323b1), which imitates Aristophanes’ speech throughout. 285 Philolaus, where first principles must be laid down before one is able to proceed with the discussion. 785 Platonic texts always function on several registers at one single time, and in this case the discussion of standard, to which the Stranger has alluded beforehand, comes within the limits of the definition of weaving. 786 Weaving functions within the Statesman as a standard paradeigma, for reasons that I will demonstrate shortly. It engages in the logic of the dialogue according to the rules established in the discussion of language that precedes this passage, as the Stranger makes clear at the outset of the definition: So what paradeigma should someone apply – one that has the same program/business (pragmatei&an) as the political art – that is extremely small in order to sufficiently discover what we are seeking? By Zeus, O Socrates, does this work? Unless we have another one in hand, why don’t we select the weaving art (th&n ge u(fantikh&n)? 787 Of particular significance in this passage to our argument is the terminology employed that makes weaving a worthy point of comparison with the political art: both of them have the same pragmateia, a word that demands closer scrutiny. As I discussed in Chapter 1, the term pragmateia in Pythagorean philosophy (as construed through the lenses of Aristotle in the Metaphysics and his student Aristoxenus in On Arithmetic) concerns the application of theoretical and ontological assumptions to applied pragmatics in business – especially mercantile trade – and in 785 See Philolaus F 1 Huffman. Recall Plato’s abrasive criticism of Dionysius II’s book On Nature; Plato refused to express his first principles as such in writing. See Chapter 2. 786 The present chapter is primarily concerned with treating the shifts in dialectic that accompany shifts in political thought throughout the dialogues and letters of Plato. I will discuss the origins of political weaving, and political weaving more generally, as historical phenomena in Chapter 6. 787 Pl. Plt. 279a7-b2. 286 politics. For Aristotle, the pragmateia of the Pythagoreans, whose goal was to render definitions, was “too simple” because it assumed ontological relationships that did not separate out things in praxis (such as “doubling”) and concepts (such as the number two). 788 The semantics here are slightly different, although not incommensurable, with the Aristotelian usage: the Eleatic Stranger is claiming that the arts of weaving and politics share one element, namely their pragmateia, and we can therefore proceed to comprehend the political art by means of paradeigmatic comparison with the art of weaving. Like the earlier discussion about letters, we can see here that the shared pragmateia is like the letter that is common between two syllables and that allows a child to apprehend those elements that are different between the two systems: if we apply the Pythagorean triad here – ontology, ideal, and pragmatic – we can see that, while the arts of weaving are not the same (an obvious point), not even formally (because formal correlation would be impossible given the prescription that Forms are always unique even if they partake of other Forms), they are pragmatically the same or similar. A shared pragmateia, then, is essentially the third term that allows a person to understand how things can be ontologically and formally different while preserving shared characteristics with other things: the result is that praxis allows human beings to comprehend the Forms 788 Arist. Metaph. 987a13-28. Cf. Aristoxenus F 23 Wehrli = Stob. Ecl. 1. Prooem. 6. 287 that would otherwise stand apart, and the Eleatic Stranger thus responds to some of the problems that arose in the Parmenides. 789 The consequences of this interpretation of Plato’s dialectical and definitional theories are wide-reaching, but what is perhaps most significant is the newfound emphasis on application (construed here as political activity). By recognizing the shared, participatory element in the praxis of things, Plato is able to synthesize the ideal and the pragmatic in ways that will affect his philosophy permanently. The dialectical proof that analogy was made possible through application is something that allows for a complete coherence in the Philosopher who practices the political or kingly art, and Plato has finally found a dialectical theory that justifies his desire, first put forth in the Republic, that the enlightened Philosopher would return to the cave and engage in political activities in the sensible world. So, then, the question arises naturally: what precisely is the pragmateia that the arts of weaving and of statesmanship share? Following the circuitous method established in the Myth of the Unwinding of the Universe, the Eleatic Statesman returns to the issue of separation and combination as a primary dichotomy that works itself into the middle of the definition of weaving itself, as Sayre has demonstrated in this diagram: 789 In this way, the paradeigma, as a tertium quid, functions like a metaphor in Aristotle’s sense of the term (Arist. Rh. 3.2.9-10). Indeed, Aristotle there claims that they must be made “of proportion” (e)k a)nalo&gou). Later on (Rh. 3.11.5), when discussing those metaphors that are made “according to proportion” (kat’ a)nalogi&an), he praises Archytas’ analogy between an arbitrator and an altar. On Archytan definition, see Chapter 6. 288 Figure 5: Definition of the Art of Weaving (Plt. 281d8-283a8), from Sayre 2006: 107. Note that this definition, which itself emphasizes the significance of the arts of separation (diakritikh&) and collection (sugkritikh&) in tandem (the Eleatic speaks of separation and collection in the dual at 282b6-8), features extensive left-handed division of the poly-tomous sort as well. Left-handed division allows one to understand what weaving is not, and it therefore functions contradistinctionally. We may agree with Sayre that “[w]eaving in effect is defined by eliminating other arts with which it shares relevant characteristics.” 790 So too, as Sayre has demonstrated, the definition of the Statesman employs right- and left-handed diaereseis in order to 790 Sayre 2006: 111. Italics original. 289 advance towards a definition of the Statesman in terms of both what he is and what he is not. 791 The mixed dialectical method proposed here therefore coheres with the identity of its proponent, whose Eleatic roots can still be perceived at the root of Plato’s discourse. Circuitous method, however, cannot provide a complete definition of a thing, if it lacks a standard by which to judge the whole process. Such is the conclusion of the Eleatic Stranger who, after he has claimed that weaving receives its name when a fabric has been completed (a)perga&zetai) from the interweave of woof and warp (eu)quploki&a| kro&khj kai_ sth&moj), he questions the periodic method that he has recently introduced: ELEATIC STRANGER: So why didn’t we just reply straightaway that the art of weaving is the intertwining of woof and warp? Why did we turn about in a circle, arranging everything in vain (perih&lqomen e)n ku&klw| pa&mpolla diorizo&menoi ma&thn)? SOCRATES THE YOUNGER: It doesn’t seem to me, O Stranger, that anything we said was said in vain. ELEATIC STRANGER: Perhaps, dear boy, it will seem so. In preparation for this sort of sickness, if indeed it should often befall us later on – and that would be no surprise – pay attention to an argument that will have some bearing on all sorts of things that will be said. 792 In keeping with the main theme of the dialogue – error – the Stranger revises yet again the dialectical method that is being practiced. Now we hear the famous discussion of excess and deficiency, which has recently been studied in a pair of 791 See Sayre 2006: 113-131. 792 Pl. Plt. 283b1-c1. 290 publications by Kenneth Sayre. 793 While a comprehensive study of excess and deficiency provides crucial insights into the shifts in dialectical theory and into the ways in which Aristotle’s account of Platonic metaphysics can be correlated with the metaphysics of the later dialogues of Plato, as Sayre has already shown, I will confine myself to those aspects of the theory of measures that are applicable to my larger project of understanding the place of Pythagorean mathematics in the revision of Plato’s whole philosophical program. First of all, we need to recall that two elements derived from the circuitous method paradeigmatized in the Myth of the Unwinding of the Universe need revision: the circuitous method itself and, consequently, the excessive length of the Myth and of the definition of weaving. Now we must emphasize that Plato was not in the business of totally excising earlier developmental aspects of his dialectical, ontological, and metaphysical theories; he preferred to continue to refine them, a process that echoes the practice of making definitions themselves. 794 A refined definition, like a refined theory of dialectic that produces the definition, must be both well-sketched and vivid (i.e. it must have e)na&rgeia). This term must be further explicated and contextualized with Fragment 4 of Archytas from the Diatribes, in which he is discussing logistic as a means to complete demonstrations: 793 Sayre 2005 and Sayre 2006. 794 Near the end of the Statesman (303d4-e5), the Eleatic Stranger will refer precisely to the metaphor of “refinement” of gold from other metals as paradeigmatic of the dialectical process. Anthropological comparisons between weaving (as female separation and combination) and metallurgy (as male separation and combination) can be found in Jenkins 1985. 291 kai_ dokei~ a( logistika_ poti_ ta_n sofi&an tw~n me_n a)lla~n texnw~n kai_ polu_ diafe&rein, a)ta_r kai_ ta~j gewmetrika~j e)nargeste&rw pragmateu&esqai a$ qe&lei. kai_ a$ e)klei&pei au} a( gewmetri&a, kai_ a)podei&caj a( logistika_ e)pitelei~ kai_ o(mw~j, ei) me_n ei)de&wn tea_ pragmatei&a, kai_ ta_ peri_ toi~j ei!desin. 795 Logistic seems to be far superior indeed to the other arts in regard to wisdom and in particular to deal with what it wishes more vividly than geometry. Again in those respects in which geometry is deficient, logistic completes demonstrations and equally, if there is any investigation of shapes, [logistic completes demonstrations] with respect to what concerns shapes as well. Huffman is correct to contextualize this fragment with Fragment 3 of Archytas, in which logistic is understood as a means to the wisdom that leads to a good life. 796 I follow Huffman in assuming that this fragment, whose primary interest is in pragmatic procedure (e.g. pragmateu&esqai, tea_ pragmatei&a), is itself part and parcel of a more comprehensive theory of political and social conduct, as evidenced in Fragment 3, where logistic is the tool that ceases stasis and increases concord by reconciling the poor and the rich and by serving as a “standard” (kanw&n) that corrects injustices. 797 Even a brief examination of Fragments 3 and 4 of Archytas reveals the significance of his mathematical theories to Plato’s discussion of measure here in the Statesman: both fragments provide a guide to achieving successful demonstrations, key to the proposition of any dialectical method (although it is disputable whether or not Archytas practiced a simpler form of dialectic). What is 795 Archytas F 4 Huffman = Stobaeus 1. Proem 4 (p. 18.8 Wachsmuth). Translation by Huffman, with some slight changes. ei!dh cannot mean “Forms” in the Platonic sense here, but means something closer to geometric “shapes” or “figures.” On this term, see Huffman 2005: 250-1. 796 Huffman 2005: 235. 797 Archytas F 3 Huffman = Stobaeus 4.1.139. 292 more, both Archytas and Plato discuss the place of logistic within political philosophy. 798 But close attention to the term “more vividly” (e)nargeste&rw) problematizes issues: whereas Archytas assumes that vividness comes from arguments that are primarily arithmetical in nature, the Eleatic Stranger seems to be saying that paradeigmata that lack an appropriate standard of measure – which has not yet been established – beget incomplete definitions that fail because they are not vivid to the observer. They fail to appear vivid due to their lack of a standard that functions to limit the Great and the Small quantitatively. One way to examine this opposition is to consider the value of geometry and logistic in the mathematical systems of Archytas and Plato. Archytas places a strong emphasis on the power of logistic and claims its superiority to geometry in ethics and politics, although he cannot complete his proof of the doubling of the cube without rotating a triangle about a fixed point; Plato, following Philolaus and contra Archytas, assumes the superiority of geometry to logistic/arithmetic in politics, at least in the Republic, where it is geometry that leads the striving philosopher up to the Form of the Good. 799 In Chapter 6, I will discuss these mathematical means and their place in formulating kinds of political structures within constitutions, but suffice it to say for now that Plato is adapting the discourse about logistic and its place in demonstrative proof from Archytas, and that this passage in the Statesman 798 Aristotle’s praise of Archytas’ use of metaphor (Rh. 3.11.5) occurs within the section that exemplifies vivid metaphors that have proportion. 799 See Chapter 2. Cf. Philolaus A 7a Huffman: “geometry is the a)rxh& and the mother-city of the other sciences.” For other ways to consider “vividness,” see Huffman 2005: 246-7. 293 involving the definition of weaving and the establishment of a standard of measurement directly engages with the philosophy of Archytas. The description of the standard of measurement is applied to the passage previously cited in which the Eleatic Stranger claims that they must “pay attention to an argument (logos) that will have some bearing on all sorts of things that will be said.” 800 The standard of measurement that follows, then, will be employed throughout the process of defining the Statesman and his pragmateia that occupies the rest of the dialogue, and its part in the revision of dialectical theory should not be underemphasized. 801 What role the appropriate or due standard of measure plays in the definition of the Statesman – especially in his pragmatic duties – remains to be discussed. But this passage may be seen as a dialectical exercise that attempts to show how the pragmateia of the weaver and of the Statesman are analogous, a process that requires a tertium quid (or an absolute standard by which these Forms, as they both partake in it, can be compared). First of all, the Eleatic Stranger presents the case for appropriate measure in adaptation of the Pythagorean contraries to which Aristotle referred in the Metaphysics; his dichotomy of “Excess and Deficiency” (th&n te u(perbolh_n kai_ th_n e!lleiyin) correlates best with the Pythagorean Alcmaeon of Croton’s “random” 800 Pl. Plt. 283b8-c1. 801 In his discussion of the “main purpose of the dialogue,” Sayre 2005: 28-35 gives cursory treatment to this passage and does not account fully for its significance to the revision of dialectic. He is more successful when concerning himself with the discussion of excess and deficiency. Interpretations of the Statesman that recognize the significance of this passage include Lane 1998: 125-136, Guthrie 1978: 169-175, and Skemp 1952: 78-9, where he concludes that Plato is engaging in “an important new application of Pythagorean principles and an anticipation of the famous doctrine of the mean in Aristotle’s Nichomachean Ethics.” 294 list of contraries, 802 where the “Great and the Small” (me&ga mikro&n) are mentioned, as emphasized by Sayre. 803 We might recall that Aristotle thought, for Plato, that the principles of the Great and the Small were analogous to the Limitless principle; Plato’s theories are distinguished from the those of the Pythagoreans by the fact that his Limitless principle is both dual and consists of the Great and the Small. 804 But Aristotle is nowhere clear about how one gets from the Great and the Small to its relative counterparts, Excess and Deficiency. An examination of the Eleatic Stranger’s argument helps us to understand the place of appropriate measure in his revised theory of dialectic: ELEATIC STRANGER: First, then, let’s examine all Excess and Deficiency so that we might praise and censure speeches concerning these occupations that are longer than necessary and the opposite [i.e. speeches that are shorter than necessary] in accordance with reason (kata_ lo&gon). SOCRATES THE YOUNGER: Of course, as we must. ELEATIC STRANGER: As long as our argument (lo&goj) happens to concern these very things, it will develop correctly. SOCRATES THE YOUNGER: What things? 802 Plato knew the medical writings of Alcmaeon of Croton and discussed them in the Phaedo; see Timpanaro Cardini 1958: 128-139. According to Aristotle (de An. 405a29 ff.), Alcmaeon also believed that the soul was immortal, “for he said that it was immortal due to its being similar to immortal things; and he predicated this on the grounds that it is always in motion, for, he claimed, all divine things are moved uninterrupted and always: moon, sun, stars, and the whole heaven.” 803 Arist. Metaph. 986a34. The “great and the small” occur nowhere in the list of the “others” from the so-called Pythagorean school, by which Aristotle means the acousmatic Pythagoreans (Metaph. 986a15-26). On this subject, see Chapter 1. Sayre’s (2005:97-8) citation of Simplicius (453.35-6) posits Porphyry’s understanding of a relationship of equivalence between the “Great and the Small” and “the More and the Less”: The same holds, says Porphyry, of “the Greater and Smaller, and as Plato calls them the Great and the Small” (to_ mei~zon kai_ to_ e!latton kai_ ta_ a)nt’ au)tw~n lego&mena u(po_ Pla&twnoj to_ me&ga kai_ to_ mikro&n). While Porphyry seems to have assumed that these elements were analogous, I will argue that he (as well as Sayre, who follows him) has failed to account for the place of “becoming” in the relationship between these sets of oppositions. 804 Arist. Metaph. 987b20-27. 295 ELEATIC STRANGER: Length and Shortness and all Excess and Deficiency; for the art of measurement (h( metrhtikh_), I suppose, concerns all these things. SOCRATES THE YOUNGER: Sure. ELEATIC STRANGER: Let’s divide it into two Parts, then. For that’s the way to get what we are currently after. SOCRATES THE YOUNGER: Would you please say what way the division should go? ELEATIC STRANGER: This way: the first Part of measurement deals with the communion of greatness and smallness as related to one another (kata_ th_n pro_j a!llhla mege&qouj kai_ smikro&thtoj koinwni&an), and the second deals with the Being that is necessary for Becoming. 805 As Taylor noted, the language here is “intentionally made to sound mysterious” and requires significant exegesis in order to make sense of the polysemy. 806 The term logos is being used duplicitously: it clearly refers to the definition of the art of measurement, but when the Stranger claims that they will need to praise and censure speeches that are too long or too short “in accordance with reason” (kata_ lo&gon), he is playing on the alternative mathematical meaning, namely “according to a standard (or, perhaps even, a ratio).” For the absolute length or shortness of an element – and subsequently any valuation of it – can only be assessed with reference to a standard, as the theory of logistic expressed in the Republic attests. Even before he has begun to discuss due measure, he is employing the concepts behind it in his methodology. Relative measurement, then, is concerned with the “communion of greatness and smallness as related to one another” and thus represents an extension of the 805 Pl. Plt. 283c2-d9. 806 Taylor 1961: 297. 296 doctrine of participation found in the pre-Parmenides dialogues of Plato. Greatness and Smallness are assumed to partake of one another, but to understand the relationship between them, we need to posit an appropriate shared element or tertium quid that allows for the establishment of absolute relationships. It appears from the subsequent comparison with the other kind of measure that relative measurement is implicitly connected to Becoming, and this inference is highlighted by the presence of a playful discourse on the logos (definition/standard) itself and its coming-to-be through dialectic. The other kind of measure, still unnamed, deals with the “Being” that is a precondition for Becoming; another way to put the point is that the yet unnamed category of measure (due measure) is to Being as relative measurement is to Becoming. 807 When the Eleatic Stranger speaks about the art of measurement, he is generally referring to what Socrates in the Republic called logistic, although the introduction of a standardized tertium quid is an innovation. In the Statesman, we 807 Or, as Miller (1979: 65-6) translates this passage, “that based on the essential being necessary to coming-into-being.” His interpretation of this passage, in which he suggests that “the mean spans the ontological gap between form and particulars,” is very similar to mine: he wants to highlight the particular significance of the mean (logos) for the diaeretic praxis of the dialogue itself: [T]he ‘being’ of forms is ‘necessary’ to such existents [(gignomena)]: as purposive, speeches and deeds are essentially defined by their aim to realize or instantiate forms. Thus, to fashion a relevant example, the statesman works to realize the just state, that is, to actualize in social-historical fact the ideal of just polity…As the fullest possible realization of the form, given the limits of context, the mean serves as the norm for praxis, the standard by which essential measure can judge speech and actions. For an examination of the argument concerning due measurement that breaks down this whole passage argument-by-argument, see Sayre 2005: 319-51. In general, I would suggest that Sayre is correct to contextualize this passage with the Philebus, but he does not sufficiently acknowledge that there is a progression from the dialectical theories of the Statesman to those of the Philebus. The Eleatic Stranger himself is not deterred from referring to the “development (i.e. Becoming)” of their argument (logos) in the Statesman. 297 can see the advancement of the mathematical study of logistic beyond the fragments of Archytas, who assumes a logistic that correlates with Plato’s concept of due measurement, and so we might suggest that it is in the area of relative measurement that Plato improves upon the Archytan scheme. 808 The Eleatic Stranger himself refers to the ways in which his distinction between two categories of measurement – indeed, accompanied by two sets of standards (one that is relative and leads to things in excess or in deficiency, and the other that is due and leads to real quantitative measurement) 809 – represents an improvement over the basic theories of logistic of people who preceded him: Indeed, Socrates, the very thing that sometimes many of the erudites (polloi_ tw~n komyw~n) say, when they think they are making some wise declaration, namely that the art of measurement concerns all things that are coming-to-be (metrhtikh_ peri_ pa&nt’ e)sti_ ta_ gigno&mena), this happens to be precisely what we were just saying. For, in some way, all things that are related to the arts partake of measure. But since they are not accustomed to examine things by division according to Form (kat’ ei!dh), they straightaway conflate things that differ extensively into the same thing, seeing as they consider them to be alike (o#moia nomi&santej). And they also do the opposite by dividing things that are different not according to Part (ou) kata_ me&rh). But, whenever someone first perceives a communion among many things (th_n tw~n pollw~n koinwni&an), he should not conclude his division before he sees all the things that exist in Forms; in turn, whenever the various dissimilarities (pantodapa_j a)nomoio&thtaj) have been seen in many things, he should not be allowed to feel able to rest before he has confined all similar things in 808 Cf. Archytas F 3 Huffman, where logistic appears to be ratios of numbers that negotiate between ontological categories of “rich” and “poor” (rather than “richer” and “poorer”). 809 Pl. Plt. 283e7: “So we must posit two standards in reality for the Great and the Small, not simply as we said a bit ago that there was need for one alone that concerned things related to one another [the relative], but just as we have just been saying, namely one that must be admitted as relative, and the other, in turn, that is in accordance with due measurement.” 298 a single likeness and circumscribed them in the reality of a single Kind (ge&nouj tino_j ou)si&a| periba&lhtai). 810 A comprehensive exegesis of this passage is beyond the scope of this chapter, but we can agree with Campbell, Skemp, and Miller that the “erudites” to whom the Stranger refers are Pythagoreans. 811 Aristotle is clear about this: he claims that Plato improved upon the crude and simple definitions of the Pythagoreans by introducing the doctrine of the Forms to dialectical theory, an advancement that addressed inconsistencies regarding the essence of contraries. 812 For Aristotle, this improvement is linked to the introduction of the “mathematical practicals” as an intermediate class between ideal numbers and sensibles. Now the fragments of Archytas make no mention of things “that are coming- to-be,” but we should not assume that he would employ the same vocabulary as the Eleatic Stranger, who is to be counted among the followers of Parmenides. But Iamblichus, when he quotes a section from Archytas’ Fragment 1, expands upon the Tarentine mathematician’s theory in a way highly reminiscent of this passage: “toiga_r peri_ tw~n kaqo&lou,” fhsi_n )Arxu&taj, “kalw~j diagno&ntej e!mellon kai_ peri_ tw~n kata_ me&roj, oi{a& e)nti, kalw~j o)yei~sqai.” dio&per ou) mo&na ou)de_ monogenh~ ou)de_ a(pla~ u(pa&rxei ta_ o!nta, poiki&la de_ h!dh kai_ [ta_] polueidh~ qewrei~tai, ta& te nohta_ kai_ a)sw&mata, w{n ta_ o!nta h( klh~sij, kai_ ta_ swmatika_ kai_ u(p’ ai!sqhsin peptwko&ta, a$ dh_ kata_ metoxh_n koinwnei~ tou~ o!ntwj gene&sqai. 813 810 Pl. Plt. 284e11-285b6. 811 Campbell 1988: 107; Skemp 1952: 173-4; Miller 1979: 68. 812 Arist. Metaph. 987a27-33 and 1078b21-27. 813 Archytas F 1d Huffman = Iambl. VP. 160. Translated by Huffman, with slight changes. 