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Lessons From Frege's Puzzle

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Lessons From Frege's Puzzle

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Content LESSONS FROM FREGE’S PUZZLE by Daniel Kwon A Dissertation Presented to the FACULTY OF THE USC GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree of DOCTOR OF PHILOSOPHY (PHILOSOPHY) August 2010 Copyright 2010 Daniel Kwon ii DEDICATION To my beautiful children, Rylie and Nathan Kwon iii ACKNOWLEDGEMENTS First, I would like to thank my committee: Elena Guerzoni, for helping me out of a jam by agreeing to a last minute request to participate in the defense. Mark Schroeder, for carefully and methodically pointing out the parts of the project that were weak or undeveloped and for suggesting ways to strengthen and develop them, and for the many meetings where he gave me invaluable advice on how to frame some of its central ideas. Nathan Salmon, for his friendship, words of encouragement and generosity and for all of the meetings at USC and UCSB where we discussed many of the central ideas of this project. I also owe him a huge intellectual debt; many of the central ideas here spring forth directly from his work. Scott Soames, for his devotion and professionalism as a teacher, for his patience, for the countless number of drafts and emails, for all of the careful and thoughtful comments and for pushing me and helping to bring the best out of me. Almost every idea in this dissertation was influenced by him either directly through my interactions with him or indirectly through his work. I would also like to appreciate the following philosophers for their questions, comments or suggestions: Brian Blackwell, Brian Bowman, Korey Declark, David Manley, Lewis Powell, Indrek Reiland, Barry Schein, Johannes Schmitt and James Van Cleve, especially David Manley for his many suggestions about the project when it was in its initial stages. iv I would like to thank Johannes Schmitt, Brandon Johns, Eddy Choi, Sam Koh and Paul Yoon for their friendship, my parents, Mike and Esther Seo, for their love and words of encouragement and my sisters, Christine Kwon-Chang and Ruth Kwon, for their support throughout the process. Most of all, I would like to thank my children Rylie and Nathan Kwon for bringing so much joy and happiness to my life and providing the motivation to keep working. v TABLE OF CONTENTS Dedication ii Acknowledgements iii Abstract vii Chapter 1 History of Frege’s Puzzle 1 1.1 John Stuart Mill on Proper Names 1 1.2 Frege/Russell Descriptivism 2 1.3 Kripke 8 1.4 Neo-Millianism 11 Chapter 2 Two Conceptions of Cognitive Significance 18 2.1 Millianism and Two Conceptions of Cognitive Significance 19 2.2 Transparent Terms versus Non-Transparent Terms 23 2.3 Non-Transparency and Two Conceptions of Cognitive Significance27 2.4 Defining the Two Conceptions of Cognitive Significance 28 2.5 Solution to Frege’s Puzzle 36 Chapter 3 How to Become a Relationist: String vs. Collapse Semantics 38 3.1 The Antinomy of the Variable 42 3.2 Response to the Antinomy 48 3.3 Frege’s Puzzle: String Semantics versus Collapse Semantics 57 3.4 Defending Relational Compositionality 61 Chapter 4 Frege’s Puzzle and Collapse Semantics 65 4.1 Why Rejecting Millianism cannot be the Answer to Frege’s Puzzle 68 4.2 Collapse Semantics 70 4.3 The Salmon and Soames Argument against the “Frege Intuition” 76 4.4 Criterion for the A priori for Singular Propositions 89 4.5 Argument that Elton John is Reginald Dwight is A posteriori 92 Chapter 5 Modify “Belief” and Partial Definition 95 5.1 Modifying “Belief” 97 5.1A Opacity 97 5.1B Kripke’s Puzzle 101 5.1C Salmon and Disquotation 103 vi 5.1D Modifying “Belief” 109 5.2 Partial Definition 114 5.2A “Belief” and Partial Definition 114 5.2B Responding to Objections to Partial Definition 116 5.2C Semantics for Partial Definition 121 5.2D 2 nd Version of Kripke’s Puzzle 122 References 125 vii ABSTRACT Although the problem in the philosophy of language known as “Frege’s Puzzle” is well known, it is not well known that 3 different, but related, puzzles have all been identified as “Frege’s Puzzle”. Each puzzle poses its own unique challenge to Millianism, the view that the meaning or propositional contribution or semantic content of a name is just its referent. It is argued here that every Millian solution to “Frege’s Puzzle” that has been proffered hitherto fails to solve it. The reason for failure is that no single solution can be a solution to all 3 puzzles. No single size fits all. The dissertation sharply demarcates each puzzle from the other two, articulates the unique challenge posed by each and draws the appropriate lessons. The first lesson is that there are two conceptions of what Frege calls the, “erkenntniswert” translated “cognitive value” or “cognitive worth”, of a meaningful expression. According to one conception, the sentences, “ketchup is a breakfast condiment” and “catsup is a breakfast condiment” do not differ in cognitive value in that they are perfectly synonymous, i.e., encode the same proposition. “Ketchup” and “catsup” are perfectly synonymous. According to another conception however, the two sentences however also differ in cognitive value in that a person who fully understands both can rationally believe that they differ in truth-value. The second lesson is that we have to move away from a standard semantics, where sentences like, “Elton John is Elton John” and “Elton John is Reginald Dwight” viii differ in the propositions they encode if “Elton John” and “Reginald Dwight” differ in their semantic contents. It seems pretty clear that these sentences differ in informational value—while the former is trivial and a priori, the latter is non-trivial and a posteriori. But, on a standard semantics, the only way to get a difference informational value between the two sentences is by rejecting Millianism. What this shows is that we have to move to a non-standard semantics, which I call, “Collapse Semantics”, where we can get a difference in the propositions encoded by the two sentences without rejecting Millianism. The third is that we have to modify our conceptions of the attitude verbs like, “belief”, “know”, “doubt”, etc. Our ordinary conceptions of these verbs lead to incoherence. On our modified conceptions, they are only partially defined. 1 Chapter 1 Frege’s Puzzle and Its History 1.1 John Stuart Mill on Proper Names John Stuart Mill, in his a System of Logic 1 , espoused the view that a proper name like, “Elton” or “Dartmouth” has a denotation but no connotation. We can understand “denotation” to be roughly synonymous with “extension” or “referent” or “designation”; we can understand “connotation” to be roughly synonymous with “meaning” or “intension” or “sense”. Let us call this view, “Mills View”. Mill’s view about names is the view that a name is a meaningless, senseless, connotationless tag. A name is therefore unlike other expressions in our language. While other expressions in our language have a meaning or sense or connotation, a name only has a referent. Mill provided reasons for his view. Consider a locality in England named “Dartmouth”. Dartmouth is the locality in England that lies at the mouth of the river Dart. Naturally, one is tempted to conclude from this that the locality is properly called “Dartmouth” because it lies at the mouth of Dart. Mill very astutely observed that this is not so. He observed that even if the river had changed course, so that the locality no longer lay at the mouth of Dart, it could still properly, albeit misleadingly, bear the name, 1 Mill, John Stuart, A System of Logic, 1843 2 “Dartmouth”. This suggests that lying at the mouth of the river is not and was not a requirement for the locality to bear the name. Now, if lying at the mouth of Dart is not a requirement for the locality to properly be called “Dartmouth”, then, there could not have been a requirement for the locality to properly bear that name. There is no requirement or constraint on something’s properly bearing that name. This suggests that the name “Dartmouth” does not have a meaning. A meaning would put a constraint on a thing to properly bear the name. The term “physician” means a person licensed to practice medicine. So, in order for something to proper fall under its extension, that thing has to be a person licensed to practice medicine. Mill concluded from these considerations that a name like “Dartmouth” or “Elton”, unlike other expressions in our language, like “physician”, is a meaningless and connotationless tag with only a denotation or designation. 1.2 Frege/Russell Descriptivism Both Gottlob Frege (1892) 2 and Bertrand Russell (1905) 3 , despite Mill’s observations, believed that Mill’s View simply could not be correct. They rejected it for more or less 2 Frege, Gottlob, On Sense and Reference, reprinted in On Sense and Direct Reference, Davidson, Matthew, Mc-Graw-Hill, 2007. 