University of Southern California Dissertations and Theses

Co-ordination of theoretical, experimental and statistical research

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Co-ordination of theoretical, experimental and statistical research

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Content CO-ORDilIATION OF THEORETICAL, EXPERIMENTAL AND STATISTICAL RESEARCH A Thesis Presented to the Faculty of the School of Education University of Southern California In Partial Fulfillment of the Requirements for the Degree Master of Science in Education by Dyon1s M . i orandini June 1935 This thesis, written under the direction of the Chairman of the candidate's Guidance Com mittee and approved by all members of the Committee, has been presented to and accepted by the Faculty of the School of Education in partial fulfillment of the requirements for the degree of Master of Science in Education. Dean Guidance Committee .... A.~ ... ~.~ ... ~ 1¥>. ~@~-~~-:r. ......... . Chairman W. H. Burton D. Welty Lefever \ foC TABLE OF CONTENTS CHAPl'ER I. INTRODUCTION •••••• • • • • • • • • • • • II. Science and its nature ••••• Objectivity in scienoe ••••• • • • • • • • • • • • • Functional relations. • • • • • • • • • • • • • • • The aim ot research and statistics. Auxiliaries and prerequisites and functional relations ••••••••• "THEORETICAL," "EXPERIMENTAL" AND "STATIS- • • TICAL" • • • • • • • • • • • • • • • • • • • Statement of the problem. • • • • • • • • • Definition ot theoretical, experimental and statistical ••••••••••• • • The interrelation ot the segregated elements ot theory, experiments and statistics, in PAGE 1 l 2 4 5 7 10 10 11 physics and psychology. • • • • • • • • • 11 III. The method of n11m1tation~. • • • • • • The role ot mathematical statistics Primary assumptions ot the thesis • • • • • Re-statement of the problem •••••• DEVELOPMENT IN PROCEDURE AND METHOD • • • • • • • • • • • • • Remarks concerning tormer investigations •• 17 18 19 20 21 21 CHAPTER IV. v. The ph1losoph1oal and the mathematical side of the problem • • • • • • • • • • • :E'unotion and structure. • • • • • • • • • • LOGIC, EXPERIENCE AND ANALYSIS •. • • • • • • The role of logic • • • • • • • • • • • • • The role or experience •••••••• Experiment and theory •••••••• So1entit1c and philosophical attitudes • • • • • • toward the question of theory and exper1- 111 PAGl!: 25 33 40 40 43 49 enoe; reality and appearance. • • • • • • 52 Scientific truth and the legitimacy criter- ion of method and co-ordination • • • • • THE n STATISTICAL" • • • • • • • ·• • • • • • • A signifioanae of statistics that point toward the unknown •••••••••• The philosophioal and mathematical sig- • • nif1oanoe of statistics • • • • • • • • • Problems and methods of ttrestricted" statistics ••••••••••••• The raotual and co-ordinating value ot • • • 61 64 64 72 80 statistics; its analytical significance • 82 VI. SIGlIIFICANCE AND PITFALLS OF CO-ORDINATION • • 86 Co-ordination and researoh. • • • • • • • • 86 CHAPTER Remarks on science, research and "human nature" • • • • • • • • • • • • • • • • • Truth, objectivity, view. • • • • • • • • • Thought, volition, emotion. • • • • • • • • vi PAGE The quest for certainty • • • • • • • • • • 95 Purpose and co-ordinating principles. • • • 99 The pitfalls of co-ordination • • • • • • • 106 VII. INTEGRAL-ANALYSIS • • • • • • • • • • • • • • 108 The two-fold uniqueness of research and knowledge • • • • • • • • • • • • • • • • A proposed co-ordination •••• Integral-analysis ••••••• • • • • • • • • • • • • VIII. ~y • • • • • • • • • • • • • • • • • • • • General • • • • • • • • • • • • • • • • Specitio •••••••••••••••• BIBLIOGRAPHY • • • • • • • • • . • • • • • • • • • • • • • • 108 109 109 121 121 124 129 CHAPTER I I:NTRODUCTIO?l Science and its nature. For the last forty years or so the so1ent1tio world has been in a state of dynamic agi tation. In an endeavor to beoome self-consistent and oategorioal, the various specialized branches of science are particularly concerned with unearthing as much data as pos sible, with oo-ordinating such data into logical systems by reasoning, and with eliminating, thereby, all that is in s1gn1t1cant and non-consistent, and finally with including • all that is signitioant and essential. "The main editace of science has grown almost beyond recognition, increasing in extent, dignity and beauty, as whole armies ot laborers added wing after wing, story upon story, and pinaole to pinaole." 1 Kost conspicuous are those activities in the depart ment ot phyaios. Eldredge gives a fascinating description ot the new world of the physioists and ot their various view poinia and aohievement. 2 But these activities are none the less feverish in psyohology or any other fields ot speoiali- 1 James Hopwood Jeans, "The new -world-picture of Modern Physics.a Science, 80:214 (September 7, 1934), p. 214. 2 John A. Eldridge, The P&sical Basis of Things (llew York: KoGraw-Hill Book compani, 1934). - 2 zation. In taot. the existence of the so-called scientific spirit may be postulated as activity itself. If further defined, it will probably be found to be identical with prevailins reasoning supported by an intense desire tor ex perimental verification. Objeotivitz _!a science. Contrary to the common be lief, however, science is not built upon the solid rock ot obJeotive reality. No matter how obJective its methods and procedure are intended to be, regardless of how quanti tatively correlated its findings become, its postulational starting point is very vague, its reality is very illusive. In the tinal analysis, in every science we come back to such oonoepts as time, space, and energy, of which we know nothing intrinsioally, even though we may feel them sub Jectively. And this subjectivity is something which belongs to the physical world, not to psyohology. 3 One may as well realize this underlying subJectivity of our scientific endeav or at the outset. And not only is this aubJective nature of science found in its origin. SubJectivity permeates science throughout. The logic itself of science, its reasoning pro cess, being a human product, is essentially subJective. As Kant asserts, "reason is the faculty which furnishes us 3 Bertrand Russell, Philosop&, (New York: w. w . Nor ton Company, 1927), p. 154. 3 with the prinoiplee of knowledge.! priori. Hence pure reason is the faculty which contains the principles of oog- 4 nizing anything absolutely.! priori." With this in mind, now one may make the seemingly paradoxical statement that purpose in science is objectivity first .ot all. Science 1s as obJeotive in this sense as electrons are essential in electricity, or as forces are necessary tor action, or the physiological gradient is active in or ganic ditterentiation. No deeper objectivity seems to be possible. ~Attempts will be made, however, in the follow- ing _ to show that the lack of fundamental objectivity not withstanding, there is a well defined obJeotivity in the quantitative relations of science, although no intrinsio or obJeotive reality may be attributed to quantity itself. The intrinsic time-space nature of quantity is not defin- able, because, as Jeans states, Space and time can not be classified as realities of nature, and the generalized theory of relativity shows that the same is true of their product, the space-time continuum •••• Space-time is not itself part of nature. In this way space and time and also their space time product, tall into their places as mere mental frameworks ot our own construction. They are of course very important frameworks, being nothing less than the frameworks along which our minds receive 4 Immanuel Kant 1 Criti*ue E! Pure Reason (London: G. Bell and Sons, 19301 1 P• l. 4 their whole knowledge of the outer world. This knowl edge comes to our minds in the form of messages passed on from our senses; these in turn have received them as impacts or transfers of electromagnetic momentum or energy • •• Thus space and time are of preponderating importance to our minds as the media through which the messages trom the outer world enter the 'gateways of knowledge,' our senses, and in terms of which they are classified. Ju.st as the messages which enter a tele phone exchange are classified by the wires along which they arrive, so the messages which strike our senses are classified by their arrival along the space-time framework. Physical science, ass\llling that each message must have had a starting-point, postulated the existence of 'matter' to provide suoh starting-points. But the existence of this matter was a pure hypothesis; and matter is in actual tact as unobservable as the ether, Newtonian force and other unobservables which have vanished from science.5 Fu.notional relations. The evasiveness of reality is fundamental. But it will be seen that it is not ·necessary, not even desirable, to attribute more obJective or intrinsic reality to quantity. The philosophic vagueness .of science for ultimate realities becomes a most valuable asset when definite oo-ordination of scientific research is achieved by means of the widefinable quantity, whenever the latter is examined in definite functional relations. The foregoing is the philosophical baokground of . · this paper. After this is made clear the question of saient1t1o obJeotivity may be expressed as tu.notional 5 James Hopwood Jeans, .2R,• cit., p. 215. co-ordination of things whose reality in themselves, that is aside trom co-ordination, may be philosophically vague and scientifically unimportant. The aim of research and statistics. The final aim ----- - ---- ------ 5 of research is thus delimited to the statement of tu.notion al relations. This is why science is called essentially mathematical. Recently the mathematical logic of science has become capable of including even general philosophioal considerations. This is the case of relativistic physics. Since Einstein nphysics has ascended to summits hitherto visible only to philosophers, whose gaze has, however, not always been tree from metaphysical haz1ness.n 6 But taken in this sense its mathematics is but a convenient symbolism for logia without the freedom that the theoretical mathematician enJoya: science is not permitted to select its postulates at will as mathematics does. Scientific postulates mu.st result in functional relations that are satisfied by data ot observation. That is, they have to be in agreement, within the tolerance of experimental error, with experience. This does not mean that experiment verifies the relations. It only means that it does not oontradiot them. As Einstein 6 Moritz Schlick, Stace and Time in ContemRorary P&s1ca. All Introduction =o the Theor,i.o? Relat:tiity and Grivltatioil(oitord: at th8C1arendon iis, 1920), p.-,::- 6 so obJectively said: "No amount ot experimentation can ever prove me right; a single experiment may at any time prove me wrong." 7 Thia is why it was stated that experimental verification is but an intensely desirable but not an achieveable aim ot the scientist. The torce of the co-ordinated functional relations of soienoe thu.s lies in their probability and the faot that they are statistically supported by experience. In some departments, as e.g. in physios, there is now a demand tor prevalence of the functional laws without exception; in others, as e.g. in physiology and psychology, exceptions are permitted for the time being, but there is a definite tendency to establish relations that hold without exception, at least as to their formality it not their detail. The primary aim ot statistic therefore, is not discovery but the checking of theory with experience. This checking, however, becomes an extremely fruitful source of new in formation, because the structure of our checking statistics embodies powerful tools of mathematical logic and directs theory towards more and more probable guesses as research goes on. This is why the research worker has to familiar ize himself with the underlying theory of statistics, or 7 Einstein's personal remark. 7 else his oonolusions and statistical interpretations may not carry definite validity. In this connection it may be said that although the recent books on statistical method will serve useful purposes in the teaching and stand ardization ot statistical practice, they have not, in general, gone tar toward exposing the nature ot the underlying theory, and some of them may even give mis leading impressions as to the place and importance ot probability theory in statistical analysis.a Atix:111aries and prere~uisites and tunotional rela tions. Here we may as well anticipate a few principles ot the methodology which is used in certain following chapters in order to substantiate the thesis as it is defined in the second chapter. It is true that aside trom functional relations there are also other things that are wiavoidable and necessary in any field of scientific research. These, however, are preliminary or constitute the connecting links with the other departments of science; it may be said that they are the inter-co-ordinators ot science, but not the subJect-matter proper of the field of specialization in question. Such prerequisites may then be classified as either introduotory or the speaitio orientation, or geography and nomenolature ot scienoe, or its ~ooe»ted methodology ot 7 Hen17 Lewis Rietz, iathematical Statistics (Chi cago: The Open Court Publishing CompaJ31', for the Mathemati oal Assooiation ot America, 1929), Preface. 8 mere description. These three, however, are not the science proper. They are only auxiliary to it, and in the same sense as.!• .i• arithmetio and algebra are to mathematics, or mathe matics, especially vector-analysis, tensor-analysis and the theory ot tu.nations are to physics, or physics, physiology and mathematics are to psychology. The specialized field itself only draws on them, but expresses its subject-matter by and in its own twiotional relations. These latter are not necessarily stated in the form ot strictly mathematical functions, although it is prefer able to have them so stated if and as soon as the progress of the science in question permits us to do so. They are quantitative and functional none the less. And in tim e they will be most probably expressible also in strict forms ot mathematical logic, so that, as it is already in physics, the explanatory text in between them 111 facilitate read ing but will not belong to the structure or oontinuity ot the science proper. As a swnmary of this introduction it may be stated now that soient1fic postulates are essentially theoretical, but the tu.notional relations obtained from them by formal logic, usually a mathematical tool, are made statistically probable from experim ental data. This 1s the essential process of scientific co-ordination, whioh, however, does g not give any information whatsoever as to the ultimate reality of the quantities co-ordinated, but it gives a de finite functional relation among them. CHAPTER II "THEORETICAL," "EXPERIMENTAL" AND nsTATISTICAL" Statement ,E! the problem. It is the purpose of this paper to find how theoretioal, experimental, and statistical research is co-ordinated in science, what detailed signi fioanoe this oo-ordination has and how it forwards the solution of soientific problems. It is also a purpose to find how and when co-ordination is achieved in a legitimate way and to point out some of the inherent dangers and pit falls ot the procedure, of which even the most eminent research workers are often victims. Finally, an attempt will be made to arrive at some definite co-ordinating prin- ciples warranted by their function (Brauch) in procedure and a probability ot their validity. !he pitfalls of co-ordinating proaedure are numerous. The increasingly involved nature of interrelations describ ing elementary "material" processes necessitates clearness ot distinction and rigor of applioation on the part of the analyzing scientist. There hardly oan be any question about science including much more than the study of directly observable method in the old sense; the new physical aspects do not lend themselves easily, if at all, to mental visual ization, that is to an understanding apart trom mathematical 11 relations. As Grozier expresses it, Until about 1900 physics had been concerned with the formulation of a oonoeption of phenomena as they might be described in terms of 'forces' acting between one body and another. More recently it has come to deal with ideas of a higher order of complexity, according to which the energy of material systems is regarded as controlled by the configuration of motion of the sys tem, and it is thus concerned with aspects ot physical systems transcending any complete analysis of detaila.l Under such circumstances it is more than desirable to have the question ot legitimacy procedure clarified, especially because experimental testimony will substantiate scientific theories only if certain logical tu.notional-requirements, of which more will be said later, are definitely fulfilled. Definition£!. theoretical, &?CJ>erimental and statis tical. In the analysis of research a three-fold groaping of its elements will be neoessary. Whatever is based on postu lates will be called theoretical; whatever concerns obser vation will be called experimental; whatever deals with method of grouping and quantitative interpretation of data, theoretical or experimental, will be called statistical. 1 a The interrelation£!. the seee~ated elements _2! !heory, ex,Periment and statistics, .!a physics and pszcholo,sy. 1 w. J. Crozier, "The tudy of Living Organisms." The Foundations ot !?eerimental Psicholoq from the Inter natioiial UnlversTty erlea in Psyo olo,sy, edited by Carl lurohlson (Woroeater, Masa.Tc!ark university Press, 1929), P• 45. la This, of course, includes the exploratory v lue or statistics. 12 The essential interrelation of these three may be illus trated by the following two examples, the first being taken from theoretical physics, the second from experimental psychology: (a) The relation among force, mass and acceleration in the Newtonian physics. Newton stated that the acoelera tional force at any instant of motion is equal to the pro duct of the accelerated mass and its instantaneous accelera tion. In mathematical symbolism, the only form for which Newtonian physics claims any validity, ( di.s J =- rn dt~ Where t ~ accelerating force m = accelerated mass ds = distance traveled by mass along its path dt ~ time in which the ds distance is covered by the mass ~';;i.:::: acoelerat1on expressed by the relation (time~rate ot change) of inf'lnltesim al quantities. This really is the definition of force, a postulated quantity. Force is here defined by mass which is, as I Poinoare stated, but a convenient proportionality factor, a useful multiplier, and by the time-rate of change of velocity, a measurable but materially non-existent vector quantity. Both mass and acceleration are experimentally observable during processe ot action; both are given by 13 relations only. It is postulated that the hypothetical toroe changes proportionally with the change in accelera tion of a given mass. It is sometimes said that in this case the force is proportional to the acceleration which it causes. But this "causal connection" has no deep sig nificance aside from the above quantitative relation and no 0 suoh causal" oonneotion need be involved for the function al description of the event in question. Thus two measur able quantities define a third whose measure is defined as the product ot the two individual measures, those of mass and acceleration. Although the relation is a theoretical one. it is made statistically probable by an exceedingly large number ot experimental observations. lhen the classi- cal mechanics ot Newton were more generalized by Einstein, it was found that this relation was stated in such a form that it rema±ned valid, that is, consistent with the new theory, although the formerly constant factors of the rela tion became themselves variable, and although "space, time and gravitation play a part fundamentally different than 2 that assigned to them by Newton." Newtonian gravitation beoame a special oase in the more general Einsteinian gravi tational relations. 2 Moritz Sohliok, S~ace and Time in Contemporary P;&sioa. An Introduotiono the Theor~ o? Rela"tlvlt1 and Gravitation"( oi?ord: at th9C1arendonriis, 1920), P• 4. 14 (b) The interrelation ot the theoretical-experiment al and statistical in the study of sensory processes of photo-receptors as studied by Hecht, 3 and of tropisms of living organisms as studied by Crozier,4 are a second ex ample. In these oases it was found experimentally that after a sensory stimulus to the photoreceptor of the animal (Mya) was applied, the time of reaction was far greater than the actual time in which the animal could have, by the nature ot its stimulus-response mechanism and nervous system, respond ed to a light stimulus. This was ascertained by experiments in which the animals reacted to stimuli after the stimuli were removed. It was then postulated that there was acer tain time, a so-called latent period, which followed the sensitization period, the sum of these two expe~imentally observable periods being equal to the experimentally ob servable reaction time of the muscular reaction. It was also assumed that the latent period was the necessary time tor the chemical decomposition in sufficient quantity of a photosensitive material in the receptor. This assumption ~ Selig Hecht, "Vision II. The Nature of the Photo receptor Process." The Foundations ot ~erimental Psich oloQ from the Internalio.nal UnlversITz8rles In Ps{c-oio lJ., edited by Carl Murchison (Worcester, Masa.:~lar Uni versity Press, 1929), pp. 222-228. 4 w. J. Crozier, .2.£• cit., pp. 100-101. 15 was made since the time ot conduction of the impulse and the latent period of muscie response was found comparatively small to explain the delay of reaction. The time ot photochemical reactions of this kind in physics varies in a well defined way with the absolute temperature at which the reaction takes place. The theo retical torm of this functional relation is the exponential function which is applicable to many transient physical phenomena. In this case it is given by 1 7 ft ~ -tr 4-c and S = s -1<.t t 0 E. where p -- the latent period in seconds R ~ the theoretical gas constant T ~ the absolute temperature in Kelvin degrees C = a threshold constant, a constant having the dimension of energy and being 16,200 for Ciona, 19,700 for Mya and 18,300 for Phola, the three experiment al animals t = time in seconds S= base of natural logarithms St= amount of photosensitive material at any time point of the reaction S =- the amount ot photosensitiv· e material 0 present at dark adaptation k = a constant 16 It was found statistically that the experimental data satisfied the theoretical requirements, and this tact indicated the probable functions and mechanisms by means ot which photoreceptive processes take place. The physical significance of this agreement between theory and experience will be even more appreciated it one considers the fundamental processes involved. The electro chemical processes that result trom light stimulations are at the base of elementary interactions between photons, that is light-quanta, and electrons, that is electrical charges with physioal mass, when the former transforms potential chemical energy into kinetio energy in the form of the lat ter. The functional relation or Einstein concerning photo emissions of electrons by light-qu.anta, the Compton-effect, the surface-work-function ot Sommerfeld, and so on, furnish the underlying principles of the actions which take place in the photoreceptors of organiams. 