299 “Therefore, having made good distinctions about universals,” Archytas says, “they were likely also to see well about particulars, what sorts of things they are.” Wherefore, the existing things are not single, of one kind, or simple, but they are already observed to be varied and of many shapes, both the intelligible and the incorporeal things, for which the name is “the existing things,” and the corporeal things and the things that fall under the purview of sensation, which by participation share in actual becoming. Extracting what is Archytan from what is Platonic or simply confused by Iamblichus is extremely challenging. Nevertheless, we might recall that the Eleatic Stranger has suggested that the “erudites” do perceive “communion” among many things, a term that seems firmly embedded in Platonic theories of Participatory Forms but might have a less technical usage in the dialectical theories of Archytas. What is clear, however, from Fragment 1 of Archytas is the presence of division according to parts, a process that appears to be similar in application to division according to universals. The Eleatic Stranger’s criticism of the “erudites” – that they divide not in accordance with the Forms – applies here to Archytas, whose ontology shows no signs of interest in Socratic or Platonic Forms as such. Archytas, like the other Pythagoreans who receive Plato’s and Aristotle’s censure, espoused a theory of division and believed that the universe could be understood by establishing ratios of analogous comparison 814 ; it does not appear, however, that these analogies were categorized according to the ontological dichotomy of Being/Becoming that is currently underscored in much of the Eleatic Stranger’s discussion. 814 On this fundamental aspect of Archytas’ philosophy, see Chapter 6. 300 Closer examination of Fragment 1 of Archytas in its entirety reveals the context for what Iamblichus is saying about the mathematician. Following the selection quoted above, Archytas claims: “Indeed, concerning the speed of the stars and their risings and settings as well as concerning geometry and numbers and not least concerning music, they handed down to us a clear set of distinctions (pare&dwkan a(mi~n safh~ dia&gnwsin).” 815 Iamblichus thus Platonizes this fragment in his exegesis, while the original fragment of Archytas reveals a confusion of phenomena and ideal systems of praxis such as geometry and music, which are subsequently considered the “sister sciences.” 816 If this hypothesis holds ground, then Iamblichus himself correlated Fragment 1 of Archytas with the argument expressed here in the Statesman. While Archytas appears to have provided the impetus for the Eleatic Stranger’s criticism of the “erudites,” other echoes of Pythagoreanism can be detected in the advancement of a theory of due measurement. The Eleatic Stranger discusses the sciences that relate to due measurement in terms that conflate ethics, time, and mathematical quantity by means of analogy: It’s clear that we ought to divide the art of measurement, as we said before, by cutting it in two in this way: we should apply one portion of it to all the arts that measure number and length and depth and width and speed against their opposites, and the other portion to all the arts that regard due measure and what is appropriate and the opportune moment and what is necessary (pro_j to_ me&trion kai_ to_ pre&pon kai_ to_n kairo_n kai_ to_ de&on) and all things that leave behind 815 Archytas F 1 Huffman = Porph. In Harm. 1.3. 816 Cf. Pl. Plt. 284a2-b1, where due measure is crucial for production of the sciences (technai). Also see Lane 1998: 128-30. 301 the extremes to colonize the middle (o(po&sa ei_j to_ me&son a)pw|ki&sqh tw~n e)sxa&twn). 817 M.S. Lane’s interpretation of this passage, in which she argues for the correspondence of kairotics and due measure, is applicable here. 818 Indeed, the temporalization of measure is a hallmark of “so-called Pythagorean” metaphysics, as reported by Aristotle: [oi( kalou&menoi Puqago&reioi] e)n de_ tou&toij e)do&koun qewrei~n o(moiw&mata polla_ toi~j ou}si kai_ gignome&noij, ma~llon h@ e)n puri_ kai_ gh~| kai_ u#dati, o#ti to_ me_n toiondi_ tw~n a)riqmw~n pa&qoj dikaiosu&nh to_ de_ toiondi_ yuxh& te kai_ nou~j e#teron de_ kairo_j kai_ tw~n a!llwn w(j ei)pei~n e#kaston o(moi&wj: e!ti de_ tw~n a(rmonikw~n e)n a)riqmoi~j o(rw~ntej ta_ pa&qh kai_ tou_j lo&gouj…[u(pe&labon] kai_ to_n o#lon ou)rano_n a(rmoni&an ei}nai kai_ a)riqmo&n. 819 [The so-called Pythagoreans] believed that they could observe in numbers, more than in fire and earth and water, many similarities among things that exist and things that are coming-to-be, e.g. such and such a characteristic of number was justice, and such and such soul and mind, and another opportune moment, and similarly, so to say, with each other number. And, what is more, since they saw the characteristics and ratios of musical scales were in numbers …[they assumed] also that the entire heaven was harmony and number. Aristotle’s description here of the mathematical Pythagoreans provides a general understanding of how the Pythagoreans supplanted the Presocratic elements with numbers in their scientific investigation into what exists or is coming-to-be. Specifically, the number seven was understood to stand for “opportune moment” (kairos) in so-called Pythagorean numerology, and in the cosmology of Philolaus it 817 Pl. Plt. 284e2-8. 818 Lane 1998: 130-136. 819 Arist. Metaph. 985b27-986a4. 302 was correlated with the Sun and with Athena, the motherless virgin. 820 Of particular significance to our argument, the number seven, which stood for kairos, was also central to the doctrine that the “music of the spheres,” cited as Pythagorean directly by Aristotle and indirectly by Plato, was related to musical theory; later on it was thought to derive from the seven-stringed lyre, and even Nichomachus believed that there was a further connection with the seven vowels. 821 This interpretation reflects Nichomachus’ familiarity with theories of dialectic found in the later Platonic dialogues: the links between vowels as elements of syllables that facilitate participation and the mixing/middle element that is due measure in Plato’s dialectical theory are demonstrable – if muted – in the Statesman, and they will be even more explicit in the Philebus. But inasmuch as Nichomachus seems to be interested in analogies between the various sciences, he is little interested in the application of music to dialectical theory: What is more, the notes of each of the seven spheres produce by nature a single kind of sound; to each of which the elementary speech sounds called vowels are referred. These individually and anything composed of them are not to be spoken aloud by the wise. Wherefore the note has the same power as the monad has in arithmetic and the point has in geometry. These elements are combined with material substances (as, for example, vowels are combined with consonants), just as the soul is combined with the body and harmonia is combined with the strings. When the soul is combined with the body, it produces living things; when harmonia is combined with the strings, it produces keys and melodies, these combinations being the active 820 On which, see Huffman 1993: 287-8 and Huffman 2005: 493. 821 See Burkert 1971: 350-6 with n. 23. This attribution of this formulation to the Pythagoreans is as old as Aristotle (Metaph. 1093a13-17). 303 and consummating productions of the gods (ta_ de_ drastika_j duna&meij kai_ telestika_j tw~n qei&wn). 822 Nichomachus’ account is full of Platonic and Pythagorean syntheses: the appeal to a body/soul dichotomy – and its consequent cultic meanings – recalls Plato’s Phaedo and Gorgias, while the notion that harmonia combines with strings to produce keys and melodies is markedly Philolaic 823 ; indeed, the application of Philolaus’ principles to dialectical theory, as Huffman has shown, is a central aspect in the development of Plato’s philosophical method in the Philebus. 824 Despite the application of this passage to especially the Philolaic aspects of the Phaedo and the Philebus, it does not directly resemble anything we have seen in the Statesman. Rather, the dialectical theories proffered by Plato’s Statesman – especially in their “second-best” state of constant revision (or “becoming”) – do not lend themselves to the kind of doctrinal teaching of the Philebus and Phaedo that later became orthodoxy for both Middle and Neoplatonists. Plato himself was all too aware of the significance of revising or “coming-to- be” of his dialectical theories and their relation to “second-best” metaphysics and politics. Mathematics itself seems to have occupied a common ground between ideals and pragmatics, and it is unclear in the Statesman whether it was to be systematically categorized among the Forms or sensible phenomena. Aristotle, for 822 Nicom. Exc. 6 p. 276 Jan. Translated by Levin. 823 E.g. Philolaus F 6 Huffman, where “since these beginnings preexisted and were neither alike nor even related, it would have been impossible for them to be ordered, if a harmony had not come upon them, in whatever way it came to be.” Translated by Huffman. 824 Huffman 2001. While I agree with Huffman that Plato is engaging the philosophical praxis of Philolaus, as I will show later in this chapter, I believe that the final dialectical theory of Plato in the Philebus owes much to Archytas and Hippasus as well. 304 his part, called these intermediaries “mathematical practicals” or “mathematical objects” (ta_ maqhmatika_ tw~n pragma&twn), which he claimed to “differ from sensible things in being eternal and unmovable, and from Forms in that there are many analogous things, but each Form itself is unique.” 825 Aristotle thus locates these “middle” terms within a larger discourse constituted by the Pythagorean triad of “what exists, what is most, what must be done,” which I discussed earlier in the Introduction and Chapter 1. Plato also identified an intermediary – the “second-best” – which was, in ethical and political terms, an imitation of the ideal that still partook of that which is base and sensible and lives in the visible world. The Forms were not to be forgotten, even if they could not be attained by a community: the Eleatic Stranger and Socrates the Younger conclude their investigation into dialectical theory by refusing to do away with Socratic division according to the Forms, thus exhibiting Aristotle’s point that Plato revised the crude Pythagorean theories of division through separation of ideals and particulars; indeed, he seems to have distingushed them only to combine them again, following the circuitous dialectical praxis of division, then remix. But proper division is the innovation, according to Aristotle, while we see multiple forms of division at work in the Statesman. The Eleatic Stranger, who, after all, is aped by Plato himself, argues that division according to due measure must be superseded by a philosophical method involving division of Forms, a procedure that is not explained in detail here: Yes, but not even all things have a view to “appropriateness.” 825 Arist. Metaph. 987b11-18. Also see Sayre 2005: 84-6. 305 For we will not need, except in a subsidiary way, to apply measures to “pleasure.” Again, in regard to the investigation into the issue, the argument (logos) recommends that sort, which allows us to make discoveries easily and quickly, as secondary for commending [a definition], but we must honor as first and above all else the method which has the capacity to divide according to the Forms. 826 The Eleatic Stranger makes allowance for division according to “what is appropriate,” which we recently noted as analogous to due measure; the logic of this passage realizes this correlation. Indeed, the negotiation of division according to the Forms and division according to due measure has not yet been addressed; this problem will be answered later in the Statesman, where the application of due measure to the Forms results in a revised but contiguous Theory of the Forms. 827 What is more, the Eleatic refers to the application of measure to understand “pleasure” quantitatively, in anticipation of a major subject yet to be undertaken in the Philebus. In the second half of this chapter, when I discuss the dialectical theory of the Philebus, we will see whether Plato changes his tune or not. But before we leave the Statesman, we are required to discuss the relationship between the praxis of dialectic (as investigated throughout the dialogue and analogized with the praxis of weaving) 828 and the pragmateia of the Statesman himself: for, if we recall what was said following the Myth of the Unwinding of the Universe, the pragmateia of weaving is paradeigmatic for the pragmateia of 826 Pl. Plt. 286d4-e1. 827 On which, see below in this chapter. 828 Cf. Sayre 2006: 135, in which he sums up his argument to this point: “Just as the warp provides the structure into which the woof is interspersed by the weaver, and just as the contingent of courageous natures provides the structure into which the “woof” of well-behaved natures is interwoven by the statesman, so the formal definition provides the structure into which the dialectician interweaves descriptive details that bring clarity to the final product of his or her inquiry.” Italics original. 306 statesmanship. 829 The explicit focus is on the activity of the dialectician/weaver/Statesman and the application of his or her science to the world. We are thus coming to be firmly entrenched in the world of the visible, where things are mutable and humans can have some effect on their environment; yet Plato never allows us to forget the visible world’s inferiority and the intelligible world’s supremacy, even though the world of things that are coming-to-be shares in the world of things that truly exist. Due measure, then, is appropriately “second” to philosophical method that adheres to the Forms, and it partakes of things that are coming-to-be, or sensible phenomena. So too with politics, where the Eleatic Stranger shifts the earlier emphasis on ideal constitutions in the Republic to “second-best” constitutions here. At this point, the preference for “second-best” becomes patent, in line with the shift away from a world of Being (i.e. the intelligible world inhabited by the Forms) that is separate to an inclusive portrait that embraces the possibility of improvement – analogous to revisions in dialectical method and to weaving – in the world of Becoming. “Best” rule by a true King appears to be remarkably difficult to achieve, distrusted by the people, and unnatural in development. 830 Rather, the Eleatic Stranger claims, “people must gather together and compose written codes (suggra&mata), so it seems, hurrying after the paths of the true polity.” 831 Coincident with the turn 829 Pl. Plt. 279a7-b2. 830 Pl. Plt. 301c6-e2. The Eleatic Stranger marks the difference between a perfect ruler’s existence and “now” when a king cannot “come-to-be and exist” (ou)k e!sti gigno&menoj). 831 Pl. Plt. 301e2-4. 307 towards the world of Becoming is the return to the discussion of “error,” the primary subtext of this dialogue: ELEATIC STRANGER: No multitude at any time or of any sort, even if it could acquire this knowledge (of statesmanship), could ever come to be capable of governing the city-state intelligently, but for that unified, correct governance (politei&an), we must seek out something small, with few persons, and unified (lit. “One”). As we said a bit earlier, we must consider the others imitations (mimh&mata), where some imitate it better, and others worse. SOCRATES THE YOUNGER: How should I understand what you’ve said? I did not comprehend what you said earlier about imitations. ELEATIC STRANGER: It wouldn’t be an insignificant thing if someone were to initiate this argument where he took it up and fail to carry it through and demonstrate the error that just happened (gigno&menon a(ma&rthma) concerning this issue. SOCRATES THE YOUNGER: What sort of mistake? ELEATIC STRANGER: It is neither familiar nor easy to see what sort of thing must be sought after; nevertheless, we must certainly make our best attempt to acquire it. Come then: although the only correct governance for us is that polity we were just discussing, you know that the others ought to preserve themselves by employing its etchings (toi~j tau&thj suggra&mmasi), 832 doing what is at the time praiseworthy, even if it is not most correct (ou)k o)rqo&taton o!n). SOCRATES THE YOUNGER: What do you mean? ELEATIC STRANGER: By not allowing anyone in the polis to dare to do anything against the laws, and by punishing the one who dares it with death and other extreme penalties. As a second-best, this is most correct (o)rqo&tata) and best whenever someone has set aside the first-best as we just now described it. We should make a thorough attempt to describe in what way the thing we’ve called “second-best” came to be (gegono&j e)sti tou~to o$ dh_ deu&teron e)fh&samen). 833 If we recall that Aristotle understood mathematical practicals as employing “participation in” rather than “imitation of” numbers – that Aristotle understood 832 Or “written codes,” as I translated it earlier. In the following four Stephanus pages, the Eleatic Stranger will play on the meaning of “writings” by drawing in a semantic range that includes artists’ sketches and written laws alike. Second-best city-states thus imitate the ideal polis by being imperfect imprints of it. 833 Pl. Plt. 297b7-e6. 308 Platonic participation and Pythagorean imitation as analogous – this passage can be read as correlating “second-best” city-states with intermediaries. Indeed, if Aristotle is right, Plato is explicitly applying Pythagorean language of “imitation,” in preference to “participation,” in the discussion of second-best polities. 834 Regarding the ontological status of “second-best” things (mathematical practicals, mixed or middle things) in the Statesman, the Eleatic Stranger is clear that they both “are” and “become” at the same time (gegono&j e)sti tou~to o$ dh_ deu&teron e)fh&samen). The mathematical practicals thus represent a tertium quid, a mixture of Being and Becoming. Likewise, “second-best” constitutions imitate the “most correct” polities according to what has been laid down in writing as the “best” constitution, later termed the “seventh” polity, described as being “like a god apart from mortals.” 835 When “second-best” polities imitate well and are governed by knowledgeable leaders, they succeed and are not overturned. 836 On the other hand, when they are navigated by “the recklessness (moxqhri&an) of captains and crews” who possess “the greatest ignorance concerning the greatest matters” (peri_ ta_ me&gista megi&sthn a!gnoian) – especially “political” matters – polities “go down 834 This argument cannot be sustained by what remains of Pythagorean writings, since mimesis does not appear among the extant genuine fragments. Nevertheless, as Huffman (1993: 60) has suggested, Aristotle might be conflating the place of homoiosis or homologia with mim1sis; I would suggest that this occurs because of the apparent paralogy between methexis and mim1sis. 835 Pl. Plt. 303b4-5. 836 Pl. Plt. 302a4-6. Just what these successful polities which endure over “limitless time (xro&non a)pe&ranton)” were goes without mention. The reference to Pythagorean “limitless” is enticing and evocative, but ultimately not sufficient evidence to suggest that Plato is referring specifically to successful Pythagorean cities like Taras. 309 like sinking ships.” 837 Success depends on the knowledge of those who navigate the city-state in its imitation of the “best” polity. Specifically, successful “second-best” constitutions are noted for their adherence to written law codes that imitate the “best” constitution: ELEATIC STRANGER: So, then, for those people who enact laws and written codes concerning anything whatsoever, a second course exists that forbids any individual or group ever to do anything whatsoever against the laws and written codes. SOCRATES THE YOUNGER: Correct. ELEATIC STRANGER: So these things (laws and written codes) would be imitations of each element of the truth if they were copied as closely as possible (to the truth) by those who have knowledge (of it)? SOCRATES THE YOUNGER: Of course. ELEATIC STRANGER: And yet, if we recall, we said that the true Statesman, who has knowledge, will do many things in his art according to his own method, not paying heed to the written laws, whenever he believes that it is better to do something against those laws copied by him and dictated to others not in his presence. 838 Second-best constitutions, then, are marked by an adherence, via imitation, to the original law codes as laid down by the lawgiver and preserved by the Statesman. But, in a highly controversial move, the Eleatic Stranger claims that the Statesman (who has knowledge of each element of the truth) is allowed to act against the laws provided that the laws, as they are composed, fall away from the truth. 839 This exemption from adherence to the letter of the laws – only extended to the Statesman – is in lieu of his art and manifests itself in his political activity (ei)j th_n au(tou~ 837 Pl. Plt. 302a6-b3. As Skemp (1952: 204n.1) notes, the metaphor of “ship of state” goes back to Alcaeus (600 BCE). 838 Pl. Plt. 300c1-d2. 839 This passage has provoked many interesting, sometimes contradictory, claims about the relationship between second-bestness and the Statesman’s method. Two representative studies are Gill 1995: 296-305 and Rowe 1995: 26-8. 310 pra~cin). But what, exactly, is this art that separates the true Statesman from those rulers of the “second-best” governments 840 and, when applied pragmatically, leads to political activity? The Eleatic Stranger and Socrates the Younger conclude the definition of the Statesman’s art by first distinguishing it as the art that circumscribes and rules over those technai practiced by people who aid the Statesman in ruling the ideal polity. 841 Those three circumscribed arts, namely rhetoric, generalship, and judgment, are comprehended by the Statesman but auxiliary to his primary art, namely the “kingly” or political art; this supreme art “should not itself act (ou)k au)th_n dei~ pra&ttein), but it should rule over the activities of the other powers (a!rxein tw~n duname&nwn pra&ttein) and become the ruler and first impulse (o(rmh&n) over opportune and inopportune time in polities.” 842 Each of the other arts concerns itself with its own 840 The Eleatic Stranger claims that “second-best” or imitative polities – including those that imitate well, we must assume – are ruled by “faction leaders,” who are distinguished from “real statesmen” (Plt. 303b8-c5): Therefore, indeed, we must distinguish those who take part (koinwnou_j) in all these governments – apart from the one based on knowledge – on the grounds that they are not real statesmen but faction leaders, and they are actually presidents of the greatest illusions and themselves illusions, and they are the greatest imitators and the greatest magicians, and they become arch-sophists of the sophists. He will go on to claim that the preceding definition of these leaders of imitative polities is “like a masque” in which “some Centauric or Satyric pageant” can be discerned. Satyrs and Centaurs, while the stuff of the final act of a dramatic sequence, are also to be distinguished from humans for their hybridity, in which mixtures of genera are noted. They thus represent the “mixed” Kind with which Plato had been grappling throughout much of his later career. 841 Pl. Plt. 304b1-c2. 842 Pl. Plt. 304c7-305d4. Interestingly, in this ideal polity, the judicial art is expected to be a “guardian of the laws” (no&mwn fu&laka) but “attendant to the kingly art.” The place of the “guardian of the laws” thus occupies a subservient position in the ideal polity of the Statesman; it will rise to the pinnacle in the “second-best” polity of the Laws (see Chapter 6). 311 praxis but cannot control itself or the others; that responsibility is left to the kingly or political art which interweaves those other arts: The art that rules over all these and concerns itself with laws and all other things that belong to the city and interweaves all of them most correctly – if we were to condense its power into a common name, we would most justly, it seems, call it the political art. 843 Having come full circle to the subject of weaving – a topic that will occupy the rest of the dialogue – the Eleatic Stranger also returns to the issue of paradeigmata; indeed, dialectically speaking, the two cannot be separated in the Statesman. 844 The process of weaving is applied paradeigmatically to the investigation of the political art, to such an extent that the final task of the dialogue becomes the definition of the “kingly interweave (basilikh_n sumplokh&n): what sort it is, and in what way, having been interwoven, its type of web is produced.” 845 At stake in the metaphor of weaving is the total revision of Platonic ethics, a notion at which the Stranger hints in the subsequent discussion of opposites. 846 For what the Stranger will suggest is that two opposing ethical qualities can each be valued as both good and equal to the other. The notion that opposite ethical qualities could be reciprocally valuable is presented as a consequence of further reflection upon the mathematical sciences that have provided partial impetus for the revision of dialectical theory in the Statesman. 843 Pl. Plt. 305e2-6. 844 Pl. Plt. 305e8-10. On paradeigmata and weaving, see the excellent and clear discussion of Sayre 2006: 92-112. 845 Pl. Plt. 306a1-3. The difference here between “interweave (sumplokh&)” and “web (u#fasma)” appears to be a distinction between activity and product, although this cannot be sustained throughout the dialogue. 846 Pl. Plt. 306a8-10. 312 It would elicit little commentary to say that “Great” was not ethically superior to “Small,” an operative assumption throughout this dialogue. But once we extend that principle of opposites beyond abstract categories that are arrived at via mathematical measure (whether subjective or quantitative), problems begin to arise. Thus we might encounter somewhat more difficulty if we say that “Right” is not superior to “Left,” and substantially more if we say “Up” is not superior to “Down” or “Heaven” not superior to “Earth;” certainly, once we suggest that “Immortal” is not superior to “Mortal,” we are but one analogous step from claiming that “Good” is not superior, but equal and opposite in its value, to “Evil.” Such are the possible consequences (via analogy) when one applies the notion that opposites are not necessarily valued within a hierarchical system. The issue of reversing hierarchical opposites points to the challenges that any philosopher will face when she attempts to apply mathematics to try to establish ethical systems of all sorts (including political values), as Archytas of Taras had done. 847 The Eleatic Stranger realizes that Socrates the Younger is not the only one confused on this issue of opposites. He elicits an example from the semantics of virtue, a favorite for the Socratic Plato of old and a continuous point of reflection for Plato throughout his career. 848 His claim recalls Archytas of Taras in several ways: temperance (swfrosu&nh) and courage (a)ndrei&a), which are both Parts of Virtue, are enemies to one another and have held an oppositional discord (sta&sin e)nanti&an 847 I will discuss this further in Chapter 6. 848 On which, see Bobonich 2002. 