3 Russell, Bertrand, On Denoting, reprinted in On Sense and Direct Reference, Davidson, Matthew, Mc- Graw-Hill, 2007 3 the same reasons, the central one being Frege’s Puzzle 4 . It is commonly thought that Frege’s Puzzle is one puzzle that manifests itself in various versions. And, the different versions are thought to be slight variations on each other. But, I do not believe that this is accurate. I believe that there are 3 different puzzles all identified as “Frege’s Puzzle”, each one presenting its own unique challenge to Mill’s View. Frege’s Puzzle 1 Consider 1a. Elton John is a musician 1b. Reginald Dwight is a musician 1a and 1b differ in their cognitive value. The cognitive value of an expression can be understood as that which every normal user of an expression grasps or cognizes when she grasps that expression. For a sentence like 1a or 1b, it is that part of it which a normal user cognizes and considers when considering whether to believe the sentence is true or false. To say that someone is a normal user of an expression is to say that that person takes the expression to mean what it in fact means. Take the expressions, “physician” and “medical doctor”. These expressions are perfectly synonymous. That is, they mean 4 A very important reason for Russell for rejecting Mill’s View was also the problem of true negative existentials. 4 exactly the same thing. So, one would expect a normal user of the two expressions to grasp or cognize the same thing when she grasps them. Insofar as they are synonymous, they have the same cognitive value. How do we judge whether 1a and 1b differ in cognitive value? That is, how do we judge whether some normal users of 1a and 1b cognize different things? To answer this, one needs to only ask whether a normal user of 1a and 1b can rationally believe that they differ in truth-value. A normal user can rationally believe that they differ in truth-value only if she cognizes different things when she cognizes the two sentences. We should agree that a normal user of those sentences can rationally believe that they differ in truth-value. If this is right, then, we seem compelled to conclude that the two sentences encode different propositions. What are propositions? We believe things, disbelieve things, doubt things, know things, asserting things, deny things, etc. Propositions are the things that we believe, disbelieve, doubt, etc.? Propositions are also what a normal user of a sentence cognizes or grasps when she grasps a sentence. If 1a and 1b encode different propositions, then, we can reasonably conclude that “Elton John” and “Reginald Dwight” differ in their propositional contributions or semantic contents. Since the two names are co-referential, the semantic contents of these names cannot just be their referents. The names must be contributing something more than just their referents to the propositions encoded by sentences that they are a part of. Contrary Mill’s view, this suggests that names are not mere connotationless tags with only a denotation or reference. The challenge presented by this puzzle for Mill’s view is this. Provide an accounting for how 1a and 1b can differ in cognitive value without positing a difference 5 in the propositions they encode. This is indeed a difficult challenge. Given the way we have defined, “cognitive value” and “normal user”, it is hard to see how 1a and 1b could possibly encode the same proposition given that they differ in cognitive value. Frege’s Puzzle 2 Consider 2a. Elton John is Elton John 2b. Elton John is Reginald Dwight 2a and 2b seem to clearly differ in their informational value. 2a seems to contain information which is trivial, knowable a priori and universally believed; 2b seems to contain information which is non-trivial, a posteriori and not universally believed. If we accept that the information contained in a sentence s is determined by the proposition encoded by s, then, 2a and 2b must encode different propositions. From this, it seems we must say that the names, “Elton John” and “Reginald Dwight” differ in their semantic contents. Since the names are co-referential, the semantic contents of these names cannot be their referent. This too suggests that Mill’s View cannot be correct. The challenge for Mill’s View posed by this puzzle is this. Provide an accounting of the difference in informational value between 2a and 2b without positing senses or connotations for names. 6 Frege’s Puzzle 3 Consider again 1a and 1b. Jones, who is a normal user of 1a and 1b, who is fully rational, has come to take himself to believe the proposition p, which he takes to be encoded by 1a, while also taking himself to not believe the proposition q which he takes to be encoded by 1b. If he takes himself to believe p then he believes it. Likewise, if he takes himself to not believe q, then, he does not believe it. So, he believes p and does not believe q. This means that 1a and 1b encode different propositions. So again, contrary Mill’s view, a names has to have some connotation or sense associated with it. The proponent of Mill’s View must block the conclusion that Jones believes the proposition encoded by 1a but does not believe the proposition encoded by 1b. So, the challenge here is to explain how Jones, who is a normal user of 1a and 1b and fully rational, takes himself to believe p but also takes himself to not believe q given that p = q. Notice that this challenge is different than the challenge posed the first puzzle. The challenge posed by the first puzzle is to provide an accounting for how it could be that 1a and 1b differ in cognitive value without positing a difference in the propositions they encode. Frege and Russell, though their views differed in important ways, provided more or less the same answers to these puzzles 5 . Reject Mill’s View. The challenges presented to Mill’s View by these puzzles simply cannot be met. Russell explicitly stated that an 5 For the purposes of my dissertation, the dispute between Frege and Russell over whether definite descriptions are singular terms or quantificational phrases is not important. Nothing I aim to do rides on it. 7 ordinary proper name like “Elton John” was an abbreviation for some definition description, e.g., “the famous songwriter who wrote Candle in the Wind” 6 . Ordinary names were merely disguised or abbreviated descriptions. The idea here is not implausible. Take the term, “physician”. It appears to be a simple term. But, very plausibly, it is really an abbreviation for, “a person licensed to practice medicine”. That explains why a simple term and a description are perfectly synonymous, i.e., have the same semantic content. In the same way, “Elton John”, like the description it is an abbreviation for, means something like the famous songwriter who wrote Candle in the Wind. Contrary Mill’s View, names are not unique. They have senses or meanings just like all other expressions. “Reginald Dwight” is an abbreviation for a different description, perhaps, “my unassuming next door neighbor”. So, ordinary names have senses or descriptive meanings. The reason 1a and 1b differ in cognitive value is that the names differ in cognitive value. And, this is accounted for in terms of the difference in meaning or sense. Though “Elton John” and “Reginald Dwight” have the same referent, they encode different meanings or senses or connotations. Appealing to different meanings or senses very elegantly solves the other two puzzles as well. Frege shared Russell’s vision for dealing with the puzzles. Though he did not explicitly state that names are abbreviated descriptions, his examples suggest that he believed that the sense of a name like “Elton John” was the same as the sense of some description. Let us call the view that a name is synonymous with some definite 6 Russell, Bertrand, Knowledge by Acquaintance and Knowledge by Description (1917), in Mysticism and Logic, paperback edition. Garden City, NY: Doubleday, 1957 8 description, “The Frege-Russell view”. The Frege-Russell view deals with the 3 puzzles simply and elegantly. 1.3 Kripke The Frege-Russell view of names, mainly because of Frege’s Puzzle, became the accepted view. But, all of that changed with Naming and Necessity (1980), the book based on the transcripts of 3 lectures at Princeton University delivered in 1970 by Saul Kripke. In that book and in those lectures, Kripke offered 3 decisive arguments against the Frege-Russell view of names—the Modal argument, the Epistemic Argument and the Semantic Argument. Modal Argument The modal argument against the Frege-Russell View is that a name is a rigid designator and therefore cannot have as its semantic content some descriptive sense. What is a rigid designator? The idea is simple. Let us take the name, “Elton John”. It refers to or designates Elton John. The idea is that if the name, a designator, designates Elton John at all, it designates him no matter what Elton John is like. Once the name locks onto its designation, it remains locked in. That is, the designation is “rigid”. It is true that Elton John is a famous musician. But, that has nothing to do with why the name designates him. If Elton John had gone into law and had become a lawyer, the name would still 9 have designated him. If he had been a hair stylist instead of a musician, same thing would be true. The designator “Elton John” is locked onto Elton John. A precise and somewhat technical definition for a rigid designator is this. A term or designator t designates an object o rigidly iff t designates o in every possible world in which o exists and never designates anything else. We can understand a possible world as a way the world could have been. There are as many possible worlds as there are ways the world could have been. In any way the world would have been and any properties Elton John would have had, “Elton John” would designate him (when used by us here and now talking about that world-state). Contrast the designator “Elton John” with the designator “The author of a Candle in the Wind”. The latter designator is not rigid. It designates Elton John, but only because he happens to be the author of the song. If Elton John had been a lawyer and never authored the song, the designator would not have designated him. Kripke concluded that since the designator “Elton John” is rigid but the designator “The author of a Candle in the Wind” is not, contrary the Frege-Russell View, the name and the description cannot be synonymous. Epistemic Argument If the name “Elton John” were synonymous with the description, “The famous musician who wrote Candle in the Wind”, then, 3a and 3b would encode the same proposition. 