5 And the action is not dis similar to those of photoelectric instruments and the chem ical reaction of photosensitive surfaces of dead matter. The nature of suoh reaction is the much more interesting since it seems to indicate that the physical co-ordination 5 Arthur L. Hugh.es and Lee A. DuBridge, Photo-electric Phenomena from the Inte~nattonal Series in P@ts!cs (New fork: McGraw-Hill Book Company, 1932), pp7 1 -181, 203~209, 215-248. 17 that man finds, in the Einsteinian physics and in quantum meohan1cs, for light-processes may, sometime in the not very distant tuture, bridge the gap between the behavior ot living and dead matter, as soon as the present inconsis tencies ot our recent physical 6 concepts are eliminated. The significance ot the interrelation of theory, experience and statistics, furthermore their co-ordination and interpretation, can not be overestimated. The method ot "limitation." - In these two examples the study of phenomena was limited to the study of their dependence upon a single selected variable, acceleration in the first case and time or temperature, respectively, in the second. This kind ot oversimplifioation .is the very nature ot soience. 7 In psychological experiments, however, the situation may not thus be controlled. The limitation to a single independent variable in the case of living organisms in general, and human beings in particular, in most instanc es is nearly impossible, and often one must be satisfied with a more or less approximate control of the detectible 6 D. M. Morandini, "What 1s Light? What is Electric ity?• Reiort for the Physiotherapy Section of the Californ ia State omeopathic Medical Society. Pacitio Coast Journ .!! El_ Homeop~tp,y, 41:484~486 (December, 1930). 7 L. L. Thu.rstone, "The Learning Function." Journal E1. General Psycholog,y, 3:469 (1930). 18 variables, so as to limit the variations ot all of them ex cept one. The variation of this one, then, 1s controlled between as wide limits as possible and the influence on the phenomenon of its oaretully controlled changes will be studied. This procedure necessarily entails the admittance ot errors, especially because usu.ally there is no way of knowing them. The role ot mathematical statistics. Our statistical ------ methods may minimize such errors, or at least those ot them which are not constant errors; but the blind application of a mathematical instrumentality will not, in general, give a more direct insight into the nature ot the examined relation that we had, before our statistical interpretation, from the theoretical and experimental data alone. Statistics, how ever, may give us the danger signals against becoming the victims of undue generalization, especially as concerns u.n warrented pet-theories for the sake of which the statistical tool is often stretched too tar. Bat these signals are given only if the tool is used legitimately, else they have the opposite result: they assist u.s in covering up our mistakes. In one of the following chapters it will be our aim to examine our statistical instrumentalities in order to point out the primarily philosophical and only secondarily mathematical nature of them and to find some characteristic 19 conditions of their use. Here it may be stated only for completeness's sake that statistical insight into function al relations is definitely possible in such oases only in which predictions are made on the basis of!. priori proba bility, as.!.•~• the calculation of chance in coin-tossing, card-dealing, drawing of balls from urns, and recently in heredity, and so on; in general in cases where the combina tion and permutation mechanisms are known previous to the performance of the experiments. In case ot .! post6r1ori probabilities, obtained experimentally, statistics can only ooordinate and interpret, they can do no more than this. Primary assumptiops ~ the thesis. Je may see thus tar that this paper is being written on the following definite assumptions: 1. ObJectivity in research oan only be approximated, and approximated to an increasingly higher and higher degree of precision with the growth and development of the research field, but obJectivity cannot be attained in any science. 2. The postu.lational foundation of a science neces sarily contains subJective elements even for the "most ob Jective" soienoes and even though experimental results are in favor of the validity of the postulates in question. 3. It is hard to realize, therefore, that scientific theories will ever be other than working hypotheses. Yet it is unavoidable and necessary to have them, or else no 20 science could ever be consistent and categoric, which two are sine qua non conditions in science. 4. Experimental agreement with theory only shows the usefulness ot the theory, but never really verities it. It is therefore a so1entif1o principle to discard such useful theories as soon as a new one is able to satisfy the de mands of usefulness and need on the basis of less or simp ler hypotheses. 5. The statistical regimentation of experimental data will have a definite bearing on the foundations of _ a hypothesis or working theory only it.! post~riori proba bilities used in such regimentation are in agreement with a priori probabilities obtained before the experiments were - I pertormed. 78 Restatement _!:!! the prob,lem. On such assumptions, this paper is trying to show that the value of research lies rather in the relations obtained by the co-ordination of its elements than in the conclusions themselves. Thus, even though the oonolusions may not be valid, or may not remain valid, the structure of the research will enable us to see in it the possibility of transition to future means of co ordination ot theory and practice, and, in general, the transition to better co-ordinated viewpoints. Such revised views are not necessarily more and more complex relational patterns, although their early stages may be7b 7a On the other hand, inductive reasonin may su est hypotheses. These , in turn, are to be stati tically verified by experience. '7b In fact, t m sir.apl a po bl . CHAPTER III DEVELORIBNT IN PROCEDURE AND METHOD Remarks oonoerning former i,nvest.1gations. Since the C time of Berkeley and Kant the methodology concerning knowl edge and 1nclud1118 logic was often made a controversial subJeot ot detailed analysis on the basis of widely differ- · ing sets ot postulates. "To postulate is simply to demand what one wants," says Schiller. 1 But "psychologically speaking, the postulate may be regarded as the most primor dial torm of truth-claim" and "the way from the postulate to the axiom is commonly long and arduous." Most of our axioms in science turn out to be, under modern scrutiny, "but methodological assumptions which are really forced upon the would-be knower by the teeling ot his helplessness when he first encounters a vast flux of happenings.n 2 With this in mind, it is not aimed here to give a complete survey of the development of procedure and method (whioh, besides, is nearly impossible), but only to point out some of the leading modern minds whose thoughts are 1 Ferdinand c. s. Schiller, Logic tor Use (New York: Haroourt Brace and Company, 1930), p.~39. 2 Ibid. The last three quotations are trom pp. 160- 164. See also pp. 352-415 tor an analysis ot "scientific method." instrumental in bringing about scientific integration in procedure and methodology, and upon whom this paper will draw frequently. Among the modern philosophers, Bertrand Russell 22 and William James, especially through his followers, Dewey and Schiller, will be referred to. By the analysis ot knowledge, logic, matter and mind, they reflect vividly the relation that man, through scientific thought, has to himself and the universe; they systematically present the the purposiveness of human thought even in its often hope less formalisms and oirculi viciosi; and they give light for the future. However, I hope to be able to draw emphatically npon the achievements of those philosophical mathematicians who partly dealt with our ·reference-frame conoepts: time and spaoe, partly with the theory of number, continuity and tu.notional relations, partly with the physi- cal application of mathematios, and partly with the mathe matical correlation of date. I am referring here especially ' to the non-Euclidean geometries ot Bolyai, Lobaohevski, and Rei~ann, and to the surface and ~eferenoe system of Gauss; to the geometrical and analytical co-ordination of / Poinoare and Levi-Civita; to the differential methods of Leibnitz and Newton; to the analysis of the infinite by Georg Cantor; to the mathematical philosophy of Bertrand Russell; to the space-time insight and gravitational theory 23 ot Minkowslcy and Einstein; to the mathematical and physical achievements ot the quantum-mechanists; to Lukasiewioa and Tarsky and their ingenious and rigorous procedure that cre ated a revolution in logia and freed logic from the slavery of its former Aristotalian "doctrinairism" and absolute-ism; to the generalizing genius, in probability and correlation problems, of Bernoulli, De Moivre, Laplace, and Pearson; and, in general, to those scientifically disciplined think ers whose philosophical insight and ability to unity created, by means ot a mathematical tool and methodology, consistent scientific systems and integrated the particulars into cate gories, thtt ts a usist e nt, em braoiv, self-cont ained units. The diffiou.lties of science and its methodology are partly pointed out in the following quotations: l. For a superficial observer, scientific truth is beyond the possibility of doubt; the logic of science is infallible, and if the scientists are sometimes mistake~, this is only from their mis taking its rules.~ 2. To doubt everything and to believe everything are two equally ooivenient solutions: each saves us from thinking. 3. The evidence for the truth of physics is that per ceptions occur as the laws ot physics would lead us to expect • ••• but physics itself never says 3 Henri Poincare, The Foundations of Science {New York: The Bcienoe Press, l9l3), p. 27. - 4 Ibid., p. 27. anything about perceptions •••• Physios must be interpreted in a way whioh tends towards idealism, and perception in a way which tends towards materialism. I believe that matter 1s less material, mind is less mental, than is com monly supposed, and that, when this is realized, the ditiioulties raised by Berkeley largely dis appear. 4. Physics in itself is exceedingly abstract ••• it does not tell us anything as to the intrinsic oharaoter of its material. Psychology is prefer able in this respect, but it is not causally auto nomous: it we asswne that physical events are su.bJeot completely to causal laws, we are compelled to postulate apparently extra-physical causes for some ot them. But in bringing physics and percep tion together ••• the traditional separation be tween physics and psychology, mind and matter, is · not metaphysically defensible ••• the two will be bro\l.gg.t together in co-ordination, not subordina tion.6 5. Physics has no need of the concepts of substance and cause, and the extent to which we employ them we darien instead of illuminating research- . The data and the whole subJect matter of science are sensation and the true method of science is analysis. It 1s from analysis of sensations that we obtain our oonoepts of the realities of physios.7 The abstract nature of all sciences, the fact that they nevertheless build upon perception, its philosophical implications, the imperative studious attention to particu- 5 Bertrand Russell, The Analzsis of attar (London: K. Paul, Trench, Trubner and Company, !9l"T) , p. 7. 6 Ibid., p. 10. 7 H. Wildon Carr, The General Prinoiijle of Relativ it1 (London: The Macmillan Company, Ltd., 1 22)P. 39. 25 lars without losing sight of all-embracing fundamental generalities and the struoture-funotion co-ordination that quantitative analysis and functional orrelation give them, all make systematic, consistent, and categorical co-ordina tion very difficult. And this despite the fact that recent ly tbe most appropriate and astonishingly precise and fruit ful tools of such co-ordination are at our disposal. If the description of co-ordination and the integral-analysis proposed in the following will serve as a contribution to the oo-ordination of the research elements in science, this paper will have served its purpose. In order to attempt to give the underlying principles ot ooordination and integral-analysis, however, the philo sophical and mathematical side of scientific methodology and co-ordination mu.st be dealt with in a rather swnmarizing manner; also the meaning and meaningfulness of "funotion structure" will have to be commented upon; all this will be undertaken in this chapter. Furthermore, the role of logic, its relation to experience and its importance and restric tions in analysis must be examined, and the postulational basis and accepted methodology of statistical procedure has to be scrutinized; following chapters are intended to ful fil this function. The philosophical and the mathematical side 2!_ the problem. In "development and procedure" the starting points 26 (postulates, assumptions) are obtained--as it is evident from the toregoing--from philosophical considerations, therefore, from thoughts modulated by subJective inclina tions. This is a fact which never mu.st be lost sight ot. On suoh philosophically derived or accepted s~art- 1ng points, then, derivations, usu.ally logical, are built, whioh derivations however can, by no means be used to Justify, expiate or substantiate the oorrectness, necessity or au.ttioienoy of the preliminary assumptions. All that any method in soientifio derivation may do is to satisfy the requirements ot self-consistency and cathegor1oal1ty by means ot tools that are, in the light of soientitio progress, best tit to draw valid (consistent, non-oontradiotory) conclusions from the aooepted assump tions. The continually developing tools of formal logic and symbolism of mathematics, and the discipline (self-discip line) it creates in the researcher are, in the view ot the writer, both the creator and safeguard of a scientific method that serves as an almost indispensible vehicle for arriving at conclusions by means that may be termed, for the present purpose, "leg1t1mate.n 8 By no means should they be construed, however, as the only legitimate means. It 8 Ct. p. b2. . 27 was shown recently (as we shall see later, when speaking of the methods ot logio developed on assumptions quite dis similar to these of the traditional or olassioal laws ot logia) that logia is the base and formalism not the result of mathematioal deductions. It is, therefore, somewhat an .! priori notion and is not crystalized in and developed by mathematical prooedure. So that it may, at least theoreti- · oally, be visualized that non-mathematioal logical systems will exceed the mathematical ones in ettioiency, dependa bility and usefulness in procedure. But at the present time, especially in view of the tact that during the recent few decades mathematics underwent an amazing revolution and housecleaning and it is now so construed that it adapts itself easily and readily to unforseeable changes without losing its oonaistenoy, mathematics and its symbolism is the most important tool of soientifio analysis. Its symbolism when contrasted with the symbolism of language, shows definition and clarity. Our other vehicle, language, on the other hand, even in its scientific termin ology is constantly open to logical mistakes and slips as a result ot often unconscious and hardly detectable, seeming ly logical demonstrations which involve the usage of two or more meanings of a word or misleading sentence construc tion, eto. With the strictly defined symbols of mathemati cal logic this is nearly impossible. 28 As an example of this, reference is made here to the methods (and to the philosophioal implications) of the infinitesimal calculus by the genius of Newton and Leibnitz. "Infinitesimals" are but useful suppositions in certain branches of mathematics, but they are not, as often thought of, indispensible necessities of analysis. In fact, as it is shown, tor instance by Weierstress 9 and others, in logical analysis the infinitesimal may be discarded entire ly and other methods of equally valid scientific approxi mations may be substituted for it. These methods, in ihe theories ot discrete, not infinitely-divisable units and in quantitioation, etc., 10 arrive at results at least as useful in p.bysioal sciences as those reached by the not less logical ass\Jllptions of the infinitesimals. In fact, there are instances of analysis in science when infinite divisibility does not seem to work, although its mathemati cal ~ogio is impeachable; it does not seem to check well g Bertrand Russell, ~sticism and Lo11c w. w. Borton and Compaiiy, l 9), pp. 82-84. (New York: 10 P. M.A. Dirac, Quantum Mechanics. In the Inter national Series of Monographs on Physics, edited by R.H. Fowler and P. Kanitza. (Oxford: Clarendon Press, 1930), pp. 18-34 (Symbolic algebra of states and observables); pp. 35~54 ("Eigenvalues" and "Eigenstates"); pp. 73-116 (Equations of motion and quantum conditions; Transforma tion theory). Also Erwin Schrodinger, avemechanios (Lon don: Blackie and Sons, 1928), pp. 7-13. 29 enough with physical experience. evertheless as a method ot analysis, it developed consistance and embraciveness to a surprisingly high degree, and it showed the way of clear analysis applicable elsewhere. In tensor-analysis~ 1 tor instance, the method of con travari~t and covariant tensors and co-ordinate transforma tions, theoretical tools of logio created by Ricci and Levi Civita,12 enabled Einstein (whose attention was called to their existence by Grossman) to formulate his useful and practically applioable General Theory ot Gravitation, on the base of the evaluation ot the line-element; he supposed that the laws ot mechanics are only to contain statements about the relative motion of bodies, and that in particular, the motion of the body under the action o~ the presence of the remaining bodies is to be symbolically described by the tormula: 11 ll Albert Einstein, Principles ot Relativity (Lon don: Methuen and Company, 1923) pp. 1· 20-161. ilso George David Birkhott, The Origin, Nature and Influence ot Rela tivity (Bew York: The Macmillan Company, 1g25), pp"; 15-17. 12 Oswald Veblen, "Spinors," Science, 80:415-419, November 9, 1934. 13 Erwin Freundlich, The Foundations ot Einstein's Theorf ot Gravitation (Cambridge: Universlty-i>ress, 1920), PP• 2 -!'T. 30 Together with the principle of equivalence, this postulate that physical events are describable by means ot quadratic terms of the above type,--the ~ ~ ~ being dependent on the gravitational space itselt and, in tact determining it,--is the fundamental assumptl.on upon which everything else mathematically (logically) depends in the General Theory of Relativity. For the Einsteinian space, however, the above formula, which makes physical laws independent of the incidental co-ordinate system from which they are ob served, oould not have been actually evaluated without the new tools, the logical instrumentalities ot Ricci and Levi Civita. The general relativity system would have remained in the form ot a mathematical hint; perhaps carrying philo sophical implications, but it would not have become a work ing physical theory and a function of scientific analysis ot things and phenomena, some of which were formerly unde tected(_!.~• the path of light in gravita~ional fields). All these were the results of a refined infinitesimal calcu lus. Again the theory ot spinors 14 shows how the still further generalization of the logical tools ot mathematics, which gave us the tensors, made it possible to connect wave-mechanics and the theory of relativity in viewpoints 14 Veblen,.!?..£• cit., PP• 418-419. 31 that satisfy both theoretically and experimentally. Another example is given by psychology in the theory of learning. Ebinghaus 15 already forwarded quantitatives relations giving an exponential quantitative law for re tentiveness, in the form i X .=Q . OOl'+~Bf-a .S-2. to 7 J/3 . C;, -x where x =- number ot meaningless syllables repeated a given number of times t -:::: the number of seconds required to fix that number (x) of syllables "upon the memory." Recently Thurstone 16 derived, from arbitrary assump tions, a mathematical function quantitatively relating postulational factors partly dependent on the learner and 15 w. M. Feldman, Biomathematics (London: Charles Griffin and Company, 1928), p. 295. 16 L. L. Thurstone, "The Learning Functi~n," Journ !!.2! General Psycholosv:, 3:469-493, 1930. He shows, theoretically, and by means of infinitesimal oaloulu.s, that attainment (p) in learning situa ions (fhat is the ratio of number of successes to the total number of trials) depends not only on the practice-time (t), but also on the nattribute" of the learner (k = a probability number) and the "attrib\lte" ot the learning problem (m.,. the product of the total number of errors and the· effective number ot suooesses). According to Thurstone 2.f<>-1 ~ k t ..,_ 2. fo -1 V ro-ra. 'f,;;; ¥ f'Jo - po where Po == the probability of suooess when t ==o. ~ This quantitative relation is arrived strictly mathematical- ly upon the assumption that in learning situations we may apply the laws ot mathematical probability. 