313 e!xeton) for some time. 849 But temperance and courage are not the only representatives of this ontological realization: other examples must be sought in which two opposite Forms (ei!dh) are themselves both good. 850 The Stranger suggests the opposite Forms of “Courage” and “Temperance” as an example; the valuation of these terms comes as a consequence of attention to what is “opportune”: If these things become swifter or sharper or harsher than what is opportune (tou~ kairou~), we say that they are hubristic and maniacal, but if they are heavier or shorter or softer, we call them cowardly and lazy. In general, we may venture to say that temperate nature and courageous nature among oppositions – Forms that make discordant divisions as if in war (oi{on polemi&an dialaxou&saj sta&sin i)de&aj) – go unmixed with one another not only in affairs that concern such things, but, if we pursue the matter further, we shall see even that people who are dominated by either of them in their souls conflict with one another. 851 Again, the appeal to due or kairotic measure is apparent here in the Eleatic Stranger’s revision of Socratic ethics and psychology, earlier called the “familiar argument (ei)wqo&ta lo&gon) in which the Parts 852 of virtue were “friendly to one another” 849 Pl. Plt. 306a8-b11. This passage elicits comparison with Archytas F 3 Huffman, where “logistic, once it was discovered, stopped discord and increased concord” (sta&sin me_n e)!pausen, o(mo&noian de_ au!chsen). For both Plato and Archytas, the assumption is that opposites are originally at war, but come to peace through the imposition of a mathematical mean. In the passage that follows in the Statesman, the Eleatic Stranger discusses frequency of the body, soul, and voice, with an accompanying reference to musical and graphic imitation; the point of comparison here is Archytas F 1 Huffman, where pitch is directly connected to frequency of blows, and speed is assumed to produce oppositions based on “high” and “low.” 850 Pl. Plt. 306c7-8. 851 Pl. Plt. 307b9-c7. 852 There is some confusion of “Part” with “Form” here, and we may best infer from this slippage that Plato believes that Parts are themselves Forms according to the new scheme, in which Parts that are “unified” (e#n) may still partake of the Form with which they share a common term (i.e. Temperance and Courage are both unified Parts that partake of the Form of Virtue, but, as unified concepts, they are Forms themselves). These Formal Parts are therefore distinguishable from each other as opposites (like consonants) and both share in a combinatory Kind (like a vowel) that we might call a ge&noj. Parts therefore do not mix naturally, even if they each have a common term. 314 (a)llh&loij fi&lia). 853 The revision here lies in the application of logistical categories of measure – the opposite but ethically equivalent Greater and Smaller – to positing a social use value for character traits that, according to a simple Formal scheme, should always and ideally be good. Or another way: measure, when applied to opposite (and indeed “warring” 854 ) ideals which are both good, allows people to understand the possibility that any virtue can be detrimental if it strays too far from the mean; also implicit in this argument is the remarkable notion that “good” traits can be opposite and warring, but remain “good” as long as they are measured according to a due standard. 855 In this way, the Eleatic Stranger’s abstract theory of logistic not only derives from but also improves upon Archytas’ formulation (F 3 Huffman) that logistic increases concord among opposite elements by eliminating discord. The Stranger’s argument, though, is not solely or even primarily concerned with revisions of Form theory or dialectic. Rather, he is constructing the formal and dialectical apparatus for understanding precisely how the Statesman will “interweave” opposite but equally socially useful elements of the community. 856 After all, it is the Statesman’s responsibility to recognize those elements of the world 853 Pl. Plt. 306b13-c1. See Miller 1979: 107, Skemp 1952: 223 n.1, and Lane 1998: 174-7. 854 Cf. Pl. Plt. 307d1-4. 855 Cf. Bobonich 1995: 315-20. 856 Of those elements that are detrimental to the community, “godless,” or impelled by the evil nature of violence, it is the Statesman’s responsibility (Plt. 309a1-3) to put them to death, expel them, or punish them greatly with disgrace. As Skemp (1952: 228n.1) notes, this “implies a mere discarding of ill-wrought strands that cannot be woven into the web.” The threat that these detrimental elements pose to the Statesman’s city is extreme: the Statesman claims that the “interweave and bond” will deteriorate. 315 that are opposite but, when measured, equally valuable: he stands above and comprehends oppositions and their differences, which can be a trifle if they only involve the temperaments of people but, when they concern the “greatest things” in city-states, become the “most hated plague of all.” 857 Those people who complete the educational training prescribed by the state, so claims the Eleatic Stranger… …whose temperaments can be molded to nobility and accept being intermixed with one another by the Statesman’s art – those who are inclined more to courage – [the Statesman’s art] will consider their tough character as the warp; but those who are disposed to modesty with suppleness and gentleness [the Statesman’s art] will consider likewise as the wooly strands. These opposed tendencies [the Statesman’s art] sets about intertwining and interweaving in some such way . SOCRATES THE YOUNGER: How? THE ELEATIC STRANGER: First the Statesman’s art fits together (sunarmosame&nh) the everlasting (to_ a)eigene_j) Part of their soul with the divine bond, according to their kinship (kata_ to_ suggene_j); then, in turn, the divine Part – the life-producing part of their soul – it fits together with human bonds. 858 Here, we see the application of the dialectical theory proposed earlier in the dialogue to human individuals to constitute a community: the Stranger claims that the shared element among these individuals, namely the divine “soul,” provides the means to reintegrate them. Like the vowels that allow one first to distinguish between syllables that contain similar and different consonants, communal “soul,” as the divine standard, functions among social groups both as a means to differentiate and as a means to integrate opposite human natures. 859 857 Pl. Plt. 307d6-8. 858 Pl. Plt. 309a8-c3. 859 See above on Pl. Plt. 278a5-b5. 316 But soul, in its function as the common element among communal opposites, also resolves the issue that has been roaming at large without conclusion since the beginning of the Sophist and the joke that involved the divinity of the Eleatic Stranger. 860 It becomes the proving ground for ethical absolutes, as the Eleatic Stranger argues, and consequently the common link (tertium quid) that unites mortal and immortal: Whenever in souls (of humans) there comes to be a resolute opinion that truly exists concerning what is good, just, and profitable, and the opposites of these, I declare that it becomes divine among a divinized Kind (qei&an fhmi_ e)n daimoni&w| gi&gnesqai ge&nei). 861 Soul then provides the standard by which oppositional but socially useful characteristics can be determined and distinguished, but it also catalyzes interweaving between those oppositions, and, in the process, it links those human elements with the divine. Soul thus functions within this scheme as the means to a standardized community of opposite but socially productive elements. That standardization takes the form of a divine mean, and it both distinguishes and connects human and divine. As such, it moderates the oppositional characters of citizens within the community and prevents them from whatever tendencies to excess or deficiency each might possess: courageous people will become welcome community members with a more gentle temperament; moderate people will engage in their public duties and abstain from cowardly or foolish behavior. 862 This goes 860 On which, see Chapter 3. 861 Pl. Plt. 309c5-8. 862 Pl. Plt. 309d10-e8. 317 both for slaves and free citizens. 863 So also magistrates, who are naturally predisposed either to moderation or excessive courage, must be interwoven as well if the community is to function properly. 864 Thus the communal soul of the polis, when moderated by the knowledgeable Statesman, forms a horizontal interweave (sumplokh&) among human opposites and establishes a vertical bond (sundesmo&j) with divinity. Once the vertical bond with the divine has been established, so continues the Eleatic Stranger, the secondary bonds among humans can be fashioned in marriage ties. Intermarriage must be established among the two warring types so as to preclude the possibility that, over generations, superlative madness (if the courageous type exceed) or crippling inactivity (if the moderate type exceed) could destroy the community. 865 Finally, the Stranger concludes his investigation into weaving by stating its function within the administration of the polity: Tou&touj dh_ tou_j desmou_j e!legon o#ti xalepo_n ou)de_n sundei~n u(pa&rcantoj tou~ peri_ ta_ kala_ ka)gaqa_ mi&an e!xein a)mfo&tera ta_ ge&nh do&can. tou~to ga_r e$n kai_ o#lon e)sti_ basilikh~j sunufa&nsewj e!rgon, mhde&pote e)a~n a)fi&stasqai sw&frona a)po_ tw~n a)ndrei&wn h!qh, sugkerki&zonta de_ o(modoci&aij kai_ timai~j kai_ a)timi&aij kai_ do&caij kai_ o(mhreiw~n e)kdo&sesin ei)j a)llh&louj, lei~on kai_ to_ lego&menon eu)h&trion u#fasma suna&gonta e)c au)tw~n, ta_j e)n tai~j po&lesin a)rxa_j a)ei_ koinh|~ tou&toij e)pitre&pein. 866 You see, I have been claiming that there is no difficulty in tying together these bonds if we premise that both Kinds have a unified 863 Pl. Plt. 311c3-4. 864 Pl. Plt. 311a4-b5. If, indeed, there is need for only one archon, the Stranger asserts that the Statesman should appoint him only if he “possesses both characteristics.” 865 Pl. Plt. 310d6-e3. The Eleatic Stranger sees these possible futures as a “natural” (pe&fuken; fu&esqai) outgrowth if not moderated by the Statesman. 866 Pl. Plt. 310e5-311a2. 318 opinion regarding good and beautiful things. For this is the unified and comprehensive duty of kingly interweaving: that it never allow the temperate characters to be separated from the courageous characters; and, by commingling them with one another through common opinions and honors and punishments and repute and gifts of securities 867 , he may bring together a web both smooth and “well- woven” from them – so goes the saying – and always entrust magistracies in the city-states to them in common. A tightly-woven polity, then, comes to exist as a consequence of the Statesman’s practice (politikh~j pra&cewj), which is carried out by virtue of his knowledge of weaving together opposite characters of humans through agreement and friendship (o(monoi&a| kai_ fili&a|). 868 What is more, the dialectical analogue is not lost on the Stranger or, for that matter, the Elder Socrates at the end of the dialogue: the Eleatic stranger claims that the kingly/political art “completes (a)potele&sasa) the best and most closely-woven of all webs” just as the Elder Socrates closes the dialogue by saying that the Stranger “has completed (a)pete&lesaj) most beautifully [the definition of] the kingly and political man.” 869 Definition by means of both dialectic and statesmanship, then, falls under the activities of the ideal Statesman, who must comprehend the Theories of Form and dialectic in order to carry out his task as ruler of the polis. This is an extension of similar concepts expressed in the Republic, no doubt, but the Eleatic Stranger’s total refashioning of the philosophical pragmateia of Plato – dialectical, political, ontological, and Formal – reflects serious reconsideration of the place of 867 Cf. LSJ: o(mhrei&a. 868 Pl. Plt. 311b7-c7. Cf. Sayre 2006: 103. 869 Pl. Plt. 311c2-3 and c9-10. Cf. Sayre 2006: 133 and Miller 1979: 112-113. 319 mathematics in the worlds of both Being and Becoming according to the Platonic political cosmology. Likewise, the analogous process of weaving provides Plato with a means to understand how to bridge the divides between oppositional types, including the traditional opposition between Being and Becoming that represents the divide between ideal and “second-best” polities. While Plato concludes the Statesman by referring once again to the ideal polity and its ideal perpetuation, the appearance of reflection upon what can be pragmatically achieved in “second-best” polities lurks in the lacunae. I will deal with revisions to Plato’s political philosophy in Chapter 6, when I will discuss the “second-best” polities of the Epistles and the Laws. There, I will examine precisely how the Archytan State provided a model for Plato in the conceptualization of Magnesia. But before Plato would come to concentrate his energies entirely on achieving what Archytas had done in Taras – successful guidance of a city-state according to philosophical precepts based in mathematics – he still needed to address the Third Man raised in the Parmenides with which he was not yet satisfied. Advances in Form Theory in the Statesman had represented notable successes for Plato, but the dialogue’s preoccupation with providing the method for governing a city-state according to appropriate measure as well as identifying methodological error in dialectic had pushed issues of ethics to the side: recall that the Eleatic Stranger raised doubts about the application of due measure to “pleasure,” a subject, as we will see, that was of particular interest to Archytas as well. It will come as no surprise to the reader, then, that Plato’s examination of these issues in the Philebus is formulated as a response to the 320 traditions of mathematical Pythagoreanism embodied in the writings of Philolaus of Croton, Archytas of Taras, and the prodigy Eudoxus of Cnidos. MEASURED PLEASURE OR PLEASURE MEASURED? DIALECTIC, MUSICOLOGY, AND METAPHYSICS IN PLATO’S PHILEBUS In his Life of Archytas, Aristoxenus describes an episode in which the Syracusan philosopher Polyarchus, called “the Voluptuary” (to_n h(dupaqh~), was sent from the court of Dionysius the Younger to visit Archytas in Taras. 870 The ensuing debate between Polyarchus and Archytas about human nature and its goal of consummate bodily pleasure reveals the substantial part that investigations into pleasure warranted for Archytas’ philosophy: in the extant fragments, Polyarchus establishes an argument in favor of bodily pleasure as a rebuttal of what we may assume were known, perhaps published, speeches of Archytas on that subject. 871 Not surprisingly, Archytas’ views on pleasure are substantially related and indeed analogous to the Pythagorean practice of a good life, rooted in temperance and rational examination. As we have come to expect with the writings of Archytas, this philosophy of temperance is demonstrably political, a fact revealed both in the hostile defense of Persian kingly ways of life in Polyarchus’ speech, preserved by Athenaeus, and in Cicero’s summary rewriting and dramatization of Archytas’ ideals 870 We must assume, with Huffman (2005: 330-1), that the context of the fragment in Aristoxenus places it during the unchallenged rule of Dionysius the Younger in Sicily (367-357 BCE). Cicero’s placement of the debate in the year 349 is anachronistic, but see below on the result of such a revision of history. 871 See Archytas A 9 Huffman = Aristoxenus F 50 Wehrli and Archytas A 9a = Cicero, Sen. 12.39-41. 321 in the De Senectute. To take the first, Polyarchus, who defends bodily pleasures (ta_j swmatika_j h(dona&j), claims that the sensible person (nou~n e!xontoj) follows pleasure and thus does not “enslave his desires,” which is the mark of a person who lacks intelligence, fortune, and understanding of the “arrangement of human nature” (h( th~j a)nqrwpi&nhj fu&sewj su&stasij). 872 Such is Polyarchus’ representation of the human ideal, achieved by the Persian, Median, Lydian and Assyrian kings; his conclusion, namely that Dionysius the Younger takes second place behind the Persian King as “happiest,” is followed by a description of the acts of the “lawgivers” who, in his opinion, enslaved human nature: But the lawgivers, wishing that human beings be reduced to one level (o(mali&zein) and that no individual citizen live in luxury, have caused the class of virtues to rear its head. And they wrote laws about our dealings with one another (peri_ sunallagma&twn) and about as many other things as seemed to be necessary for political commonwealth (pro_j th_n politikh_n koinwni&an) and in particular about dress and the rest of our lifestyle so that it would be uniform (o(malh&j). Therefore, since the lawgivers were at war with the clan of those who wanted more than their share (tw~| th~j pleoneci&aj ge&nei), first the praise of justice was magnified and I suppose that some poet spoke of “the golden face of Justice” and again of “the golden eye of Justice.” And then even the very name of Justice was deified, so that altars and sacrifices to Justice appeared among some peoples. After this Temperance and Self-control joined the revel and gave the name of greed to any preeminence in enjoyment (pleoneci&an e)ka&lesan th_n e)n a)polau&sesin u(peroxh&n), so that it is the one who is obedient to the laws and the voice of the multitude who is moderate in bodily pleasures (metria&zein peri_ ta_j swmatika_j h(dona&j). 873 As Carl Huffman demonstrates, Polyarchus’ summary of the political and ethical theory of the “lawgivers” recalls the arguments of Archytas, especially those 872 Archytas A 9 Huffman. 873 Ibid. Translated by Huffman, with slight changes. 322 preserved in Fragment 3. 874 What is more, the appeal to a “leveling” of society elicits comparisons with the description of the Tarentine Constitution as preserved by Aristotle (Pol. 1320b12), wherein property is rendered communal for the sake of the poor. 875 The process of economic “leveling” in this fragment of Aristoxenus is reiterated later on, where laws have been composed by the “lawgivers” with an eye to promoting uniformity (o(malh&j) of dress and of way of living among correlative elements of the polis (peri_ sunallagma&twn). 876 Economic and social leveling occurs in Archytas’ political philosophy as a consequence of the discovery of calculation, 877 which is said to serve as a “standard” (kanw&n) and “preventative” (kwluth&r) through which justice and injustice can be decided. What is more, obedience to the laws and to the will of the multitude – a markedly democratic ideal – allows one to moderate (i.e. to judge according to due standard: metria&zein) bodily pleasures; 878 the process of moderating one’s bodily pleasures by means of calculation is thus contrasted to monarchical ideals, manifested in the character of the Persian King; the Tarentine democracy, which is marked by adherence to 874 See Huffman 2005: 314-317, where he convincingly demonstrates that this speech cannot be simply modeled on those of Callicles in the Gorgias or Thrasymachus in the Republic. 875 On the Tarentine constitution, see Chapters 4 and 6. 876 Cf. Archytas F 3 Huffman: “Once calculation (logismo&j) was discovered, it stopped discord and increased concord. For people do not want more than their share, and equality exists, once this has come into being. For by means of calculation we will seek reconciliation in our dealings with others (peri_ tw~n sunallagma&twn).” 877 Ibid. 878 Cf. a comparable usage of this verb at Arist. Pol. 1323b2. 323 mathematical models, is thus understood as opposite to Persian monarchy, a subject that Plato will himself discuss further in the Laws. 879 We are not the only ones who have seen anticipations of Archytas’ political and ethical pragmateia in Plato’s later political writings: Cicero, in the de Senectute, claims that Archytas’ speech on pleasure took place in 349 BCE – on the fourth and final visit of Plato to Taras – in the presence of a Samnite named Gaius Pontius. 880 While we should be skeptical about the actual chronology, Cicero wants us to locate this speech late in the life of Plato and thus far beyond the political philosophy of earlier writings such as the Gorgias or the Republic. 881 The natural point of comparison, then, would be a late work 882 of Plato on pleasure with Pythagorean overtones and a sensitivity to the place of logistic in measuring pleasure: the Philebus. Here, as I will demonstrate, Plato’s project of revising his entire pragmateia by basing both dialectical and political method on mathematical Pythagorean precepts takes its form as a debate about pleasure and intelligence. Indeed, in the writings of the mathematical Pythagoreans, as in the later Platonic dialogues, the debate about pleasure is coordinate with the investigation into methods of organizing political communities, based in the macrocosm-microcosm relationship of body to state. As I shall argue, Plato’s Philebus epitomizes an ultimate theory of dialectical procedure that is rooted extensively in the philosophical 879 See Chapter 6. 880 Archytas F 9a Huffman. On the date and the presence of the Samnite Pontius, see Humm 2005: 530-1. 881 On which, see Huffman 2005: 330. 882 On the late date, see Guthrie 1978: 197. 324 ideals of the three most prominent mathematical Pythagoreans of the first half of the 4 th Century BCE: Philolaus of Croton, Archytas of Taras, and Archytas’ extremely influential student Eudoxus of Cnidos. 883 Specifically, I will suggest that the divine dialectical method attributed to Prometheus and Theuth refers to the philosophical activities of the father of mathematical Pythagoreanism Hippasus of Metapontion and Pythagoras, respectively. This interpretation is significant for our understanding of the Pythagoreanizing of Plato’s pragmateia because it unites what were two sundered forms of philosophy in accordance with the synthetic process of weaving. Finally, I will conclude my study the of the development of the Platonic Theory of the Forms in this chapter, with careful consideration of the place of Eudoxus’ theories of mixture in the last work of Plato’s that deals extensively with the praxis of dialectic and its ramifications for Formal Theory. The Philebus, despite its secondary function as an investigation into the nature of the Good, is primarily a dialogue about the relationship between pleasure and a happy life within the individual soul. W.K.C. Guthrie notes its place within the later traditions of Platonic philosophy, especially those that involve conscientious attention to the place of Pythagorean analogizing: The Philebus is an excellent illustration of Plato’s talent for combining the ethical and the metaphysical, the human and the cosmic. The whole of reality is his province, and he is unwilling to separate any of its parts since for him they are parts of an organic whole. Man’s soul is a fragment of the universal soul (30a), order is 883 It is worth recalling, with Huffman (2005: 316), that Aristoxenus’ speech probably borrowed some elements of the “Polyarchan” view on pleasure from Heracleides of Pontus (e.g. F 55 Wehrli). See Gottschalk 1980: 88-93 and 145. 325 the same in individual souls, in the city-state and in the universe at large. The Philebus treats of it in the individual, the Politicus in the state, and the Timaeus in the universe at large, but all alike are at pains to put mankind in his setting as an integral part of the cosmic order. 884 While Pythagorean analogies between micro- and macrocosm are nothing new to Plato, the Philebus begins with an echo of the Statesman’s juxtaposition of opposite traits, recalling the Pythagorean Table of Opposites. The Elder Socrates has returned from his Pythagorean and Parmenidean education at the hands of the Eleatic Stranger, and he remains puzzled by the argument that opposite Forms that are good ought to be interwoven in definitions as well as in society. The discerning and interweaving of opposites, made possible through dialectic and its sister-art logistic, functioned by means of due measure; but Socrates here wishes to indict due measure itself – a proposition that recalls the investigative avenues of the Third Man argument in the Parmenides – and to understand the ideal relationship between pleasure and reason: Well, Philebus declares that what is good is for all living things to take enjoyment of pleasure, delight, and however many things are concordant (su&mfwna) with that Kind; but for us, these are not valid points, but intelligence and thought and memory and all things kin (suggenh~) to these – correct belief and true logistic applications (logismou&j) – are better and preferable to pleasure for all things that have the power to partake of them (au)tw~n dunata_ metalabei~n). For those things that have the power – now or in the future – to partake (metasxei~n) of them, this is the greatest benefit of all. 885 884 Guthrie 1978: 203. 885 Pl. Phlb. 11b4-c3. Note Gosling’s (1975: 73) interpretation: “It would be quite possible to hold that both pleasure and intelligence are good. It is only when at least one is proposed as the good that dispute arises. Note that Socrates only claims thought, etc. are better.” 326 While Socrates is currently expressing his support for intelligence, thought, memory, correct belief and logistic, the unresolved issue of opposites that are both good hearkens back to the challenge to measuring pleasure in the Statesman. He initially proposes pleasure and intelligence, et al. as opposites, a concept reiterated soon thereafter by the discussion of opposite colors that recalls the issue of proper distinction according to Form or Part found in the Statesman. 886 At issue again is the proper identification of opposites. We recall that, in the Statesman, the Eleatic Stranger argued that “…we will not need, except in a subsidiary way, to apply measures to ‘pleasure.’” 887 Socrates’ philosophical questioning of reason, colored by the emphasis on logistic here, represents a direct challenge to Archytas’ unquestioned preference for logistic as a means to enact political, economic, and ethical leveling; this Socratic challenge to logistic also poses questions to the dialectical method – rooted in kairotics and due measure – proposed by the Eleatic Stranger in the Statesman. In the Philebus, however, the answer to whether pleasure or intelligence is better – and the consequent questions of whether one or both are good or the Good – cannot be achieved without another revision to dialectical theory; Socrates also 886 Pl. Phlb. 12e3-13a5. The discussion here refers to mathematical figures as well: That would follow for color with color, O happy one: indeed, every color differs in no way from another inasmuch as it is a color, but we all know that black differs from white in that it happens to be most opposite regarding difference. The same holds regarding figure with figure: each is the same according to Kind, but, regarding Parts, some are the most opposite with one another while others happen to have thousands of differences, and we will discover that this holds for many other things. So don’t trust in this argument, which renders all most opposite things unified; I suspect we will discover that particular pleasures are opposites of others. 887 Pl. Plt. 286d4-6. 327 allows for the possibility that the Good is neither simply pleasure or intelligence, “but some other third thing.” 888 He tells Protarchus that the successful investigation into this issue 889 relies upon an explication of the dialectical method (o(do&j) from which many things have their art (te&xnh), one that is “not terribly difficult to demonstrate (dhlw~sai), but especially difficult to employ.” 