10 3a. Elton John wrote Candle in the Wind if there is a unique famous musician who wrote the song. 3b. The famous musician who wrote Candle in the Wind wrote Candle in the Wind if there is a unique famous musician who wrote the song. If they encoded the same proposition, then, one of them would be a priori iff the other was. But, they differ in epistemic (a priori/ a posteriori) status. 3b is clearly a priori. Of course the person who wrote the song wrote the song. We do not need any empirical evidence to figure that one out. In contrast, 3a is not a priori. There is no way to figure out which particular person wrote the song without some empirical information. In order to know that Elton John wrote the song, I need some empirical information which confirms that he did. For instance, I need to read the back cover of a compact disc and see that the song is credited to him. From this we can conclude that 3a and 3b encode different propositions. This too confirms that, contrary The Frege-Russell View, the meaning of a name is the not same as the meaning of some description. Semantic Argument If the name “Elton John” and the description, “The famous Musician who wrote ‘Candle in the Wind’” were synonymous, then, if it turned out that Elton John did not write the song, then, the name “Elton John” would not refer to him. Suppose it turned out, unbeknownst to the general public, that Billy Joel wrote the song instead. We would then 11 say that the description designates Bill Joel and not Elton John. Billy Joel is the one that really wrote the song. We believed all along that the description designated Elton John. But, we were just wrong about this. The description designates whoever was the famous musician who wrote the song. In contrast, even if it turned out that Billy Joel was the author of the song, we are inclined to say that “Elton John” still designates Elton John and not Billy Joel. This too suggest, contrary the Frege-Russell View, that names are not synonymous with descriptions. As I mentioned earlier, I believe these Kripke arguments against the Frege- Russell View are decisive. But that leaves us in a really tough spot. Without the Frege- Russell View, there seems to be no way to deal with Frege’s Puzzle. 1.4 Neo-Millianism Kripke’s arguments against the Frege-Russell view have sparked a revival of Mill’s View. Neo-Millianism or just “Millianism” is the view that names are directly referential. A term is directly referential iff its semantic content is just its referent. If names are rigid designators and there are no descriptive senses associated with them, then, a reasonable conclusion is that names are directly referential. Kripke’s arguments and conclusions seem to strongly suggest Millianism. It is true that we are then faced anew with Frege’s Puzzle. But, neo-Millians feel confident that they can meet the challenges of the puzzle. 12 In subsequent chapters, I examine responses given by 3 prominent Millians, Kit Fine (2007) 7 , Nathan Salmon (1986) 8 and Scott Soames (2002) 9 to the puzzles. However, as I see it, none of their responses is completely satisfactory. There are various reasons for this. But, the main reason is that the 3 puzzles present 3 distinct challenges to the Millian each calling out for a unique answer. No single answer can adequately deal with all 3 puzzles. Kit Fine and String Semantics Fine proposes to resolve the puzzle by appealing to a new kind of semantics, what I identify as, “String Semantics”. A semantic theory tells us what kind of meanings the simple expressions of a language have and provides rules for calculating the meanings of the complex expressions out of which the simple expressions are constructed. For instance, one semantic theory will tell us that the meaning of a general term like “physician” is a function from world states to sets; another theory tell us that the meaning of the term is a property, etc. A semantic theory will also tells us how to calculate the meaning of sentences like 2a and 2b in terms of the expressions that make up those sentences and their syntax. Without getting into too much detail, according to String 7 Fine, Kit, Semantic Relationism, Blackwell, 2007 8 Salmon, Nathan, Frege’s Puzzle, Ridgeview, Atascadero, California, 1986 9 Soames, Scott, Beyond Rigidity: The Unfinished Semantic Agenda of 'Naming and Necessity, Oxford, 2002 13 Semantics, propositions encoded by sentences like 2a, with two or more occurrence of the same term are what Fine calls, “coordinated”. Here is how it works. Assuming Millianism, given 2a’s syntax, it encodes the proposition that Elton John and Elton John stand in the identity relation to one another. This suggests that the proposition is the ordered pair of the ordered pair of EJ, EJ, and the identity relation. However, that is not the whole story. Since 2a has two occurrences of the same term, the members of the ordered pair EJ, EJ stand in the coordination relation. String Semantics represents this fact by assigning a string that attaches these members. So, we represent the proposition as, <<EJ---EJ>, =>. In contrast, since 2b does not have two occurrences of the same term, the proposition it encodes lacks coordination and so no string gets assigned to it. 2a encodes, <<EJ, EJ> =>. The main selling point of String Semantics is that it yields a difference in the propositions encoded by 2a and 2b without rejecting Millianism. It looks like it can accommodate the difference in informational value between 2a and 2b while maintaining Millianism. Frege’s Puzzle 2 solved. Alas, I do not believe that moving to String Semantics provides an adequate Millian response to any of the 3 puzzles. It is not designed to even address puzzles 1 and 3. Neither 1a nor 1b has more than one occurrence of the same term. Plus, as I argue in chapter 3, String Semantics does not even adequately address puzzle 2, the puzzle it is custom tailored to address. 14 Nathan Salmon and Guises In dealing with Frege’s puzzle, Salmon appeals to the notion of a guise. The person Elton John appears to Jones under two distinct guises. The term “guise” comes from the term “disguise”. Elton John appears to Jones as a musician, songwriter, performer, the person named “Elton John”, etc. This is one guise under which Elton John appears to Jones. He also appears to Jones as his neighbor, loner, the person named “Reginald Dwight”, etc. This is a different guise under which Elton John appears to Jones. Jones does not recognize that the person(s) that appears to him under these two guises same person. Jones, through a failure of identification, believes that the guy named “Elton John” and the guy named “Reginald Dwight” are different guys. He takes the first guy to be a musician but does not take the other guy to be one; he takes the first to be famous, the second guy not, etc. Salmon’s appeal to guises provides a fully adequate solution to the third puzzle. The reason Jones take himself to believe the p he takes to be encoded by 1a but does not take himself to believe the q he takes to be encoded by 1b is that Elton John appears to him under different guises. When Elton John appears to Jones under one guise, Jones takes himself to believe that he is a musician; under a different guise, Jones takes himself to not believe he is a musician. However, in chapter 2, I argue that Salmon’s appeal to guises does not do so well with respect to puzzle 1. The challenge posed by the puzzle 1 is how 1a and 1b could differ in cognitive value if 1a and 1b are supposed to encode the same proposition. In chapter 2, I argue that the answer to this challenge is that there are 15 two conceptions of “cognitive value”. On one conception, if 1a and 1b differ in cognitive value, they encode different propositions. But, on a different conception, even if 1a and 1b differ in cognitive value, they can still encode the same proposition. The challenge posed by this puzzle can be met without appealing to guises. In chapter 4, I argue that Salmon’s framework does not do so well with the second puzzle either. The challenge presented by the second puzzle is how it can be that 2a and 2b differ in information value given Millianism. Roughly, Salmon’s answer is that though 2a and 2b encode the same a priori proposition, this proposition is presented under different guises. An important idea for Salmon is that propositions, like objects, appear to agents under different guises. Since singular propositions or object-containing propositions are constructed out of objects and objects appear under guises, singular propositions appear under different guises. Salmon’s idea then is that the proposition encoded by 2a and 2b are presented to agents under the following guises. It is presented as the proposition encoded by 2a; it also presented as the proposition encoded by 2b. When this a priori proposition appears as the proposition encoded by 2a, its a priori