32 partly on the thing to be learned. Upon the acceptance of his assumptions the relations logically follow. The method ot analytical reasoning employed by Thurstone involves only mathematical oonsiderations and his procedure is imbedded in mathematioal symbols and tools which were not specific ally developed for his purpose but readily lend themselves to application in his as well as innumerable other cases. The experimental checking of the "validity" of the Thurs tone learning-curve, will pass Judgment upon his assumptions only but not upon his method. It must not be forgotten, however, that scientific aohievements through mathematics and its usefulness were increased in an extreme measure only after it had been freed of much ot the dogmatism in its assumptions, especially those of absolute certainties. The last of the latter was discarded when the non-Euclidean assumptions ot · Lobaohewsk.y, I Bol,ai and Riemann furnished as valid and as useful geo- metries as that ot Euclid who ruled supreme before. As it will be referred to,an equally important step in 1930 freed logia from its dogmatism in a way similar to the delivery of mathematics from certainties a century earlier. It may be stated, in views contrary to the foregoing, that there are fields of science that do not lend them selves, or do not lend themselves entirely, to methodologi- 33 cal procedures of quantitative m athematical relations. These alleged scientific fields so far as they are non mathematical or are not able to employ quantitative tools ot analysis, may not be included in the word "science" (as this word is used in this paper) sinoe quantitative analy sis (even of qualities) is taken here as a sine-qua-non ot science. Soienoe reveals itself chiefly in its method ology, not in dealing with questions, ntruths," or "true existences" (realities). Its content may or may not be looked upon as truths or realities depending on philosoph ioal inclinations and viewpoints. But method, as described above, is its strength. "Scienoesn which are either merely descriptive .or which employ speculative reasoning without a very strict and self-consistent metho~o· logy \throughout, may be looked upon as science-in-embryo; or as a system of information systematized by speculative and philosophical rather than scientific methods; or as viewpoints put forth tentatively and to be scrutinized and scientifically system atized later. Fu.notion and structure. M ethodology, as a tool of research, reaches its present height of development by means of a strict symbolism which is essentially, it not always formally, based on the sam e or similar considerations as those ot mathematics. A "unit of research" may be looked 34 upon as a procedure in which theoretical or observational starting points through logical means of the researcher, furnish scientific conclusions which "follow" in a sequen tial way from those starting points. This does not mean that suoh conclusions are the only possible ones; or that they necessarily carry soientific validity; or that they exhaust, as a rule, all that may be involved in the theo retical and observational start. But it does mean that they are consistent in the sense as this word is being used in mathematics and, especially since 1930, in logic. It is on account of this latter that our procedure in scientific research has influence also on metaphysics and, therefore on philosophy. As Alfred North Whitehead expresses it in a foreword to one of the best and recent treatments of log ic, which contributes greatly to the vast generalization of logic during the last few years, "logic prescribes the shapes ot metaphysical thought.nl7 When a methodology may carry such generality with it, when it provides for suitable treatment of things and events that differ in degrees that may not be forseen and when the co-ordination ot whatever is involved seems to remain possible under greatly differing circumstances, then 17 Willard Van Orman Quine, A Szstem ot Lo,istic (Cambridge, Mass.: Harvard University Press,-r934, p. x. 35 it is little wonder that it has so wide application. The sequential consistency of our method in scientific research is fundamental; it is, perhaps, the only fundamental char acteristic that survives even the most recent onslaught of rigorous scrutiny upon methodology, the scrutiny itself being based essentially upon this sequential ordination only. The nature of the logical discipline by means of which &11 that proved to be either non-essential or non mandatory in method is being now weeded out will be referred to later; here it will be pointed out only the supreme offioe ot the new scientific method in reference to two as peots ot research, namely function and structure. Research essentially deals with these two. Up to recently they were considered to be two distinct, though fundamentally inter related things. The new analysis does not readily permit such a differentiation anymore; and while a superfioi&l distinction often persists as a modus dicend1, closer scrut iny clearly shows that it is nothing more than this. Neither philosophically, nor tn usu was ever found one without the other. Their theoretical separation, which caused so much fruitless argwnent and unsurmountable diffi culties (hindrance to analysis), especially in psychology and biology, is only a fiction, a fiction whose det1n1tion itself was never made clear. In language they are used ith 36 speoitio meanings differing for different cases. In this respect, they have, of course, indepen4ent but special de notations. But when they are used as contradistinctions of one another, they both lose all denotation and become useless symbols that are not defined in their use. Function is denoted 18 be means of action or activity; structure by means of "arrangement of parts." The way the new analysis is built up, as, for instance, for logic by Russell, Lukasiewicz, 19 Tarsky, 20 uine and others, 21 for mathematics by Lobatchewsky,22 Bolyai, Riemann, Cantor, Dedekind, Ricci Lev1-Civita 23 and others, tor physics by 18 Webster's Dictionar1. 19 Lukasiewioz,"Philosophische Bemerkungen zu mehr- wertigen Systemen des Aussagenkalkuels," Comptes Rendu.s des Soeanoea de la Sooiete des Soienoes et des Lettres de Varsovla,,-3:'!o-78, 1930. - - 2 0 Lukasiewicz and A. Tarsky, "Untersuchungen ueber den Au.ssagenkalkuel," Ibid., 23:30-78, 1930. 21 Quine, .2£• cit., pp. 50-160. 22 Erio Temple Bell The Search for Truth (New York: Reynal and Hitohcook, 1934f, pp. 204-217. 23 Tullio Levi-Civita, A Sim£11fied Presentation of Einsteins Unified Field Equations ( onaon: !iackle and - Sona, 1929). 37 Planck, Bohr, Einstein, 24 Lorentz, 25 i.nkowski, 26 Schroed- 27 28 29 1nger, Heisenberg, Dirac , van der Waerden, and others , demonstrates beyond doubt that function and structure are the two, fused but inseparable aspects of a single "funotion struotu.re" concept. Statements, whenever produced in strictly defined symbols, as in the examples quoted above, so that there is no misunderstanding admitted, always con cern both ot them inseparably; whenever conclusions may be drawn tor what is, in common parlanoe, called structure, then conclusions or prophecies may also be dra n and made for function. In this lies one of the most invaluable advantages ot the new analysis. 24 Albert Einstein, On the ethod of Theoretical PMsics (oxtord: The Clareno1>n Press, 193~. llso Prill o1}les ot Relativity, collected original papers by H. I. Lorentz-;-A. Einstein, H. Minkowski, and H. Weyl~ (London: Methuen and Company, 1923), 216 pp. See pp. 37-65, 99-108, 120-160. 25 Ibid., pp. 7-34. 26 Ibid., PP• 75-91. 27 Erwin Schroedinger, Four Lectures on w ave ech- anics, delivered at the Royal Institute, Lona0n, on March 5-14 1 1928. (London: Blackie and Sons, 1928), 53 pp. 28 P.A. M. Dirac, The Princilles of ~u.antum Mech anics (Oxford: The Clarendon Frese, 930)-;-2 7 pp. 29 Veblen • ~. C 1 t • J 1-:>t'. 'tt!> -.lf 19 . 38 It is not the purpose of this paper to give a de tailed description of the new analysis aa it is evolved through the work of those mentioned above and others; it may be stated here, however, that, after the postulates are made, every research unit is developed by means ot rigorous sequences, the symbolism of which does not permit mental or !!. faoto separation of structure and function. So tar as sequence 1s concerned, our new methodolo gy~-the embryo of which may be traced back to Descartes- works very similarly to a well deviced automatic machine to which sufficient power is applied and· suitable working material is fed. In a flash Descartes saw the possibility of devis ing a method which would irove (or disRrove, if false) any known or conJectured heorem of geometry, no matter how oompliaated or abstruse, by a purely mechanical process •••• The method is so unerring that even a dullard cag 0 make it work with sufficient pa~ience and obstinacy. Yet, as the same author remarks, "taste, efficiency and in telligence are needed to bring out the best of it." Nevertheless, there is nothing in the new method, even in its latest refinements that would assure a oategoric (all-embracive) use of it. The fact that derivations satis fy the rules of consistency gives no assurance whatever that it develops categoric scientific systems, which necessarily 30 Bell,~• cit., pp. 153-154. 39 provide pigeonholes for all that there is or may be ascer tained in the research field in question. Categoricity depends on postulates and genius. Yet it is proposed here that the integral-analysis, approach to which will be made in this paper, provides a possibility ot such "pigeon holing of reasearch" that is provision of proper place, irrespective of postulates, for whatever genius may discover, by partly automatic processes, although intuition may pro vide tremendous short outs. Aside from the role of mathematics and sequential ordering in general and apart from the function-structure unity, first the role of logic, its relation to experience and its place in analysis will have to be dealt with, however, in the next chapter. CHAPTER IV LOGIC, EXPERIENCE, AND ANALYSIS The role El_ logic. Systematic human thought is a result of arbitrarily though purposefully accepted primary limitations. In soience, where mathematical and other logi cal formalisms are used, it is agreed, among other things, that whatever is admitted as an organic part of research be consistant, that is it be in harmony with all other admitted things within an arbitrarily delimited scope or field of investigation. Consistency is the postulational base of logio. It is a subJective imposition. 1 In order to put the consistency postulate to work a tool had to be found, which serves, as tar as possible, as an instrwnent of secur ity of the strict observance of the postulate. Such a tool tor logic has been evolved, through thousands of years of use, in the logical symbolism especially, of the recent years 2 whioh saw a renaisance of logic and its liberation l Cf. pp. 2-3. 2 The work of Whitehead and Russell, PrinoiRia M athe matica (1910) started the avalanche of rigorous scruting of the principles of logic, by its strict symbolism and th8 establishment of the three "primitive categories," namely: propositions, terms in general and propositional functions. 41 from most of the deadwood of the past. 3 The symbolic tool of logic is similar in its for malism to that of mathematics which is natural, since both logia and mathematics are formal deductive reasoning. Fur thermore. both express tautologies. uM athematios is the set of all propositions of the form 'P implies Q', where P, Qare any propositions whatever." And "roughly, mathematics is a branch of logic (on this theory)." 4 This implies the sequential consistency of both mathematics and logic, and it gives a fine example of mutual stimulation and correla tion of two fields of human thought. Logic necessarily preceded and created mathematics; mathematics, then, after and in its evolution, recreated logic,--a mutual reaction similar to that between philosophy and the mathematical and and psychological sciences. 2 (continued) See also Lukasiewicz and Tarsky, 2..£• cit., pp. 30-78, and Quine,~- oit., pp. 11-49. These works are based on the Principl"a but they break away--espeoially the work of Lu.kas Iewioz--?rom certain postulates of the Aristotalian (classi cal) logia. These postulates (called axioms) are mentioned here on the following page. In Quine's system the Principia Mathemati~becomes a special case of a tar more generar system ot 'logic. 3 Erio Temple Bell, The Search for Truth (New York: Reynal and Hitchcock, 1934), pp. 132-137, 155, 187-191, 198- 203, and especially 204-217. 4 Ibid., pp. 108• 238. 42 The new logic, as developed by Lukasiewicz in 1930, and as embodied by him and others in a rigorous symbolism, opens vistas hitherto unseen. The Aristotalian absolutes, two ot his three maJor axioms (namely: A is A, and A is either true or false) are banished. Consisteno1 (namely that A may not be true and not tru.e at the same time) seems to remain the only postulate. Classical logic thus reduces to a small special case among the infinitely many possible and valid logical systems. It 1s not difficult to see, therefore, that the delicate and strictly defined symbolic tool ot logic may, by means of its operational calculus, establish always closer and closer interdependence between science and phil osophy, each of these having a fundamental subJectivity despite the professed aim at ob jectivity in science. 5 Aside from its consistency postulate, logic carries an other source of continual subJeotivity in its modern primary operation called "ordination," "congeneration," and "abstraotion." 6 This is to be seen by the following consid erations: these fundamental operations define their consecu tive steps by supplying means of ascertaining the formal validity of the results of the operations themselves; but 5 Ct. pp. 2-5. (ObJeotivity in science and fwiction al relations). 6 Quine,~• oit., pp. 11-49. they do not provide necessarily for unique research ave nueslmostly they leave considerable freedom and leeway 43 for the researcher, although they usually furnish automatic checks ot correctness of procedure and means to avoid or retrace our steps from blind alleys. The very freedom of direction, thus is not only in the way of oategoricity but also leaves logic permeated by subJectivity; in view ot this it is really surprising how symbolic logic of modern times is able to attain such many times infinite, although not absolute, embraciveness, as it certainly does attain. When all this is considered, the arbitrariness and the limitations of logic are evident. Within its limita tions, however, it fulfills its role eminently: it provides a systematic procedure for human thought, even though the system thus provided is not in itself categorical. either is the system such that its instrwnentalities result neces sarily in scientifically valid conclusions, although the conolu.sians may be valid logically. The role of experience. The essential difference between scientitio and logical validity is that the former usually is required to be also a validity of experience: it has to check with results of controlled experiments. As 7 Loo. cit. 44 Schiller expresses it in his Logic for Use: Their 'truth' (the truth of loGioal Judgments, es pecially in their linguistic form) is only truth olaim, and, if this sense of •truth' is adopted, one can only say that such formal 'truth' is not exclusive ot falsity, and so is scientifically worthless. Nevertheless it is in this sense that truth has to be taken by the Formal Logics, because they do not wish to have to wait to consider the oiroumstanoes of actu al oases but desire to lay down logical 'laws• a ~riori. This involves them in terrible oontradTotion, eoauae they also need a sense ot 'truth' in which it excludes falsity, and because they frequently confuse this formal •truth' with absolute; but they prefer to wallow in these confusions to renouncing the ambition to dictate to the sciences •••• So we distinguish between the mere putting forward of a claim and the 'verification,' •validation,' or 'confirmation' which it has to undergo before winning social recognition, between a truth-claim and an estab lished truth. This distinction is of the greatest practical importance. Important, however, as the distinction is, it is not absolute. It is a matter of degree •••• A verified truth may always be improved and revised by further veritioation, and no amount of verification ever renders it absolutely true •••• No Judgment, and a fortiori no proposition, is true or false in itself; Tts value is always dependent on its use in the content in which it becomes a vehicle of meaning •••• Absolute accuracy is not possible, if only because no human instrument and no human sense can measure it. But neither is it needed: what is needed is accuracy sufficient for the purpose in hand •••• Of course it may be obJected that when the 'same' question is considered with different purposes it is not strictly the same question, and ought not to be called so; but this will only bring out the cognate fact that, still more strictly, the least change in the person, interests, times, places, and contexts ot a question may imperil its identity. For it may constitute a differ ence relevant to the purpose in hand. Thus any asseftion of •sameness' is always a (disputable} claim that certain differences may be neglected. A s identity never occurs 45 as a 'fact,' and has always to be extracted from the differences in which it is immersed, it is always an identity-for-a-purpose, and a hypothesis to be verified. The value, therefore, of a truth-claim can never be determined in advance of its use: it always remains dependent on experience of its working •••• If we have sufficiently made clear the vital import ance of truth, and the practical impossibility of ig- • noring et by accepting formal truth-claim as a substi- tute tor real truth, we have made out a cogent case for demanding from every logic an ade~uate theorl of truth. Now, no theory of truth wilDe a equate nnlesSit suc ceeds in distinguishing truth from error (in conception 8 at least) and can suggest a way of testing truth-claims. The role of experience, therefore, is of prim ary i m - portance in scientific investigations. hatever logic through its extremely useful formalism {whether mathematical or any other kind) is capable of achieving has to undergo verifications by experience, before it may become a part of our human treasures and used for ~efinite human purposes; on the other hand, 'verification' only m eans in this sense, as we have stated it earlier, 9 that no definite contradic tion of the logical achievement was found, that is no such contradiction was discovered which would render the results of the forwarded logical system untenable under the circum stances in which they are proposed to be used. 8 F. c. s. Schiller, L~io for Use. An Introduction to the Voluntarist Theory otowledge. (New York: Harcourt, Brace and Company, 1930), pp. 105-111. g Cf. pp. 5-6. 46 To illustrate this statement, reference is made here to three logical (mathematical) and at the same time philo sophical problems which fruitlessly ocoupied thinkers over three thousand years. These are the problems of the infin itesimal, the infinite, and continuity. The work of Jeier strass, Dedekind and Cantor,10 at the end of the last century and the beginning of the present, clarified these oonoepts, putting thereby order in place of former confusion in mathematical thinking. It was also shown, especially by deierstress, that the philosophical concept of the infinit esimal may be banished entirely without reducing the scope or impairing the functioning and results of mathematical reasoning. The role of the infinite, on the other hand, was accentuated and worked out in detail by Dedekind and Cantor. Since in modern physics, whenever laws are stated, they usu.ally concern an infinite collection of things, there was a possibility to turn the new mathematical tool into use and apply them to time, space and motion, all of which were clearly defined through our new conoept and clear statement of the infinite and without any necessity to resort to the concept of continuity, a thing not physi cally demonstrable in conneotion with time, space and motion. lO Bertrand Russell, Mysticism and Lo~i.o, PP• 79-91. 47 The discrete units, quanta, of modern physics are members of such non-continuous infinite collections. The new no tion of oontinu.ity, on the other hand, fits in very well with events in 'empty space,' the medium whioh, in the theory of relativity, is the transmitter of gravitational and electro-magnetic disturbances. Under suoh conditions of practical applicability of theoretical investigations, it is understandable why the mathematician and philosopher Bertrand Russell calls the achievement of eierstrass, Dedekind and Cantor "probably the greatest of which our age has to boast; and I know of no age {except perhaps the golden age of Greece) which has a more convincing proof to offer of the transcendent genius of its great men.nll But not only in sciences has the new foundation achieved so much: it brought new light into philosophy it self. The view of men's relation to his Universe is chang ing fundamentally as a result of the experim entally import ant theoretical analysis of time, space and motion. The new analysis is based on an extremely strong fundation: it does not rest on alternative methods of reasoning or upon identifioation procedures that are involved; it rests on elementary steps only, euoh as ordination, sequence, one to-one oorrespondanoe, that is upon methods universally 11 Ibid., pp. 81-82. 48 accepted in both science and philosophy. And, of course, upon clear definitions of 'infinitesimal,''infinite,' and •continuity.' Definitions that reinstate, and lead to the clear solution of, the so-oalled four problems of Zeno. In order to accentuate also the philosophical importance ot the mentioned achievements, the statements of Russell will be quoted here: The philosophy of the infinitesimal, as we have Just seen, is mainly negative. People used to believe in it, and now they have found out their mistake. The philosophy of the infinite, on the other hand, is wholly positive. It was formerly supposed that infin ite numbers, and the mathematical infinite generally, were selt-oontradictory. But as it was obvious that there were infinities--for example, the number ot num bers--the contradictions of infinity seemed unavoid able, and philosophy seemed to have wandered into a "oul-de-sao." This difficulty led to Kant's antinom ies, and hence, more or less directly, to much ot Hegel's dialectic method. Almost all current philosophy is upset by the tact (of which very few philosophers are as yet aware) that all the ancient and respectable oontradiotions in the notion of the infinite have been once tor all disposed of. The method by which this has been done is most interesting and most instruotive.12 Thus, we may conclude that the power of organization of thought in science lies, in a great measure, in the logi oal tool that is employed in systematic (soientifio) re search; but logic alone is not capable of arriving at scien tifically valid results: the logical oonoluaions in science attain validity by means of experimental (experience) veri- 12 Ibid., pp. 84-85. 