890 Here, Socrates calls upon a pair of interconnected historical myths that function paradeigmatically – in a manner comparable with the Myth of the Unwinding of the Universe found in the Statesman – to exhibit divine dialectical method, which allows humans to “investigate, learn from, and teach one another.” 891 The subject of the first myth, of course, is the gift of the “certain Prometheus”: Qew~n me_n ei)j a)nqrw&pouj do&sij, w#j ge katafai&netai e)moi&, poqe_n e)k qew~n e)rri&fh dia& tinoj Promhqe&wj a#ma fanota&tw| tini_ puri&: kai_ oi( me_n palaioi&, krei&ttonej h(mw~n kai_ e)ggute&rw qew~n oi)kou~ntej, tau&thn fh&mhn pare&dosan, w(j e)c e(no_j me_n kai_ pollw~n o!ntwn tw~n a)ei_ legome&nwn ei}nai, pe&raj de_ kai_ a)peiri&an e)n au(toi~j su&mfuton e)xo&ntwn. 892 As it appears to me, it was a gift of the gods to humans, cast down from the gods by a certain “Prometheus” along with a most brilliant fire. And our forefathers, being stronger than we are and living closer to the gods, passed on the tradition that the things that are said to be eternal have come from one and many, but they had Limit and Limitless inherent 893 in them. 888 Pl. Phlb. 14b4. 889 I cannot sufficiently explain the application of this method to the one/many problem found in chapters 14-16 of the Philebus. See the useful summaries of Gosling (1975: 143-153) and Guthrie (1978: 206-8). For an excellent in-depth analysis of this passage and its antecedents in Plato’s dialogues, see Sayre 2005: 118-128. 890 Pl. Phlb. 16c1-2. 891 Pl. Phlb. 16e2-3. 892 Pl. Phlb. 16c5-10. 893 Sayre (2005: 118) translates su&mfuton as “connaturally” while Gosling (1975: 7) suggests “inherent.” It may be said that Plato’s usage here recalls the Myth of the Unwinding of the Universe, 328 Now commentators have noted that the “forefathers” in this passage refer to the later Pythagoreans, 894 but Plato is vague about who exactly these people were; for that matter, Socrates does not demonstrate precisely who this “certain Prometheus” was, leaving it to the reader and Protarchus to interpret. Pythagoras has been offered up as a possible referent, although, as Huffman demonstrates, this doctrine cannot be original with Pythagoras at all. Instead, on Huffman’s reading, the “Prometheus” here possibly refers to Philolaus of Croton. 895 This is problematic, since it is not clear that Philolaus was punished (as Prometheus was) for disseminating the divine method nor that Philolaus was the first to ascribe such significance to fire in his cosmological universe. 896 Now, we need to keep in mind that the doctrine of “co-generated Limit and Limitless” is not attributed directly to the “certain Prometheus”: while it is apparent that this concept is related to the gift of Prometheus, it is explicitly understood to be on the authority of the “forefathers” (oi( palaioi&), who pass it down; these, I suggest, can be correlated with Philolaus and other second generation mathematical Pythagoreans. 897 Instead, we must address the fact that the method/way (o(do&j) of when “destiny and innate (su&mfutoj) desire” take hold of the universe again (Plt. 272e6). Also see Pl. Lg. 771b7, where su&mfuton refers to the inborn (or connatural) proclivity for being religious, known as the “gift of the god.” 894 Gosling 1975: 83, 165; Huffman 2001: 70-1. 895 Huffman (2001: 71), citing the traditions of Proclus (Plat. Th. I.5) and Syrianus (Metaph. 10.2). 896 Even Huffman (2001: 71n. 11) is unclear about the significance of fire in this myth. Fire, there is no doubt, plays an important role in the philosophy of Philolaus, but it is not considered a first principle. 897 I will argue this below. Cf. Huffman 2001. 329 the gods is passed down by Prometheus along with fire. 898 Indeed, the focus on fire here in the Philebus was assumed by later Neoplatonist commentators to refer to the means of human ascent to the divine. 899 Of course, the Promethean gift is as old as Hesiod; 900 the version in which it functions to separate gods and men appears in the Aeschylean Prometheus Bound, where the description of the gift of Prometheus resounds with the mathematical Pythagorean emphasis on astronomy, number, and memory: …a(ll’ a!ter gnw&mhj to_ pa~n e!prasson, e!ste dh& sfin a)ntola_j e)gw& a!strwn e!deica ta&j te duskri&touj du&seij. kai_ mh_n a)riqmo&n, e!coxon sofisma&twn, e)ch~uron au)toi~j, gramma&twn te sunqe&seij, mnh&mhn a(pa&ntwn, mousmh&tor’ e)rga&nhn. 901 …But everything they did was Without thought, until I showed them the risings and The settings of the stars, hard to distinguish; And then number, eminent among wisdoms, I introduced to them, and combinations of letters, Memory of everything, industrious mother of the muses. We know that Aeschylus has Prometheus pass down his gift of technai to human beings by means of fire, 902 but this passage suggests the prominence of number in 898 Cf. Huffman 2001: 71 n.11. Both Pythagoras and Homer are said to espouse a way (o(doj) in the Republic (R. 600a9-b5), but there is no mention of fire there. 899 Cf. Damascius’ Lectures on the Philebus, where the commentator claims: “The fire that Prometheus stole and gave to man is all elevatory existence and elevatory perfection, not viewed in its upward motion, but in the process of being distributed through him to the lowest stratum of the universe. This is why it is said to be stolen, because, though elevatory, it is brought down; and through him, because only its descent is effected by Titanic powers, while its existence as form is due to other Gods.” Fire begins to sound very much like Soul in later Plato, according to this interpretation. See Dam. in Plt. Phlb. 61(ed. Westerlink). 900 Hes. Th. 521-616 and WD. 42-89. 901 Aesch. PV. 456-61. 902 Aesch. PV. 253-4 and 110-1. 330 tandem with the teaching of astronomy; the triad is completed by the introduction of the “combinations of letters,” all of which may be related to fire. Prometheus first fixes on the “risings and settings of the stars,” which are considered “hard to distinguish” (duskri&touj); method, as we might recall for Plato and the Pythagoreans, is called a “path” (o(do&j) that is correlated with the paths of the stars. 903 Pythagoras is not to be considered among those who were responsible for educating about the stars; this distinction falls instead, in the eyes of Aristotle, to the “so-called Pythagoreans,” whom we have identified with the mathematical exoteric Pythagoreans. 904 Now, if we recall, the philosopher responsible for the schism that occurred among the Pythagoreans was Hippasus of Metapontion, who, like Prometheus, was branded a heretic and put to death by sea; Hippasus, however, was punished for having publicized the secrets of mathematics 905 that led to the discovery of geometry and its promulgation through the work of Theodorus of Cyrene and Hippocrates of Chios. 906 Generally, scholars have understood these lines as reflecting Pythagorean concepts. Even Mark Griffith, who attempts to demonstrate that there are very few 903 See, e.g. Philolaus F 5 Huffman = Aetius 2.29.4. Generally, see Burkert 1971: 299-337. 904 Philolaus F 1 Huffman = Arist. Cael. 293a18ff. See Chapter 1. 905 Specifically, we hear (Iambl. VP 88) that Hippasus was punished for having been “the first to publicize and demonstrate visually the sphere from the twelve pentagons.” On the dodecahedron as a sphere made of twelve pentagons, see Von Fritz 1945: 256-260. 906 Iambl. De Comm. Math. 77-8. Other heretics who were said to have publicized the secrets of the mysteries include Empedocles, Plato, and, interestingly, Aeschylus (Arist. EN 1111a9; see Griffith 1978: 110 with n.44). We might consider the probability that Horace’s Odes 1.28 (Archytas A 3 Huffman), on the death of a Tarentine philosopher by sea, refers to Hippasus of Metapontion and not, as the scholiasts thought, to Archytas of Taras. Clearly the figure presented in the poem cannot be absolved from the crime he has committed, and the scholiasts (Archytas A 3a and A 3b Huffman) make explicit connections between number, geometry, and astronomy, in which Hippasus seems to have engaged. 331 Pythagorean elements in Aeschylus’ Prometheus Bound, allows for the possibility that these lines (alone among the extant works of Aeschylus) might refer to Pythagorean teachings: Prom. likewise offers little of substance, except of course for the emphasis placed on numbers as ‘choicest of sciences’, and on writing as the ‘reminder of everything, worker and mother of the muses (Prom. 459f.). Here there is no hint of metaphysical significance, merely a statement of their practical value as tools of civilization. 907 Indeed, Griffith’s formulation of numbers as the practical “tools of civilization” could not be closer to Hippasus’ formulation of number: we recall that Hippasus and his students understood number to be the “discerning tool of God the cosmiourge” (kritiko_n o!rganon kosmourgou~ qeou~). 908 The discernment of the risings and fallings of the stars may be implied in both the fragments of Hippasus 909 and the Aeschylean Prometheus. What is more, the element of fire was central to Hippasus’ philosophy – it was the first principle of all (a)rxh_n tw~n a(pa&ntwn to_ pu~r) 910 – and Aristotle considered his philosophical concepts more in line with the propositions of Heraclitus than with those of other Pythagoreans; 911 we might see Hippasus as a 907 Griffith 1978: 110-1. 908 Iambl. In Nicom. arithm. 10.20 Pistelli = Timpanaro Cardini 1958: 96-8. The term “tool” in Hippasus recalls the fragments of Gorgias Defense of Palamedes (DK B 11a30, 36), who suggests that “letters are the tool of Memory” (gra&mmata& te mnh&mhj o!rganon) and “number is the guardian of possessions” (a)riqmo_n xrhma&twn fu&laka). Palamedes, of course, is a famous Prometheus himself, though no Pythagorean, on which see Griffith 1983: 166-170. Edith Hall (1997: 97), following J.A. Davidson, assumes that this passage refers to another punished “Promethean” figure, the political thinker and lawgiver Protagoras, whose links to democratic Thurii have been demonstrated in Chapter 4. 909 On Diogenes Laertius’ authority (8.84), Hippasus was interested in the relationship of time and change in the cosmos. 910 Aet. 1.3.11 = Timpanaro Cardini 1958: 96 (F 5.9). 911 Arist. Metaph. 984Aa7. On the place of Heraclitus in the development of dialectical theory, see Lloyd 1979: 68-9. 332 Heraclitean Pythagorean, who accented teachings of the acousmatic Pythagoreans with Heraclitean natural physics. 912 In the absence of other fragments relating the doctrine of Hippasus, Heraclitus’ fragments provide us a means to posit a bridge between fire and measure that might refract Hippasus’ ideas: ko&smon to&nde, to_n au)to_n a(pa&ntwn, ou!te tij qew~n ou!te a)nqrw&pwn e)poi&hsen, a)ll’ h}n a)ei_ kai_ e!stin kai_ e!stai, pu~r a)ei&zwon, a(pto&menon me&tra kai_ a)posbennu&menon me&tra. 913 Neither did some “god” or “human” make the cosmos – that which is the same for all – but it always was and is and will be an eternally living fire, kindled in measures and snuffed out in measures. This fragment has produced much aporia: the place of measurement in the continual motion of the cosmos is not easy to infer. 914 But if we recall the shared doctrine of Heraclitus and Hippasus that fire was “unified, in motion, and limited” (e$n…kai_ kinou&menon kai_ peperasme&non), 915 we can deduce that fire is understood to be an eternally activated principle that has already been limited (by an unknown agent); as a limited entity, it thus is kindled and snuffed out according to measure, since limited entities – by the very nature of their being focused by a limiting standard – increase 912 Griffith himself notes (1978:111) that harmonia (PV. 551) cannot be simply Pythagorean but “might be by a Pythagorean (or Heraclitean).” The relationship between Hippasus and Heraclitus is secure, but it is difficult to separate out their doctrines or writings. The Suda even suggests that some believed Heraclitus to have been the disciple of Hippasus the Pythagorean! Heraclitus (Philodemus, Rhetoric 1, coll. 57, 62 = Robinson F 81a), of course, also criticized Pythagoras as a “captain of swindlers.” 913 Clem. Al. Strom. 5.103.6 = Heraclitus F 30 Robinson. 914 See, e.g. Robinson 1987: 96-8. 915 Simpl. In Phys. p. 23.33 = Timpanaro Cardini 1958: 94-5. 333 or decrease according to spatial and temporal measures. 916 Measure, which follows from Limit, thus exists into perpetuity along with the transformative power of fire. While it would be possible to consider Heraclitus as the “certain Prometheus” cited by Socrates, there are two problems with this interpretation: first, Heraclitus seems not to have been considered an exoteric who was punished for his divulging of divine secrets; and second, he is called by name elsewhere 917 in Plato’s oeuvre, and there would be no reason to hide his identity behind a mask. Instead, we can posit that the “certain Prometheus” of Plato’s Philebus, who was responsible for the passing down of the divine 918 gift of dialectical method as well as fire to the Pythagorean “forefathers,” recalls Hippasus of Metapontion and his pyrarchy: in both we see the correlation of discerning method with fire that led to the intuition of the mathematical arts; both were punished as a consequence of their publication of divine secrets; 919 both are seen as figures whose divulgence of the divine method led to technical discoveries in mathematics, especially geometry and astronomy. The presence of the “certain Prometheus” in Plato’s Philebus thus suggests the significance of mathematical Pythagorean method as derived from the teachings of Hippasus of Metapontion to the shifting theories of dialectical procedure in Plato’s late dialogues. 916 Such are the reversals of fire that operate temporally and spatially in measures. See Kahn 1979: 134-144. 917 Pl. Cratyl. 401-402. 918 Huffman (2001: 71) reminds us that it was Pythagoras who was considered “divine,” and that the “certain Prometheus” distributed to humans the divine method itself and was punished for having done so. 919 Interestingly, Socrates in the Philebus does not place emphasis on the punishment of the “certain Prometheus,” but it is assumed in all treatments of the Titan’s philanthropy. 334 Plato’s Prometheus, to be sure, recalls the Aeschylean paradigm. While we have investigated the significance of number and astronomy to the gift of Prometheus, it remains to discuss how the Aeschylean “combinations of letters” (gramma&twn te sunqe&seij) bestowed upon humans plays a role in the divine dialectical method of the Philebus. After relating the Pythagorean “forefathers’” application of Limited and Limitless to the problem of the One and the Many, Protarchus, perhaps like the reader, is in need of a simple paradigm in order to understand what the divine method is. 920 Specifically, he is having trouble conceiving of the relationship of logistic to the One/Many issue. Socrates has complained that “the wise among humans of today” – in contrast with the Pythagorean forefathers – “make a unit into a plurality either more quickly or more slowly than is necessary” and “straightaway proceed from the One to the Limitless;” they thus fail to proceed methodologically in accordance with due time (kairos), and this passage recalls the Eleatic Stranger’s discussion of ill-proportioned paradeigmata in the Statesman. 921 Indeed, “the means escape them” (ta_ de_ me&sa au)touj e)kfeu&gei), and it is the means that “separate out whether we posit the relationships of arguments in dialectical or eristic fashion.” 922 Dialectic, then, has come to be entirely formulated as a practice of logistic that demands attention to means, which prevents a definition from being too long or too short. Socrates in the 920 Pl. Phlb. 16e9-17a7. 921 See above. Socrates imitates the formal argumentative structure of the Eleatic Stranger here by proceeding from discussion of misapplication of logistic to the parsing of elemental syllables as a proper paradeigma. 922 Pl. Phlb. 17a3-5. 335 Philebus, in contrast to the arguments of the Eleatic Stranger in the Statesman, no longer believes that pleasure cannot be assessed according to due measure; 923 nevertheless, it remains to see precisely how one can do so, and Socrates calls upon further paradeigmata to illustrate this method. The divine dialectical method is first explained with a now-familiar paradeigma: language. Socrates treads over familiar ground from the Meno and the Statesman: any sound that can come out of a mouth is itself limitless, and we need to deduce whether it is either totally limitless – as a vowel – or unified – as a consonant; the knowledge of the “quantity and quality” (po&sa…kai_ o(poi~a) of any sound is what makes a person learned in grammar. 924 Socrates initially hesitates to go into further depth, and what follows is a significant digression from the argument that prepares Protarchus and the reader for yet another modification to the Platonic dialectical praxis. Socrates here distinguishes earlier treatments – which could include Aeschylus’ – of writing as a tool to understand philosophical method from this one, in which musical sound is understood as the paradigm. 925 The emphasis on sound (fwnh&) shifts away from the visual model of the written syllable, a marker of Plato’s heightened interest in the methodological application of phonic science. 926 Here it is worth recalling Fragment 1 of Archytas, in which the Tarentine 923 Pl. Plt. 286d4-e1. We might here recall that the Archytan “democratic” mode criticized by Polyarchus (Huffman A 9) assumes the need to measure bodily pleasures (see above). 924 Pl. Phlb. 17b3-9. On the indeterminate nature of vowels, see below. 925 Pl. Phlb. 17a8-b1. 926 Pl. Phlb. 18b3-4. Plato adopts mechanical investigations into pitch at Pl. Tim. 67a7-c3 and 79e10- 80b8. 336 philosopher begins his treatise Harmonics by referring to his predecessors who make good definitions by employing the sister-arts – including music – to understand the difference between wholes and parts: Those who distinguish the sciences seem to me to do so well, and there is nothing strange (in suggesting that) they understand individual things correctly, what sort they are. For, after they made good distinctions between the nature of wholes, they were on their way to see well concerning things, what sort they are, part by part. In fact, concerning the speed of the stars and their risings and settings, they handed down to us a clear distinction; the same goes concerning geometry and numbers and – not least (of all) – music. For these sciences seem to be akin. So they first noted that sounds could not exist unless impacts of things against one another were to happen. And they said “an impact happens whenever things in motion collide and fall upon one another. Some moving in opposite directions, when they meet, make a sound as each slows the other down, but others moving in the same direction but not with equal speed, being overtaken by the ones rushing upon them and being struck, make a sound. In fact, many of these sounds cannot be recognized because of our nature, some because of the weakness of the blow, others because of the length of the separation from us, and others because of the excess of the magnitude. For the excess of the magnitude of sounds does not slip by into our hearing, just as nothing is poured into the mouths of cups whenever someone pours out too much.” 927 Huffman has noted, rightly, that the switch from indirect statement to direct statement in line 18 of this passage demarcates the boundary between the opinions of “those who distinguish the sciences” and Archytas’ own views. 928 I follow Huffman, Burkert, and Barker in assuming that this passage, in which we hear about the speeds of colliding objects and experiments with pouring liquids into vessels, illustrates the 927 Archytas F 1 Huffman = Porph. in Harm. 1.3. Translation adapted from Huffman. 928 Huffman 2005: 139. 337 advances made in phonic science by Hippasus of Metapontion. 929 One incomplete fragment, from Theon of Smyrna, describes how Lasus of Hermione and the followers of Hippasus of Metapontion: … [thought it best?] to pursue the speeds of objects in motion and their slownesses through which consonances…(lacuna)…thinking that these sorts of ratios come from numbers, he [Hippasus? Lasus?] derived them from vases. For, using vases all equal and of like figure, he left one empty and filled another half-way full of water; he struck them together and produced consonance of an octave. And again, leaving one of the vases empty, he filled up another one-fourth of the way, and striking them together he produced consonance of a fourth. And he produced consonance of the fifth when he filled up one third of another. Thus the emptiness of the first vase was in a relation to the second of 2 : 1 in the consonance of an octave, and 3 : 2 in the consonance of a fifth, and 4 : 3 in the consonance of a fourth. 930 The deduction of mathematical ratios (which correspond with basic concords) from banging vessels together was thus one of the discoveries in musical theory attributed to Hippasus. 931 Comparable fragments demonstrate that Hippasus also investigated the sounds that could result as a consequence of striking bronze disks whose dimensions were mathematically proportional; the results were empirically successful, in that, if the bronze disks featured equal diameters, the thicknesses of each would be proportional to their peculiar frequencies. 932 Hippasus, then, may be credited with having first engaged in experiments that led to a comprehension of the mathematical ratios of phonic frequencies. His 929 Huffman 2005: 135. 930 Theo Smyrn. 59.4 Hiller = Timpanaro Cardini 1958: 100-1 (F 5.13). Translated by Barker. 931 See Barker 1989: 30-2 and Burkert 1971: 206-7. 932 Schol. ad Pl. Phd. 108d4. The authority here is Aristoxenus. See Barker 1989: 31 n.6 and Burkert 1971: 377. 338 experiments and discoveries are relegated to the understanding that speed of blow (i.e. quickness or slowness) combined with the mass of the colliding objects elicits a mathematical frequency which can or cannot be heard by a listener (depending on the distance between the blow and the listener). 933 In the Philebus, these kinds of investigations into pitch retain their Pythagorean value. There, however, Socrates is only interested in pitch theory inasmuch as it leads to harmonics, a science for which both Philolaus and Archytas were pioneers in the 4 th Century BCE: But, O friend, whenever you understand phonic intervals both in their numerical quantity – in their quickness or slowness – and in quality, in the notes of their intervals, and in however many arrangements come about from these – recognizing these arrangements, our predecessors passed down to us (their followers) the name of “harmonies;” and they declared that other sorts of characteristics which also come to be in the movements of bodies ought to be measured through numbers and called “rhythms” and “measures,” and, likewise, that we ought to realize that this was the proper way to deal with everything, both unified and many. 934 Socrates thus understands pitch to refer to numerical quantity and the arrangements of notes to refer to musical quality, called by their predecessors “harmonies.” Harmonies, then, are understood to refer to qualitative arrangements that, on Mitchell Miller’s reading of this passage, are congruent with the mathematical ratios produced by measured intervals on a monochord. 935 Comprehension of a true 933 Cf. Huffman 2005: 139-40. In this way, Hippasus’ theory of pitch is superior to that of Archytas, his follower, whose theory that high pitch corresponds with a faster speed of sound and lower pitch with a slower speed of sound is empirically incorrect. All sounds move at the same velocity, but the frequency that occurs at the moment of impact – a mathematical ratio – marks pitch. 934 Pl. Phlb. 17c11-d7. 935 Miller 2003: 28-9, contra Barker 1989: 64-5 notes 41-2. Barker does not take into account, while interpreting this passage, the role it plays in understanding the relationship of the Limit and Limitless terms or, for that matter, dialectical procedure at all. 339 harmonic mode requires the knowledge of the mathematical ratios that occur when one creates a note by applying a pause (i.e. Limiting) to an otherwise Limitless continuum of possible pitches that occur on the continuum of a string. The basic principle of Philolaus of Croton, in which “Nature in the cosmos was fitted together (a(rmo&xqh) from limitless and limited things (e)c a)pei&rwn te kai peraino&ntwn),” is thus applied here to a monochord in order to explain how one can understand a metaphysical process in pragmatic terms. 936 In the Philolaic scheme, harmony is understood as the catalyst that produced a synthesis of limitless and limited principles (a)rxai&), “in whatever way it came to be”; Philolaus thus does not account for how harmony came upon the oppositional principles, nor can we detect in his fragments any sense of how one has come to this knowledge. 937 In the Philebus and the Timaeus, however, the authoritative speakers employ the Platonic paradeigma of the monochord – and of dialectical procedure itself – to illustrate how harmony functions. 938 Thus, the identification of a harmonic arrangement, as with dialectical procedure, requires attention to the quantified aspects of any given matrix on a single continuum; the process of limiting a limitless continuum by establishing a spatio-temporal pause (i.e. a point) on the continuum (such as a string), then, is 936 Philolaus F 1 Huffman = D.L. 8.85. 937 Philolaus F 6 Huffman = Stob. Ecl. 1.21.7d. On this whole passage, see Huffman 2001: 80-2. 938 Also see Pl. Tim. 34b10-d7. It is worth comparing this passage of the Philebus with the composition of the universe in the Timaeus, a subject that must be undertaken comprehensively at a later date. 340 understood as a paradeigma for the successful dialectical application of Limit to Limitless. 939 What is more, as is implicit in Miller’s argument, harmonic arrangements correlate according to graduated relationships of notes in cyclical transfer following, and collectively spanned within, any octave. 940 Indeed, this discovery may be attributed to Philolaus of Croton, who, on Nichomachus’ account, understood the octave to be the fitting together (h(rmo&sqh) of the fourth and the fifth; this “magnitude,” then, was the first concord known as “harmony (a(rmoni&a).” 941 The discovery of Philolaus represents an extension of Hippasus’ discovery that eighths, fifths, and fourths existed when one caused the collision of bronze disks or vessels. Such an interpretation suggests that, while Plato understood Prometheus to be a mask for the heretic Hippasus of Metapontion, the “forefathers” and “predecessors” of this revised Platonic dialectical procedure were the mathematical Pythagoreans who, 939 Cf. Huffman 2001: 76-81. 940 Miller 2003: 29 provides a useful diagram of this Philolaic principle, which I reproduce here: Figure 6: Diagram of Modes Derivable from the Dorian Diatonic 941 Philolaus F 6a Huffman = Nicom. Harm. 9. ed. Jan. 341 following Hippasus’ experiments in phonics and harmonics, engaged in harmonic and pitch theory: Philolaus of Croton and Archytas of Taras. 