status is obvious. When this same proposition appears as the proposition encoded by 2b, its a priori status is not obvious. This is what explains the apparent difference in informational value between the two sentences. I do not think that Salmon’s appeal to guises to explain away the apparent difference in informational value between 2a and 2b is plausible. In chapter 4, I argue that 2a and 2b indeed differ in informational value. In that chapter, I argue that the 16 Millian can and should accommodate the clear intuition that 2a and 2b differ in informational value. Scott Soames and Pragmatic Enrichment Soames makes a distinction between what he calls, “bare singular propositions” and what he calls, “pragmatically enriched singular propositions”. Let us say that Jones and Smith are conversational participants and share beliefs about the man they both refer to as, “Elton John”. They both believe that he is famous, extremely talented, “original”, stylish, a musician, etc. They also happen to share beliefs about the man they both refer to as, “Reginald Dwight”. They believe that he is dull, Jones’s next door neighbor, a hermit, etc. Soames’s idea is with these shared beliefs in place, when Jones assertively utters 2b, in addition to asserting the proposition semantically encoded by 2b or the bare singular proposition that Elton John stands in identity to Reginald Dwight, he also asserts the pragmatically enriched proposition that Elton John, the famous and talented musician is identical to Reginald Dwight, my boring next door neighbor. Given his adherence to Millianism, Soames accepts that “Elton John” and “Reginald Dwight” have the same semantic content. But, they differ in their pragmatic potential. The exact same thing is true for 2a and 2b. Soames, like Salmon, holds that the proposition semantically encoded by 2a and 2b is a priori. Thus, 2a and 2b do not differ in informational value. The reason it seems 17 that they do is accounted for in terms of the difference in pragmatic potential between 2a and 2b. In chapter 4, I argue against the Salmon and Soames position that 2a and 2b do not differ informational value. I also argue that Soames’s apparatus is inadequate to address puzzle 1 or puzzle 3. As I see it, the problem with each neo-Millian attempt to resolve the puzzles hitherto is that each attempt is an attempt to resolve all 3 puzzles with a single framework. No single framework can meet the challenges of all 3 puzzles. This fact alone justifies my dissertation. In my dissertation, for each puzzle, I provide a framework custom made to answer the challenge presented by that puzzle. In constructing each framework, appropriate lessons are drawn. 18 Chapter 2 Frege’s Puzzle and Two Conceptions of Cognitive Significance In this chapter, I argue that the main lesson of Frege’s Puzzle is that there are two conceptions of what Frege calls “erkenntniswerte” or “cognitive significance” or “CS”. The CS of a meaningful expression e is supposed to be that which every normal user “grasps” when she grasps e. If what I argue is correct, then, at least some meaningful expressions have two CS’s not one. As I see it, the reason Frege’s Puzzle has been so intractable is ultimately due to a failure to notice this fact. The argumentative strategy is the following. In part I, I argue that Frege’s Puzzle decisively shows that Millianism is false if there is only one conception of CS. In part II, I define “transparency” and argue that there are two different kinds of terms—transparent and non-transparent. In part III, I argue that if some terms are non-transparent, then, there must be two conceptions of CS. In part IV, I define the two conceptions of CS. In part V, I employ the two conceptions of CS to show that Frege’s Puzzle does not militate against Millianism in the least. 19 2.1 Millianism and Two Conceptions of Cognitive Significance. Let us start with Frege’s Puzzle. Consider 1a. Hesperus is a planet 1b. Phosphorus is a planet Here are some claims: Claim1: 1a and 1b differ in CS (Cognitive Datum). Claim2: For any two expressions e and e*, if e and e* differ in CS then e and e* differ in meaning (Frege’s Principle). Claim3: If 1a and 1b differ in meaning then “Hesperus” and “Phosphorus” differ in meaning (Compositionality). Claim4: For any two proper names n and n*, if n and n* differ in meaning then n and n* differ in reference (Corollary to Millianism) Claim5: “Hesperus” and “Phosphorus” are not co-referential (1-4) Claim6: “Hesperus” and “Phosphorus” are co-referential (empirical premise) Claims 5 and 6 are inconsistent. Claim 6 is an empirical premise which we know to be true. Claim 5 simply follows from claims 1-4, so at least one of them must be false. Claim 4 is a corollary to Millianism, so, if we cannot resist at least one of the first 3 claims, then, Millianism is false. Resisting claim 3 is not a viable option. Surely, if 1a and 1b differ in meaning, the difference must be due to a difference in meaning between the subject terms “Hesperus” and “Phosphorus”. 1a and 1b share the same predicate, and they have the 20 same syntax and the same form. The syntax for both is NP, intransitive verb. They both have the form Fa. So, by any reasonable principle of compositionality, if “Hesperus” and “Phosphorus” have the same semantic content, then, 1a and 1b encode the same proposition. If we accept any reasonable principle of compositionality, then, we must accept claim 3. The Millian is really down to two options—resist claim 1 or resist claim 2. Let us consider claim1. There are two tests by which we can determine whether or not two expressions have the same CS. The first test let us call, “Cognitive Significance Test1” or “CST1” CST1: For any two sentences s and s*, s and s* differ in CS iff a normal user A of s and s* can take herself to believe this: the unique thing encoded by s is true, while also taking herself to not believe this: the unique thing encoded by s* is true. Let us say that a speaker A is a normal user of an expression e iff A takes e to semantically encode what e in fact semantically encodes. The idea behind CST1 is this. If sentence s encodes proposition p and s* encodes q, then, a normal user A of s and s* will take s to encode p and s* to encode q. And, A can rationally take herself to believe p while taking herself to not believe q iff p and q do not represent the same fact. So then, A can rationally take herself to believe “the thing uniquely encoded by s is true” while also taking herself to not believe “the thing uniquely encoded by s* is true” iff s and s* encode propositions that differ in their representational content. If the CS of an 21 expression e is e’s representational content, then, CST1 will tell us whether or not two expressions have the same CS. Let us call the second test for determining sameness of CS, “CST2”. CST2: For any two sentences s and s*, s and s* have the same CS iff s and s* have the same representational or informational content. If there is an independent means of determining whether or not two expressions have the same representational content, then, we can employ CST2. We know that “doctor” and “physician” both mean, a person licensed to practice medicine. They are perfectly synonymous. Since the representational content of an expression e supervenes on e’s semantic content, the two terms have the same representational content. Thus, by CST2, we know that they have the same CS. Careful reflection on the two tests suggests that they are equivalent. That is, for any s and s*, a normal user A of s and s* can rationally take herself to believe “the unique thing encoded by s is true” while also taking herself to not believe “the unique thing encoded by s* is true” iff s and s* differ in their representational content. To confirm this, consider 2a. Every medical doctor has a license to practice medicine 2b. Every physician has a license to practice medicine 22 Notice that Jones, who is a normal user of both 2a and 2b, cannot rationally take himself to believe “the unique thing encoded by 2a is true” while also taking himself to not believe “the unique thing encoded by 2b is true”. Of course, it can happen that he is not sure that he is a normal user of at least one of them. So, he could suspend judgment about whether 2a and 2b have to be co-extensional 10 . But, that is not a case in which he takes himself to believe “the unique thing encoded by 2a is true”, while taking himself to not believe “the unique thing encoded by 2b is true”. That is a case in which he suspends judgment. The reason Jones cannot rationally take these contrary attitudes towards 2a and 2b must be that he grasps the same thing when he grasps 2a as when he grasps 2b. The terms, “medical doctor” and “physician” are perfectly synonymous, both meaning, a person licensed to practice medicine 11 . Thus, by CST1, 2a and 2b have the same CS. And, since we know that they have the same representational content on independent grounds, they have the same CS according to CST2 as well. The important thing to notice here is that they have the same CS according to both tests for the same reason—they are synonymous and therefore have the same representational content. It would be question begging against Millianism to simply posit that 1a and 1b differ in their representational content. So, we cannot appeal to CST2 to determine 10 It is important to rule out these kinds of cases because of an example due to Stephen Rieber. Rieber imagines someone who is a normal user of the synonymous pair of words, “bet” and “wager” but does not take himself to believe that they are synonymous. The reason is that the person is not confident that he is a normal user of both. So, he is reluctant to take himself to believe it. Rieber, Stephen, Understanding Synonyms without Knowing that they are Synonymous, Analysis, 1992. 