49 ficationa only. EXJ)eriment and theo,ry. y hether experiment or theory is the "real" source of knowledge was a permanent question ot dispute, especially through the last four centuries. Since the time ot Francis Bacon, Galileo and Descartes, that is since the time of the first applications of systematic scientific methods, the question of theory and experiment was kept alive constantly. Those leaning toward the abstract assumed and contended that theoretical human thought is the real source of knowledge, and that experience, if it is to be considered at all, is secondary. Those whose "practical" inclinations led them toward the specific or concrete main tained that experience is the primary sou.roe of all knowl edge, although thought may be involved later, especially when the systematization of knowledge is desirable in sci ences and philosophy. As Dewey states, "the dispute as to whether reason and oonoeption or perception and sense are the source and test of ultimate knowledge is one ot the most enduring in the history of thou.ght.nl3 Empiricism, rationalism and Kantianism (a compromise, aooording to Dewey, between the two former) are the three ohiet doctrines in regard to experience and theory. It is 13 John Dewey, The guast tor Certaintl: A Stu~ of the Relation of Knowledfe an Action (New York:-Irtoii, Balch and Compiny, 19!9 , p. 110;· 50 not necessary for our present purpose to describe the his torical evolution of thought which led to the view now pre vailing in science. It will be sufficient to point out briefly the main features of scientific attitudes regard less the often philosophical differences and the variations in beliefs concerning the "best method of approach." Heither empiricism, nor rationalism (nor Kantianism} may serve today as fundamental doctrines when sources of knowl edge are looked for in modern scientific investigation. Knowledge in science is the result of doing; doing both theoretically, that is by logical analysis, and experiment ally, that is by controlled experience; and the two are not merely co-ordinated (as in the Kantian conception) but in terrelated, fused, so that "the distinction of sense and thought occurs within the process of reflective inquiry, and the two are connected together by means of operations overtly pertormed." 14 "In the Kantian scheme the two or iginally exist in independence of each other, and their con nection is established by operations that are covert and are performed in the hidden recesses of the mind, once for all~ 15 It follows from these statements that knowledge de pends essentially ~pon the method by means of which it was 14 Ibid., pp. 171-172. 15 Ibid., p. 172. 51 reached. There is not such a thing as absolute knowledge, knowledge independent of the knower and his approach ot the knowing problem. fhat is more, this is not a matter of philosophy alone: it was found in modern science that our observation and the view we are taking influences the re sult of the observation. As Eddington stated it, in con nection with the relativistic shortening of distances in motion with respect to an observer, "when a rod is started from rest into uniform motion, nothing whatever happens to the length ot the rod. e say that it contracted; but length is not a property of the rod; it is a relation be- tween the rod and the observer. Until the observer 1s specified the length of the rod is quite undetermined.n 16 A further example of scientific knowledge being a relational thing, that is,a relation between observer and observed and not the discovery of intrinsic (material) properties, is given by the famous Heisenberg's principle of indeterminaoy. 17 It was found in modern physics by quant um theoristio methods that it 1s impossible at any given instant to determine both the position and the velocity of 16 oritz Sohliok, Space and Time in Contem!orarz P&sios. An Introduction to the Theorl orRelatlV ti and Gravltatioil(oxf'ord: The c'!irendon Press, 19201, p.5. 1 7 A somewhat abstract and philosophical description of this is tou.nd in Dewey's ~uest for Certainty, pp. 200-07. 52 a moving electron with certainty. If the position is de termined, the velocity will remain known only approximat ively; again, if the observer chooses to ascertain the velocity, the position will become only approximately de terminable. And the interesting thing is that this mutual indeterminacy ot Heisenberg is not the result of any limit ations in exactness of measurement: it seems to be a theo retical uncertainty, something that follows from the nature of the things involved; from the relation of the observer and the observed phenomena; from the mere fact that an ob servation has been made. As Bridgeman says in an article in the March, 1929, number of Harper's Ma69:zine, entitled "The New Vision of Science," "A cat may look at a king but at least one bullet of light mu.st pass if any light at all passes, and the king cannot be observed without the exer tion of that minimum amount of mechanical repulsion which corresponds to the single bullet (of light)." 18 Scientific and philosophical attitudes toward the questions _2! theory and experien~e; reality and appearance. Contradistinction between theory and ·experience on a class ical (Greek) or on the Indian (mystic) fu.ndation today is hardly possible. Such rigid philosophioal distinctions lead us only to pseudo-problems, that is to problems which 18 Ibid., p. 204. 53 have no solution beoau.se they do not properly exist. Ten dencies of this kind, which, on one part, created the con cepts of "intrinsic reality" and "extrinsic appearance" as contrasts in philosophy, and, on the other hand, introduced 11 absolute, space, time and matter" and its classical anti thesis, the mere "classical ~elativity of things" (a rela tivity that measured relations with absolute yardsticks), --thus tar proved to be unsuited and incapable of achieving their aim: the giving of olear criterions of the verbally claimed distinotions. Thu words were uttered, but their meaning was vague. "Always, no matter where one turns in the field of philosophy he finds that it deals with the con trast of reality and appearance, with what the world is and what it seems to be.n 19 Thus philosophy always recognized the problem. Modern philosophy, while using the distinction as a convenience, seems to have given up, however, the definite tendency of trying to find a unique solution of what reality and of what appearance is, and it seems to be satisfied in presenting its material in such a manner that rigid distinction is either not necessary or else, it is left to the individual to deoide what the distinction, de pending on his own taste and preJudices, may be. As Dewey 19 A. MeikleJohn, Philosop& (Chicago: American Li brary Association, 1926), p. 30. 54 states: nsubJect and object antithetically defined can have logically no transactions with each other ••• SubJective and obJeotive distinguished as factors in a regulated effort (italics not in the original) at modification of the en- vironing world have an intelligible mean1ng.n 2 0 And appear- - ance and reality hinge on the same thing. Their separation may be a convenience, but it is not a philosophical necessity anymore. In science, especially in pre-relativistic physics, this problem was not clearly and generally recognized. Science was dogmatic and absolute in its materialism. Its reference-frame of time and space was believed to be a part of nature, an unalterable certainty, not a mere convenience for description, or an important but arbitrary coordinating system as it now is. Newton said: "Absolute, true and mathematical time flows in virtue of its own nature uniform ly and without reterenoe to any external obJect, always re mains the same and immovable.n 21 But the concept of the absolute, as a result of Einstein's rigorous logical analysis of the concept and in consequence of the experiencial veri fication following it, was abandoned in science: the question Court 20 John Dewey, EJg>erienoe and Nature (Chicago: Open Publishing Company, 1925), PP• 24l.242. 21 Sohliok, .2.lt• oit., p. 2. 55 of reality and appearance and the question of obJectivity and subJectivity are but methodological expressions, Justi fied in use by arbitrary definitions and convenience, but as underlying principles ot scientific investigations or of theories, working hypotheses, physical laws, etc., are en tirely eliminated. 22 As Einstein expressed it: "Space and time are deprived of the last vestige of obJectivity.n 23 And in Minkowski's words: "From hence forth tim e by itself and space by itself are mere shadows, they are only two aspects of a single and indivisible manner of coordinating the facts of the physical world.n 24 Theory and Experience, therefore, are clearly dis tinguished from one another on logical and methodological bases only; but not as perfect antitheses. The scientific and philosophic pseudo-problems, which were unavoidable with rigid contrasts, disappear. Theory and experience in science do not deal with intrinsic realities or with appearances any more; they deal with their arbitrary realities of relations only; and it is only the procedure, the methodological con- ~e5~lts venience that distinguishes them. Science does not deriv~ 22 Cf. PP• 2-4. 23 Schlick, £R.• oit., P• 52. 24 Erwin Freundlich, The Foundation of Einstein's Theorz of Gravitation. Preface by Einstein-;-translated by t. Bros.-:- (Cambridge: The University Press, 1920), pp. 15, 19. 56 today, as Lou.is Roug1er 25 points out in his laureate essay. by transforming a simple analogy into an absolute identity, or by changing a partial difference into a perfect contrast. The absolutes in science do not work. The objective es sence of things, their "real" nature, if such concept of philosophy was made ever clear at all, does not lend itself to scientific descriptions: reality only admits arbitrary and one-sided definitions, such as the methodo1ogical as sumption ot physics: "Whatever is measurable is real," which enables the scientist to describe, or, at least, to attempt to describe, the so-called physical universe "ob Jectively." His reality, then, is one to suit his purpose; descriptions in symbolic relations; quantitative descriptions without quantity being intrinsically defined; tautologies ·that live up to and exhaust the assumption. But the scien tist must not say anything about the "real," or .the "intrin sic" nature -of his world, or the ultimates that underlie it. "When a scientific theory claims to tell us what heat, eleotrioity or what life really is, it stands convicted at the outset." 26 The reality of the scientist (as far as the physical 25 Lou.is Rougier, Philosop& and the New Physics. Essay for the French Academy; translated by Morton Masius. (Philadelphia: P. Blakiston's Sons and Co., 1930). 26 Henry Poinoar8 1 s statement. See Rougier,~• cit. 57 world is ooncerned) is in the functional relations of quan tities whose objective reality, as it was already pointed out, may be philosophically vague and is scientifically un important. This statement, however, is not a dogma of mysticism. On the contrary, it is but the acknowledgement of the very essence of our human characteristics, the realization of the fact that all what we may know of the world and our selves is obtained through a mental process (thought) which 1s based on perception and the realization that the funda- mental source of what we may term the "intrinsic knowledge of the world" is mental. Also upon the realization that thought processes are not, or not yet describable in terms ot physics and chemistry. Bertrand Russell will be quoted here concerning the previous statements: Percepts are the only part of the physical world that we know otherwise than abstractly. As regards the world in general, both physical and mental, everything that we know of its intrinsic character is derived from the mental side, and almost everything that we know ot its oausal laws is derived from the physical side. But from the standpoint of philosophy the dis tinction between physical and mental is superficial and u.nreal.27 This shows definitely why no rigid distinction, no .! priori distinction may be made between reality and appear u5~~~ anoe in science, if any other than common parlance'«'"'of these 27 Bertrand Russell, The Analisis ot Matter (New York: Harcourt Brace and Company, 19 7), P. 4~2. 58 terms is permissable at all as scientitio contrast. We perceive things, but our perceptual world is in our mind, an there only. This is why the most obJective soientifio knowledge is essentially subjective. Yet the minute agreement, both experimental and theoretical (men tal), anl agreement which, although is based on postula tional foundation, exists among an exceedingly large number ot individuals who are capable to explore the physical world, definitely and convincingly shows that the quantita tive oo-ordination of our physical experiences created such a mental realization of the physical world that the inter relations in it of events will be quantitatively the same tor allot us, regardless hat and what kind of qualitative sensations we may obtain individually, what speculations e may have philosophically and what beliefs we choose to en tertain religiously. This non-material, arbitrary, but well-defined and uniquely co-ordinated orld constitutes the obJective physical sciences. hatever else there be is mental. Which means that it 1s not based upon those direct perceptions alone among which soienoe, despite the individual differences of the experimenters, is capable of finding quantitatively defined agreement. They are qualities and abstract concepts, the products of thought, reflection and speculation. henever any of them will be (as it is from time to time) quantita- 59 tively correlated to the findings of physical sciences, it becomes "real" in the sense of the soientist, who holds whatever is measurable is real. All the foregoing will also show hy the soientist as scientist abhors metaphysical speoulations of the DJY'Stic kind. Since matter and energy are reduced to a matter-energy oonoept (just as body and mind to body-mind), the new science is not materialistic, but, for the very same reason, neither is it sp1r1tualist1o, nor idealistic in the old sense. Soienoe !! ~ unified (or so intended), consistent and cate so,ic, and qU;B~titative viewing EL the ~hysioal universe!!! our relation 12_ ll• Therefore b11man values, which do not lend themselves to quantitative analysis, m ental h1unan values of artistic, metaphysical or teleological nature, values thatjneither oonstitute quantitative processes nor are described in such processes, and any other imaginable but quantitatively non-relatable h11man values are outside the realm of soienoe. The scientist, as and usually thr,i-t does acknowledge his hwnan existance and importance; the beauty of a poem, the redness of certain frequencies in the optical spectrum, the quality ot musio, the sensation of friendship, of love, eto., are realized by him. He realizes -th;.t' well~that "emergent" something whioh we have with us besides our physical nervous system and human body, which we call "mind" and which we develop with oonsoiousness and environ- 60 mental modifioation (as we grow up and live) 1 w111 "experi ence" and oreate things for us whioh are none the less real for us than our physical world, and which, perhaps, on ac count of their subjective nature and on account of being mostly our own creations, may be called "intrinsic" in the sense that they are for us (always tor a single being only) what they are, since we created them so. And as Russell says: "I hold that self-observation oan and does give us knowledge which is not part of physios, and that there is no reason to deny the reality ot 'thought.'" 28 Here is where Watson's otherwise practical approach of scientific study breaks down as an ultimate philosophy. - The world which is described and arbitrarily called "mental" here, is not, however, that world of the scientist, ot which he may or will speak ex oathedra. It 1s well to keep this in mind ----- whenever scientific authorities speak of their o· ther than scientific beliefs. such clearly defined distinction of the concept of reality, theory, appearance, experience, experiment, and so on, (which concepts, however, are not intended here to be oontradistinguished in any absolute or classical sense) is indispensibly essential whenever one attempts to realize, describe or point out characteristics of scientific method 28 Bertrand Russell, Philosophy (New York: w. Norton and Company, 1g2?), p. l75. • 61 and oo-ord1nat1on. Scientific truth and the ~egi~imacr oriter1on ~ method and co-ordination. Logic 1s not a tool ot absolute truth. It is a consistent tool of purposive truth; ot truth already postulationally involved and to be made more evi dent by means of some accepted arbitrary rules of thought procedures. Logic, whatever kind (as long as it is consis tent, and consistency is 1n the very definition ot logic) analyzes and quasi demonstrates such truths sequentially; that is, the demonstration establishe~ a ''logical sequence" from postulates to conclusion throughout. But by no means does logic verify such truths experienoially. Experienoe verifications are established by scientifically controlled experiments, as a rule, which corroborate theoretical (pos tulational and logical) truth only for such a period or human experience in whiob no contradictory experiencial evidence is found. Contradictory scientific evidence dis proves former scientific truths whose validity was made probable earlier. Theref6re, scientific validity is not ab solute: to make them suoh, an infinite nwnber of corrobor ating evidence without a single exception would be necessary; and this is not humanly possible. But if the number or such evidences, in the opinion of the scientific world, is con sidered great enough for the purpose in question, then the "truth" in question is accepted valid for the time being. This way truths may remain valid sometimes for centuries. 62 When a soientifio truth 1s contradicted by experi ence, and cannot be m odified so as to inolude the new ex perience, it will be discarded; it will not be used as truth in science anymore, regardless how flawless its logi cal validity may be. This is how tar science, soientifio m ethod and co ordination oan go. This is how far modern scientists may ever hope them to go. Logic and experience in science thus fuse into a unity of method, a method which has arbitrary but accepted and well-defined purposive postulates underly ing it. The relation of theory (postulates, logic, etc.) and experience in scientific analysis, as described in this chapter, involves the earlier mentioned "criterion or legiti macyn29 of method and co-ordination. Whenever scientific method and co-ordination establishes or interrelates scien tific truths consistently, that 1s , tbey do it from postulates by accepted sequential steps and verification by experience (controlled, as a rule), then the method or co-ordination 1s said to be le5itimate; the "truth" is said to be establish.ad by let3i.tima.te means. 29 Ct. pp. 1-10:I0-ll. 63 The fact that scientific truths are m ade only prob able (therefore practically useful) by co-ordination, but not absolutely certain, commands us to examine some of the questions ot "probability." This will be done in the fol lowing chapter. CHA.PrER V THE "STATISTICAL" ! sisn:ifioanoe .2!, statistics that £Oints toward the 11nknown. It was stated earl1er 1 that the fundamental evas iveness ot reality notwithstanding, science expresses itself in well-defined functional relations or quantities whose in trinsic character is unknown and supports such relations by finding a sufficiently large number of oases of experience which satisfy such functional relations. It was also stated that in some department of science, as~•,&• physios, "there is now a demand for prevalenoe of the functional laws without exception." This latter statement must not be misunderstood. The recent, so-called laws ot physics still have this char acter, simply beoause they do not state anything ot the in dividual phenomena the aggregate of which 1s considered,!.! an aggregate, in those statistical laws. The tact that they do not apply to individual histories ot eleotrons, photons, eto., is merely an other way of saying that they are "laws" ot aggregates; such they are made intentionally, and the un certainties involved in the "behavior" ot individuals ot an aggregate do not concern the prevalence ot the laws them selves. l Cf. pp. 3-6. 65 "A sufficiently large number ot oases"--when the ex pression 1s taken in this sense--does refer, in connection with statistical laws of physics, to the observation of ag gregates the tendenoies of whose individuals give the aggre- gates in question the statistically detinible oharacteristics which the laws express. But it is only the cumulative inter action of the individuals that we are dealing with in this case, not their individual histories as such. Therefore, ''sufficiently large number" refers only to our h,1man limit ations that we are not able to perform infinitely many ob servations in order to ascertain whether or not those physi cal laws hold without exceptions. To this it may be added that those laws of nature are not expressing what "actually" happens in nature, but they do express what human beings, keen and qualified, see to happen, when they make their ob servations in the physical and social environment infahich they happen to be. Which faot, again, seems to support the beliet that sooner or later all such "previously unexoep tionally-prevailing laws" will be upset, modified or replaced. The writer, furthermore, 1s unable to avoid the thought that every human research or investigation is alosely connected with intent, if for no other reason than for the fact that every, no matter how objective, observation and every, no matter how logical, thought-process unavoidably involves the ass11ming of a well-defined though ori tical yet 66 purposive position relative to the problem in question. The nature of human will to deal in some definite way with the uncertainties and, perhaps, indeterminacies that present themselves gives research this purposive character, by which is not meant only that research is made with purpose but al so that purpose is present in research throughout. As Dewey states it: Contingency of will would mean that uncertainty was uncertainly dealt with; it would be a resort to chance for a decisiqn. ~e business ot 'will' 1s to be reso lute; that is~tttfi!er the guidance ot thought, the in determinateness ot uncertain situations. Choice wavers and is brought to a head arbitrarily only when circum stances compel action end yet we have no intelligent clew as to how to act. 2 Human intent, then, together with will and our limitations toward the infinite, precondition statistical statements as results of observation and thought. It is a definite oharacter of the "statistical," whether it is!. ~riori or!. posteriori, whether it is a rather rigorous mathematical method or a philosophical con cept, that it deals with probabilities not with certainties. The fact that both purposive theoretical guesses (initiative, intuition) and results of observational situations fused with them, render things probable but not absolutely certain 2 Dewey, The ~gjt for Certaintz (New York: Milton Balch and · company, 1 , P• 250. 