942 On his way to uncovering a new and revised dialectical process informed by the teachings of the Eleatic Stranger in the Sophist and Statesman, Socrates forges a bridge between the paradeigmata of musical harmony and vocal sound; this bridge functions as both a summary of what he has earlier suggested about music and an extension of its principles to dialectical procedure: Just as: if someone at any time grasps any unity whatsoever, then, I suggest, he ought not to look immediately at the nature of the limitless, but at a certain number; so, conversely, whenever someone is forced to start by grasping some limitless thing, he should not immediately look to the One, but instead he should note a certain number that possesses each plurality; and he should end up at a unity made up of many things. 943 Socrates thus understands number as the mediating category between limited and limitless terms. For dialectical procedure, a person is forced to begin with a unity or a plurality; that person should then advance upon the subject by considering number as the mediating characteristic through which s/he might approach the opposite of the initial subject, and dialectical procedure thus becomes either: Unity Number Plurality or: Plurality Number Unity. 942 Archytas, too, was responsible for advances in diatonic theory that display advancements over Philolaus and Plato. On these, see Barker 1989: 46-52. I will discuss the matter of Archytan mathematical means and their relation to his political theory in Chapter 6. 943 Pl. Phlb. 18a7-b2. 342 Number, in this pair of sequences, functions as the mediating factor, due measure, or the tertium quid, that establishes difference and similarity between Plurality and Unity. Again, following the periodic dialectical scheme proposed in the Statesman, the practicing dialectician might be required to move in one direction or another, and to reverse the vector in the opposite way; knowing when to do so and under what circumstances constitutes the kairos. Here, though, the mathematicization of dialectical procedure is emphasized, and any appeal to weaving to locate it within Greek cultural traditions – both in oral poetics and in material production – is absent from this treatment. Even so, Socrates recalls the paradeigma of vocal sound once again, eliciting comparisons with the Statesman and extending the incomplete discussion from 17b3: Once, indeed, either some god or divine man noticed that vowels were limitless. The tradition in Egypt is that there was a certain “Theuth” who first noticed that, among the limitless type, vowels were not unified but plural, and then that there were other sounds that, while they partook of some articulation, were not vowels, and that there was a number of these. And he distinguished a third Form, namely those we now call mutes. Subsequently, he distinguished the inarticulate and mute sounds as far as each individual unity, and he did the same with the vowels and with the mean sounds, until, grasping a number of them – individually and collectively – he called them letters/elements. Realizing that none of us could learn each one itself according to itself without all the others, he, in turn, calculated that this was a bond on the grounds that it somehow rendered both each individually and all of these together as a single unity, and he gave utterance to this, calling it the “art of letters,” as it were. 944 This passage reveals Plato’s correlation of the distinction of language by letters (or elements) with the distinction of musical modes through mathematical means. In 944 Pl. Phlb. 18b6-d2. 343 both paradeigmata for dialectical procedure, the emphasis is on starting with a limitless quantity and moving via number to unities. The ascription of this theory to the Egyptian god Theuth/Thoth is perplexing and has elicited surprisingly little commentary. 945 Nevertheless, Phiroze Vasunia’s investigation into the Egyptian traditions that predate Plato confirms the positive image we receive of the technarch in the Philebus: Thoth is responsible for maintaining the cosmic order, or maat, by exercising knowledgeable control over language. 946 To be sure, in the Philebus, Socrates forces the pliable and ambivalent myth of Theuth into a Pythagorean framework: Aristotle ascribed to the Pythagoreans correlations between the distances between the letters A and W, the distance between the lowest and highest notes on an aulos, and the constitution of the heavens. 947 A little later, Aristotle’s student Aristoxenus (F 23 Wehrli = Stob. Ecl. 1 Prooem. 6) assumed that Pythagoras was, indeed, the individual who discovered the logos for numbers that exhibits their correlations; it is remarkable that Aristoxenus then claims that the Egyptians believed that Thoth made this discovery. 948 We note that, in contradistinction to the discovery of the “certain Prometheus” whom we have identified as Hippasus of Metapontion, the current cataloguing of letters and investigation into distinguishing elements attributed to Theuth carries with it no disastrous prolepsis for human 945 It has been the tradition of scholars and critics, both ancient and modern, to focus on the myth of Prometheus. Damascius, for instance, never discusses Theuth in his commentary; Huffman (2001: 77) glances past by devoting only one paragraph to Theuth, and it essentially recapitulates the argument of Gosling (1975). 946 Vasunia 2001: 146-155. 947 Arist. Metaph. 1093a29-b7. The “some” here refers back to the acousmatic Pythagoreans earlier chastised (1093a13-15) for analogizing the seven vowels, strings on a heptachord, and Pleiads. 948 On this fragment of Aristoxenus, see Chapter 1. 344 beings, and the “divine man” to whom Socrates refers here is most likely Pythagoras himself. If this is the case, we may see the digression that correlates and synthesizes the methods of the “certain Prometheus” and the “divine man” who resembles Theuth as Plato’s attempt to reconcile the philosophical processes of the mathematical and the acousmatic Pythagoreans: thus, the divine “way” (o(do&j) of the Philebus represents the combination of two oppositional philosophical approaches that, thanks to the political schism that occurred in Magna Graecia during the first half of the 5 th Century BCE, had been distinguished by competing ideological communities among the Pythagoreans. Following this pair of paradeigmata that allow Protarchus and Philebus to understand how to employ a Pythagorean dialectical procedure – it is interesting to note that Philebus, the proponent of geometric hedonism, accepts the process ascribed to Theuth but disapproves of the one ascribed to Prometheus – the interlocutors return to the issue of pleasure, and they will occupy themselves with this and the problem of the Good for the rest of the dialogue. As J.C.B. Gosling has argued convincingly, the issue of attaining the preferred life here is predominantly a response to the influence of the geometer and astronomer Eudoxus of Cnidos, who we are told was a student of Archytas and perhaps also of Plato. 949 The application of his theories of pleasure to the Philebus is immediately manifest and recalls the arguments of Polyarchus and Archytas aforementioned: 949 See especially Gosling 1975: 139-42 and 166-70. On Eudoxus as student of Archytas and Plato, see D.L. 8.86 = Eudoxus T 7 Lasserre and Capizzi 1984: 169-171. 345 Eudoxus believed that pleasure is the Good, justifying his claim on the following grounds: he saw that all things, whether rational or irrational, gravitated towards it; but in every case, he believed, that which is sought-after is reasonable (e)pieike&j), and that which is especially sought-after is best. Therefore, the fact that all things are brought (fe&resqai) towards it indicates that this is the most noble thing for all (for each thing discovers its own particular good, just like it discovers food), but that which is good for all things and to which all things gravitate (ou{ pa&nt’ e)fi&etai) is the Good. 950 What marks Eudoxus’ theory of the Good as distinctive from the philosophical ideals of his Pythagorean predecessors is the prominent placement of astronomy – and not the logistical oppositions of Limit/Limitless – in his philosophical system. Here, in his ethical philosophy, we perceive that Eudoxus employs terms of astronomical motion in order to understand the Good. Regarding astronomy, Eudoxus’ primary contribution was a hypothesis of four rotating spheres centered on the earth. 951 As we may recall, the mathematical Pythagoreans believed that the heavenly bodies rotated around a central fire, and thus Eudoxus departs from the teachings of Philolaus and (probably) Hippasus. Plato himself, if we are to accept the testimonia of Theophrastus, was ambivalent about whether to place fire or earth first, because he assumed that the heavenly bodies were composed of both. 952 While it is clear that Plato found fault with Eudoxus’ conceptualization of the Good, as was noted by Aristotle in the Nichomachean Ethics, 953 he and his successors in the Academy came 950 Arist. EN. 1172b9ff. = Eudoxus D 3 Lasserre. 951 Arist. Metaph. 1073b17ff. = Eudoxus D 6 Lasserre. On this fragment, see Heath 1931: 188-90. 952 Philoponus, De aeternitate mundi contra Proclum 13.15 = Theophrastus F 160A Fortenbaugh. 953 Arist. EN. 1172b29-35, referring to Pl. Phlb. 60d. 346 to be influenced by Eudoxus’ astronomical models. 954 Despite its long-living appeal, Eudoxus’ hypothesis about the concentric circles of the universe – which supplied Plato with a mythical system for interrogation and paradeigmatic borrowing – was incommensurable with the observable phenomenon of retrograde planetary motion, to which Timaeus refers (for the first time among extant Greek texts) in the eponymous dialogue. 955 Conclusions are difficult to draw from the paucity of evidence, but if Plato recognized the fault of Eudoxus’ theory of concentric circles, then the application of his peculiar astronomical ideas to the Good would have been problematic. 956 On the other hand, Eudoxus was perhaps able to provide Plato with suggestions about how to resolve the problem of participation among the Forms. What we know about Eudoxus’ Formal theory is filtered through Aristotle’s eyes: Most of all, someone might be at a loss to say what in the world the Forms contribute to the everlasting sensibles (toi~j a)idi&oij tw~n ai)sqhtw~n), whether they are coming-to-be or being destroyed. For they (i.e. Forms) are not causes of motion or change for them (i.e. sensibles). Indeed, they (i.e. Forms) neither give aid to the knowledge of other things – they are not the substance of things, since they would be in them – nor to their existence, since they are not present in the things which partake in them. If this were to be the case, perhaps they would seem to be causes, e.g. something is white when it is mixed with White. But this argument, which was first suggested by Anaxagoras and then later by Eudoxus and some others, is easily refutable. 957 954 On which, see Lloyd 1979: 174-79. The evidence for influence is strongest for the Epinomis, probably composed by Philip of Opus following the death of Plato. 955 Pl. Tim. 40c3-d3. On observable retrograde motion and its contradiction of the Eudoxan theory of concentric spheres, see Negebauer 1957: 154-5. 956 Generally, for Eudoxus’ theory of concentric spheres and the criticisms of other ancient philosophers, see Evans 1998: 305-312. 957 Arist. Metaph. 991a8-18. 347 Aristotle’s summary of Eudoxus’ conceptualizations of the Forms is frustratingly condensed and conflates the views of Anaxagoras and the Platonic/Pythagorean astronomer. 958 Now Anaxagoras held no definable theory of the Forms, nor anything like it, and he is especially famous for believing that the astronomical bodies were stones, thrown off from the spin of the earth. 959 Indeed, the elements of Aristotle’s summary that resonate with the extant fragments of Anaxagoras are: (1) the doctrine of mixture and (2) the use of color to determine relationships between different things. Mixture and participation appear to be the issues under examination here, and Aristotle goes on to criticize the Platonic doctrine of paradeigmata as an ill- suited reformulation of the problem of meixis. 960 We are therefore looking for a pre- Statesman formulation of mixture that is Eudoxan: the notion that Forms could contribute to the “everlasting sensibles,” by which Aristotle means the heavenly bodies, is a remarkable elision of Platonic Formal Theory with astronomical observation. Eudoxus, then, assumed a relationship between Forms and heavenly sensibles based on mixture. 961 From what we can deduce negatively from Aristotle’s account, Eudoxus held that (1) the heavenly bodies, which are subject to coming-to- be and to decay, partake of the Forms; (2) the Forms are causes of motion and 958 Alexander of Aphrodisias (In Arist. Met. Comm. p. 97 Hayduck = Eudoxus D 2 Lasserre) attempted to unpack this fragment. 959 For Anaxagoras’ astronomical theories, see KRS 380-82. 960 Arist. Metaph. 991a20-991b1. 961 Ross (1924: 198) describes the relationship between the Eudoxan and Platonic Form Theories thus: “…his theory seems to have been an ideal theory which rejected the transcendence ascribed to the Ideas by Plato and described them as immanent in particulars.” The problem with this interpretation is that Aristotle focuses on not simply particulars, but eternal particulars, or the heavenly bodies. 348 change; (3) the Forms, in some ill-defined fashion, do promote human knowledge of themselves; (4) the Forms have substance. Where mixture figures in this scheme is unclear in Aristotle’s account. If we return to the Philebus, we note that Socrates proceeds – following the description of the dialectical gifts of Prometheus and Theuth – to discuss the best form of living. On the way to deducing the top prize that is to be given for this para- Olympic competition for the most preferred way to live – the award will go to the life that mixes pleasure and intelligence 962 – Socrates and Protarchus investigate the ways of distinguishing Forms from other concepts within the universe; this approach represents a final revision of the Theory of the Forms as developed from the criticisms of the Parmenides through the dialectical procedures of the Statesman. Here, we see the synthesis of the divine gifts of Prometheus and Theuth with a Formal theory that both appropriates and extends Eudoxus’ contributions. Socrates embarks on this theory that examines “things that currently exist” by appealing to the first principle: SOCRATES: Let’s try to respect the argument by positing a starting point/principle (a)rxh_n)for it. PROTARCHUS: Of what sort? SOCRATES: Let’s divide all things that currently exist in the whole world into two or, even better, into three, if you wish. PROTARCHUS: According to what, would you say? SOCRATES: Why don’t we take up some of the things we were just saying. PROTARCHUS: Which ones? SOCRATES: Well, we were saying that the god has demonstrated that things in existence have a Limitless, and, on the other hand, a Limit. 962 Pl. Phlb. 20b7-9 and 27d1-2. 349 PROTARCHUS: Definitely. SOCRATES: So let’s posit these as two of the Forms, and a third, a unified thing mixed up from both. But, in my opinion, I seem to be a ridiculous person when I divide according to Forms and enumerate them. PROTARCHUS: What do you mean, my friend? SOCRATES: Actually, it appears that we need to add a fourth Kind. PROTARCHUS: Tell me what it is. SOCRATES: Notice the cause of the intermixing (th~j summei&cewj …th_n ai)tia&n) of these with one another, and posit this for me as a fourth Kind in addition to those three. PROTARCHUS: Wouldn’t you need to add a fifth Kind, which has the capacity for distinction (dia&krisi&n tinoj duname&nou)? SOCRATES: Perhaps, but I don’t think so now…. 963 Socrates thus modifies the earlier Theories of the Form by positing a fourth Kind, namely the class of causes that are responsible for catalyzing mixture of the Limit and Limitless. Limitless is understood as the first Form, and Limit the second; the third, mixed Kind, which forms a unit, is described as “the entire progeny” of the Limitless and Limited, a “coming-into-Being (ge&nesin ei)j ou)si&an) from the measures completed following the Limit (e)k tw~n meta_ tou~ pe&ratoj a)peirgasme&wn me&trwn).” 964 It is understood to be analogous to the best form of life – the mixed life – which involves Limitless pleasure measured by the Limit intelligence in a harmonious compound. 965 The fourth Kind, however, requires much more detailed investigation. Indeed, the addition of a fourth Kind to the Theory of the Forms, a Kind that is responsible for activating the mixture and genesis of things into their existence, is an attempt to resolve the problem of the 963 Pl. Phlb. 23c1-d11. 964 Pl. Phlb. 26d7-9. 965 Pl. Phlb. 27d1-10. 350 Third Man argument from the Parmenides: the fourth kind, which causes the combinations of Forms and sensibles to occur, governs what mixed Kinds can be formed from the application of a Limit to a Limitless. The end result is that the perpetual Limitless that can occur from innumerable combinations can be controlled by a higher power. This addendum to the Theory of the Forms recalls the prominence of Mind in the fragments of Anaxagoras 966 combined with the Eudoxan identification of divinity with movement of the celestial bodies and their eternal existence: SOCRATES: Should we declare that the universe and what we call its entirety are controlled by the power of irrationality, chance, and the concept that “whatever happens, happens?” Or is the opposite the case, as our predecessors used to say, that some amazing Mind and Intelligence organize and navigate it? PROTARCHUS: What a difference, my dear Socrates! What you are now saying seems beyond irreverence! But to say that Mind orders all these things does justice to the observable cosmos: the sun, the moon the stars, and all their circuits. 967 In this presentation, while Socrates promotes the Anaxagoran position, Protarchus (who is representative of the Eudoxan perspective) adapts the Socratean notion of Mind as the helmsman of the universe – a notion that recalls the Myth of the Unwinding of the Universe – by making Mind the director of the movements of the celestial bodies in the observable heavens. But the influence of Eudoxus does not end there: if we recall, Aristotle criticized Eudoxus for believing that the Forms were the causes of change in the heavenly bodies. When we recall that this argument 966 And, of course, both Diogenes of Apollonia and the author of the Derveni Papyrus. On Mind in the Derveni Papyrus, see Betegh 2004: 185-191. Generally, on this passage, see Skemp 1967: 21-30. 967 Pl. Phlb. 28d5-e5. 351 concerning the power of Mind to govern and navigate the cosmos is itself an explication of the Fourth Kind, we are not surprised when Socrates declares that the cosmic Mind is the cause of the ordered mixing of the Limit and Limitless: If this isn’t the case, then it would be better for us to say – in response to the argument – as we have said several times that there is a great amount of Limitless in the universe, and a sufficient amount of Limit, and a certain not illegitimate Cause for them that arranges and orders the years, seasons, and months, which would most justly be called Wisdom and Mind. 968 Socrates has welcomed the influx of Eudoxus’ theories of the Form by allotting Mind as the Fourth Kind, a divine power that, like Love in the Empedoclean cosmos, brings things together in the universe in mixture 969 ; but this is no capricious commingling, as Mind regulates the Limitless expanse by applying an appropriate Limit, thereby creating a balanced and measured mixture that is the Third Kind. Proof of this is in the circuits of the observable heavenly bodies, a shared doctrine for Eudoxus and Plato that would continue to develop among these competing but complementary philosophical minds. A fifth Kind is hinted at, even given a name: the power of distinction (dia&krisi&n tinoj duname&nou), but Socrates sees no need to move beyond the Fourth Kind. This Fifth Kind appears nowhere else among the works of Plato, and it receives no further commentary here in the Philebus. Some have speculated that it is correlative with Strife in Empedocles’ scheme; 970 this would be concordant with the revised dialectical procedure of the Statesman, 968 Pl. Phlb. 30c2-7. 969 Thus, as Greg Thalmann suggests to me, Socrates “ends up incorporating nou~j into the framework, whereas Plato (in the Phaedo) represents him as rejecting it at the end of his life.” 970 Skemp (1967: 28) quotes R.G. Bury for this suggestion, but he goes no further with it either. 352 wherein the student is required perpetually to distinguish and combine, only to distinguish again, in a dialectical circuit. But the term itself, diacritics, comes closer to Hippasus’ belief that Number was the “discerning tool of God the cosmiourge” (kritiko_n o!rganon kosmourgou~ qeou~). 971 If Mind, the divine potentate who is in command of all of the first four categories of Form, were also subject to the cycles of the universe, then a return to diaeresis would lead back to the breaking down of Limitless and Limit once again. So runs the cosmic physics and metaphysics of this hypothetical scheme; we can only speculate, to be sure, because Socrates will go no further in describing the Fifth Kind. It holds no significant place in this dialogue. On our own voyage through the dialectical and Formal theories of the Statesman and the Philebus, we have found ourselves, as Plato did late in life, looking back in time for systematic models to understand the universe while he progressed with scientific investigations into astronomy and geometry. In the process of revising his dialectical theory, he consequently found himself revising his theories of ontology, ethics, and even the Forms. All of this occurred in response to the philosophical innovations of the mathematical Pythagoreans, descended from the Promethean heretic Hippasus of Metapontion, including Philolaus of Croton, Archytas of Taras, and Eudoxus of Cnidos. These revisions occurred in two demonstrable spheres of thought: (1) regarding the world of the Intelligible and the Forms themselves, Plato produced an answer to the Third Man criticism of the Parmenides by positing a divine Mind that regulates the mixture of the oppositional 971 Iambl. In Nicom. arithm. 10.20 Pistelli = Timpanaro Cardini 1958: 96-8. 353 Limit and Limitless within the universe; (2) and regarding the earthly, visible, “second-best” world, Plato adduced the kingly Statesman, whose responsibilities included the mediation of the communal, mixed soul of the polis by interweaving the oppositional characters (courageous and temperate) that constitute the political commonwealth. And so, when we finally find ourselves prepared to reexamine Kallipolis and its constitution, we are firmly entrenched in a reflective analogy involving the intelligent Mind and the human Statesman; what remains, then, is sketching the “second-best” polis of Magnesia herself and the demonstrable reliance upon mathematical Pythagorean political philosophy. 354 _______________________________________ CHAPTER 6: THE TARENTINE TAPESTRY: MAGNESIA AND PHILOSOPHICAL POLITIES IN MAGNA GRAECIA _______________________________________ ‘The Lawgiver will assume that it is common sense that numerical distribution (ta_j tw~n a)riqmw~n dianoma_j) in every variety will be applicable to all things, those variegated among themselves and those variegated in length and width and especially in sound and motion (both straight up-and-down progression and circular revolution). The Lawgiver should turn his attention to all these things and instruct every citizen, to the best of his ability (ei)j du&namin), not to neglect the structure of these things.’ – The Athenian Stranger (Plato, Laws, 746e6-747a7). It has been a recurrent preoccupation of Plato to seek out a means to distinguish successfully between the noetic, existent world of the Intelligible and the changeable, sensible world of visible phenomena. This Parmenidean battle between reality as it is understood and reality as it is perceived established the boundaries for metaphysics and determined the difference between Being and Becoming; but Plato was never really comfortable with this systematic divide, first allowing for the possibility that the things that are coming-to-be imitate those that exist ideally, then attempting to account for the means by which sensible phenomena could participate in their Formal progenitors; finally, he hypothesized a navigator for the universe who could control the relationship and balance the mixture between Being and Becoming, the cosmological Demiourge of the Timaeus or Mind of the Philebus. Mathematics was the tool for mediation. In these figurations, Plato’s comprehensive and recurrent 355 engagement with the writings of Presocratic and Pythagorean philosophers occurred alongside technical advances in mathematics and astronomy made within the Academy and across the Adriatic Sea, in a competitor school of mathematical Pythagoreans centered in the Southeastern Italian polis of Taras. We may consider that a primary stimulus for these revisions of Platonic dialectic and ontology was the oft-unscripted factor in Plato’s life, well-known but traditionally ignored in analytical treatments of the development of Plato’s philosophy: his failures in the world of politics. 972 In this final chapter, I will investigate the place of contemporary politics in the revision of Plato’s philosophical pragmateia. Specifically, I will examine how Plato’s failures in Sicily at the court of Syracuse led to a rejection of the ideal polity that he had imagined in earlier works such as the Republic and the Timaeus-Critias in favor of a “second-best” polity that is illustrated in Epistles VII and VIII and the Laws. The combination of Plato’s failures in Syracuse with Archytas’ notable success in governing Taras prompted Plato to abandon the simple ideal model of a polity for one that was a synthesis of ideal and pragmatic, formulated in Plato’s writings as a combination of the polity that exists perpetually and the polity that is able to undergo change without being corrupted or destroyed. Ontologically, this new model represents the negotiation of Being and Becoming, to which Plato’s ethical and dialectical theory had led him in the Philebus. 973 Politically-speaking, 972 Notable exceptions are Morrow 1993 and Capizzi 1984. 973 On which, see Chapter 5. 356 the synthesis of ideal and pragmatic was manifested in the unification of the primary models for Plato’s political thought, the traditional polity represented by “best- lawed” Epizephyrian Locri, whose laws, composed by Zaleucus, were celebrated in antiquity for never changing. 