11 This definition comes from dictionary.com. 23 whether 1a and 1b have the same CS. That is precisely what is at issue. However, we can, without question begging, appeal to CST1. Let us consider Datum2. Datum2: It is possible for a normal user of 1a and 1b to rationally take herself to believe “the unique thing encoded by 1a is true”, while taking herself to not believe “”the unique thing encoded by 1b is true”. The Millian must concede Datum2. And, by Datum2 and CST1, 1a and 1b differ in CS. I do not see any way the Millians can resist this. Thus, Millians cannot resist claim 1. What about claim 2? If CST1 and CST2 are equivalent, then, claim 2 follows. If by CST1, they differ in CS, then, by CST2, they differ in representational content. If they differ in representational content, then, 2a and 2b encode different propositions. It is hard to see how Millians can resist claim 2. Thus, Millianism is false if CST1 and CST2 are equivalent, and there is only one conception of CS. 2.2 Transparent Terms versus Non-Transparent Terms Let us begin with the definition of “transparency”. Definition of transparency: For any expression e, e is transparent iff for any e*, if e and e* are synonymous then it is not possible for a normal user A of e and e*, who is confident that she is a normal user of both and who is not apprehensive, to rationally withhold judgment about whether e and e* are synonymous. 24 To say that A is confident that he is a normal user of e is to say that he has no doubts that he is. To say that A is not apprehensive is to say that A does not withhold making a judgment about whether e and e* are synonymous because of extreme caution. Consider again the synonymous pair of words, “doctor” and “physician”. Can Jones withhold judgment about whether they are synonymous? In order to rationally withhold judgment, he needs some reason for withholding. There are 3 potential reasons. The first is that he is extremely cautious. No matter how justified he is in making a judgment, he will not do it. Why? He is crippled by extreme caution. We might say that he is unreasonably cautious. So, perhaps, in some sense, he is irrational. But, perhaps, he is not. Perhaps, being wrong with one of his judgments is something he wishes to avoid at any cost. He would rather forgo 1000 opportunities to be right than risk being wrong even once. So, he is rarely right. But, he is even more rarely wrong. This is no way to live, but it is not immediately clear that that is in any way irrational. Let us stipulate that Jones is not apprehensive in this way. The second potential reason for witholding judgment is that he is not confident that he is a normal user. He is not in any way apprehensive, but he does not like to go too far out on a limb either. He will make a firm judgment about things so long as there are no good reasons to doubt it. Perhaps, he doubts that he is a normal user of “physician”. On many occasions he thought that he was a normal user of a term but then later found out that he was not. He worries that “physician” is not perfectly synonymous with “medical doctor”, but he cannot see that because he is not a normal user. Let us stipulate 25 that Jones is confident that he is a normal user of both terms. So, we do not have to worry about him having these kinds of doubts. The third reason is that he sees some difference in meaning between the two terms. If he is not apprehensive and he is confident that he is a normal user of both, then, in order to rationally withhold judgment, he must see some difference in their meaning. The reason for this is that “doctor” and “physician” are non-Twin Earthable. “Medical doctor” means the same here on Earth as it does on Twin Earth. That is, its meaning is unaffected by changes in non-linguistic external facts in the environment. Given that Earth and Twin-Earth differ only in non-linguistic external facts, “medical doctor” as used on Earth and “medical doctor” as used on Twin Earth are synonymous. “Medical doctor”, as used on Earth, means, a person licensed to practice medicine; “medical doctor”, as used on Twin Earth, also means, a person licensed to practice medicine. The same goes for “physician”. Thus, in order for him to be justified in suspending judgment about whether “doctor” and “physician” are synonymous, he must notice a difference in meaning. But, that is ruled out if we stipulate that he is a normal user of both. For these reasons, given our definition of “transparency”, “doctor” and “physician” are transparent. They are “transparent” in that anyone who meets all the relevant conditions is in position to see and judge that they are synonymous. There are many terms that are transparent in this sense, e.g., “bet”/”wager”, “bachelor”/”unmarried man”, “cordate”/”creature with a heart”, etc. However, there are also many that are non-transparent. A term t is non-transparent iff t is not transparent. 26 Examples include “water”/”agua”, “London”/”Londres”, “ketchup”/ “catsup”, etc. Consider Nathan Salmon’s example of foreign born Sasha. Suppose that foreign-born Sasha learns the words “ketchup” and “catsup” not by being taught that they are perfect synonyms, but by actually consuming the condiment and reading the labels on the bottles. Suppose further that, in Sasha’s idiosyncratic experience, people typically have the condiment called “catsup” with their eggs and hash brown for breakfast, whereas they routinely have the condiment called “ketchup” with their hamburgers at lunch. This naturally leads Sasha to conclude, erroneously, ketchup and catsup are different condiments that happen to share a similar taste, color, consistency, and name. He thinks to himself, “ketchup is a sandwich condiment, but no one in his right mind would eat a sandwich condiment with eggs at breakfast; so catsup is not a sandwich condiment 12 . We should expect that Sasha will assent to 3a but dissent from 3b. 3a. Ketchup is a sandwich condiment 3b. Catsup is a sandwich condiment Does Sasha’s pattern of assent and dissent show that he is irrational or that he is not a normal user of 3a and 3b? The answer here must be “no”. He is a normal user of “ketchup” in that he takes it to mean ketchup. The same goes for “catsup”. He thinks that catsup happens to look, taste, feel, etc. like ketchup, but is different. He thinks that 12 Salmon, How to become a Millian Heir, Nous, p. 216, 1989 27 perhaps, there is a difference between the two kinds of stuff that he simply cannot detect. Perhaps the stuff he calls “ketchup” is tomato based while the stuff he calls “catsup” is twin-tomato based. Tomatoes and twin-tomatoes are qualitative identical but different vegetables (or fruits?). “Ketchup” and “catsup” are Twin-Earthable in this way. Thus, even if Sasha is a normal user of both terms and he is confident that he is and he is not in any way apprehensive, he can rationally take himself to believe what he takes to be encoded by 3a while taking himself to not believe what he takes to be encoded by 3b. Thus, “ketchup” and “catsup” are non-transparent. Thus, there are two kinds of terms—transparent and non-transparent. 2.3 Non-Transparency and Two Conceptions of Cognitive Significance By CST1, 3a and 3b differ in CS. 3a and 3b are synonymous, thus, by CST2 3a and 3b do not differ in CS. Thus, there must be two conceptions of CS. The simple terms “ketchup” and “catsup” differ in CS in that a normal user of both can take herself to believe that they differ extensionally. Thus, CST1 and CST2 are not equivalent tests. The reason we thought they were is that there are many terms which are transparent, and we generalized from this and concluded that all terms are transparent. The generalization is faulty. Let us call the following seductive but faulty underlying principle, “The Transparency Principle”. 28 The Transparency Principle or TP: For any two propositions p and q, if p and q are the same or have the same representational content, then, an agent can see this simply in virtue of grasping them. If TP were true, then, for any two expressions e and e*, e and e* would have had the same CS according to CST1 iff they have had the same CS according to CST2. But, TP is false. That is why the two tests give us conflicting results about “ketchup” and “catsup”. Since some expressions like “ketchup” and “catsup” are non-transparent, there must be two senses of “CS”. 