67 for the use to whioh they are put clearly shows the proba bility-aspeot of "statistical, .. even aside from its mathe matical significance. The probability-aspect of statistics often points toward some unknown future achievements the na~ure of which may not, and usually is not, made definite or clear by this aspect itself. The tendency of progress through search tor the probable (not for the dogmatically certain) is such that it gives prophetic cues to future searoh which may be based on methods "little known or unfamiliar to our minds." To illustrate this statement the Heisenberg indeterminacy principle and its prediction by Maxwell (a olassioal physi cist) may serve as one of the best examples. I prefer to have this example stated by Dewey who refers to it in a different relation near the end of the ohapter on "The su premacy of I v lethod" in his g,uest for Certainty: It has long been recognized that some physical laws are statistioal instead of being reports of behavior ot individuals as such. Heisenberg's principle, to gether with the discovery that mass varies with veloo ity, mark the generalized oonolusion that all physical laws are of suoh oharacter. They are, as we have noted, predictions or the ~robab1~1ty of an observable event. They mark the oulmination of a qualified prediction of Maxwell's so remarkable as to be worth quoting in full. 'The theory ot atoms and void leads us to attach more importanoe to the doctrines of integral numbers and definite proportions; but, in applying dynamic prin ciples to the motion of irmnense numbers of atoms, the limitation of our faculties forces us to abandon the attempt to express the exact history ot each atom and to be content with estimating the average conditions 68 ot a group of atoms large enough to be visible. This method of dealing with groups of atoms, which I might oall the statistical method, and which in the present state of our knowledge is the only available method ot studying the properties of real bodies, involves the abandonment of strict dynamic principles, and an adop tion ot the mathematical methods belonging to the theory of probability. It is probable that important results will be obtained by the application ot this method, which is, as yet, little known and is not famil iar to our minds. If the actual history of soienoe had been different, and if the soientifio doctrines most familiar to us had been those which must be expressed in this way, it is probable that we might have oonsid ered the existanoe of a oertain kind ot contingency as a self-evident truth and treated the doctrine of phil osophical necessity as a mere sophism.'3 That which Maxwell felt that he must look upon as a trait due to the 'limitation of our faculties' turns out to be a trait of natural events themselves. No mechanically exact science is possible. An individual is a history unique in character. But constituents of an individual are known when they are regarded not as qualitative, but as statistical constants derived from a series ot operations. As regards Dewey's closing sentences in this quota tion it will be pointed out presently why the writer cannot take a view identical with that of Dewey. But the prediction ot Maxwell who could not have had any knowledge whatsoever ot the involved mathematical instrumentalities which had to be developed later on (suoh as eigenvalues, theory of matrio- 5 6 7 es, Heisenberg's matrices, Schroedinger's wave equations, 3 Dewey takes this quotation from "J. c. [axwell, Soientitio Papers, Vol. II, p. 253." 4 . Dewey,~• cit., pp. 248-249. 5 P.A. M. Dirac, The Pr1nc1~les of guantum. eohan ics (Oxford: The Clarendon Pre'ss , ■ 1 30). -- 69 de Broglie waves, wave equations for arbitrary fields, 8 eto.} in order to present a "symbolio algebra of states and observables," "probability theorems of systems in given states," "perturbation theories," eto., is more than -a re markable faot. The analytic mind of Maxwell, who developed olassioally his rigorous set of equations tor electromag netic and light distur.bances propagated in continuous empty space, predicted here the coming of abstract theories of discrete quanta, of electron spins, eto., whose physical realization itself seems to be impossible in those modern theories of wave mechanics which make such an excellent and fairly consistent use of their pioturally unrealizable "physical objects." Herein lies that significance of stat istics which points toward the unknown; the unknown whose sudden introduction may throw in the monkey-wrench into a well-developed and seemingly complete mechanism ot soientif- io representation at any time and may oompel us to res ru t1n1ze our former, no matter how recently acquired soientitio prejudices. But this is the nature ot progress which does 6 w. Heisenberg, "Ueber kinematisoher und mechanisoher fur Physik, 33:879-893, 1925. tentheoretische Kinematik und Annalen, 95:683-705, 1926. quantentheort,tisohe Umdeutung Beziehungen." Zeitschritt Also Heisenberg, "Ueber quan echanik," M athematische 7 E. Schroedinger, W ave-mechanics (London: Blackie and Sons, 1928). 8 Dirac,~• oit., pp. 23?-256. 70 not know traditional security. These last sentenoes contain the argument which com pel the writer to take Dewey's closing remarks in the formEr quotation very cautiously. The statement that "a trait due to the limitation of our faculties turns out to be a trait ot natural events themselves" must be regarded with due pre caution, even though they come trom such a thoroughgoing pragmatist and able philosopher as Dewey. There is no traditional security aecn•t•r in progress, as we just stated, and Dewey himself professes this view when he says that "no one discovers a new world without for aking an old one; and no one discovers a new world who exaots guarantee in advance for what it shall be, or who puts the act ot discovery under bonds with respect to what the new world shall do to him when it oomes into vision." 9 What is more, the quantum the ory, even in its modified and unified form, 1s not as yet complete. The method of causality and indeterminanoy is still unsettled. 10 The classical theory ot physics was con sidered, at least by its proponents, to be complete and theoretically perfect instrument which will be always suit able tor the description ot the physical universe in man's 9 John Dewey, §xperienae and Nature, p. 246. lO D. M. Morandini, "What is Light? What is Electri city?" Paoitio Coast Journal ,21 HomeoRathy, 41:486, 1930. 71 relation to it, regardless phenomena and events to be dis oovered in the future. The universe was considered mechani oally presentable in the Laplaoian sense, that 1$ on the base of strict (mechanical) causality. 11 Today there is on1y one thing that seems to be perfect in the classical dogma: our d1sa pointment in it. Even the genius or a New- ton could not secure tinal security for us. And strangely enough one of the fundamental statistical laws ot modern physics was formed and stated, by means of the logic of a classical physicist, in a rational form by an innovator, who abhors the lack of oausality: Albert Einstein. 12 The 11 Ibid., P• 485. 12 Einstein was awarded the physical Nobel prize for the fundamental law ot energy absorption and emission, name ly that: in elementary absorption processes the energy ab sorbed depends o~l on the frequency of the radiation ab sorbed, and not a all on its intensity (as it would be ex pected on a classical basis). For photo-eleotrioity this is stateA, for an electron (of mass m) moving with velocity v, in the form NIA ~1... 1 _ rr, ::.. % 1'-W- 2- where h ~ 6.5. 10- 11 e~g- sec., the universal con stant ot Planck, \t = the frequency (color) of light which caused, by its being ab sorbed by a light-sensitive material, the emission of the electron~and w 1s the work that was necessary to liberate the electron from its emitting material (matter); his the fundamental statisti cal constant of statistical physics. When asked how he, an essentially causalistio theoretical physicist, came to state this "law" which was statistically 72 statistical aspects themselves of the universe, therefore, must be accepted not as a trait of natural events them selves, but only as a novel, useful and probably valid form ot representation of our view of, and relation to, the physical world; they must be taken as scientific truths which may, and probably will, be replaced by other unforseen relational aspects. The philosophical and mathematical significance· S!.!_ statistics. The widest imaginable scope of m athematical statistics is practically limitless. It may include "all the mathematics applied to the analysis of quantitative data obtained from observation." 13 When taken in such a wide sense, mathematical statistics rests on fundamental philosopioal assumptions and involves all a-dimensional arbitrary variables. It is, furthermore, usually conneoted with the concepts ot "infinite," ''infinite number," "infin ite number ot observations,'' etc.; oonoept~ that exist only in form of philosophical considerations, mathematical definitions, or inferential statements of "facts of observa- 12 (continued) verified years later, Einstein jokingly remarked: "It was convenient and 'reasonable.' Furthermore, why should the right hand know what the left is doing?" 13 Henry Lewis Rietz, · thematical Statistics (The Carus ~thematical onogra~hs No. 3. Chicago: The Open Court Publishing Co., 1g27), p. 1. 73 tions"; but these infinite-oonoepts do not rest on experi ence through perception: the infinite is an elusive, al though mathematically strictly defined concept of the h11man mind, a concept only recently defined by the mathematical genius ot Dedekind and cantor. (By rejecting the maxim that it any collection is part ot another, the one whioh is a part has fewer terms than the one of which it is a part, they obtained a precise definition ot 1nfinity 14 ). When we connect, therefore, statistical probabilities with infinite, as we often do, we are entirely oft of an experience-founda tion which we usually take pride in when ''speaking statisti cally." Yet the empirical statistical results, whatever they may mean, may be taken as results of procedures that are, all in all,~ facto practical procedures, as we shall see later. 15 14 Bertrand Russell, .rqstioism and Losio. See chapter on nMathematics and etaphysicians," pp. 80-92. 15 Empirical (a ~osteriori) statistics is ab natura based on orude approxTniations of the conoept of infinity and also on h11msn purposiveness both in the grouping of data and their interpretation. An "objective" example which seems to be fairly beyond human control (at least as concerns the ob jects whioh serve the data and their motion) will clearly show this. L. Silberstein, in his recent book, The Size of the Universe (Oxford: University Press, 1930) shows that---rhe aurvature-radius (dl) of the universe is statistically obtain able by the formula - where Li.x == .X.1. - X , _; 74 For the time being it will suffice to say that in view of our purpose in hand (the co-ordination of research) we may. conveniently accept suoh "practical knowledge" or "scientific experience" of infinity as is given us by the mathematical definitions "greater than any assignable num ber," "extensions without limit," "oollection of continuous aggregates satisfying certain given boundary conditions," 15 (continued) o is the light velocity; rand v are distances and velocit ies, respectively and are astronomically observable. From three groups of data we have statistically that R's value depends oµ observational methods and also on the distances, from us, of star-groups considered; accordingly: R =-3.0lxla1' astronomical units trom one group (Cepheid, p. 185) R ==3.25xlOH a.u. from an other group (0-stars, p. 187), and . R =4.03:xl0H a.u. from a third, the most n,unerous (in number to infinitely "nearest")group (459 stars from Young and Harper's list, pp. 19g-211). . This shows the uncertainty and approximate nature ot .! ~os teriori statistical oo-ordination, although the case con sidered is fairly sate from "undlil!? h,1mau interference" except in observation itself. lhe great difference between mathe matical (a priori) and a posteriori "infinites" acoounts tor a good part of the numerical disagreement. R could be called valid only by considering all stars of the universe. This is impossible, therefore there is no hope that we may ever"experience" the actual R; beside this, what intrinsic meaning this four-dimensional radius could, in form ot interpretation, convey to us? What is beyond this radius, one may ask with the 'insensible" layman. Or is it to be interpreted that space, as experienced, ceases, Ez. definition, to extend beyond it? If so, it still remains unexper!enoeable, or only may give intormation regarding the nature o~ light-rays. 75 eto. But we must not forget the entirely theoretical nature and arbitrariness of such "experiences." With this in mind, some or the most important philo sophical assumptions that underlie statistics may now be pointed out. What is meant by the probability of an ooour ance? or, more definitely speaking, what is meant by the probability of succeeding to seleot a certain single event, oocurance, trom among an aggregate of events that are "equal ly likely" to ooour? This question involves, first of all, the assumption that we know or are able to define what "equally likely" means. I shall not attempt to give any definition of the phrase, and do not know of any which withstands rigorous scrutiny. Statements which in final analysis amount to say ing that events which by no human effort or other agencies (as deus ex machina?) may be shown to be not equally likely ------- / ,·kel'f are considered equally lipia7, is, ot course, only begging the question. Accepting therefore, "equally likely" on its tace value, probability as an answer to the question above may be defined as follows: it t 1s the frequency of the oo- ouranoe ot a oharaoter or event among s possible ooourrances, then t/s is called the relative frequency of suooess, by definition in statistics. "If the relative frequency of suc- cess approaches a limit when the trial is repeated indefin itely 'under the same set of oircumstanoes' {?), this limit 76 is called the probability of success in one trial." 1 6 The process ot arriving at a probability is as follows: "If all of an aggregate of ways of obtaining successes and failures can be analyzed into s' possible mutually exclusive ways each of which is "equally likely"; and if f' of these ways give successes, the probability df a success in a single trial may be taken to be t'/s•." 17 It is evident that the phrases 11 indetini tely," "under the same set of circ11mstanc es," and ''equally likely" are subject to unavoidable cri ti aisms based upon the foregoing introduotory remarks of this subtitle. Granting these definitions their questionable rigor we offer them as postulational statements justified only by use as working hypotheses and supported, in a way that is normal in science, by statistical result, experience of ap plications. Peculiarly, ho ver, these experiences may be established in very few actual oases, the cases of schemata, only. These schemata are mechanical arrangements intended to oreate the conditions of "same set of circwnstances" and "equally likely," and even after granting them this charac ter (the existence of which may be always seriously doubted), 1 6 Rietz, 2R.• cit., p. s. 1'7 Ibid., p. 10. 77 they realize the trial,!!_ indefinitely repeated by means of subsequent mathematical reasoning (by means of the the ory of limits) only, and not by, of course, actual practice. To establish a mathematically fair knowledge, however, in any other practical case of application, a knowledge that would show, in a scientific manner, that our definitional requirements are fulfilled; that necessary and sufficient conditions are present in a given case for a bona-fide scientific application of the so-called "statistical machin ery" that is derived logically (consistently) from the defin itional postulates: is nearly impossible. We face here s01m:tthing that seems to be a methodolog ical impossibility; a demand on our "human nature," which it cannot comply with. Perhaps we are pondering on nature's gates, through which we gain aocess to what we call knowl edge, tor secrets which it does not ·have, and, therefore, cannot give us. Our exertions, as suoh exertions usually did in the past, may lead us to such discoveries (realiza tions of relational circumstances) which may compel us to destroy suddenly the wonderful and ingeniously constructed statistical machinery itself on behalf of which our anal ytic queries are made. But the only way science can destroy values is by replacing them by others that we call and feel to be better ones. The act of destruction is carried out by and in the process of building more beautiful, more con- 78 sistent and oategorio, and more convenient edifices during the ceaseless search for scientific truths. There is hardly any single statistical theorem whioh is not directly based upon undefinable postulates that are similar in character to those that were already mentioned. Desire and tendency seem to prevail even more in statistics than they do in other research fields of science. On the other hand, statistics gives, perhaps, more opportunity to the intuitive and creative genius and to the analyzing faculties of suoh genius, than any other soientitio field of creative character. A Bernoulli, a Laplace, a De Moivre, a Tohebycheff, a Pearson and a Charlier, in the domain of statistics proper, or a axwell, an Einstein, a Bohr, a Heisenberg, a Schroedinger, a de Broglier and a Dirac in the realm of symbolic description of a "statistical" material universe,--represent the most outstanding examples of human ingenuity and ability of dealing with problems which seem, especially on account of their elusiveness of olear defini tion, involve nearly unsurmountable difficulties at the outset. Other postulates that are demanded by specific branch es of statistics are defined similarly to those already mentioned. uantum. mechanics, for imstanoe, sets up the oondition for the compatibility of two observations as a "symmetr1oal oondition between them," defining the latter by means of probability and average probability. 18 In the very large literature of statistios, different authors use different wording to give these uncertainties a more pleas ing appearance. Arne Fisher connects his introductory ex planations regarding statistical probabilities, eto., with the theory of integral equation , 19 and, follows in this the methods of the Scandinavian mathematioia~ especially of Gram and Charlier, because definite integrals appear to him (as it is now generally accepted in m athematics) a more elementary and primitive operation, than the infinitesimal and the derivative, the approaches of Pearson. 20 The fun damental difference in deriving statistical tools, especial- ly the frequency curves and functions (which are of funda mental importance), is the difference between the Gauss Pearson approach and the Gram-Charlier approach, namely that the functional relations of probabilities are expressed as closed algebraio or transcendental functions and curves in the former, while they are infinite series in the latter. Aside, however, from some major differences in the hypothes es, the approximation formulae of both theories may be made 18 Dirac,~- oit., pp. 11-14. 19 Arne Fisher, Frequency Curves and Their Application in the Analysis of Death Curves and Life Tables (New York: !he Macmillan Coiiipany, fg22), pp. l-25. 20 Rietz, op. cit., pp. 50-60. . . 80 to reduoe into each other by si ple and conveniently selec ted mathematical changes. The questions llt underlying probability, equal likelihood, eto., are discussed and il lustrated with many direct calculations, by the late Wil liam Burnside, whose posthumous work 21 is an interesting, clever though not exhaustive discussion of the theory of probability taken from the viewpoint from which they are usually considered in oonneotion with research problems other than those of statistical physios. Problems and methods of "restriotedrr statistics. - Leaving aside the problem of statistical physics, of which the necessary remarks for the pur poses of this paper were already made, some problems and methods of statistics in a restricted sense will now be s11mroe.rily considered; they are coming to an expression in connection with frequency func tions and correlation of data of observations. Whenever a sucoess of a single trial is defined as given earlier, and the probability of an event may be de fined by analysis from the nature of the problem without carrying out aotual trials (as,!.•.&• in the case of throwing a die) we refer to the oaloulated probability as an~ priori probability; when suoh definite probability may not be 2 1 i1111am Burnside, F.R.S., Theory of Probability (Cambridge: The University Press, 1928). - 81 theoretically predicted, the approximate probability whioh 1s obtained from actual statistical data (results of trials), is oalled !. 