974 This new polity was in a state of coming-to-be, which, as “second-best,” preserved the original intentions of the lawcode it imitated and was guided by a knowledgeable and effective leader: this constitution, I suggest, was that of Taras. Indeed, as I will argue, while the Spartan and Locrian lawcodes presented Plato with an ideal, timeless model for his polity, the method of political “weaving” that significantly characterizes his post-Republic political philosophy and appears in tandem with mathematical method in the Laws is in dialogue with traditions involving Pythagoreans in Southeastern Italy. I will conclude this chapter by demonstrating that this model of political philosophy, characterized by mathematics and weaving, is derived substantially from the philosophy of Archytas of Taras. PLATO’S SKETCHES FOR THE “SECOND-BEST” POLITY AND THE MIXED CONSTITUTION OF MAGNESIA The story of Plato’s unsuccessful attempts to instantiate a philosopher-king in the figure of Dionysius II of Syracuse is well-known and can be gleaned from his Epistles, especially numbers VII and VIII, both of which are addressed to the 974 See Chapter 4. 357 followers of Dion in Syracuse. If they were written by Plato, as I think they were, 975 these letters were composed, respectively, immediately following the death of Dion in 354 BCE and within a year of that time, once Dion’s party and Hipparinus, the half-brother of Dionysius II, caused the expulsion of Callippus – the assassinator of Dion – from the city: they thus appear to have been composed in 354 and 353 BCE. 976 Epistle VII is a complex work of philosophy and autobiography that reveals Plato’s failure to achieve a “best-lawed” community, a theme that we have noted develops throughout the later dialogues of Plato, especially the Statesman; there, we noted the presence of a movement towards theories of the “second-best” political organizations as Plato reconsidered how contemporary polities, which are subject to Becoming, would change throughout time. In Epistle VII, we detect a recurring trend in Plato’s political philosophy, namely the realization that the “first-best” kinds 975 Such is the conclusion of Morrow 1962: 45, 81-2. Charles Kahn (1996: 48 n.22) has put the issue of authenticity in its proper place: “I have no doubt that the letter was written by Plato. Most twentieth-century Plato scholars have recognized the letter as authentic, but in the last generation the doubters were more conspicuous. The communis opinio seems now to be swinging back in favor of authenticity.” Even further, Kahn identifies precisely why people have doubted its authenticity, an issue that recalls the first few pages of this study: the failure of scholars to engage seriously with Plato’s political project. So Kahn (p. 50): “This is a document of extraordinary importance for anyone who assumes, as I do, that the letter was written by Plato…[O]nce we comprehend Plato’s passionate concern for political action, many things fall into place. The deep yearning for political reconstruction explains why his three longest works, spanning his whole career, are devoted to the question of how to impose a moral order on the life of the city: Gorgias, Republic, and Laws.” The same could be said of Epistle VIII, where an acute awareness of the unified project of philosophy and politics is exacerbated in Plato’s heated advice to the followers of Dion. The argument (b) of Schofield (2006: 16-17), that Epistle VII is pseudonymously written because it speaks in the first person (‘I’), and not in the voice of another character (e.g. Socrates), is absurd. Are we to imagine (the only alternatives that correspond with his logic) that Plato would compose political correspondence to his embattled compatriots in Sicily in the voice of Socrates? Or of the Eleatic Stranger? Or as Timaeus? Indeed, should we attribute authenticity to a letter that was written “Socrates, to the followers of Dion?” 976 For the dating of Epistles VII and VIII, see Morrow 1962: 45 and 82-3. Even if the letters are spurious, they reveal remarkable similarity to the later political philosophy of Plato, especially in the Laws, and as such they represent, at the very least, Plato’s contemporary thought in the late 350s. 358 of political organization are impossible to sustain even if they can be momentarily put into effect: If, in his [i.e. Dionysius II’s] rule, philosophy had come to be truly unified with power, it would have shone forth through all Greek and Barbarian peoples as a sufficient testament to the truth that never will any city-state or man come to be happy if he does not conduct his life with intelligence and under the eye of justice, whether it is achieved personally or through just rearing and education in ethics from reverent leaders. 977 Throughout his later career, Plato’s disappointment with contemporary philosophical polities is manifest on two levels: first, he criticizes monarchs’ failures to conduct themselves as temperate leaders of their communities; and second, contemporary historical events provided a sufficient challenge to the earlier idealizations expressed most eloquently in the Republic. Both of these disappointments are tied directly to Dionysius II himself: as a failed experiment in the philosophical education of a young royal, Dionysius not only exemplified the tyrannical ethos at its most acute; he was also responsible for abrogating the “best- lawed” constitution that provided Plato with a model for the traditional polity throughout his later career: the Zaleucan constitution of the Epizephyrian Locrians. 978 The other contemporary imperfect city-states that provided Plato with 977 Pl. Ep. 335d1-e1. 978 On Locri’s constitution, see Chapter 4. It is the only constitution that Plato deems “best-lawed” (eu)nomwta&thj ; eu)nomw&tatoi) in the superlative (Lg. 638b2; Tim. 20a2), in contrast to even “well- lawed” Sparta, a tradition to which Plato probably subscribes although he never refers to Sparta as “well-lawed” (eu)nomoume&nh). On Spartan Eunomia, see Morrow 1963: 40-49 and Thommen 1996: 22-53. Strabo (6.1.8) claims that the Locri Epizephyrii, who were responsible for the first written law-code in Greece, were ravaged by the excesses of the exiled Dionysius II, who was, at that time, still allied with the Tarentines. Cf. Arist. Pol. 1307a34-40, where Aristotle claims that Locri shifted 359 models for imitation and development of his ideal polity – Athens and Sparta – had disappointed Plato for some time, and it became a topos in Plato’s later works (from the Timaeus forward) to call to witness the lost ideals of Solonian Athens and Lycurgan Sparta. 979 Yet, until his death, Plato maintained a vision of a “second- best” or imitative polity that would be governed by laws in the absence of a true monarch to guide the city-state according to philosophical precepts. 980 Perhaps the earliest notification of his intention to propose a second-best polity as the desired goal of a community is found in Epistle VII, addressed to the followers of Dion: Whenever they get the will to save their city, let those men who are in authority counsel themselves to select those from among the Greeks who they learn are the best: first, let them select old men, with wives and children at home and descendents who were especially numerous, good, and illustrious; each should possess a sufficient amount of property (a sufficient number of these old men for a city of ten- thousand people is fifty). Let them, by personal requests and honors as great as possible, induce these old men to leave their homes. Once the old men have been relocated, let them direct the old men to make laws, binding them in oath to distribute no more to the conquerors than to the conquered, but to distribute equally and commonly to the entire city. Then, once the laws have been established, everything depends on this: if the conquerors offer themselves as more subservient to the laws than the conquered, everything will be full of safety and happiness and escape all evils. But, if this does not happen, let nobody who does not obey these current principles call upon me or anyone else for support. These proposals are akin (a)delfa_) to those which Dion and I attempted to put into effect for the benefit of the Syracusans, but second-best. 981 from an aristocratic to an oligarchic constitution during the period of Dionyisus II’s sojourn there. See De Juliis 1996: 251-2. 979 The best treatments of Plato’s reflection upon Sparta and Athens remains Morrow 1993: 40-92. 980 For a useful summary of the traditions of “second-best” polities in Plato’s later work, see Klosko 1986: 198-241. 981 Pl. Ep. 337b3-d6. 360 Rule under written laws, as established in the Statesman, provides the background for this “second-best” polity recommended by Plato to the Syracusans in 354 BCE. This set of provisions, however, imitates the ideal constitution proposed by Plato and Dion during their discussions that occurred previously, perhaps in 355 BCE. Dion, as Plutarch tells us, had proposed to invite legislators from the mother-city of Syracuse, Corinth, in order to draw up a mixed constitution for the Syracusans: In actuality, Dion did send for some Corinthians, hoping that it would be easier to set up his intended constitution with their presence. He was intending to slacken the indomitable power of the people (dhmokrati&an), on the grounds that it is not properly a constitution but a bazaar of constitutions, according to Plato. Instead, he was hoping to establish and organize an aristocracy that would preside over and arbitrate the greatest things by forging a Laconian/Cretan model, mixed up from the people and the monarchy (meica&menoj e)k dh&mou kai_ basilei&aj). 982 While Plutarch is frustratingly vague here, it is clear that the ideal constitution proposed by Dion is itself a mixture of democratic and monarchical elements, called an aristocracy (a)ristokrati&an). This form of aristocracy does not appear among the types of aristocracy enumerated by Aristotle in the Politics, in that Aristotle presupposes that aristocracies are types of constitution that take into account the people and either virtue or wealth, both of which are markers of a small class of citizens. 983 In Aristotelian aristocracies, the mixture is of democratic and oligarchic – not monarchical – elements. Indeed, Dion’s ideal “aristocratic” constitution differs 982 Plut. Dion 53. Plutarch cannot be cribbing his material from Polybius, who believed that a mixed constitution was made up of monarchical and oligarchic elements. See Von Fritz 1954: 184-5. 983 Arist. Pol. 1298b15-22. The two exempla of aristocratic constitutions are Carthage, whose constitution has an eye to wealth, virtue, and the d1mos, and Sparta, which represents “a mixture” of virtue and democracy. 361 also from the aristocratic constitution of influential Rhegion, for which Heraclides Lembus (following Aristotle) claims a boule of one-thousand selected according to the value of each citizen’s property. 984 On the other hand, Dion’s mixed constitution has more in common with the description of Athens following the formation of the assembly of the five-thousand in 411 BCE, as described by Thucydides, in the second-oldest extant textual reference to any kind of mixed constitution (first expounded by Hippodamus of Miletus in On Polity) 985 : Many other assemblies were held afterward, from which lawmakers were elected and other things were voted upon for the establishment of the constitution. During this first period, Athens appears to have been governed better than it ever had been in my lifetime, since the mixture between the few and the many was moderate (metri&a ga_r h# e)j tou_j o)li&gouj kai_ tou_j pollou_j cu&gkrasij e)ge&neto)… 986 We may therefore suggest that a predominant form of mixed constitution in the second half of the 5th Century BCE in Athens was the combination of an oligarchy and a democracy, and this became the traditional “aristocratic” constitution of Aristotle and his followers. 987 But the ideal “aristocratic” constitution conceived jointly by Dion and Plato in the mid-350s is composed of monarchical and democratic elements. It is likely an attempt by Plato and Dion to interweave the two 984 Heracleides Lembos F55 Dilts. On the constitutional development of Rhegion, see Hölkeskamp 1999: 234-7. 985 On Hippodamus, see Chapter 4. 986 Thuc. 8.97.2. For Thucydides, the Athenian “moderate” mixture is in contradistinction to that of Syracuse during the same period, which is described as “mixed-up mobs of all kinds of people (o!xloij…cummei&ktoij poluandrou~sin)” and did not preserve the aristocratic mean (Thuc. 6.17.2). For the Athenian constitution after the establishment of the five-thousand, see Bordes 1982: 345-6. 987 Aristotle (Pol. 1266a2-5) criticizes the constitution of Plato’s Laws for being a mixture of democracy and tyranny, although Plato calls this “monarchy.” His criticism follows from his belief that a better politeia will occur when the government is mixed from even more constitutional types. 362 dominant historical forms of governance in Syracuse: democracy (which was the dominant constitutional element – even if Syracuse was a mixed constitution – from roughly 466-413 BCE) and monarchy (in effect from 412 BCE until the death of Dion). 988 This mixed constitution, however, was never put into effect; the failure is attributed to Dionysius II by Plato, to the popular party and its leader Callippus by Plutarch. 989 Following the death of Dion, Plato exhorts the followers of his party to put into effect the “second-best” constitution, one that is “akin” (a)delfa&) to Dion’s proposed mixture of democratic and monarchical elements. Indeed, Plato’s Epistle VIII reveals his vision of the original plan: in Epistle VII, Plato proposes a panhellenic committee made up of Greeks 990 – not simply Corinthians – to establish a new constitution and see to it that the land is distributed equally among both those who have benefited from the revolution in Syracuse and those who have not. His temporary solution is thus directed at settling land to avert any further internal dissent among Syracusan factions. The treatment of this subject is further elaborated in Epistle VIII, where Plato is concerned with the comprehensive and long-term structure of the mixed constitution as well as the immediate measures to save Syracuse from internal stasis; it thus represents – as we will see shortly – an extension of the policies of Dion and Plato from Epistle VII. 988 On Syracuse as a democracy from 466-413/12, see Robinson 2000. 989 Plut. Dion 54-8. 990 Plato is not concerned about the differences between individual Greek communities; he proposes a synthetic model that (1) first integrates the Greek communities themselves and (2) extends that integration to the “Barbarians” of Sicily, by which he means Near Eastern peoples, such as the Carthaginians. See Ep. 332a3-c2. 363 The words of Dion in Epistle VIII, expressed in direct discourse, partake of a long-standing tradition of preambles to laws ascribed to the lawgiver himself. 991 Prooimia to the Laws of Charondas and Zaleucus testify to the traditions in Sicily and Magna Graecia of recording, for posterity’s imitation, the laws of the community as written documents. Plato thus elevates the status of Dion to an original Lawgiver or thesmothet1s whose words survive in death as a manifesto for the conduct of the polity and its timeless goals. 992 In this way, the prelude of Dion recalls lawgiving traditions from texts that were probably composed around the mid-5 th Century BCE. 993 What makes this speech particularly resonant with the political philosophy of Plato late in life is its adherence to a mixed paradigm, directly inherited from the Spartan constitution of Lycurgus, as Plato understood it. Preceding what we might want to designate the Prooimion to the Laws of Dion, Plato sua voce expresses his hope that Dionysius II will be able to “flee the name and deeds of a tyrant” and “change into a King”; 994 the analogy is then drawn with Lycurgus, who, unlike his relatives in Argos and Messene, wanted to preserve himself and his polis from degenerate forms of rule. Plato claims that Lycurgus “instituted a remedy (fa&rmakon), the rule of the elders, and that of the ephors as the saving bond 991 In the possibly spurious Epistle III (316a3), “Plato” claims that he worked with Dionysius II on “Preambles to the Laws.” Other testimonia suggest that these prooimia might have been used in the drafting of constitutions for Phoebia and Tauromenion in 358-7 BCE. On these, see Morrow 1962: 92-3. 992 On the term thesmos and the traditions of Charondas and Zaleucus, see Farenga 2006: 267-279. 993 See Chapter 4. 994 Pl. Ep. 354a6-8. 364 (desmo_n…swth&rion) 995 of the Kingly rule.” 996 We can thus suggest that Plato understood the development of a mixed constitution in Lycurgan Sparta as a preservative for the legitimate and uncorrupted monarchy; the goal of instituting a system of tri-cameral rule in Sparta, in Plato’s eyes, was to preserve the monarchy, to keep Lycurgus himself from becoming a tyrant. The Spartan constitution was preserved in this original form, so claims Plato in a compact and paradoxical sentiment, “since Law became King and Lord of the people, and the people did not become tyrants over the laws.” 997 We may thus understand Plato’s view of the establishment of the gerousia and ephorate in Sparta as modifications to the constitution made by Lycurgus that correspond with and, more importantly, develop the political philosophy of “second-best” city-states from the Statesman: after expressing the ideal of political rule, the Eleatic Stranger asserts that, following the death or departure of the Lawgiver from the community, the “second-best” polities, if they wish to imitate the polity laid down by the founder “as closely as possible” (ei)j du&namin), 998 must never allow transgression of the “written and ancestral traditions.” 999 Adherence to the written laws is thus a marker of the imitative polity 995 Recall the use of this term in the “bonds” that connect human to human and human to divine in the Statesman. See Chapter 4. 996 Pl. Ep. 354b6-7. Compare the vertical bond that the Statesman forges between the human community and the divine through measured interweaving in the Statesman, on which see Chapter 4. 997 Pl. Ep. 354b8-c1. The Athenian Stranger also proposes that law should be despot over the rulers in the Laws (715d), on which see Morrow 1993: 544-72. 998 This term, we should recall, has semantic resonances with mathematics, particularly with the issue of commensurability that was so significant to Hippasus and Archytas. I will discuss this later in the Epilogue. 999 Pl. Plt. 300e11-301a4. 365 that will preserve its constitution from corruption and promote a measured community. 1000 Dion’s sketch for his Prooimion commences with a trope familiar from the Philebus: the assignment of positions of honor to the soul, body, and property. The first laws that should be laid down, so claims Dion, involve the establishment of a hierarchy in which soul comes first, followed by body, and finally wealth; the order is justified by which element is naturally subordinate to the others. 1001 We are invited to understand that another Hellenic council invited from all over will be responsible for the new constitution of Syracuse. 1002 Once these laws have been drafted and established, the Syracusans are expected to strike a balance between liberty and servitude by establishing a monarchical rule that is liable to audit: ‘So now let there be freedom for one party, but under Kingly rule; and for the other let there be a Kingly office that is liable, whereby the laws will punish kings and citizens alike, if they act against the law.’ 1003 By rendering the kings subject to the laws, Dion substantiates the Pindaric claim that Law is King over all and firmly characterizes the new Syracusan constitution as of 1000 Cf. Pl. Ep. 354e5-355a1: “Due measure is obedience to God, and the absence of measure is obedience to people; the Law is God to the wise, as is Pleasure to fools.” A similar hierarchy appears in the general Prelude to the Laws of Magnesia (Lg. 726a2-29b1), where the gods are superlative, while the places of honor given, in order, echo Epistle VIII: the gods, soul, body, and property. 1001 The Prooimion to the Laws of Charondas features a similar focus on proper hierarchy and subordination, although Dion’s is more directed towards internal human conduct than administrative order. The fragments of Hippodamus also concern themselves with the corrupting influence of wealth. See Chapter 4. 1002 Pl. Ep. 356c6-8. 1003 Pl. Ep. 355d8-e3. 366 the “second-best” type. 1004 He advises his followers to institute three coordinating kings whose responsibilities are predominantly religious in nature, following the model established by Lycurgus in Sparta. 1005 Dion is ambivalent about whether these three kings are to have the same power as the Spartan kings or a power more limited. 1006 The three kings of Syracuse are expected to represent a synthesis of the warring factions within the city-state, with the goal to eradicate stasis and to preserve the city from barbarian incursions. These kings appear to be Dion’s son Hipparinus, 1007 Dionysius II, and Dionysius I’s other son (and step-brother to Dionysius II) Hipparinus. Following the establishment of the responsibilities and powers of the three kings, Dion advises that the lawcode stipulate that “thirty-five Guardians of the Laws ought to be appointed to rule over matters of war and peace, ruling in conjunction with the assembly and the council (meta& te dh&mou kai_ boulh~j).” 1008 The Guardians of the Laws are further expected to preside over judgments involving punishment through exile, imprisonment, and execution in 1004 Cf. Rowe 1995: 26-8 with n. 98. Rowe’s interpretation exposes potential differences between the valuation of “second-best” polities in the Statesman and the Laws. Generally, Rowe wishes to focus on differences between the political philosophy of the Statesman and the Laws, specifically that the laws of the Statesman would be philosophically-based, and those of the Laws would not. I tend to agree with Rowe, in the sense that practical application is a distinguishing factor; but I would temper his conclusions with the view given by Christopher Gill in the same volume (1995: 303-4), which sees the Laws as an “expression of continuing argument” of the program of politics in the Republic and the Statesman. Nevertheless, I do detect a greater focus on the use-value of the “second-best” polity based primarily on shifts in dialectical and mathematical theory. This change in focus towards approval of “second-best” states appears to occur with the possibilities that Syracuse afforded to Plato in the 350s. 1005 Pl. Ep. 357d1-2. For the Spartan constitution, see e.g. [Xen.] Lac. 15.1-9. 1006 Pl. Ep. 356b5-7. 1007 On the identity of this son, see Morrow 1962: 83-6. 1008 Pl. Ep. 356d4-6. 367 cooperation with select judges who undertook magistracies in the previous year. 1009 Dion distinguishes these powers from those of the kings, on the grounds that monarchs, as priests, should not be defiled by imposing punishments; 1010 keeping the kings’ hands free from blood would have also fulfilled a necessary function in the preservation of political order in a city-state beset with stasis. We may thus conceive of the mixed constitution proposed by Dion as a combination of four elements: a monarchical triad, a council (of an unspecified number), an assembly (also of an unspecified number), and an oversight committee composed of thirty-five Guardians of the Laws. In this way, the constitution of Dion is mixed from monarchical, aristocratic, democratic, and oligarchic forms of rule attributed to Sparta and present in the ideal polity for Taras in the writings of Archytas. 1011 In composing Epistle VIII, Plato was not concerned whatsoever with the functions or structures of the council and the assembly; his primary interest and goal was to define the roles of the kings and the Guardians, and we may imagine that he did not assume a need to revise the other spheres of political authority. Of course, the definition of the rights, responsibilities, and election of the Guardians of the Laws was of supreme importance to Magnesia, the “second-best” state of the Laws; there, however, the description of the Nomophylakes and their duties to the court is 1009 Pl. Ep. 356d6-e3. 1010 Pl. Ep. 356e3-357a1. 1011 This is the same combination as exhibited in the Archytan constitution of On Law and Justice (on which, see below). There, we see that the Spartan ephors – who as magistrates had executive, judicial, and disciplinary powers, like the Nomophylakes of the Laws – represent the oligarchic element. This is a markedly non-Aristotelian understanding of oligarchy, which for Aristotle was defined by property-requirements for the Council (Pol. 1292a39 ff.). 368 undertaken with far more enthusiasm and detail, 1012 while this speech of Dion, which resembles the speeches of the lawgivers of the nearly-mythological Prooimia of Charondas and Zaleucus, abbreviates this definition and lays out the basic four-part structure of the new Syracusan politeia. Preludes to the laws only appear in one other dialogue of Plato, the Laws, where the Athenian Stranger both provides a theory for how to compose Prooimia and a model for imitation, one that can be understood to lay the foundation for what will become the “second-best” constitution of Magnesia. In Book IV of the Laws, the Athenian Stranger discusses the proper structure of law-giving with Cleinias and Megillus by appealing to music theory, in a trope that recalls the place of music as analogue to other elements in the pragmateia of the Pythagoreans and to the divine dialectical process as illustrated in the Philebus: I was hoping to say that for every summation of arguments (lo&gwn) in which voice participates (fwnh_ kekoinw&nhken) there is a prelude and some “sparring,” as it were, which establishes an approach according to the rules of the art. 1013 For instance, preludes that have been masterfully labored upon precede the so-called “melodies” (no&mwn) of songs for the harp and for every kind of music. But for real laws (no&mwn), that is to say the ones we call “political” laws, nobody has ever proposed the term “prelude” nor forced one, once composed, into the light, because they considered that it was unnatural. But our discussion up to this point indicates, in my opinion, that it is natural: thus the laws we were just discussing appeared to be double (diploi~), but in reality they are not double in the simple sense (a(plw~j), but they are dual (du&o), being both law and prelude. 1014 1012 On these details, see Morrow 1993: 251-272. 1013 See England 1976: ad loc. 1014 Pl. Lg. 722d2-7. 369 While this passage recalls the divine dialectical method of the Philebus (with its paradigmatic use of voice and analogous application), its primary effect is to argue that laws composed synthetically with preludes are not contrary to nature: law and nature can coexist in metaphysics as well as in politics. Here, as elsewhere in the dialogues and letters of Plato, mixture is a pervasive idea. Indeed, the principle of mixture functions analogically throughout the Laws as a means to a unified polity at many levels: first of all, as Jean-Marie Bertrand suggests, the Athenian Stranger advocates laws that are mixed naturally with prooimia, in contrast to an otherwise unmixed and simple lawcode; 1015 such a doctrine of properly 1016 composed laws substantiates the positive reflection on the mixed life in the Philebus and mixed kinds of dialectic, as well as the synthetic polity, in the Statesman. 