2.4 Defining the Two Conceptions of Cognitive Significance Here I provide definitions for the two conceptions of CS. Let us call the conception that corresponds with CST2, “Cognitive Significance Information” or “CSI”. Let us call the conception that corresponds with CST1, “Cognitive Significance Mode of Presentation” or “CSM”. Let us begin with CSI. Definition of CSI In determining whether I take myself to believe that a sentence s is true, I first determine whether I take myself to believe the information I take to be encoded in s. If I do, then, I take myself to believe that s is true. The information encoded in s is the primary thing that I grasp when I understand s. Also, s is true but only insofar as the information 29 encoded by s is true; s is a priori but only insofar as the information encoded by s is a priori; s is necessary but only insofar as the information encoded by s is necessary. The CS of a sentence s is s’s “knowledge-worth” or the information or representational content semantically encoded in it. Here then is the first attempt at defining CSI. Definition #1 of CSI: the CSI of a sentence s is the proposition encoded by s Definition #1 seems like a reasonable proposal for defining CSI. But, Salmon has given reasons to think that definition#1 of CSI is unsatisfactory 13 . The main reason has to do with something first noticed by Ali Kazmi 14 . Consider two ways of formulating Church’s theorem: CT-formulation#1: First order logic is undecidable CT-formulation#2: It is not the case that first order logic is decidable Frege was of the opinion that thoughts or propositions were individuated compositionally. A proposition or the sense of a sentence, like any complex sense, is determined and composed out of the senses of the constituents of the sentence which encodes it and the manner in which the constituents are composed. But then, the proposition encoded by CT-form #1 and that of CT-form #2 are distinct. CT-form #1 and 13 Salmon, On Content, Mind, Vol.101, No.404, (Oct., 1992), 733-751 14 Kazmi, Ali, Reference, Structure and Content, unpublished comments on Richard, Mark, Propositional Attitudes: An Essay on Thoughts and How We Ascribe Them, Cambridge Press, 1990. (Kazmi’s comments were delivered to a symposium of the American Philosophical Association). 30 CT-form #2 differ in their constituents. For one, the second formulation has negation while the first does not. Therefore, on this very fine-grained way of individuating propositions, the propositions semantically encoded by these different formulations are distinct. Thus, by definition #1, CT-form #1 and CT-form #2 differ in CSI. Yet, this does not seem right. The proposition encoded by CT-form #1 and the proposition encoded by CT-form #2 are such that one is true, a priori iff the other is and one is believed by Jones iff the other is and they are co-intensional. The reason is that the propositions have something in common—their information content. They represent the same fact. Thus, a single fact makes them both true. Just as sentences have propositions semantically encoded in them, propositions have information contents encoded in them. And, the information content(s) encoded in the two propositions are identical. The suggestion then is that though the two propositions are distinct, they have the same CSI. There are plenty more examples of this sort. Murphy’s Law has many formulations. Here are 3: MLformulation#1: whatever can go wrong will go wrong. MLformulation#2: whatever might not go right will not go right. MLformulation#3: whatever does not go wrong cannot go wrong. From a compositional standpoint, each of these four formulations encodes a distinct proposition. The first formulation is about things going wrong; the second has nothing to do with things going wrong. Rather, it is about things not going right. The third has 31 negation and the concept of something going wrong. Salmon justifiably worries that if we carve things up strictly in terms of propositions then we will be carving too finely. The crucial fact to notice here is that each formulation essentially says the same thing. That is, they contain the same information content. Thus, if an agent believes one then she believes them all. To believe one of them is to believe them all. Whatever fact about the world makes one of these true, makes them all true; whatever fact makes one of these a priori makes all of them a priori, whatever makes one true at an arbitrary world w makes them all true at w, etc. Further examples are Gödel’s incompleteness theorem, the Heisenberg uncertainty principle, Leibniz’s law, Goldbach’s conjecture, dualism, logicism, behaviorism, functionalism, theism, atheism, etc. There are many formulations of Gödel’s incompleteness theorem, but there is only one theorem. There are many formulations of Leibniz’s law, but there is only one law, etc. Here is the Salmon proposal for defining CSI 15 . Definition#2 of CSI for sentences: The CSI of a sentence S = the informational or representational content encoded by the proposition encoded by S 16 Definition of CSI for expressions: The CSI of an expression e = the informational content encoded by the semantic content of e. 15 Of course, Salmon does not put things in terms of defining CSI. He does not make a distinction between the two notions of cognitive significance. Salmon sees himself as just defining “cognitive significance” simpliciter. 16 I believe that instead of propositions, we should think of CSI’s as the primary objects of the attitudes. 32 Definition#2 is the one we want. Given this definition of CSI, we can see the sense in which CSP2 and claim 2 are true. CSP2 is true as a matter of definition. As for claim 2, two expressions can differ in their semantic contents without differing in their information content but not the other way around. If two expressions e and e* differ in their informational content then e and e* differ in semantic content. Let us add that this definition of CSI goes for both transparent and non- transparent terms. For any expressions e and e*, e and e* have the same CSI iff e and e* represent the same fact. Definition of CSM Though a single definition of CSI is enough for both transparent and non-transparent terms, two different definitions of CSM are needed. The definition of CSM for transparent terms is different from the definition of CSM for non-transparent terms. Definition of CSM for transparent terms: For reasons already given, we know that CST1 and CST2 are equivalent for transparent terms. Thus, we need only a single definition of CS for transparent terms. The CSM of a transparent term t = t’s CSI. 33 Definition of CSM for non-transparent terms: We know that “ketchup” and “catsup” have the same CSI. But, they differ in CSM. Thus, the definition of CSM for a non-transparent term cannot be its CSI. So then, what is it? Well, here is something everyone seems to notice. Any two simple non-transparent terms t and t* differ in CSM iff t and t* are distinct. The pair of terms “ketchup” and “catsup” differ in CSM in that they are distinct terms. These terms differ in CSM but two occurrences of “ketchup” do not differ in CSM. Free occurrences of “x” and “y” differ in CSM even when they are assigned the same object, but two occurrences of “x” have the same CSM. The names “Hesperus” and “Phosphorus” differ in CSM but two occurrence of “Hesperus” have the same CSM. Notice an important difference between transparent and non-transparent terms. Consider 4a. Ketchup is a condiment 4b. Catsup is a condiment 4c. Ketchup is not a condiment Notice that Jones, a normal user of 4a – 4c, can rationally take himself to believe that 4b and 4c are both true. However, insofar as he recognizes that the occurrence of “ketchup” in 4a and the occurrence of it in 4c are merely different occurrences of the same term, he cannot rationally take himself to believe that 4a and 4c are both true. Though 4a and 4b 34 have the same CSI, the fact that 4a has an occurrence of “ketchup” while 4b has an occurrence of “catsup” means that they differ in CSM. In contrast, consider 5a. All medical doctors are wealthy 5b. All physicians are wealthy 5c. Some doctors are not wealthy Just as Jones, who is a normal user of “medical doctor” and “physician”, cannot rationally take himself to believe that 5a and 5c are both true, he cannot rationally take himself to believe that 5b and 5c are both true. So, the fact that “doctor” and “physician” are different terms makes no difference in terms of CSM. The pair “doctor” and “physician” have the same CSM in just the way two occurrences of “doctor” do. Is there a semantic difference between “ketchup” and “catsup” which explains the difference in CSM? The answer is “yes”. Any two distinct terms, transparent or non- transparent, differ in logical content. The logical content of a variable can be thought of a function from assignments to values. So, the variables “x” and “y” differ in their logical contents. But, two occurrences of “x” have the same logical content. The logical content of a name is a function from model structures to values. So, “Hesperus” and “Phosphorus” differ in their logical contents even though two occurrences of “Hesperus” do not. If we think of general terms as predicates, then, the logical content of a general 35 term like “ketchup” is a function from model structures to functions from objects to truth- values. The same goes for “doctor”. My suggestion then is that while the CSM of a transparent term like “doctor” is its CSI, the CSM of a non-transparent term like “ketchup” is its logical content. Here then is the definition of CSM for non-transparent terms. Definition of CSM for non-transparent terms: the CSM of a non-transparent term t = def. t's logical content. Here is one way of thinking about the difference between what a normal user does when she understands a set of transparent terms versus what she does when she understands a set of non-transparent terms. When a normal user A considers any term t, transparent or non-transparent, the first thing A considers is t’s CSI. She goes “straight for the CSI”, so to speak. And, when it comes to transparent terms like “doctor” and “physician”, grasping the CSI is good enough. Understanding the CSI is enough to settle whether the CSI’s are the