12sosterior,i {empirical). It is required in re search that these two probabilities of a soientifio hypo theses agree with each other when a theory of convenience is turned to practical use, or else the experimental (statis tical) data will not be considered as supporting the theory. When data of observation of a variable~ (~•.S• ther mometer readings) are considered as a set (of fre quencies) and y signifies frequenoies, it is said that a frequency function or probability density (or law of distribution) ex ists for the values of x, it, and only if, there is a func tion F(x) such that the ratio of a number of x values within any arbitrary interval to the number of x values in another b arbitrary interval is / F{rj dx ~ b' F {x) rlx t!' tor all intervals ab and a'b' ot the given variable. j = F {x) is the frequency function (theoretical) or sim ply the fre quency curve. This curve, when evaluated under the assumption of "random'' or "natural" sampling of theoretioally infinitely many observational data of a variable, takes the Gaussian form: 82 where is a measure of dispersion of the data, called "standard deviation" and is defined by the process ot deri vation of this function, or is obt.ainable from this func tion by substituting corresponding (x,y) value-pairs into it. The Gaussian frequency curve is ot fundamental import ance in statistics. Pearson and Gram and Charlier derived independently generalized sets of frequency functions. The tactual and co-ordinating value of statistics; its analytical sisnifioanoe. When sets of more than one interdependent variables are considered in such a manner that from the behavior of one or more sets conclusions are drawn, mostly on an!!. posteriori basis, for the remaining sets, problems of simple, multiple ~nd partial correlations are dealt with. These are especially useful for finding such laws of empirical experience regarding objects and liv ing organisms (including oonsoious behavior), which laws are extremely diffioult to discover or approach by direct analy sis. Whenever correlated data of statistical experience indicate such positive interdependence of the variables {oharacteristios, traits, events, phenomena, eto.) we hope to have obtained some cues for the better understanding of their interdependent existenoe and operation. ~ ithout going into the description of correlation theory and technique (the nature of which is evident from 83 the foregoing and is conoisely and extremely ably explained in the quoted "Mathematical tatistios" of Henry Lewis Rietz) the following statements are offered here without any further proof of their probability than that which may be inferred on the strength of this chapter. The systematic tabulation of observational data is made under the assumption that it is possible to approximate, to a satisfactory degree of precision, the idealized theo retical conditions whiah are mathematically (logically) de rived from probability assumptions and are indicated on previous pages. The tools of approximation constitute a mathematical instrwnentality which, in toto, is a useful --- counterpart of rigorous and idealized analysis. Therefore it gives mathematically correct results within the precision of the approximation. Correlation tools operate similarly. But it must not be forgotten that the very structure of the statistical postulates, as it was made alear earlier, prohibits the unconditional use of the tool, because hardly ever may it be ascertained whether or not the intrinsic or unknown nature of the problem for whose solution statisti cal data were correlated, actually involves a fair approxi mation of the conditions upon whioh the permissable use of the tool is based. Only skill, judgment and "intuition" are our guides in this respect. 84 Again, the pliable statistical mechanism is a blind tool. Muoh more blind than differential calculus, because its operational character does not supply us with direct analytic values. It is a synthetic tool, which puts fre quency numbers, this nameless mosaics of uniformed empiri cal data, together in a symposium which may be impressive. But it is not in itself convincing or dependable. e may trust its mathematics, we may even rely on the practical validity of its postulates, but we hardly may ascertain that its postulational requirements are actually satisfied by the individual case which we study. It is faith, faith in our own discretion and research ability, the addition of our individual human values first of all that convinces us of the correctness of its use and, therefore, the de pendib111ty of its results. rihen this may be supposed, new difficulties follow: the interpretation of the statistical results; the oorrelated mosaics must be given collective names. And this mass-baptism does not follow so naturally; it is often easy to isname the collections, to misinterpret the measureless numbers. The only cases which may be called exceptions to these unproven rules are those in which theoretical,~ pri ori probabilities, agree with observational statistics. Aside from schemata, most of these cases, especially those which are scientifically interesting are connected with 85 infinite aggregates and are thus established by a large number of comparisons. Educational problems usually are not of this character. The restricted number ot cases, their "population," is not near enough to a "practical infinity" whioh oould fairly well substitute the mathematically de fined theoretical infinity upon which the statistics of indefinitely repeated trials is based. Besides, in most cases one cannot even guess how near the supposition of equal likelihood is approached. All these difficulties notwithstanding, the co-ord ination values that derive from the statistical mechanism which was directed by skillful hands and able brains, hardly can be surpassed by any other single factor of co-ordina tion. Furthermore, the intuitive foresight that guesses well upon the cues of the statistically co-ordinated yet analytically unknown data directed searoh to new discoveries in more than one occasion. In this lies the co-ordinating and analytical significance of the statistioal. 22 22 Statistical method, as considered in this chapter, is applicable to social- science researches without any essential elaboration. The uniqueness of social reeearch lies in the constant presence of the 'Wl known, hidden or not well controllable variables interfering with the research procedu~e and hindering conclusions to be drawn by means of the controlled variables. In this, however, social research is not dissimilar to recent physical r se~rohes of statistical nature. The reat difference lies in that the complexities of indeterminacy in physics are no reduced to few primary processes, of hich all other processes are readily anal ysable. (For clearer vision the primaries are concentrated upon.) But in social sciences the complex nature of consciousness, ill, purposive ac tion, etc., of research media are bein taken -ranted ab ovo and serve as (necessarily) accepted indeterminacies. s far as metho is concerned, however, this is only a difficulty which is diff erent in e ree, not in kind from those of hy · s. CHA.PrER VI SIGNIFICANCE AND PITFAI,I.S OF C0--0 DINATION Co-ordination and research. The fourth chapter of this paper analyzed some major questions of theory and ex periment in their philosophical, logical and experienoial aspects; the fifth chapter, the chapter on "The statistical,t' dealt with theory and experiment from the point of view of their interrelation, especially as concerns the aspects of the!. priori and the empirical. Both chapters were intend ed, 1'rlrthermore, to characterize what may be referred to as the philosophical and physical environment in which re search takes place, and to show the nature of scientific • • truth aimed at by w 11-directed yet well-defined methodo- • 1, logical means. These means, in turn, themselves are prog ressive; they often have rigorous conventions and definite symbolism but never a rigid and unchangeable conformity to methods of the past. Research, therefore, when carried on by such m eans, will be called progressive. Reasearch effects oo-ordination. Under co-ordination is meant in this paper the combined steps or results of a method by means of which a consistent unity is established or is intended to be established among whatever may concern given scientific phenomena, their 87 relations and implications, when these, in our relation to them, are viewed and oonsidered in auoh a manner that the "oo-ordinating principles'' enumerated near the end of this chapter are, in general, complied with. In this definition co-ordination has two denotational aspects: one is method ological, the other resultative. The latter does not neces sarily mean that the results are there in either positive or negative form as a oonsequenoe of the above mentioned combined steps, but it does m ean that in lack of such re sults the research was not successful. Research 1s our means in science to obtain results; co-ordination is our method to that end. Remarks on science, research and ''human nature." An --------- interesting and striking description of science and its mathematical character is given by Hudson Hoagland who looks upon science especially from a biological and psychological point of view. In! Handbook of General Experimental Psych olofiY tor 1934, he expresses himself as follows: By science one understands the unresting attempt to obtain a comprehensive, satisfying aocount of the uni verse and all that it oontains; the essence of this, as science, is that it must be based upon the fewest possible assumptions. fuy such an attempt should be found satisfying presents a problem into which we need not now inquire •••• The description and interpreta tion of the properties of living organisms encounter hazards more varied and insidious than those attending the scientific treatment of non-living objects. Even in the latter case, to be sure, description and inter pretation are statements of properties of the ob, erver and the theorist. • • • The biological system presented by a single indiv idual, no less than that which may be conceived to be presented by any association or society of different individuals is obviously not a 'thing,' a single 88 event, but a system of relations. It is these rela tions which mµst be defined through investigation. To do this there~5required a procedure whioh is essentially quantitative and mathematical in character. uantita tive treatment is not iperely a matter of numbers and arithmetic. It is fundamentally and primarily con cerned with relationships of funotional dependence • • • • (Then he quotes a:xwell) 'The most important step in the progress of every science is the measurement of quantities •••• , The measurement of quantities (con tinues Hoagland) which is neoessary for the production of statements of functional dependence, implies units ot measurements possessing definite dimensions, using 'dimensions' in the sense of physics. The relationship between measured features of the performanoe ot an organism and values pf a known controlling variable supply the materials for statements of functional de pendence. To be really satisfying and productive, these formulations must be rational, not merely empiri cal; the constants they contain must have a testable s1gnif1oanoe.l In Chapters I to III, these features of science were discussed somewhat in deta11 1 and definitions of soienoe ere given in Chapter IV. 1th all this in mind, before the principles of oo-ordination in science will be enumerated and commented upon, it is necessary to make a few remarks concerning research and the researcher. In our view of the physical world temporal relations 1 Hudson Hoagland, "The Study ot Living A Handbook of General Experimental Psyoholof. Ilassachusetti: Clark University Press, 1034~ national University Series in Psychology. p. Organisms." (Worcester, The Inter- 3-4. 89 play a unique part among the relational co-ordinators, usu ally four, used in such views. This will be evident by the following: three of these oo-ordinators are spatial, one is temporal. It is a psychological peculiarity of man that, although he intends to use these arbitrary co-ordinators of his "objectively" in science, he usually wishes to have as much subjective feeling of them as possible. As Noble says As the 'time' aspects of objects are aspects of differ ences; as it is the prooession of an object from one stage of its existence to another and not its continu ing existence, which most excites ou#attention--it was inevitable that when the human mind began to reach out for a deeper and wider acquaintance with objects whioh are to be gained only from a knowledge ot their connec tion with each other, it should have been overwhelming ly impressed, not with the faot of their relation in ~space,' but with the phenomena of their relation in 'time. And if it be asked why the mind has simultan- eously fallen short in the equally necessary process of • realiz•~- taat objects as totalities in their exten- sion asp~ct, the reply is that the field is here not one of difference that shock the oonsciousness because they embody change, but of resemblances cognizable by the intellect rather than by the senses •••• The result of this failure to complete our succession of 'evolutionary' knowledge of objects with an equally radical insight into the extension aspect of Iature has been, as tar as the fundamental method of thou~t is conoernid, toreta!n soienoe in a stagewhlch 8s acT vanoed little beyond that represented by the mind of primitive men.2 (Italics not in the original) Only after a "radical insight" into the extension aspect of the world, became a scientific spatio-temporal ordination of objects, events, and their relations possible. 2 Edmund Noble Pur?osive Evolution; the Link between Soi9noe and Religion (Nework: Henry Holt and Company, l926), PP• 148-149. 90 As a result of his primitive desire for a deeper feeling of the temporal, man often forgets (no matter how cautioasly he tries to avoid this), that subjective time and objective time are two entirely different entities which have very little to do with each other. This results in a mental confusion: the intermixing of the physically tempral with the subjectively (psychologically) temporal, and vice-versa. As to spacial relations, the ohance for such contus ions is far less; physioal and psychological extensions, when and if they are compared, are quite distinct. It is only with duration that we unwittingly try to identify their physical and psychological (subjective?) aspects with each other. This Bergsonian feeling of the temporal 3 reacts upon our peroept of, and attitude toward, physical time. On the other hand, it renders subjective time conceptually more elusive than a similar distinction is in extension. lfe feel the nnow" more keenly than we feel the "here. tt e disting- uish past and future uniquely, while we do not distinguish right-lett, up-down, foreward-backward in this way. Instead of the two things: past and future as related to "now," we 3 Ct. Charles Fox, The nd and Its Body; The Founda tions ot Psicholof: (New York: Harcourt, Brace and Company, 1932),"pp. 46-24. Al.so see Henri Bergson, ind-Ener~, translated by H. ildon Carr. (New York: Henry Hoit an Company, 1920), pp. 20-22. 91 have only one thing: "elsewhere" as related to "here." This uniqueness of the temporal brings the objective time-sequen tial ordering of things subjectively much nearer to us, mudl more keenly felt by us, than the ordering of things in a spacial sequence. :Furthermore, we feel that we live "nowtt and feel that the process which takes us from the past to the future is an irreversible one; but we feel that although we may live "here" we could live elsewhere, fairly as a mat ter of o- hoice (within limits), and the process which takes us trom "here" to "there" is a reversible one. Aside from the uniqueness of the temporal, there is another fact that interferes with soientific investigation in such a way that it probably spoils our fair chance in viewing everything equally objectively. This has relation to the quantitative and qualitative asp ots of our human existence. There are phenomena (events, objects, etc., both physioal and mental) which are of such an order that they are comparable by means of our own human scales. Broad ly speaking: they are of human size. And there are other phenomena which are not. Investigations relating to phenom ina that are either physically of the order of human magni tudes or are philosophically or psychologically ot our own qualitive nature, have advantages, both methodologioal and resultative, !. priori, above investigations oonoerning either micro- and macrooosmic things or teleological and epistomo- logical considerations. 4 The uniqueness of the temporal on one part, and the three compartments of the physical and mental extensions (human, sub-human, superhuman) on the other, seriously interfere with our scientific research and supply some ad ditional reasons why scientific objectivity 1s difficult to define, and why co-ordination may not be mechanically fixed or prescribed in detail. Truth, 9bJectivity, view. The previous remarks show that for the reasons mentioned above (and also for other reasons to be dealt with later in this chapter) is rather difficult to define scientifio objectivity. What objectiv ity in science is may be better desoribable by the method of soientifio investigation than by direct definition. In vestigation and research in science is carried out for the purpose ot arriving at scientific truths. The sum total ot suoh truths at any given time is scienoe. Science, as truth in this sense, however, is not absolute truth; the method ology and co-ordination exclude this possibility. "To arrive at new truth and vision is to a~ter," says Dewey. 5 4 See Dorcas and Shaffer, Textbook of Abnormal ~41oh- ~ (Baltimore: The 1ill1ams ana Wi!kinsCompany, 19 , ~ (The statistical determination as a criterion ot abnormality). 5 John Dewey, EXJ2!rienoe and Nature, p. 245. 93 "Only by identification with remaking the objects that now obtain are we saved from oomplaoent objectivism •••• Identification of the bias and preference of selfhood with the process of intelligent remaking achieves an indestruc tible union of the instrumental and the final." 6 Such a purposive achievement of the knowing by doing clearly shows that absolute truth is unattainable because of our lack of "absolute objectivity" and our purposive interaction (active participation) in the knowing process. It would be extremely useful if the relative ~bjeot ivity and its result, relative scientific truth, were more generally recognized. There are objective features in re search and co-ordination, but they are there by the "rules of the game," by a voluntary discipline and silent agreement among researchers, not by any absolute relation between phenomena (object) and method. The voluntarily accepted principles of co-ordination are called here co-ordination principles. They are, or should be, in the writer's view, nothing more and nothing less than an arbitrary harmony which the researcher (all researchers ot science) chooses to interpose, as his system of reference, between phenomena and himself. ''Till we understand the operation of the self as the tool 6 Ibid., P• 246. 94 of tools, the means in all use of means • • • so ience i·s incomplete and the use made of it is at the mercy of an un known factor, ••• the psycho-physical mechanism and func tioning of individual centers of action." 7 This is the background upon which we intend to paint, in the following, the picture which depicts the fundamental reference-frame, the self-imposed objectivity of the soien tist. The composite picture has the principles of co-ordin ation as its component and is colored by the purposive interference of the researcher with his phenomena of invest igation. By agreement he can not, however, use any kind of oolor: in accepting certain rules of his game(!_.~• that of oonsistenoy) he willingly limits his activities to what he oalls legitimate means of scientific research. Thougqt, volition, emotion. Researoh deals with ques tions to be answered. Uncertainty, therefore, of situations is the challenge whioh stimulates action from the part of the researcher. Whenever action is the result of emotion, it necessarily takes the oharacter of emotion; it is imme diate, non-analytic, unreliable, often. random. such action i~ h~Y~eci .from ,e 5e6,--rc.J,. The ~ef/o n 'Of the researoher is mediate, analytic, reliable and assured. He defers his aotion, does not aot under the impulse of the 7 Ibid., p. 247. 95 moment. This manner of acting in researoh gives it its SY! tematio oharaotar. System, however, involves not only in tellect but also volition; the researcher makes his plan but also has a purpose at hand. Thought, systematic thought, is the reaction or the researcher to a problem, but he not only thinks ot his problem ''as it 1s," but also thinks ahead and iaakes plans how to get rid of his problem; he creates his method of attack. When he does this, however, he defers his action and scrutinizes his purposes, desires and choices, thereby trying to free them trom their chaotic emotional attributes. This is his individual approach to whatever he decides to face scientitioally. And his approach is a very commendable one, because "the volitional phase or mental lite is notoriously connected with the emotional." 8 The quest for certainty. In putting his individual emotions, but not his volition, as tar aside as possible, the researcher must realize a fairly recent doctrine of modern science, namely that he is not supposed to look for final certainties. During the long reign of classicism "the idea ot a universal reign ot law, based on properties immutably inhering in things and or such nature as to be capable of 8 Dewey, The ~uest tor Certaintz, p. 226. 96 exaot mathematical statement was a sublime 1dea.n 9 And "a universe whose essential oharacteristic is fixed order and oonneotion bas no plaoe for unique and individual existen ces, no place tor novelty and genuine change and growth. It is, in the words ot 1lliam James, a blook universe." 10 Modern science does not present us such a world. In this it has no choice. Both its history and present status oontra dicts this possibility, and do so with the only standard whioh science accepted as its measure ot validity, that is, by experience. All former truths, the most certain oertainties changed. But this alone would not be enough to justify our supposition: the lack of absolute and final in the queries ot science. There are, however, other more profound reasons to support the belief just forwarded. First, not only we have nothing established in modern soienoe as absolute, but there are very serious indications (as!!.•~• in the difticul tiea and amazingly rapid changes or the quantum theory, or in the consistent but some hat isolated serenity of the relativity of empty space) that absolute finalities are, fortunately, not the share of men. If by any torm ot speech the question may be worded ''What is the intrinsic (absolute) 9 Ibid., p. 208. lO Ibid., p. 209. 97 reality of the universe?" science is not called upon to answer it. Secondly, the general theory of relativity, or rather the method by means of which it was established by Einstein, shows the peculiar nature of measurement, the very foundation upon which every investigation in soienoe necessarily and by definition rests. The arbitrary reality of science is quantitatively measurable. Standard yardsticks are necessary for absolute measurements. A centimeter, a second, a gram that is the same always and everywhere. 'I'he classical physicist was sure that he had it. The modern physicist tound that he had it not. Eddington, who in his peculiarly absolute relativism uses his genius not only for mathematioally correct symbolic deductions but also for the putting forth ot much less cor rect metaphysical guesses, maintains that there are a few absolutes left in the system of the modern physicist. For instance, number (of discrete 1ndividuals) 11 , or the velo city of light to which "in the general theory of relativity is no longer assigned the same constant value, but (which) continues to correspond to the grain of absolute world struoture."12 He, however, conveniently forgets that, on 11 A. s. Eddington, The Nature of the Physical orld (Cambridge: University Press, 1929), p:-23. 