1017 We must recall, however, that this passage’s treatment of “double” (diploi~) and “two” (du&o) is directly related to the criticisms that Aristotle levels against the mathematical Pythagoreans’ dialectical procedure in Book A of the Metaphysics: …while they began to speak and create definitions about the “what is” (tou~ ti& e)stin), their putting it into practice was too simple (li&an d’ a(plw~j e)pragmateu&qhsan). For they rendered superficial definitions, and they believed that the essence of a thing is that to which the asserted definition is referred (u(pa&rceien) in the first place; for instance, if someone should think that “double” (dipla&sion) is the same as “two” (dua&da), because, the first “double” refers to “two.” But perhaps to exist according to the principle of “double” is not the same thing as to exist according to the principle of “two.” 1015 Bertrand 1999: 280-1. 1016 Pl. Lg. 723a7-b2. 1017 Indeed, the Athenian Statesman follows the political philosophy of the Eleatic Stranger in the Statesman by suggesting (Lg. 721a3-5) that the “first principle” (a)rxh&) for this city-state ought to be the “intermixing and commonwealth of marriages” (tw~n ga&mwn su&mmeicij kai_ koinwni&a). 370 Otherwise, many things will be One, which is a consequence of these things…The pragmateia of Plato followed upon these aforementioned philosophies. 1018 Plato thus employs the theories of his Pythagorean predecessors in suggesting that the laws are “double” by representing them as a synthesis that is both plural and unified. 1019 The abstract unification of the single and the plural is of utmost significance to the Athenian Stranger’s project of political integration, and this project justifies the crucial analogy between metaphysics and politics in Magnesia: even the first law presented, on marriage, features both a shorter preludic form (called “simple” [a(plou~j]) and a longer exposition (called “double” [diplou~j]) that is decorated with persuasion and threats. 1020 Such an integration ought to be understood as a marker of Plato’s continued interest in Pythagorean arithmology. If we are willing to accept that the Prooimion to the Laws was a literary topos invented in the mid-5 th Century by citizens of Locri and Croton who wished to extol the program of their own political mythology, then the contextualization with Pythagoreanism would not be problematic to Plato a century later; indeed, his adoption and defense of the prelude as an indispensable element of his own Laws justifies adaptations of Pythagorean concepts throughout his later career. The Prooimion to the Laws of Magnesia appears in two segments in Plato’s Laws: first, in a section that precedes the defense of the prelude, where the oral 1018 Arist. Metaph. 987a20-30. 1019 One of Aristotle’s primary criticisms of the Platonic politeia (Pol. 1261a17-31) is his misuse of the concepts of unity and plurality. He argues that Plato’s error is to mix things that are of different categorical nature. 1020 Pl. Lg. 721b1-e3. 371 document is considered a hypothetical address to the new panhellenic colonists of the polis. 1021 This section is only identified as the commencement of the prelude later on, but its literary style resembles what we have seen in the Prooimia of Charondas and Zaleucus as well as that of Dion in Epistle VIII. The initial topic is proper hierarchy and appropriate reverence towards the gods: ‘What conduct (pra~cij), then, is attendant upon and dear to God? There is only one, epitomized in the saying of old, “Like is attracted to like through true measure (tw|~ me_n o(moi&w| to_ o#moion o!nti metri&w| fi&lon a@n ei!h), but things that are unmeasured are not attracted to one another nor to things in due measure (ta_ d’ a!metra ou!te a)llh&loij ou!te toi~j e)mme&trioij).” In fact, God is definitely the measure of all things for us, much more than some man, as they say.’ 1022 This explicit contradiction of the Protagorean doctrine that man is the measure of all things takes on a particularly Pythagorean color here: the God, whom the Athenian Stranger calls the “measure” (me&tron), is earlier referred to in the first argument of the prelude, where the Athenian claims that “according to the ancient story, God, who possesses the beginning, end, and middle of things that exist, advances straight by rotating (eu)qei&a| perai&nei periporeuo&menoj) according to nature.” 1023 This God, the inspiration for lawgiving, resembles the divine helmsman of the Statesman and the Demiourge of the Timaeus, and his cosmic activity recalls the divine power over time and cyclical motion illustrated in those dialogues. 1024 The proper way to 1021 On the function of this Prooimion in the Laws, see Bobonich 1991: passim and Bobonich 2002: 97-108. 1022 Pl. Lg. 716c1-6. 1023 Pl. Lg. 715e7-716a2. The scholiast (ad loc.) identifies this as an Orphic sentiment, and a similar statement appears as a line from the Orphic Hymns in the Derveni Papyrus (Col. XVII.12). 1024 On which, see especially Chapter 5. 372 become affectionate to the God – to show reverence to the divine – is to honor the gods, but this too receives the stamp of Pythagoreanism: First, [establish] honors for the Chthonian gods next after the Olympian gods, whose provenance is the city; one may celebrate most correctly by honoring the former secondarily and ‘even’, and, for the latter whom we’ve just discussed, contrary and superior honors that are ‘odd’; thus may one chance upon the target of piety. 1025 It is worth noting that Plato has appropriated the Platonic Table of Opposites to reflect the proper religious hierarchy of his state: the Olympian gods, who are patrons of the polis, are to be honored in the first place as the ‘odd’; similarly, the Chthonian gods are understood as secondary and honored as the ‘even’. Porphyry attributed this structure of worship to Pythagoras, and the full account preserved in his Life of Pythagoras suggests that the honoring of Olympian gods with ‘odd’ offerings and the Chthonian gods with ‘even’ offerings was understood as related to both the ordering of the universe and to the Table of Opposites. 1026 Worship according to these precepts adheres to the acousmatic emphasis on religiosity and mysticism. Thus, we can substantiate the place of traditional acousmatic Pythagoreanism in the Platonic “second-best” city-state: just as Epizephyrian Locri and Croton were historical centers for acousmatic brotherhoods, so the Prooimion to the Laws of Magnesia regards the solemn religiosity of the Table of Opposites not 1025 Pl. Lg. 717a6-b2. 1026 Porph. de Vita Pythag. 38. 373 simply in its mathematical use, but also in its possible cultic functions. 1027 Plato, unlike his student Aristotle who wrote several treatises on the Pythagoreans (distinguishing the acousmatic from the mathematical types) 1028 , promoted a politeia of proportionate interweavings between two kinds of constitution: if Plato knew that a schism occurred among the Pythagoreans a century before this composition, it is possible that he felt the need to reunite, through mixture that has been balanced by means of due measure, the warring sides in an attempt to reconstitute a unified polity, in the same way he extolled the comparable divine methods passed down by the Titan Prometheus and the God Hermes (or Theuth) in the Philebus. In this way, the polity of the Laws represents the unification of the ancestral constitution that is best represented by Epizephyrian Locri with, as we will soon see, the modern mixed constitution of Taras; thus, as I will demonstrate, Plato’s later political philosophy attempts to negotiate between the oppositions of Being and Becoming by unifying them in a single principle of existence, Magnesia, according to standardization by means of due measure. The process of establishing the proper mixture by employing due measure as a standard is understood within two otherwise distinct paradeigmata in the Laws: weaving and the process of composing music. Conversely, both of these methodological applications – which are, at their core, representations of the process 1027 According to Iamblichus (VP. 156), Pythagoras required his followers to enter temples on the right and depart on the left, postulating that right was coextensive with “Odd” and left with “Even.” For other cult activities involving “Odd” and “Even,” see Burkert 1972: 474-5 with n. 56. 1028 See Chapter 1. 374 of philosophical dialectic – provide the Athenian Stranger with comparative models for the political art that the Lawgiver is expected to carry out. Indeed, weaving and music are correlative and analogous activities in the Laws. Following the exposition of the prelude, the Athenian Stranger returns to the metaphysics of music from the Philebus and compares it with the praxis of political weaving of the Statesman: Let’s leave the prelude to the laws there, spoken as it has been and complete in its argument. Following the “prelude” must be the “tune/law” (no&mon), or, to be more precise, the outline of the true laws of the constitution. Now, just as when we are dealing with the web or with any woven composition, it is impossible to complete a warp and woof made of the same materials, and we must ascertain that the Kind of the warp is directed towards virtue – for it is strong and endowed with a firm character – and the other is both softer and suitably and justly workable; so, we must distinguish (diakri&nesqai) in the same way, according to logic, between the magistrates who will rule among the citizens and those who are tested, from time to time, at a lower educational level. Indeed, let us assume two Forms of the polity: the installation of offices for individuals and the laws granted to those offices. 1029 The Athenian Stranger’s progression from prooimion to musical mode or outline of the constitution is explicated paradeigmatically through the practice of weaving: one must initially card the wool (to which the Athenian Stranger will refer immediately thereafter) 1030 and remove the unworkable threads, then undertake the diaeresis of warp and woof, and finally interweave these opposite threads into the composition of the community. Weaving, then, becomes the primary paradigm for the process of constructing a lawcode and for the perpetuation of the community by means of rule. 1029 Pl. Lg. 734e3-735a6. 1030 Pl. Lg. 735a7-736c4. For the “purging” (kaqarmo&j) of the community of colonists, the Athenian Stranger employs the metaphors of medicine and shepherding, both of which appear in the Statesman as analogous practices for the ideal Statesman. 375 For the Eleatic Stranger of the Statesman, weaving was directed towards the integration of the courageous and the moderate elements of the community with particular emphasis on the characters of individuals: this goal was to be achieved pragmatically though the combination of courageous families with temperate ones in ties of marriage. In the Laws, though, Plato has shifted the analogy from the unification of social equals to the interweaving of individuals selected as “courageous” or “soft” based on their level of education. The immediate goal is a political hierarchy in which the educated are understood as appropriate for magistracies, whereas the less-educated ought to be ruled. Plato understands this negotiation between ruler and ruled as “concord” (sumfwni&a), a relationship that is analogous with the hierarchy established between reason and emotions. 1031 Concord, which is based on the preservation of hierarchy, is established by means of education. Education thus functions within the Laws as the element that distinguishes rulers from ruled and, for that matter, king from tyrant. The issue of proper hierarchy and the integration of the ruled with the rulers is understood within the bounds of the Kingly art (basilikh_ texnh&) of political administration by the ideal Statesman. Magnesia takes on its most basic significance as a polity mixed up from the two most traditional warring opposites – both of which, I think, are “good” in the sense proposed by the Statesman – in the Greek political world: democracy and monarchy, which for the Athenians had long been 1031 Pl. Lg. 689a5-e2. In this way, the principle of harmony between ruler and ruled recalls the natural distinction between classes in the Republic. Nevertheless, there are differences between these models, on which see Bobonich 2001: 116-119 and 199-203. 376 embodied in the opposition between Athenian and Persian. 1032 We recall that the constitution proposed by “Dion” in Syracuse involved the mixing of democracy and monarchy; here, however, Plato provides a historical reason for the combination of these elements that is mediated through mathematics: There are, as it were, two mother-constitutions (politeiw~n oi{on mhte&rej), from which someone, if he were to say so, would say correctly that the others are derived: one is rightly called monarchy, and the other, in turn, is democracy. The former Kind is represented in the extreme by the Persians, and the latter by us [the Athenians]. Nearly all the others, as I have said, are varieties of these. It is especially necessary that one partake of (metalabei~n) both of these if freedom and friendship are to be combined with intelligence. 1033 The mixture of monarchy and democracy is desired only when moderate (me&tria), as the ancient Laconian and Cretan polities had been, so claims the Athenian Stranger. 1034 As with the descriptions of political philosophy in the Statesman and the Epistles, the subsequent exegesis of this statement focuses more on the Kingly or monarchical element (i.e. the “political” element) than the democratic one. The Athenian Stranger discusses the rules of the Persian monarchs Cyrus, Cambyses, Darius, and Xerxes in order, noting the cycles of good and bad rulers and understanding education as the means to halt the cycle. Cyrus, a successful ruler, was able to unite both ruler and ruled into a synthetic blend that promoted a measured harmony of freedom and subjection: 1032 Interestingly, this opposition takes us back to pre-Periclean Athens, when the vestiges of the Solonian code continued to be traceable. Plato, of course, was hostile to the changes that occurred under many 5 th Century BCE Athenian statesmen like Pericles and Themistocles, on which see Brauer 1986: 9-10 and Schofield 2005: 197-99. 1033 Pl. Lg. 693d2-e1. Note the correlation with Philolaus A 7a: “geometry [is] the source and mother- city of the other mathematical sciences (gewmetri&a…a)rxh_ kai_ mhtro&polij ou}sa tw~n a!llwn).” 1034 Pl. Lg. 693e5. 377 The Persians, when they took the especially moderate course (to_ me&trion…h}gon) between subjection and freedom under Cyrus, first came to be free and then rulers of many other people. As rulers, they granted freedoms to those people they ruled and observed fairness (e)pi_ to_ i!son a!gontej), and consequently the soldiers were more affectionate towards their generals and offered themselves as willing participants in the dangers of war. Also, if someone among them were intelligent and able to give advice, the King would not be jealous, but he allowed free speech and honored those who were able to contribute advice on any matter. He offered the power to aim for the mean in thought (fronei~n ei)j to_ me&son) as a common gift, 1035 and he improved everything for them by means of freedom, friendship, and common thought. 1036 Here, the Athenian Stranger’s emphasis on fairness (to_ i!son) might typically be considered a quality that resonates with democratic governance; to be sure, the Athenian is attempting to visualize the reign of Cyrus the Great as a perfect measured blend of proper ruling structure and freedom for the citizens of the Persian state. Such is the understanding given by, for instance, Archytas of Taras in Fragment 3, where mathematical calculation (logismo&j) increases communal agreement (o(mo&noia) and halts internal stasis by bringing about “equality” (i)so&taj): the result is a system of proper justice and mediation between the rich and the poor. 1037 Nevertheless, as I will discuss later in this chapter, the kind of leveling is significant: in no way would we assume that the “fairness” that is promoted under Cyrus the Great is the same as the democratic “leveling” of Archytas. Indeed, several kinds of “leveling” and “equality” or “fairness” are possible in the 4 th 1035 Greg Thalmann reminds me that the phrase “ei)j to_ me&son” could also mean “publicly.” This is remarkable because it is logically one step further than the basic Platonic application of mathematical ideas to political thought: the possibility of free speech is thus guaranteed by moderation in thought. 1036 Pl. Lg. 694b3-6. 1037 Archytas F 3 Huffman. 378 Century BCE. Still, both the political systems of Cyrus in the Laws and Archytas assume that some shift in class organization – a “leveling” – must occur in order to stabilize the community (which, paradoxically, preserves the hierarchy and deters the corruption of the polity). 1038 This sort of leveling is comparable to the reforms of Lycurgus, which made the king subordinate to the law and allowed for class distinctions among those subordinate to the king. As we will investigate in the design of the Platonic colony of Magnesia, intra- and inter-political unity is made possible by means of equalization, which can mean either (1) the establishment of economic parity or (2) the development of a system of mathematical ratios: the first kind of “equality” is the hallmark of a democracy, and the second of a moderate aristocracy. The city of Magnesia itself, like the panhellenic colony of Thurii whose city plan was laid out by Hippodamus of Miletus, is to be designed according to mathematical precepts that involve basic proportions. 1039 First of all, the Athenian Stranger claims, the “second-best” city’s population should be regulated at 5040 households, a number that he arrives at because it allows for the possibility of being divided mathematically by every number from the decad (1 to 10), further testament to the Pythagorean numerology of this city-state; 1040 land will be distributed (to 1038 Cf. Eur. Phoen. 535-42. 1039 Specifically, the orthogonal design of Thurii featured lots that measured 37m X 74m, in a proportion of 1:2. See Cerchiai et al. 2004: 119-20. 1040 Pl. Lg. 737e1-738b1. 379 catalyze the development of the “second-best” polity) 1041 to each household’s hearth in two parcels: one within the city and one outside of the city. The land within the city and in the chora must be divided into twelve sections – for the twelve Olympian gods – that are constituted in a circular fashion (ku&klon periba&llonta a)f’ ou{ ta_ dw&deka me&rh te&mnein) that radiates outwards from the acropolis, which is located at the center of the island. 1042 In this way, the city with its manufactured layout resembles other imagined circular or radiating poleis in the ancient world, including Atlantis as described in the Critias and the Persian and former Median capital of Ecbatana, a radiating structure in the eyes of Herodotus and his mythographers; 1043 it resembles the circular bouleuteria of Acragas and Poseidonia, and, most importantly, the ekklesiasterion of the mathematical Pythagoreans at Metapontion. 1044 The distribution of land in Magnesia imitates the organization of the citizens into four property classes, an adaptation of the class structure of Solonian Athens 1045 and Kallipolis in the Republic: for the “second-best” polity, the Athenian Stranger adjudicates that the portions of land to be distributed to each household must “become equal parts” (i!sa gi&gnesqai me&rh) inasmuch as smaller lots will be 1041 Pl. Lg. 739e3-6. 1042 Pl. Lg. 745b3-e6. 1043 On the plans of these cities, see Friedländer 1958: 314-322. Archaeologists have not yet been able to locate the walls of Ecbatana. 1044 On these, also see Chapter 4 and Mertens 2006: 334-9. 1045 Although, given what we know of the Solonian reforms, there was no redistribution of land in tandem with the “leveling” that occurred as a consequence of the abolition of debt. See Morrow 1993: 102 n.14. On the comparison between the four classes of Solonian Athens and of Magnesia, see Morrow 1993: 135-6 with n.118. 380 assigned to land with good soil, and larger lots to land with poorer soil. 1046 This kind of “equalizing” of land parcels represents a mixed judgment based on both qualitative and quantitative elements, and as such it is not a policy of simple numerical equivalence: in this sense, it goes beyond the quantitative proportions of 1 : 2 in the distributional plots of the panhellenic colony of Thurii. What we have, instead, is a kind of ‘proportional inequality’ that Plato adapted from Pythagorean experiments in economic class structure. This is nowhere more explicitly the case than with the economic organization of the property classes: So for the sake of many things, especially because there will be fairness of opportunity (kairw~n i)so&thtoj) throughout the city-state, there must be unequal property classes (timh&mata a!nisa), in order that the status of worth for each citizen – offices, taxes, and grants – will be distributed not only according to the virtue of himself or his ancestors, nor his bodily strength or good looks, but also according to his wealth or poverty; in short, honors and offices should distributed as fairly as possible (w(j i)sai&tata) by ‘proportional inequality’ (tw~| a)ni&sw| summe&trw|), to prevent disparity (mh_ diafe&rwntai). For these reasons, four classes must be established according to the greatness of wealth: first, second, third, and fourth, or whatever other names we might assign to them. 1047 This statement presents us with a remarkable illustration of how “fairness” (i)so&thj) can be complicated paradoxically with its opposite “inequality” (a!nisoj): the mixed term – the Athenian Stranger later calls it the “middle” (me&son) 1048 – is “proportional inequality” (tw~| a)ni&sw| summe&trw|), a phrase that receives further explication. In Book VI, when the Athenian concludes his description of how the magistracies 1046 Pl. Lg. 745c2-3. 1047 Pl. Lg. 744b4-c6. 1048 Pl. Lg. 756e9-757a4. Note in this passage the accumulation of terms of measurement: me&son, meseu&ein, me&trou. 381 (including the Council) should be filled, 1049 he pauses to reflect more generally on the method of selection: A system of selection thus constituted will achieve the mean between the monarchical and the democratic constitution, a polity that must be mediated continually. For, even if someone were to declare that slaves and despots were of equal status, they could never become friends; so too with honest men and scoundrels, since things that are equal become unequal with unequal things, if someone fails to hit upon the mean: in both cases, polities are frequented with strife. How true is the saying of old, “equality produces friendships” (i)so&thj filo&thta a)perga&zetai), spoken correctly and in tune. But deducing what kind of equality is able to do this problematizes things for us significantly because it is not altogether clear: there are two “equalities” in existence which have the same name, but they are opposites in many respects in deed. The first – the equality (i!shn) that is achieved by means of measures, weights, and numbers – can be applied by any polis or lawgiver to the property classes by equalizing the distributional adjustments through allotment (klh&rw| a)peuqu&nwn ei)j ta_j dianoma_j). But the truest and best equality has not yet been very easy for everyone to visualize: for it is the discernment (kri&sij) of Zeus, and it gives minimal aid to the human race; but when it gives aid to city-states or to individuals, it makes all things good (pa&nt’ a)gaqa_ a)perga&zetai). It distributes a greater amount to the great and a lesser amount to the lesser, giving measures to each in regard to its nature; specifically, it distributes greater honors always to those who are greater in terms of virtue, but to those who are opposite in terms of virtue and education, it renders what is appropriate in accordance with reason (kata_ lo&gon). 1050 This version of “proportional inequality,” called the “discernment of Zeus,” refers to what is generally called the “geometric proportion” to which Socrates had appealed in the Gorgias when chastising Callicles for his failure to attend to geometry: Socrates understands the “geometric proportion” in opposition to the system of 1049 On the selection of magistrates, see Morrow 1993: 159-168. 1050 Pl. Lg. 756e9-757c5. 382 Callicles, which adheres to pleonexia. 1051 As Dodds notes in his commentary on the Gorgias, 1052 the notion of applying proportions to deduce property classes is Pythagorean and hearkens back to the political philosophy of Archytas of Taras; closer examination of the treatment in the fragments of Archytas, however, reveals some differences between these forms of political proto-economics. As I will demonstrate in the second half of this chapter, for Archytas, adherence to alternative models of proportional class-structure both reflects the Tarentine constitution – insofar as we can reconstruct it for the first half of the 4 th Century BCE – and extends the whole of his philosophical pragmateia to political organization in the philosophical polity, a kind of mixed constitution that favors democracy in concert with the general ambitions of the mathematical Pythagoreans. In this way, as I will show, the “aristocratic” mixed constitution of Plato’s “second-best” polity in Magnesia represents an ideology that competes against the “democratic” mixed constitution of Taras. ARCHYTAS AND POLITICAL WEAVING: THE PEPLOS OF ZEUS AND POLITICAL LEVELING IN PLATO’S LAWS AND THE ARCHYTAN ON LAW AND JUSTICE Before I am able to continue with the investigation into how precisely Magnesia features a constitution extensively founded on mathematical principles, it will be helpful to illustrate the character of governance of Taras under the philosopher and strategos autokratCr Archytas with reference to the extant fragments 1051 Pl. Gorg. 508a4-b3. Cf. the scholiast ad loc. 1052 Dodds 1959: ad loc. 383 that sketch out a vision of Archytan political philosophy. In this second half of this chapter, I will argue that Archytas, like other “democratic” Pythagoreans before him, proposed a philosophical pragmateia that was founded on principles of mathematical proportion (in this case, ratios involving the Limited and Limitless). We detect the importance of proportions in several analogous spheres of his philosophical program: theories of motion, language, and finally political organization. Upon further reflection on the pseudo-Archytan 1053 treatise On Law and Justice, we discover precisely how theories of proportion and ratio – which are fundamental to the theories of motion and language in the genuine fragments of Archytas – constitute the structure of the Tarentine state and its governance under Archytas himself. Remarkably, the political philosophy of the On Law and Justice justifies its mixed constitution through political weaving, and we will demonstrate how political weaving is the common methodology by which the mixed constitutions of both Taras and Magnesia are produced. Finally, we will return to Plato’s Laws and suggest that Magnesia and Taras are both constituted by the geometric proportion or “discernment of Zeus”, which for Archytas designated a “democratic” mixed polity, but for Plato was the hallmark of an “aristocratic” mixed polity. Let us begin with Fragment 3 of Archytas, from the lost work On Sciences (Peri_ maqhmatikw~n), where he draws explicit connections between equality and concord within the polis: 1053 On the authenticity of this text, see below. 