same or not. The reason is that the CSI’s are transparent. The fact that the terms differ in their logical content makes no difference in terms of CSM. This suggests that a normal user of 2a, when determining its extension, [needs to] grasp(s) only one thing when she grasps it—its CSI. When it comes to two occurrences of a non-transparent term like “ketchup”, since their CSI is non-transparent, a normal user A, wanting to properly judge whether they have the CSI or not, shifts her attention from their CSI, to their logical content. In other 36 words, since their CSI does not provide enough guidance to properly judge whether they are the same or not, after initially going for their CSI, A turns to their logical content for guidance. In this case, since the logical content of the two occurrences are the same, A is able to properly judge that they must be synonymous and co-extensional. This explains why two occurrences of “ketchup” have the same CSM but “ketchup” and “catsup” do not. If two non-transparent terms have the same CSI but differ in logical content, then, without more (empirical) information 17 , A cannot properly judge that they are synonymous and co-extensional. This is the sense in which a speaker grasps two different things when she is determining whether 3a and 3b have to be co- extensional—their CSI and their logical content. Though they have the same CSI, because they differ in logical content, they differ in CSM. 2.5 Solution to Frege’s Puzzle We are now ready to solve Frege's Puzzle. Claim 1 is CSM true. 1a and 1b do differ in CSM. And, Claim 2 is CSI true. If two expression e and e* differ in CSI then e and e* differ in their semantic contents. These are things the Millian can readily admit. However, there is no sense of CS whereby they are both true. Insofar as Millianism is true, claim 1, though CSM true, is CSI false. At the very least, to posit that claim 1 is CSI true is to beg the question against the Millian. Claim 2, though CSI true, is CSM false. Thus, there is no single sense of “CS” whereby the Millian has to accept both 17 In my chapter 4, I argue that the extra information needed here is empirical. 37 claims 1 and 2. If all of this is right, then, Frege’s Puzzle does not militate against Millianism in the least. Frege’s Puzzle has been a particularly intractable puzzle. The reason is that there is something right in the thought that since 1a and 1b differ in CS, they must differ in meaning. When it comes to any two transparent terms t and t*, t and t* have the same CS iff t and t* have the same CSI. And, if some terms are transparent, then, it is very natural to think that all terms are transparent. Therefore it is very tempting to think that Frege’s Puzzle decisively shows that Millianism is false. If all terms were transparent and there was only one conception of CS, then, Frege’s Puzzle would show that Millianism is false. 38 Chapter 3 How to Become a Relationist: String Semantics versus Collapse Semantics The question I am interested in answering in this chapter is how one should become a “Relationist”. To be a Relationist is to subscribe to a principle of compositionality, first introduced by Hilary Putnam 18 , we will identify as, “Relational Compositionality”. Compare Relational Compositionality with what we will call, “Standard Compositionality”. Standard Compositionality: There are 2 factors that determine the proposition p encoded by a sentence S relative to a context C and assignment A—S’s syntax and semantic contents of S’s constituents relative to A and C. Relational Compositionality: The are 3 factors that determine the proposition p encoded by a sentence S relative to a context C and assignment A—S’s syntax, the semantic contents of S’s constituents relative to A and C and whether or not S has more than one occurrence of the same term. The central motivation for favoring Relational Compositionality over Standard Compositionality is Frege’s Puzzle. Consider 18 Putnam, Hilary, Synonymity and the Analysis of Belief Sentences, Analysis, 1954 39 1a. Elton John is Elton John 1b. Elton John is Reginald Dwight 1a and 1b seem to clearly differ in their informational value. While the former is a trivial and a priori, the latter is non-trivial and a posteriori. So, they must encode different propositions. But then, by Standard Compositionality, contrary Millianism, “Elton John” and “Reginald Dwight” differ in semantic content. But, as we saw in chapter 1, there are very powerful reasons to think that Millianism is true. This is the puzzle. Also, as we will see in chapter 4, rejecting Millianism simply cannot be the solution to this puzzle. Rejecting the intuition that 1a and 1b differ in informational value is simply not credible. The only genuine option left is to reject Standard Compositionality in favor of Relational Compositionality. According to Relational Compositionality, because 1a has two occurrences of the same term, and because two occurrences of the same term relate differently to each other than the way two distinct terms relate to each other, 1a and 1b differ in the propositions they encode. That is, differences in the way the constituents of a sentence relate to each other affects semantic content. Kit Fine (2007) 19 and I are both Relationists. We both think that the way to deal with Frege’s Puzzle is to abandon Standard Compositionality in favor of Relational Compositionality. But, we disagree about how to become a Relationist. Fine believes that the correct way to become a Relationist is to abandon standard semantics in favor of 19 Fine, Kit, 2007 40 what we will identify as, “String Semantics” 20 . I believe that the proper way to become a Relationist is to abandon standard semantics in favor of what we will identify as, “Collapse Semantics”. On a standard semantics, for a language L, we assign objects to the names of L, properties or sets or n-tuples to the predicates of L, functions to the functors of L. And, we determine the semantic content of a complex expression strictly in terms of syntax. So, though a standard semantics can support Standard Compositionality, it cannot support Relational Compositionality. In addition to what we do in standard semantics, on String Semantics, we assign relational or “coordination” schemes, a wire or a string, to the semantic contents encoded by complex expressions with two occurrences of the same term to represent the fact that the semantic content is “coordinated”. The idea is that two occurrences of the same term get their values assigned to them in coordination. And, this coordination gets reflected in the semantic content. The semantic content is coordinated. The strings represent the coordination. So, set theoretically, we can represent the coordinated proposition encoded by 1a as the ordered pair consisting of the ordered pair of EJ, EJ, the identity relation and a string attaching the members of the ordered pair or <<EJ—EJ>, =>. The proposition encoded by 1b is the same ordered pair minus the string, <<EJ, EJ>, =>. The two differ in that while the former has a string as one of its constituents, the latter does not. 20 It should be noted that what we are calling, “String Semantics”, Fine calls, “Relational Semantics”. The reason for calling it what we are calling it and not what Fine is calling it is the similarity between “Relational Semantics” and “Relational Compositionality” and a possible tendency to confuse the two. 41 On Collapse Semantics, in addition to the rules for calculating the semantic contents of complex expressions given by standard semantics in terms of syntax, there is an additional rule that states that expressions having two or more occurrences of the same term induces a structural collapse so that a sentence like 1a with a dyadic predication encodes a structurally collapsed monadic proposition with reflexivity. On Collapse Semantics, 1a is ambiguous. It encodes both the dyadic proposition that Elton John and Elton John/Reginald Dwight stand in the identity relation represented as the ordered pair, <<EJ, EJ>, => and the structurally collapsed reflexive proposition that Elton John stands in self-identity represented as, <EJ, self-ID>. I do two things here. I argue that the way to be a Relationist is to accept Collapse Semantics not String Semantics. Plus, I defend the Relationist position against the charge that it cannot be the answer to Frege’s Puzzle. Here is the argumentative strategy. In part I, I present what Fine calls, “the Antinomy of the Variable”. The antinomy is supposed to be an independent argument for String Semantics. In part II, I offer a rebuttal to the argument from the antinomy by pointing out two problems with it. In part III, I argue that Frege’s Puzzle cries out for Collapse Semantics not String Semantics. In part IV, I respond to the charge that Relational Compositionality cannot be the answer to Frege’s Puzzle because it is useless when dealing with more general versions of the puzzle. 