12 Ibid., p. 56. 98 one hand, counting is not a physical thing, but a process • which has, in the oonneotion he refers to it, definite ar~ bitrary rules of performance: its discrete operational se quence; and on the other hand, that number is a non-entity, a mere methodological convenienoe and depends, in its Edd1ngton1an absolute character upon the existence of a oonsaious counter. There is no such thing as one, two, three, etc., but only one thing, two things, three things, eta. As to his seoond absolute, the velooity ot light, he himself has to admit its magnitudinal and directional (vectorial) variability, yet he asserts that it is "the grain of absolute world structure." Probably he only refers to light in this allusion as our universal means to experi ance and explore a little more or the world than a few miles of our immediate physical environment, and, again, he conveniently forgets that even in this sense light is only a relational aspect in the observer-observed relation, and that light-experienoesexist for us only in light-emmissions and light-receptions (absorptions) but nowhere else, or not 1nbetween. Thus truth is not absolute in soienoe, not even tor Eddington. It will be seen however in the following chapter that soientifio truth has, not in its intrinsic character, but in the methodology by whioh it 1s pursued, a feature which guides man toward it, without the necessity of "having nailed it 99 down for good" or without crystalizing it into an immobile, unalterable, preconceived,_!. priori goal. A beautiful pas sage ot Dewey conveys to us the spirit ot research and progress 1n the very sense of this paragraph: Abandon oompletely the notion that nature~ to conform to a aertain definition, and nature iiitrI'iisic ally 1s neither rational nor irrrational. Apart from the use made ot it in knowing, it exists in a dimension irrevelent to either attribution, just as rivers in herently are neither located near cities nor are op posed to such location. Nature is intelligible and understand•ble. There are operations by means of which it becomes an object of knowledge, and is turned to hurnan purposes, just as rivers provide conditions which ma{ be utilized to promote human activities and to s isfy h1unan need. l.3 Pur~ose and co-ordinating ~rinciples. tethod is born of intent, method is oreated for purpose. This 1s evi dent trom the foregoing. Sinoe one of the chief purposes of science 1s discovery, scientifio method must aooommodate this purpose, regardless what other aspeots are to be specifically considered. Soienoe strives for knowledge planningly and systematically; in fact, plan and system are the essence ot its procedures. Through them it contemplates and experiences the world. "The criterion of knowledge lies in the method used to seaure consequences and not in meta physical conceptions ot the nature of the real." 14 Soien- 13 Dewey, The 9.uest for Cer.tainty, p. 210. 14 Ibid., P• 221. 100 tifio oonsequenoes are m easurable by comparisons; therefore, also so1entifio knowledge is, indirectly, measurable. eas urements, on the other hand, are based on the observation of ooinoidenoes and are, as suoh, expressed in quantities and their relations. As to the intrinsic nature of our measure- ments, they only oan give us suoh tautologies as~-~• the statements that "light is light," "length is length," be cause quantity itself 1s not physically definible. But relationally they give us such state ents as "five light units of light" or "seven length-units of length." It 1s mathematics that is built up logically upon such relation ally speoitio but intrinsically meaningless oonoept of quan tity. It is little wonder, therefore, that the tools ot research, these essentially relational means, are, first ot all, expected trom the measurer, the physicist, and the creator of systematized relations, the mathematician. "In the end thinkers of all lines are dependent upon the mathe- . matician and the physical inquirer for perfecting ot the tools in their respective ~allings." 15 In view of purpose, therefore, and the nature of the tool toward it, the coherent totality of the steps in re search, that is, co-ordination, is laid down in the follow- 15 Ibid., p. 221. 101 1ng on principles which are those of mathematics and physics, respectively. Without any o.laim to absolute inclusiveness, the following principles of soientifio oo-ordination are here enume~ated: l. Procedure, both specific and general, should be based upon as few assumptions (postulates) as possible. There is no causal reason for this, but it is aooepted as desirable to reduce "explanations" to as tew logically non substantiated ideas, or as few "unexplainables" (if this is the oase) as possible. 2. The procedure should be consistent, that is: se quentially well ordered and non-contradictory in its des criptive and logical (deductive or induotive) part; and cap- able of verification or refutation by experience. (Consis tency is, of course, a logical conoept. Today it is, per haps, the only attribute of logic which 1s still adhered to in the recent multivalued logics whioh replace The Logic of classical tame.) 3. The theoretical results which are obtained from the postulates consistently, must be compared with experience (usually controlled experience, called experiment). After it has been found that theory and practice are in agreement, that is: experience statistically supports theory, theory is considered practically valid, verified, which only m eans that 102 it is not contradicted by experience. In logic and mathematics proper there is a conven tion (a well satisfied arbitrary requirement) that not only statistioal but unexoeptional verification 1s demanded. This is, however axiomatic, given by definition. A similar tendency exists in physics and more or less in physi~al scienoes, but it may be questioned whether or not such ten dency is more than statistical, even though theory and prac tice may agree in 999,000 cases out of a million. 4. The organic unity of 1, 2, and 3, as a reference frame-mechanism, will be considered (by definition) as the criterion of oo-ordination, as the word is used in this paper. Whenever l, 2, and 3 are accomplished with positive resul.t, the oo-ordination will be called valid. The valid unity of these three principles assures l~a what we may term the "asymptotioity of researoh" ·\and ot knowledge). This is expressed to some extent in the excerpt from Dewey (see page g9) and it will be examplified by "integral-analysis'' in the next chapter. The major principles of co-ordination, aa they are considered here, are already given above. It is only for the sake of guidance and greater explicitness that the fol lowing points are added: 5. The method of limitation. The researcher is a limited h11man being who may not be, and usually is not, able 1 5 a A oharacteristio by means of whioh the researcher seeks to establish things through closer and oloser, definite approximations of tendenoially set ideals. 103 to comply with the above requirements ot co-ordination without resorting to simplifications of his problem. Such simplifications, nevertheless, are not entirely arbitrary, although considerable freedom prevails in the determination of their nature. They have to oomply with l to 4, and also have to satisfy point 6 below. 6. Satisfactory "re-assembling" of the individual results obtained through the method ot limitation or other wise. This means that (a) the knowledge gained does not change its essent ial character when the simplified studies are considered in their complexity within an aotual phenominon "as it is," (b) the knowledges gained of various limited studies and their re~assemblies are in harmony with possibly all other results within a certain scientific oategory or branch (as.!•£• physics, or psychology), (o) there is nothing in our chosen methodology, as tar as it 1s known, that would exclude other phenomena of the category trom such assembly as here described. The point 6 (a,b,o) may be called the principle of categorioity. It is one of the aims of the following chap ter to outline distinctly one of suoh possible methods, which is applicable both as oo-ordination within a specific problem, and as oo-ordination of problems within a category. Although in the latter oase, as it is expectable, the method 104 becomes fairly complex. 7. The discrete, proper and legitimate use ot "intui tion" (originality, ingenuity, eto.). "Legitimate" here means consistent with purpose at hand and oomplianoe with other co-ordinating principles. We have to remember that "the eventual purpose in knowledge is observation of a new phenomenon" 16 and that in a fixed-order-universe ttthere is no place for unique and individual existences, no place tor novelty and genuine change and growth." 17 It is the business or intuition, etc., to extort novelties by whatever legitimate means it finds possible. What is more, it is the privilege and duty of intuition to scrutinize rigorously (that is to start a rigorous scrutiny ot) former, accepted and seemingly valid soientifio truths, methodologioal assumptions or methodology itself. The validity of scientific truth lies in its postu lates and its establishing methods; therefore, •1••• science jealously guards its right to destroy the old and to build 1tecmew, whenever it hopes to gain more consistent or more embracive knowledge thereby. In this intuitional principle have those reorientation effects their origin, which recent ly permeate philosophy. 16 Ibid., p. 207. 17 Ibid., p. 209. 105 This principle assures scientific progressiveness by providing for the introduction or recognition of novelty. 8. Purposiveness, as it is admitted in objective studies. We dealt with this principle earlier. Let us add only that it is ttpurpose for an end," but it must not falsi fy facts or the method by whioh taots are attained or oo ordinated. It really is the opposite of "disinterestedness," but by no means does it involve uncontrolled or designing emotional influence from the part of the researcher. 9. "Objectivity.•• This is included here only so far as it may be defined. Its aspects were mentioned earlier, but the writer is not able to define it otherwise than by saying that objectivity is a tendency of the researcher to interfere in a "due manner" and not to interfere 1n •• ''unduly" with his observations. What "due manner" and "unduly" mean I cannot tell. :Except that it .involves circumspection, carefulness and the avoidance of negligence and uncontrolled emotional dispos_ i tion toward the object and method ot research. But then, this is a question of ethics, temperament and ability, and is, therefore, without the scope of this paper. It is reiterated here, at the end ot this enumera tion or co-ordinating principles, that conformity is defin itely not a scientific co-ordinating principle. The formal ilm ot science is both convenient and necessary, but never 106 is finally uniform or irreplacible. The conventionalism of scienoe is willing, not submissive. Conventions (symbolic or other kinds, and including logic) are rationally accepted formalities, not compulsions. 1e mays :y. that the tyranny of science is very democratic; anything in it may be replaced by better things, that is, consistently and progressively. The ~itfalls .Q! co-ordination. After what has been said in this chapter and the eDumeration of the principles or oo-ordination not much is needed to be said of this sub ject. The previous 11st could be taken point by point and shown that non-compliance with its essentials involves dangers of going astray. It may be said, however, that the lack ot preparedness, skill, intuition and self-discipline implant research with pitfalls well hidden and often un aviodable. In particular, the lack of fundamental knowledge of the auxiliary sciences that are necessary prerequisites ot a certain research field (See page 7) will, almost al ways, revenge itself. Aside from this, the following are mentioned as ser- iously interfering, retarding or frustrating co-ordination: l. Lack of purpose and system. 2. Taking postulates as self-evident truths. 3. Assumptions carelessly ad.mi tted as working hypo-~ theses. 4. Implicit dependence upon the logical tool. Un- 107 oonditional acoeptanoe of its results as truth. 5 •. Implicit dependence on the statistical instrument alities or the improper {inappropriate) selection of them. In particular, haziness or lack or distinction between the ~ priori and the empirical{!!_ ~osteriori); and the misin terpretation or numbers of correlation or of statistical prediction. 6. The improper fusion ot the co-ordinating princi ples, especially of the first three. 7. Disregard of the method of limitations; also, undue dissection of the problem into parts. A proposed co-ordination based on the assumption of funotion-struoture unity, 1s outlined symbolically in the next ohapter. CHAPTER VII INTEGRAL-ANALYSIS The two-fold uniqueness of researoh and knowledge. As it was a~oentuated in the previous chapter and elsewhere, co-ordination, as used for establishing synthetic unity in research, is not an absolute sohematism. It may not be mechanically applied to a situation that may exist between researcher, his system of reference and the problem. Reference-systems are instruments emergent partly from vol itional attitude and judgment and partly from the condition ing environment. fuat is more, the relation may change d~ing investigation. Knowledge, therefore, as obtained in quest is, at best, a quasi-tensor·ial representation of the knowing situation: a view that lends itself to covariant transformations to other systems uniquely. At worst, it is a dogmatic picture, inflexible and incapable of transforma tion-changes. Co-ordination is re garded here as a flexible method, providing numerous approaches and differing detail; a method that suits ability, individuality, disposition, will, and purpose. Still it means a unique relation. Its uniqueness is twofold: in its above mentioned as pect it is unique for the individual; and in an other (let us say: objective) aspect it is unique for the totality of 109 human individuals,--mankind. This second aspect of unique ness I shall call asymptoticity and shall try to examplity in the following. ! ~reposed oo-ordination. In the following a pro cedure, general in application yet unique in character, is given in the form of ooncise symbolic outline. Symbolism is chosen for clear definition and brevity. The leading principle in this co-ordination is the proper and effective fusion of the "theoretical," "experi mental" and "statistical," without the stultification of originality, intuition and initiative. There 1s an extreme- ly great degree of freedom in the selection of "procedure subunits," whioh, however, are required to remain in harmony with each other and the scientific category to which a problem-in-question belongs. This check of unity of the analysis suggested the name: integral-analysis. The procedure of co-ordination is based on the philo sophical supposition of function-structure unity, and is developed in outline as follows. I.ntesi:,al-ar+al;y:sis.A.Let whatever be made the subject or investigation be called a phenomenon P. Let us suppose, as a working hypothesis, that every phenomenon.f may bear- bitrarily simplified, in an infinite number ot ways, into sub-phenomena i , ~ , n:. , eto. , in suoh a manner that each I :t' 1. :t:' .3 110 of these oarries in itself some (so-called) charaoteristios '/ ot !2. Since !P, , :P._, ef:>,, etc. , are but arbitrary simplifi cations ot <.i, they may be defined, arbitrarily, by the re- searcher as consisting of characteristios 't:~j and their relations, so that where j = 1, 2 , 3, • • • 1> i . The j, now are finite numbers, the numbers ot arbitrary characteristics which the researcher selects to define bis sub-phenomena 'P,,·. And the symbol P,· U {i) is to be read "sub-phenomenon ~- is defined by the observed oharacteris tics 'lc,i, where j takes the arbitrary values from l to "1. ;_ • " The criterion of any 'P, being defined, for our purpose, by the Y::,i is the fact that a sufficient number of situations ~ ~' (called in their relational totality, P) "caused" by the presenoe 01' the c/,;j and their relations as stated in ( i/) will "always" result in~-. We shall symbolize this statement by which 1s to be read "arrangement P1 whioh is caused by the presence of '/,.;_,/ and their relations, tends to predict /,; •" The words "caused," "suffioient" and "always" are used for oonvenienoe; "causen involves only sequenoe, "suf- h H tioient" involves only sufficient tor the purpose in hand, 111 or "suftioient in the judgment of the researcher"; and "al ways" implies only "always whenever attempted," or ''always whenever the thing in question occurs." In this manner any desired nwuber of convenient sub phenomena of a given phenomenon may be examined without the necessity of drawing any final or absolute conclusions tor the phenomenon pin question; or without any tendency, on the part of the researcher, to look tor intrinsic oharao teristios ot the phenomenon ~ itself. The positivum that is definitely involved in such preliminaries of procedure as above proposed is the clear and unambiguous although ar bitrary definition of the seleoted sub-phenomina ~ "- • Their definition is given by the tact that the researcher intentionally defines them as they are defined; but it re mains to be seen what bearing such arbitrarily defined sub phenomena have upon the phenominon ~ under investigation. "]3. The methodological assumptions and their consequences as stated up to this point are that we have P, ( i, ••• JQQ. The ~ , contrary to the ~ '-; , are not experimentally establiahable. Any ~ i , however, is to be oonsidered--by definition- as implying a finite number of characteristics t.~/, and, therefore, eaoh of the series 'I/: I f,, • • ' I L 0 '1_ · ~ _,,) (,~ t.. .J / .J L --(11 1 being the number of characteristics arbitrarily ad- mitted into any of the series of the above type, and1' 1 be ing in general, different number for different 1, and 11 JG being the number of such series)--is exhaustive for their - respective~. The relation of the~~;· within any P t" is uniquely defined by the fact that ~ ( Ye~;) • ► ~- - 113 C, It is pointed out here that the methodology thus far described, although serving as a general arrangement, does not suppose anything especially as to the selection ot those ~. which are defined by the fusion of theory and i practice in • Therefore, it is not claimed here that this method- which, in its entirity, will be called integral-analysis- will lead to a "perfect," "intrinsio" or even "necessarily satisfactory~knowledge of~. The knowledge gained for~ shall depend, as it will be seen in the following, upon the judgment of the researcher, by means of which he detines his arbitrary Pi. This 1s only an other way of stating that knowledge is relational between phenomenon and observ er. As in any other method, here also there are an infinite number or possibilities of attack for the solution of a given problem. fuat is more, it is the very intention of integral-analysis not to eliminate intuition or arbitrary original seleotion of the "arrangements" P 1 , regardless whether those selections were made on the base of some fav ored theory or otherwise. It 1s considered an advantage 114 that such selections may be made freely and as the research er may see them best fit for his purpose in hand. on -the other hand, it is suggested here that the re searcher make his selections in such a way that he has the best chance, as far as he knows, to have his arbitrary~· satisfy the requirement which will be defined in the fol lowing as "asymptotioity"; or else he will have to abandon his selections almost as fast as he makes them. It is pointed out, furthermore, that ~he procedure does not encourage so far {and it intends to discourage al together, as far as possible) selections that are anything else except "simplifications" of IP' • Under "simplifica tion" is meant selection of characteriatios d · and of their I L~; relations such that in the <pi the essential or allegedly essential ahracteristicsfot £ are still recognizable ex perimentally, or that at least some of them are so recog nizable. It is not necessary, at this stage of the investi gation, to have any of the / (which are considered as 1, , '/,_, .. 'Ji., ... ) individually recognized or relationally clari fied through any '/c,j·(and their relations) of any~-. But if the researcher was unable, at the beginning of the investigation ot ~, to make up his mind as to what might be at least some of the characteristics ot ~ for the purpose in hand, for which he wants to know ~, then he may 115 have to take a rather round-about way and may have to retrace his steps from numerous blind alleys before he will be able to say definitely that he attained knowledge under the ex isting oiroumstanoes of the phenomenon in question. The principle of asymptotioity will lead him to negative results, until, by some cue or thought that may have ocou.rred to him as a subjective by-product of his attempts to know P, finally he finds himself' approaching his goal. That this ap proach is or is not an aotuality for him, the principle of asymptoticity will for him define. Attention 1s oalled especially to the fact, before further methodologioal steps are introduced, that "knowledge with purpose in hand't and "knowledge, a relation between phenomenon and knower" are such methodological concepts which serve as more than useful guides for the selections ot ' lc:,i to determine ~i by the practical check of° /1.,. ~ .£,·. In biologiaal or psyohologioal investigations, for example, Pi that predict ~ ,· so that ~ 1.,· essentially establish sub phenomena not experimentally similar, in the studied aspects to~, will be discouraged by the abo~e concepts of knowl edge. More speoifioally, bacteriological studies, for in stance, by first killing the bacteria by staining, may not lead to essential oharaoteristics of such Tin whioh it is essential that those bacteria are alive. 116 - D. As shown earlier under B, the !Pl: are defined by a tinite number ot 'lc.