384 sta&sin me_n e!pausen, o(mo&noian de_ au!chsen logismo_j eu(reqei&j. pleoneci&a te ga_r ou)k e!sti tou&tou genome&nou kai_ i)so&taj e!stin: tou&tw| ga_r peri_ tw~n sunallagma&twn diallasso&meqa. dia_ tou~ton ou}n oi( pe&nhtej lamba&nonti para_ tw~n duname&nwn, oi# te plou&sioi dido&nti toi~j deome&noij, pisteu&ontej a)mfo&teroi dia_ tou&tw to_ i}son e#cein. kanw_n de_ kai_ kwluth_r tw~n a)dikou&ntwn <e)w_n> tou_j me_n e)pistame&nouj logi&zesqai pri_n a)dikei~n e!pause, pei&saj o#ti ou) dunasou~ntai laqei~n, o#tan e)p’ au)to_n e!lqwnti: tou_j de_ mh_ e)pistame&nouj, e)n au)tw| dhlw&saj a)dikou~ntaj, e)kw&lusen a)dikh~sai. For, once discovered, calculation stopped discord and increased likeness/concord. For, once this has come into being, pleonexia does not exist and equality does exist. For, by means of this, we reconcile concerning dealings with one another. So, through this, the poor take from the powerful, and the wealthy give to those in need, since they both believe that they will have equality through this. As it is both a standard and a hindrance to unjust people, it stopped those who know how to calculate from committing injustices, because it convinced them that they would not be able to escape unnoticed whenever they undertake it; as for those who do not know [how to calculate], it prevented them from committing injustices since it made clear that they were committing injustices in it. In this fragment of Archytas, the notion of “calculation” (logismo&j) eliminates stasis within the community by eradicating pleonexia. We may recall that in the debate between Polyarchus, the Sicilian “Voluptuary,” and Archytas (discussed earlier in Chapter 5), Polyarchus criticizes the “lawmakers” for having declared war on pleonexia and attempted to “level out (o(mali&zein)” society; in doing so, Polyarchus implicitly attacks the political philosophy of Archytas himself. 1054 Logismos may be understood as the basic concept employed by Archytas to promote economic and cultural uniformity within the polis, and it thus functions to promote the democratic element of the constitution of Taras. As we will soon see, this basic 1054 Archytas A 9 Huffman = Aristoxenus F 50 Wehrli. 385 concept of “calculation” is a generic term that refers to the application of three formulas of mathematical proportion to the class structure in order to constitute a community. In the opinion of Aristotle, Taras, which was a “democracy” at the time of the composition of the Politics (1320b9-14), featured a program of communal property for the people – a particularly democratic principle that allowed for distribution in equal shares – and a division of magistracies into two classes: those who were elected (who would ensure that political affairs would be “better conducted”) and those who were chosen by lot, facilitating democratic participation. In this way, the Athenian Stranger’s belief that magistracies in the “second-best” city-state of Magnesia needed to be “mixed” and assigned both by lot and by election imitates the political philosophy behind the Tarentine constitution. 1055 But how precisely does Archytas’ logismos effect economic parity in the community? In Chapters 2, 3, and 5, we demonstrated that logistic, as it developed in the metaphysical and dialectical theories of Plato, became the tool by which opposites could be compared and contrasted and, with the addition of due measure, successfully mediated. In the fragments of Archytas, it is most likely, as Huffman argues, that the science of logismos “studies the properties of numbers that form the basis for practical calculation and in particular studies proportions.” 1056 The general theory about logismos put forth in Fragment 3 of Archytas refers to a basic principle 1055 Pl. Lg. 759b4-7. The terms employed here are significant: “meignu&ntaj pro_j fili&an a)llh&loij dh~mon kai_ mh_ dh~mon.” On the mixture of selection by lot and election by voting in Magnesia, see Morrow 1993: 157-64. 1056 Huffman 2005: 189. 386 of leveling and to the socio-political function of calculation to promote harmony within the community; it is the mathematical study of music that provides us with further insight into the categorization and application of proportional ratios to Archytas’ philosophical and political pragmateia: There are three means (me&sai) in music: one is the arithmetic (I), the second geometric (II), and the third sub-contrary (III) [which, they call harmonic]. The mean is arithmetic (I), whenever three terms are in proportion by exceeding one another (kata_ ta_n toi&an u(peroxa_n a)na&logan) in the following way: by that which first exceeds the second, by this the second exceeds the third. And in this proportion it turns out that the interval of the greater terms is smaller and that of the smaller greater. The mean is geometric (II), whenever they [the terms] are such that as the first is to the second so the second is to the third. Of these [terms] the greater and the lesser make an equal interval. The mean is subcontrary (III), which we call harmonic, whenever they [the terms] are such that, by which part of itself the first term exceeds the second, by this part of the third the middle exceeds the third. It turns out that, in this proportion, the interval of the greater terms is greater and that of the lesser is less. 1057 The mathematical formulations for the three means, then, can be summarized in this way: (I) Arithmetic: a – b = b – c (e.g. 12, 9, 6) and a/b < b/c (II) Geometric: a/b = b/c (e.g. 12/6 = 6/3) (III) Subcontrary/Harmonic: (a – b)/a = (b-c)/c (e.g. a=12, b = 8, c = 6). The testimony of Iamblichus is significant here: he claims that the school of Hippasus and Archytas – the mathematikoi – was responsible for changing the name of the “subcontrary” mean (III) to “harmonic” because “it appeared to embrace ratios 1057 Archytas F 2 Huffman = Porph. in Harm. 1.5. 387 (lo&gouj) of what is harmonic and melodic (e)mmele&j).” 1058 Later on, so claims Iamblichus, the mathematikoi who followed Eudoxus discovered the subsequent three means and assigned the term “subcontrary” to the fourth mean. The seventh through tenth means were discovered by Eratosthenes, according to Nichomachus. 1059 For our purposes, it suffices to discuss only the first three means, since these are the only mathematical formulas that seem to have influenced Plato at the end of his career: whether or not he knew about the means contributed by Eudoxus is impossible to deduce, since his dialogues and letters exhibit no knowledge of them. 1060 But the first three means appear to have been available at least as early as Hippasus of Metapontion in the first half of the 5 th Century BCE, and we may assume that the application of mathematical principles to political organization commenced following the schism that occurred along political lines among the Pythagoreans themselves. 1061 Be that as it may, the abstract principle of calculation (logismos) appears to have been a vehicle for leveling the Tarentine community under the guidance of Archytas during his tenure as strategos autokratCr in Taras from 367-61 BCE. As a Pythagorean philosopher of the mathematical type, Archytas’ pragmateia was comprehensive and attempted to establish philosophical systems that were concordant by means of applied analogy: in this way, Aristotle’s comment that 1058 Archytas F 2A Huffman = Iambl. In Nicom. 100.10-101.11 Pistelli. On the issue of renaming the subcontrary mean as harmonic, see Huffman 2005: 174-7 with bibliography. 1059 See Zhmud 2006: 172-4 with n.28. 1060 See Barker 1989: 53-61. 1061 On which, see Chapter 1. 388 “proportion is the equality of ratios/arguments” (h( ga_r a)nalogi&a i)so&thj e)sti_ lo&gwn) betrays its Archytan heritage. 1062 We might recall that with the democratic revolutions that occurred during the second quarter of the 5 th Century BCE in Western Greece – Acragas, Syracuse, Taras, Metapontion, Croton, and others – came the introduction of “democratic” forms of rhetorical discourse: the need for redistribution of land to establish “fairness” among the inhabitants catalyzed innovations in rhetorical debate and concluded in the establishment of civil courts especially in Syracuse and Acragas, where Tisias, Corax, and Empedocles were credited with supplying the discursive method whereby stasis would be expunged from the polis; 1063 Plato, in Epistles VII and VIII, assumed the need for this kind of radical redistribution of property at the initial stages of the revision of the Syracusan constitution, in the process of moving from political Becoming to Being. Likewise, the mathematical Pythagoreans under Archytas appear to have extended and adapted “democratic” rhetoric to their peculiar advances in mathematical theory: the result, as I will demonstrate, is the proposal of a mathematically-based language theory that is analogous to Archytas’ theories of circular motion. The operative term of the fragments that preserve both Archytas’ theories of physics and of language is “proportion of equality” (a( tou~ i!sou a)nalogi&a). As Carl Huffman has clarified, the term most generally refers to “any similarity between 1062 Arist. EN. 1131a31-2. Here, Aristotle too is attempting to argue (in a particularly Archytan light) that “justice” (to_ di&kaion) is “a certain proportion” (a)na&logo&n ti) that is not simply a numerically quantitative proportion (ou) mo&non e)sti_ monadikou~ a)riqmou~) but a generally numerical proportion (o#lwj a)riqmou~) composed of at least four terms, like a metaphor. 1063 On which, see Chapter 4. 389 two ratios so that A has a relation to B that is similar to the relation C has to D.” 1064 It thus refers to at least four terms and realizes a relationship between two separate ratios; in this way, it accords with all of the harmonic means discussed in Fragment 2, but this presents us with a problem: to which mean (arithmetic, geometric, or harmonic) does the “proportion of equality” refer in the extant fragments of Archytas? Aristotle (Problems 16.9 915a25-32 = Huffman A 23a), in discussing how nature makes non-instrumental body parts rounded, exposes the significance of motion to Archytas’ philosophical program by appealing to the “proportion of equality”: Why is it that the parts of plants and animals, which are not instrumental (mh_ o)rganika&), are all rounded (of plants the stem and the shoots, of animals the calves, thighs, arms, and trunk), but neither the whole nor the part is triangular or polygonal? Is it, just as Archytas used to say, because the proportion of equality is present in natural motion (dia_ to_ e)n th~| kinh&sei th|~ fusikh|~ e)nei~nai th_n tou~ i!sou a)nalogi&an) – for he said that all things are moved in proportion (kinei~sqai ga_r a)na&logon pa&nta) – but this proportion alone bends back on itself, so as to make circles and curves, whenever it comes to be in something? 1065 There has been much controversy in grasping Aristotle’s interpretation of Archytas’ theories of proportion, which, as I have suggested, are at the core of his entire philosophical program, including politics and language. 1066 Initially, the terms here appear to suggest that the “proportion of equality” would denote geometric proportion, since the term “equality,” when taken politically, draws us into the 1064 Huffman 2005: 179-81. In general, my interpretation of these fragments owes much to Huffman’s treatment in his recent edition. 1065 Translated by Huffman, with minor changes. 1066 For an excellent examination of this problem, see Huffman 2005: 529-37. 390 semantic range of democracy during this period in Athenian political writings. However, as Carl Huffman has ingeniously argued, the term “proportion of equality” cannot refer to the geometric mean, whose motion (mathematically) would be a straight vector: motion according to the geometric mean will result in a straight line with a constant slope, the slope having been determined by the proportionate ratio that is itself constant (e.g. 4/2 = 8/4 = 16/8 etc.). 1067 As we continue to extend the geometric mean by creating new ratios in accordance with the formula – that is to say, as we apply motion to a series of ratios in order to derive a magnitudinal line – the slope remains constant, as illustrated in this diagram: Figure 7: Geometric Mean with Applied Motion (a/b = b/c, b/c = c/d, etc.), from Huffman 2005: 539. On the other hand, when motion is applied to a succession of ratios according to the arithmetic mean (a – b = b – c and a/b < b/c), each segment will have a reduced slope. Now while the ratios will decrease over time, and this leads to a slope that gradually tapers off, we cannot fault Archytas for assuming that it would lead ideally 1067 Huffman 2005: 532-3. 391 to a circle, as he seems to have assumed. 1068 After all, the mathematical Pythagoreans – like Plato in the Timaeus and Philebus – sought to justify their philosophical program by finding mathematical concepts that would reflect their own first principles. 1069 For Archytas, as well as for the mathematicians among the Pythagoreans, the first principles of the Pythagorean Table of Opposites (in this case, Limited and Limitless) continued to be central to their philosophical pragmateia. In spatio-temporal terms, the point represents the Limited, and Limitless motion, when applied to the point, leads to rotation, as displayed in this diagram: Figure 8: Ideal Arithmetic Mean with Applied Motion (a – b = b – c and a/b < b/c), leading to Rotational motion. 1068 The operative term employed is a)naka&mptein. Cf. Huffman 2005: 538, where he claims: “The basic meaning of this verb is ‘to bend back’ or ‘to return.’ It does not appear in the Presocratics, occurs only once in Plato, but is used over thirty times in Aristotle. In some contexts a)naka&mptein clearly refers to circular motion which bends back to its starting point (e.g. Arist. De An. 407a28 of Plato’s view in the Timaeus that thinking involves circular motion).” While Huffman is right to point out that the proportion of equality “does not literally move in a circle but bends back on itself in that it produces a smaller and smaller ratio,” I assume that Archytas failed to grasp this and used this theory of circular motion despite its inaccuracies. 1069 Another 4 th Century BCE Pythagorean named Caeneus argued that fire consists in a multiple proportion, which is to be identified with the geometric proportion. His idea was that fire spreads outwards (i.e. horizontally) and upwards, which would create a constant slope (i.e. the terms would increase as the fire spread at a constant rate). On Caeneus, see Huffman 2005: 534-5. 392 Once we understand that the Archytan “proportion of equality” or the arithmetic mean leads to circular motion, we are forced to consider the relationship between circles, the arithmetic mean, and political organization: as we discussed in Chapter 4, circles and circular motion are a fundamental part of both the Pythagoreans’ and Plato’s cosmological systems, and the polis ought to find its place, in various ways, within the organization of the universe. 1070 The political significance of circular civic space, as we have demonstrated in Chapter 4 and above, was contested among those city-states of Southern Italy and Sicily that constructed circular meeting-places, and the difference between a “democratic” or “aristocratic” circular space depended on the proportion of citizens who could be seated inside relative to the general population at large: in Poseidonia and Acragas, the relatively small circular meeting- places represented bouleuteria, and in Metapontion – one of the original mathematical Pythagorean polities – the massive circular ekklesiasterion appears to have signified cosmic democracy. A visual comparison between these Southern Italian and Sicilian buildings and the Pynx at Athens demonstrates the significance of accurate geometry to the Italian and Sicilian meeting-places: 1070 See, e.g. Pradeau 2002: 114-132 and Caraone 2005: 150-1. 393 Figure 9: Circular Monumental Meeting-places in the Ancient Greek World, from Mertens 2006: 339. We have not yet been able to locate any circular buildings in Taras; archaeological research there continues to be hindered by the presence of a thriving modern downtown placed directly on top of the ancient city. For instance, we do not yet know where the ekklesia or boul1 met, and, in the absence of archaeological proof, we cannot be sure that the Theatre of Dionysus to which Polybius and others refer was a circular or semicircular building. 1071 Circularity and circular motion for Plato were manifestly representative of the monarchical and divine during his later career. In the Timaeus, the motion of the 1071 Cf. Wuilleumier 1987: 248-9 and 612 . Hesychius (s.v.) reports an Auleterion in Taras. In 1881, engaged in excavations in Taranto, L. Viola discovered a semicircular building with a diameter of 10.5 meters incorporated into a rectangular structure. The nature and structure of this building cannot be further deduced from what remains. See Mertens 2006: 369-71. 394 whole axis of the universe emanates from and imitates the self-rotation of Mind; likewise, in the Laws, the Athenian Stranger suggests that “the entire path (o(do_j) and movement of heaven and all that is in it has the same nature as the motion, rotation, and calculations (logismoi~j) of Mind and operates accordingly (suggenw~j).” 1072 To take the analogy further, as Gabriela Caraone has recently argued, the connections between the God of the Myth of the Unwinding of the Universe in the Statesman and Mind are implicit. 1073 Likewise, as we demonstrated in Chapter 5, the ideal Statesman operates coordinately with Mind by engaging in the “political art,” which Plato understood to be the same as the “kingly art.” The monarchical navigation of the cosmos is paradeigmatic of the navigation of the state, and these macrocosm-microcosm relations are common to later Plato. Magnesia, as a “second-best” polity that is drawn up according to the mixture of monarchical and democratic elements, is itself circular and is architectonically similar to both Persian (recall the description of the Persian-Median capital Ecbatana by Herodotus) 1074 and Athenian political organizations (e.g. the Pynx). For Plato, the “geometric proportion” or “proportional inequality” of Magnesia is the primary system that promotes “fairness” within the polis and leads the community, ideally, from the fluctuating and unstable state of Becoming to the divine reality of Being. We are thus forced to consider the “proportion of equality” that leads to circularity in the fragments of Archytas as a competitor system to the Platonic “monarchical” 1072 Pl. Lg. 897c4-7. 1073 Caraone 2005: 43-4 and 150-1. 1074 I discussed this in greater depth in Chapter 4. 395 circularity that dominates his understanding of the layered rotations of the heavenly cosmos, 1075 the civic design of his “second-best” colony, and his understanding of the internal motion of the soul in the Timaeus and the perceivable force of the soul in the Laws. 1076 How then can we apply this understanding of circular motion and the “proportion of equality” to Archytas’ political philosophy? In order to investigate the relationship between proportions and political organizations in Archytas’ fragments, we should examine the other kinds of proportion as they relate to political ideology in the extant writings. One place to look is the notion of proportionate language – adapted in Aristotle’s writings in his discussion of metaphor – and its correlative political system. Interestingly, Archytas seems to have followed his “democratic” Pythagorean predecessor Empedocles in positing a kind of language theory that cohered with his theories of motion and ratio. Aristotle, in the Metaphysics, discusses combinatory “tertiary” (tri&th) definitions that are both form and matter: here we find something akin to Archytas’ “geometric proportion” at work: Wherefore, some of those who give definitions, when they say what a house is, say it is stones, bricks, and wood and speak of the potential house (th_n duna&mei oi)ki&an), for these things are matter. Others, proposing that it is a receptacle that shelters property and people or some other such definition, speak of the actuality (th_n e)ne&rgeian). Some, combining both of these, speak of the third essence that is composed out of these…Archytas also approved the same sort of definitions. For they are of both. For example, what is windlessness (nhnemi&a)? Stillness in a quantity of air (h)remi&a e)n plh&qei a)e&roj). For the air is matter, but stillness is actuality and essence. What is 1075 On which, see chiefly Pl. Lg. 897b7-899b9. 1076 Caraone 2005: 46-9. 396 calm-on-the-ocean (galh&nh)? Levelness of sea (o(malo&thj qala&tthj). The sea is what underlies as matter. But levelness is the actuality and form. 1077 Since we are forced to filter Archytas’ theories of language through Aristotle, we must remove the terms “actuality” and “matter” in order to posit a coherent theory of definition not tainted by Aristotelian innovations. Carl Huffman’s approach has yielded many insights: his proposition that the term “matter” is best understood as “Limited” and “actuality” as “Limitless” exposes the proportional structure at work in the definition of the terms “windlessness” and “calm-of-the-ocean.” 1078 Both of these terms are equivalent (windlessness = calm-of-the-ocean), as Aristotle attests elsewhere (Topics 108b26), because they are analogized with “quiet” (h(suxi&a). As Huffman suggests, Archytas’ point is not to make this kind of simple equivalence. Indeed, Archytas is interested in the relations between the proportions whereby these terms exist in some syntax, i.e., the relations between the Limited and the Limitless terms. We can understand this relationship, then, according to the something akin to the geometric mean, but not quite the same. 1079 We recall that the geometric mean, which featured a constant slope, was constituted thus: 1077 Archytas Fragment A 22 Huffman = Arist. Metaph. 1043a14-26. Translated by Huffman, with slight changes. 1078 Huffman 2005: 496-9. 1079 The difference lies in the number of terms: when there are four terms (A, B, C, D), the proportion is discontinuous; when only three (A, B, C), it is called continuous. On these terms, see Huffman 2005: 179. 397 (II) Geometric Mean: a/b = b/c (e.g. 12/6 = 6/3) If we substitute the terms relating to “quiet” (which may be considered the “slope” of the mean here), then the formula looks like this: (IIa) The Mean of “Quiet” a:b :: c:d where a:b = c:d (a=Stillness, b=Quantity of Air, c=Levelness, d=Sea; Slope = “Quiet”) Stillness : Quantity of Air :: Levelness : Sea (h)remi&a : plh~qoj a)e&roj :: o(malo&thj : qa&latta) Limited : Limitless :: Limited : Limitless (peperasme&non : a!peiron :: peperasme&non : a!peiron) Windlessness :: Calm of the Ocean (nhnemi&a :: galh&nh) Quiet :: Quiet (h(suxi&a :: h(suxi&a) Quiet = Quiet (h(suxi&a = h(suxi&a) As this kind of definition functions to create a sustained equivalency among ratios, it works in a way related to the geometric mean, although it functions as a discontinuous analogia. The notion of “levelness” (o(malo&thj), of course, recalls the principle of “leveling” that occurs as a consequence of the discovery of calculation in Fragment 3 of Archytas’ works. As we argued earlier, “leveling” is vaguely but perceptibly tied to the democratic element of the Tarentine constitution, and we may thus assume that the type of geometric proportion exhibited in Archytas’ theory of definitions is related, in some fashion, to democratic ideology. In the cases of the geometric and “quiet” proportions, the slope is constant, and each term in the proportion of “quiet” is semantically related to the pacifying of otherwise tumultuous forces within any system, whether it be political, linguistic, or related to motion. 398 If we can posit a correspondence between the geometric proportion and the notion of “leveling” in the political philosophy of Archytas, how do the other proportions – especially the arithmetical mean that produces circular motion – fare in regard to other constitutional forms? In order to investigate this problem, we must consider a treatise ascribed to Archytas whose authenticity has been considered doubtful: the pseudo-Archytan On Law and Justice, a series of fragments preserved among the Stobaean collection. 1080 Generally speaking, scholars have considered this treatise to be spurious on many grounds, which Carl Huffman has analyzed and refuted convincingly. 1081 Nevertheless, he does not consider these fragments genuine. His reasons to doubt the authenticity – demonstrable correlations between On Law and Justice and other certainly spurious works and failure to replicate the terminology of the ethical fragments A 9 and A 9a – are justified, although he himself allows that each of these arguments can be easily challenged: there is no reason to assume that later pseudo-Pythagorean works did not imitate the Archytas text, and the compositions of A 9 and A 9a – penned by Athenaeus and Cicero, respectively – need not be expected to preserve the actual terminology of Archytas’ missing works. Perhaps we can find a middle ground: the fragments of On Law and Justice function, like the Prooimia to the Laws of Charondas and Zaleucus, to substantiate and legitimize a particular mode of Pythagorean political thought that 1080 The best edition remains Thesleff 1965: 33-36. 1081 See Huffman 2005: 599-606. In particular, Huffman challenges arguments against authenticity made by Zeller, Moraux, and especially Aalders. His conclusion is far from definitive: “My conclusion is that, given our present understanding of the evidence, the arguments for the authenticity or spuriousness of On Law and Justice are about equally balanced. Accordingly it cannot be treated as a genuine treatise of Archytas.” 399 mathematical Pythagoreans, during the constitutional debates especially of the mid- 4 th Century BCE, were attempting to legitimate. In this way, On Laws and Justice ought to be considered within the genre of pamphleteering works such as the constitutional treatises ascribed to the Old Oligarch, Xenophon, and Aristotle. 1082 On this reading, advocates of the Tarentine league were distributing works of Pythagorean political philosophy throughout the 4 th Century BCE in order to legitimate the Tarentine form of governance and to offer up Archytas as a competitive model for the p