~j , therefore, the oharaoteristios '/:_;/'· , in virtue of their index numbers 1 and j, •l ■e may be con sidered without reference to their relations in P l· • They may thus be classified into rows and columns ot a "prelim inary soheme, 'lc.i . " In this sense they will be individually spoken of as being in the "preliminary pigeonhole if t?J. •" The H~ ; ·will now be considered with regard to the similar ity ot their oontent. They will be re-olassitied with res pect to their second index j, eaoh kc;/ being arbitrar.tly transformed into an llci)X in such a manner that 11 ~ ;/~ which are considered to have essentially similar content will be given the same secondary index j~ regardless of their first index 1. This involves that the contents, the characteris tics ,A·, are thus transformed into identical but position- T 1.,~) ally ohanged characteristics 'It;/' • re must not forget that JI,~/ and I-Iii~ are identical in content, but. differing in their oolumnal positions; this statement will be expressed by the symbols Hli -< > H1,/ " . . Ca >-- t,. 'j- l1/ "Hi) 1s identically shifted into the " <l. • 1s identically shifted into the 1,,, tively. w hich are to be read position," and position," respec- 117 A two-told reclassification of the "preliminary scheme ~~/ " is afteoted in this manner. The c/c.~/ did not lose their position in relation to their respective sub- phenomena ~ -, but similar characteristics of different - l ~ are arranged in the same class; such classes will be spoken ot as "vertical classes" of the "seoondary scheme" which latter is defined by the re-classification itself. Classification with respect to indices 1 is hereby defined as olassitioation into "horizontal classes." The "secondary scheme" of t he Hj,J * with contents thus constitutes a scheme of pigeonholes Htj* such that the number of the horizontal classes is the same as the greatest I 1, called lm , and t he number of the vertical classes is the same as the greatest of the 11 1 called nt- ~ • e have, . therefore, l 1'K,q_t, times n". ~ pigeonholes in the secondary scheme altogether. The secondary scheme includes also "~mpty pigeonholes;·" because the characteristics P, _; meaning that " P2, is a nearer simpli fication of ff thd\ ~ , " or meaning· that "~ z. approaches f better than ~ • " F. The whole procedure from A to Eis repe~ted now with new~ (which may be oalled ~", whereas the original~- now 119 I . I/ may be referred to as ~- ) • The ~ t.- are defined by new (J)II -0 Q (,A '') I/ T ~; 1 · such that r t. T1.J· -;, 1.·• The procedure leads finally, through the pigeonholing process, to a ?_x°'-;•J such that 7; ~ f/4;~ ) ~ ~ )(. rx ~ xx Then the process is repeated to define new y 3 ..J ~ ~ •-~~,, on similar principles. G. It' 1 t will be found that the series £,.. ~,,,, ... _, ,I'., x I .,J .- ../ 11 ./ except for a permissible number of exceptions (or except for a number of exceptions which are negligible when con sidered with respect to the purpose in hand), are such that they may be re-arranged in an order so that for the new ~ )( X )( order P,- .) if:;: .) ~S' .) ... .J p-fi it is found that - x - 2. .J I I I / then it will be stated that the investigation which was made in regard to satisfies the requirem ent of asymptotioity. It is a postulational assumption in integral-analysis that knowledge or phenomina is asymptotical; Therefore, it will be declared upon the requirements of asymptoticity having been satisfied that knowledge of € is attained. · The measure ot the degree of such knowledge is said to depend on the nature of the relations considered under ; the smaller are the differences between oonsecutive X - X p_ p _ ) I•'_) I ~ 2. - as the numbers 7; -_; .. ~ if increase, the "nearer" or "bettertt is the knowledge sa rtd to be for the purpose in hand. 120 In case the asymptotioity requirement is found not satisfied, the investigation is to be repeated, perhaps by utilizing the u1nsight" gained by the previous failure. It is seriously hoped that integral-analysis, espec ially when worked out in more detail, complies with all the principles of co-ordination, as they are stated in the previous chapter. CHAPTER VIII SUMMARY General. It is evident that the argument of the thes is has been based throughout, and its oonclusions in Chapter VI established, on certain general philosophical tendencies, metaphysical convictions, scientific faith and methodologie~I inolinations of the writer. Aside from the speoific attri butes, th~refore, of the thesis there are generalities which are worth while being summarized, so as to emphasize these general tendencies, convictions, faiths and inclinations. This is being done with the purpose ot warning the reader where the prejudices of the writer may lie. 1. Absolute certainties do not prevail in science. 2. Structure and function, when separated in thought J are only convenient aspects of an inseparable structure function unity. The validity of conclusions drawn from either aspect alone is far more questionabie, as regards soientifio truth, than the validity of oonolusions attained through analyses based on structure-function unity. 3. Methodology, whatever it is otherwise, must be consistent. 4. Postulates are convenient, arbitrary starting points in research. They are modified and remodified as a result of 122 researoh. 5. Logic, especially as recently freed from classi cal prejudices, is a consistent theoretical tool of co-ord ination in establishing (tautological) relations from postulates. 6. Functional relations, as shaped by a logical tool: mathematics (or similar} serve co-ordination definitely only when their logical content has been experimentally verified. 7. Experimental verifications consist of statistical co-ordinations of observations for the purpose of abstract (mathematical) comparisons of functional relations with this statistically correlated domain of data. a. Statistioal (~ posteriori) probability carries the muoh more weight in co-ordination the more it is in agree ment with!.. priori (mathematical, philosophical) probability. 9. The theoretical functional relations, as derived from arbitrary postulates by logical (mathematical) sequence and checked by experience (scientific experiments), are considered as soientific truths, that 1s, first, second, thirda, eta., approximations of only tendenoially set ideals. They represent the results of our best mathematical efforts to make, as far as possible, exhaustive and probable con sistent statements of the physioal universe in our relation to it. 123 10. Our scientific view of the universe is purpos ive. Our statement of it, therefore, is not absolute but dependent on the use (theoretical or practical) to which it is intended to be put. 11. On the principle whioh may be referred to as "asymptotioity of progress," views are constantly changed by means of statistical comparisons of what may be roughly called theory and experience; the statistical procedure it self being subject to similar changes. 12. Changes in view, method and co-ordination are intrinsic necessities. They follow from the fact that our participation, as observers of things and events, is an ao- - tivitz which has definite (though not necessarily and pre ferably not predetermined) influence upon the observed. Furthermore, changes, being the only fundamental objects of observation, define quantitative relations without defining quantity pe~ !.!• 13. The fact that consecutive changes may be compared quantitatively with one another serves to define the concept of "asymptoticity of progress," whenever the relative prob abilities of t'unotional relations are ascertained by intu itively arranged sequences which are made, intentionally, the bases of auoh comparisons. 14. The asymptotic approach to "unknown scientific truths" is the result of conscious action. Therefore, it is 124 esentially subjective. Furthermore, it is modulated by purposively controlled desires according to rules that are tentatively fixed as accepted scientific method (or are in augurated as suoh). This latter is itself a variable func tion of physical and sooial environment. 15. Asymptotio progress, in virtue of the changes trom which it derives, necessitates also a constant change of those postulates and working hypotheses upon which pre oeeding steps--which led to those changes--were based. 16. Thus, the method of scientific progress which co-ordinates knowledge, is essentially a reiterating one, although not identically recurring. In this sense it is a cyclic procedure, although human tendency gives them a spiral asymptotic character. 17. Progress involves risk; it does not give certain ty. And despite the predictability of immediacies, it is such that in the aggregate of steps unpredictable novelties occur. 18. Novelties, in our scientific and philosophic view ot them, are catalytic agents in ou~ constantly changing, active view of (participation in) the Universe. S~eoitic. Both as its subject-matter and speoifio aims this paper deals with the establishment of the tollowing as regards science and its method: 125 1. Intrinsic (ultimate) oharacteristios of the world are not within the soope of scientific investigation. 2. Soience arbitrarily defines its realm as that of realities of an arbitrary nature: "fuatever is measurable is real." Science deals with such physically measurable reali ties, and with them only. 3. Suoh arbitrary (and one-sided) realities do not establish fundamental intrinsic-properties of (material) things; they only bring about, by means of so-called scien tific methods, quantitative funotional-relations (usually in mathematical symbols). The "real" nature of quantity itself is not ascertained by science; quantities are relationally compared without any !!. priori or deduced intrinsic. llllllS knowledge of quantity. 4. The "objectivity" of science is formal; not funda mental. It is a result of convenient, voluntary agreement among scientists; not a rigid, unchangeable thing. It 1s patent in the method (approach) rather than in the problem or its "solution." 5. The question of materialism - and idealism does not, in the sense of oontra-distinction, enter into the defini tion of soienoe. A non-material, arbitrary, but quantita tively well-defined and uniquely co-ordinated world consti tutes the "objective" physical sciences. This world, however, 126 is based on perception, therefore its non-materialistic con tent is experimentally verifiable. Science is a unified (or so intended) consistent and categoric, and quantitative viewing of the physical universe in our relation to it. 6. Thus, scientific knowledge is the result ot rela tion between the world and the investigator. The criterion of such knowledge lies in the method used to secure conse quence, not merely, and not so much, in the results of such method. ?. Scientific truth, therefore, is not absolute; it may be said to be rather "asymptotically progressive." a. Scientific method means co-ordination of theory and experience: theoretical postulates and their logical results must, by postulational requirements, be tested and be found in at least statistical agreement with experience (experiments, usually controlled), before any scientific truth is accepted as "valid-for-the-t1Ine-be1ng." 9. Principles,--steps and results--of such co-ordina tion are systematically developed in this paper by means of a three-fold grouping into "theoretioa~," "experimental" and "statisticaltt aspects. These, however, are considered to constitute the interrelated, or rather, fused parts of a methodological unity, the co-ordinating reference-frame of the researcher. 127 10. SUoh reference-frames, however, are not entirely arbitrary. First of all, they, as relations between viewer and viewed, depend on the object of investigation; secondly, the free ohoice of the researcher 1s limited by his volun tary aooeptance of certain general co-ordinating principles, especially those or parsimony of assumptions, consistency of derivation and checking by experienoe. 11. The subjectivity of the researcher becomes, through him, a part of his reference-frame; therefore abso lute objectivity in soience is 1 possible. Objectivity is a goal whose asymptotic approach is always hoped for in soienoe but not finally attained. Purpose, will, desire always remain a part, although a well-controlled part of scientific objectivity. 12. The thesis as a whole 1s not merely theoretical; neither 1s it a survey of the past only. Aside from cons tant authoritative references, it develops its conclusions in agreement with its "primary assumptionsn; and it constant ly refers to experimental verification. In such spirit the thesis outlines, as a further support _ of 1 ts conclusions, a definite but tentative method which, it is hoped, may be practical and satisfactory. This method of approaoh--co-ordination based upon funotion-struoture unity--is schematically developed in this paper and named "integral-analysis." This co-ordination 128 of the "theoretical, " "experimental" and nstatistioal" is a flexible plan, intended to insure great generality and wide application without interfering with, or limiting, intui tion, initiative, originality--these essential and integral parts of research. Integral-analysis is derived in agree ment with developed co-ordinating principles. BIBLIOGRAPHY BIBLIOGRAPHY I. PBDURY SOURCES Bell, Erio Temple, The Search for Truth. New York: Reynal and Hitohoook, l934. 879 PP• Bergson, Henri, "Mind-Energy," Lectures and Essays. Trans lated by H. Wildon Carr, Hon. D. Litt., Professor in the University ot London. 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Brose; Preface by Einstein. Cambridge: The University Press, 1926 • . 140 PP• 132 Heoht, Selig, ttVision II. The ature of the Photoreceptor Process," The Foundations of Experimental Psychology. The International University Series in Psychology. Worcester, Mass.: Clark University Press , 1929. Pp. 216-272. •• Heisenberg, w., 'ttJber quantentheoretische Umdeutung k1nemat1soher und meohanisoher Beziehungen," Zeit sohritt fflr Physik, 33:879-893, 1925 • • • , "Uber quantentheoretische Kinematik und echanik," --~Ma~thematisohe Annalen, 95:683-705, 1926. Hughes, Arthur L., and Lee A. DuBridge, Photoelectric Phenomena. International Series in Physics. The McGraw-Hill Book Company, 1932. 531 PP• James, William, Prag1natism. LA ne name for some old ays of thinking.J New York: Longmans, Green and Company, 1907. 309 PP• --~-' Some Problems of Philosophy. Green and Company, 1911. 237 PP• ew York: Longmans, jeans, Sir James Hopwood, "The New orld-pioture of odern Physics," Science, 80:213-222, September 7, 1934. Jennings, H. s., The Biological Basis of Human Nature. New York: W.W. Norton and Company, Inc., 1930. 384 PP • Kant, Dmnanuel, Critique of Pure Reason. Translated by J.M. D. Me1klejohn. London: G. Bell and Sons, Ltd., 1930. 617 PP• Lev1-Civ1ta, Tullio, A Simplified Presentation of Einstein's Unified Field Equations. Translated by John Dougal!. London: Blaokie and Sons, 1929. Lukasiewioz, J., and A. Tarski, "Untersuohungen ttber den Aussagenkalkttl" (Calculus of Propositions), Comptes Rendus des seances de la Societe des Sciences et des Lettres de Varsov1e-;-23: Class II!: pp. 30-78.- 133 Lukasiewioz, Jan, "Philosophische Bemerkungen zu mehwertigen Systemen des Aussagenkalkttls," Comptes Rendus des seances de la Societe des Sciences et des Lettres de Varsovie-;-23: 30-?8, 1930. - - Meiklejohn, Alexander, Philoso~hy. Chicago: The American Library Association, 1926. 56 pp. Morandini, D. Iii., " tlhat is Light? hat is Eleotrici ty?" Report for the Physiotherapy Section of the California State Homoeopathic !edical Society, ay 14, 1930. Pacifio Coast Journal of H omoeopathy, 41:479-487, December, 1930. , "Philosophy and Science." Unpublished lecture --~~ delivered for the Severance Club and the Saturday Lunch Club, Los Angeles, California, April, 1931. Morgan, c. Lloyd, The Emergence of Novelty. N ew York: Henry Holt and Company, 1933. 207 pp. Murchison, Carl, editor,_ Handbook of General Exrerimental Psychology. The International University er es in Psychology. · orcester, ~ss.: Clark University Press, 1934. 1125 PP• --~-' Psyo~ologies of 1930. The International University Series in Psychology. oroester, ass.: Clark Uni versity Press, 1930. Noble, Edmund, Purposive Evolution. N ew York: Henry Holt and Company, 1926. 5?8 PP• I Poinoare, Henri, The Foundations of Scienoe; Science and Hypothesis; The Value of SciellCe;· Soienoe and ethod. Translated by George Bruce Halstead, with a special prefaoe by Poinoar~ and introduction by Josiah Royoe. New York: The Science Press, 1913. 553 pp. Principles of Relativity, collected ori ginal papers by H. A. Lorentz, A. Einstein, H. inkowski, and H. eyl. London: Methuen and Company, 1923. 216 pp. 134 Quine, Willard Van Orman,_ System of Logistic. Cambridge, Mass.: Harvard University Press, 1934; and London: Humphrey Milford, Oxford University Press . 204 pp . Rietz, Henry Lewis, dathematioal Mathematical onographs, o. Publishing Company, for The America, 1929. 181 pp. Statistics . The Carus 3. Chicago: The Open Court athematioal Assooiation of Rothschild, Richard, Reality and Illusion. New York: Har court, Braoe and Company, 1934. 442 pp . Rougier, Louis, Philosophy and the New Physics. Essay for the French Academy; translated by orton asius. Philadelphia: P. Blackiston's Sons and Company, 1930. Ruark, Arthur E., and Harold c. Ursy, Atoms, oleoules and ~uanta. International eries in Physics . New York: he M cGraw-Hill Book Company, 1933. 790 PP • Russell, Bertrand, Introduction to athematical Philosophy. London: G. Allen and Unwin, Ltd., 1920 208 pp . Russell, Bertrand, and Alfred ~hitehead, Principia ·athe matioa. Cambridge, Eng.: The University Press, 1925. 2l9 PP• Russell, Bertrand, Philosophy. N ew York: • • Norton and Company, 1927. 307 pp. ____ , The Analysis 2.f. atter. London: K. Paul, Trench, Trubner and Company, 1927. 408 pp. , Mysticism and Logic. New York: •• Norton and --~c-om-pany, Ino., 1929. 234 PP• Schiller, F. c. s., Formal Logic. A scientific and social problem.J London: Maomillan and Company, 1912. 423 pp. Schiller, Ferdinand Canning Scott, Logic for Use. ew York: Harcourt, Brace and Company, 1930. 469 PP• Schlick, M oritz, Space and An Introduction to the tition. Translated by Clarendon Press, 1920. ime .!!!. Contemporary Physics . Theory of Relativity and Gravi Henry L. Brose. Oxford: at the 120 PP• 135 SohrOdinger, Erwin, Four Lectures on ave Mechanics delivered at the Royal Institute, London, M arch 5-14, 1928. London: Blaokie and Sons, 1928. 53 pp. Silberstein, Ludwik, The Size of the Universe, Attempts at a Determination of the curi'ature Radius of Space-time. Oxford: The Unive'rsity Press, 1930. 215 pp. Smuts, J. c., Holism and Evolution. N ew York: The mc millan Company, 1926. 362 PP• Thurstone, L. L., "The Learning Function," Journal of Gen- ---- - -- eral Psychology, 3:469-493, 1930. Tolman, R. c., Statistical eohanics. ew York: The Chemical Catalog Company, 1927. 334 pp. Veblen, Oswald, "Spinors," Science, 80:415-419, ovember 9, 1934. Weatherburn, c. E., dvanced Vector Analysis ( vith Appli cation to ·at ematical hysics). London: G. Bell and Sons, Ltd., 1924. 222 pp. eyl, Hermann, Space, Time and atter. Translated by Henry L. Brose. ew York: E. P. Dutton an4 Company, 1921. 330 PP• II. SECONDARY SOURCF.s Adler, Alfred, The Neurotic Constitution, Outlines of a Comparative Individualistic Psychology and P~cho- therapy. Translated by Bermand litck and Jo E. Lind. New York: offat, Yard and Company, 191?. 456 pp . --~~' The Science of Living. 264 PP• e York: Greenberg, 1929. Aveling, F., ttEmotion, Conation and · 111," Feelings and Emotions. The ittenberg Symposium, The International University Series in Psychology. orcester, ass.: Clark University Press, 1928. Pp. 49-57. Boring, E.G., "Mathematical ersus Scientific Signifioance,tt Psxchological Bulletin, 16:335-338. Brown, Ralph R., "The Time Interval Between Test and Re test in Its Relation to the Constancy of the I •• ," Journal or Educational Psychology, 24:81-96. 136 Camp, B. H., "Probability Integrals for the Point Binomin al," Biometrika, 16:163-171. Curie, Irene, Joliot F. and Preiswerk P., "Neutrons from Artifioially Radioactive Elements," Paris ~oademy of Sciences Report, July, 1934, and Scienoe--Supplement, 80:192, August 24, 1934. Dove, Patriok Ed ard, The Theory of Human Progression. Abridged by Julia Kellogg. New York: Isaac H. Blan chard Company, 1910. 142 PP• Dunlap, Knight, The Elements of Scientific Psychology. St. Louis: The c. f . osby Company, 1924. 368 pp. ______ , Mysticism, Freudianism and Scientific Psyohology. St. Louis: c •• osby Company, 1928. 173 pp. Fisher, R. A., Statistical ethods for Research orkers. London: Oliver and Boyd, 1925. Forsyth, c. H., An Introduction to the Jf.athematical Analy sis of Statistics. New York: John ~iley and Sons, fg24-;- 241 PP• Freud, Sigmund, The Problem of Lay-Analyses. IntrodQction by Dr. s. Ferenezi. New York: Brentano's, 192?. 316 PP• Garrett, Henry E., Statistics in Psycholor, and Education. Introduction by R. s. oodworth. ew ork: Longmans, Green and Company, 1926. 317 PP• --~-' Statistics in Education and Psychology. Longmans, Green and Company, 1927_ . 31? pp. ew York: Harnwell, G. P., and J. J. Livingood, Experimental Atomic Physios. International Series in Physics. Ne York: MoGraw-Hill Book Company, 1933. 4?2 pp. Heyl, Paul R., The Fundamental Concepts of Physics in the Light of odern Discovery. Baltimore": The \lilliams and ilkins Company, 1926. 112 PP• 137 Hinton, James, Chapters on the Art of Thinking (and other essays). London: c.Kegan Paul8nd ·company, 18?9. 393 PP• Holzinger, Karl John, Statistical ethods for Students in -------- Education. Boston: Ginn and Company, 1928. Hull, Clark L., "The Goal Gradient-hypothesis and 1"aze Learning," Psychological Review, 39:25-43, 1932. Hunter, qalter s., "Learning II. Experimental Studies of Learning," The Foundations of Experimental Psychology. The International University Series in Psychology. , orcester, 1ass.: Clark University Press, 1929. Pp. 564-627. Johnston, G. A., The Development of Berkeley's Philosophy. London: Macmillan and Company, 1923. 400 pp • • • Jorgensen, Carl, "A Theory of the Elements in the Emotions," Feelin~s and Farnot1ons. The i' ittenberg Symposium, The International University eries in Psychology. or cester, ~ 1 ass.: Clark University Press, 1928. Pp. 310- 315. Jung, c. G., Psychology of the Unconscious (A Study of the transformations and symbolisms of the L1bido.--A con tribution to the History of the Evolution of Thought). Translated by Beatrice ·• Hinkle. New York: .offat, Yard and Company, 1916. 566 PP• , Psychological Types .2.!: The Psychology of Individu ---a~t--ion. 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Creator Morandini, Dyonis M. (author)

Core Title Co-ordination of theoretical, experimental and statistical research

School School of Education

Degree Master of Science

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Degree Conferral Date 1935-06

Publication Date 06/08/1935

Defense Date 06/08/1935

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Advisor Raubenheimer, A. S. (committee chair), Burton, W. H. (committee member), Lefever, D. Welty (committee member)

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