42 3.1 The Antinomy of the Variable: In generating the puzzle Fine appeals to the notion of a “semantic role”. We can understand “semantic role” to be roughly synonymous with the generic term, “semantic value” or “semantic feature”. He writes that in any meaningful expression, “there is something conventional…and something non-conventional…‘semantic role’ is [the] term for this essentially non-conventional aspect of a meaningful expression” 21 . What is the semantic role of a variable? An essential, non-conventional fact about a variable is that it ranges over a domain. A term would not be a variable if it did not do that. So, “x” and “y”, qua variables, essentially range over a domain. Fine then observes that any two variables of a single language essentially range over the same domain, assuming the logic to which the language belongs is one-sorted. Combine these two facts and we get the result that “x” and “y” have the same semantic role. Consider 2a. x > 0 2b. y > 0 The only difference between 2a and 2b is that while 2a has an occurrence of “x”, 2b has an occurrence of “y”. But, the only difference between “x” and “y” is that while “x” is written and pronounced the way it is written and pronounced, “y” is written and pronounced the way it is written and pronounced. But, this difference cannot a semantic 21 Ibid. p. 7. 43 difference. Surely, it is merely a “conventional”, “notation” difference. Insofar as “x” and “y” are both variables of a single language, they both range over the same domain. Thus, we get Semantic Sameness. Semantic Sameness (SS): Any two variables (ranging over a given domain of objects) have the same semantic roles. However, notice also that 3a and 3b clearly differ in their semantic roles. 3a. x > x 3b. x > y 3a relative to any assignment is false. 3b relative to some is true. The reason is that there is no way to take an object from any domain and assign it to “x” so as to get 3a to come out true. For no object is greater than itself. But, there is a way to take objects from a domain and assign them to “x” and “y” so as to get 3b to come out true 22 . This semantic 22 If the fact that “x” and “y” essentially range over the same domain is enough to establish that 2a and 2b do not differ semantically, then, this fact should be enough to establish that 3a and 3b do not differ semantically. But, of course, the fact that “x” and “y” essentially range over the same domain is not enough to establish that 3a and 3b are semantically identical. Fine correctly observes that it might be thought that the specification of the range is sufficient to fix the behavior of the variables. But this is not strictly so. For we should specify not only which values each single variable can assume, when taken on its own, but also which values several variables can assume, when taken together. We should specify, for example, not only that “x” can assume the number 2 as value, say, and “y”, the number 3 but also that “x” and “y” can simultaneously assume the numbers 2 and 3 as values; and, in general, we should state that the variables take their value independently of one another (Ibid. p.23). In other words, insofar as “x” and “y” can simultaneously take on different values while two occurrences of “x” cannot, 3a and 3b differ semantically despite the fact that the variables of a single language essentially range over the same domain. 44 difference between 3a and 3b needs to be accounted for. But, notice that the only difference between 3a and 3b is that while the former has a second occurrence of “x”, the latter has an occurrence of “y”. So, this difference must be the difference which accounts for the semantic difference between 3a and 3b. But that can only be if “x” and “y” differ in semantically. So then, we get Semantic Difference. Semantic Difference (SD): Any two variables (ranging over a given domain of objects) have different semantic roles. As Fine sees it, the reasoning for either SS or SD is hard to resist. This is the antinomy. This is where the argument begins. The argument is that if we want a solution to the antinomy, we have to abandon standard semantics in favor of String Semantics. For a solution, Fine asks us to make a distinction between the intrinsic semantic role and the extrinsic semantic role of an expression. The intrinsic semantic features of an expression e are those semantic features of e that do not depend on e standing in any semantic relationship to any other expression. So, for example, it is an intrinsic semantic feature of “medical doctor” that it is true of all and only medical doctors. It is also an intrinsic semantic feature of it that it means, a person licensed to practice medicine. These facts But, notice also that “x” and “y” can take on different values and 2a and 2b can differ in truth-value relative to a single assignment. So, “x” and “y” differ semantically despite that fact as well. The point is that we have two different standards for establishing SS and SD. If “x” and “y”’s essentially ranging over the same domain is enough to establish that 2a and 2b are semantically the same, then, it is enough to establish the same for 3a and 3b. So, we only get SS. If “x” and “y”’s essentially ranging over the same domain is not enough to establish that 3a and 3b are semantically the same, then, it is not enough to establish that for 2a and 2b. So, we only get SD. By either standard, there is no way to get SS and SD. It is only by using different standards for SS and SD do we get both. 45 do not depend, for instance, on the fact that it is synonymous with “physician”. Rather, it is the other way around. It is synonymous with “physician” because it and “physician” have the same intrinsic semantic features. They both mean, a person licensed to practice medicine. The fact that “x” ranges over the domain it is assigned to range over does not depend on how it relates to any other expression. The same is true of “y” ranging over the domain it is assigned to range over. As Fine sees it, these intrinsic semantic features of “x” and “y” are enough to establish SS 23 . The suggestion then is that SS is true when “semantic role” is understood in the intrinsic sense. SD is false when “semantic role” is understood in this sense. The variables “x” and “y” do not differ in their intrinsic semantic features. However, they differ in their extrinsic semantic features. Notice that an occurrence of “x” stands in a different semantic relation to a second occurrence of “x” than the semantic relation born by an occurrence of “y” to that second occurrence “x”. That is, an occurrence of “x” and an occurrence of “y” stand in different semantic relations to a second occurrence of “x”. This semantic difference between an occurrence of “x” and an occurrence of “y” is not an intrinsic semantic difference. It is an extrinsic semantic difference. They relate differently to a second occurrence of “x”. So, SD is 23 Here is a minor problem with Fine’s suggestion here. The rationale for thinking that “x” and “y” have the same semantic role(s) was supposed to be that they range over the same domain. But, the fact that “x” essentially ranges over the same domain as “y” does not seem to be an intrinsic semantic feature of ‘x”. The variable “x” essentially ranges over the same domain as the variable “y” because it belongs to the same language as “y”. I would have guessed that “x” belonging to the same language “y” belongs to is an extrinsic semantic feature of “x”. If Fine disagrees, then, it is hard to make sense of the intrinsic versus extrinsic semantic role distinction. 46 true but only when “semantic role” is understood in the extrinsic sense. So, the principle Fine is urging us to resist is Semantical Intrinsicalism. Semantical Intrinsicalism (SI): For any two complex expression E and E*, if E and E* differ in their intrinsic semantic roles, then, if E and E* are composed in the same manner, then, at least one constituent of E and its corresponding constituent in E* differ in their intrinsic semantic roles 24 . Fine contends that, “though this view of meaning (or principle of compositionality)—‘Semantical Intrinsicalism’—seems hard to dispute…it is false all the same” 25 . There is no need to insist on an intrinsic semantic difference between “x” and “y” to account for the intrinsic semantic difference between 3a and 3b. The extrinsic semantic difference between the occurrences of “x” and “y” in the two formulas is sufficient. Again, the variables differ extrinsically in that an occurrence of “x” relates to an occurrence of “y” differently than it does to another occurrence of “x”. Two occurrences of “x” get their values assigned in “coordination”; an occurrence of “x” and 24 The expressions E and E* are expression types. But, their constituents are occurrences of expression types. For instance, 1a is an expression type. But, one of its constituents, “Elton John” is merely an occurrence of the expression type “Elton John”. 1a has two occurrences of “Elton John”; 1b has only one. So, if we are to properly judge whether to hold onto or reject Semantic Intrinsicalism, we need to be told about the semantic roles of occurrences of expressions. Perhaps Fine is thinking that the semantic role of any occurrence of an expression type e = the semantic role of the expression type e. But, this is cannot hold generally. Consider the occurrence of the variable “x” in the formula “Fx” and an occurrence of it in “∃x Fx”. Relative to an assignment A, which assigns the number 1 to “x”, the occurrence of “x” in the first formula refers to 1. But, relative to A, the occurrence of “x” in the second formula does not refer to 1. Given that the two occurrences, relative to the same assignment, differ in this way, they cannot have the same “semantic role”. So, we cannot just assume that the “semantic role” of an occurrence of a variable v = the “semantic role” of v. For a full discussion on the significance of the semantic difference between bound occurrences and free occurrences of variables, see Nathan Salmon’s, A Theory of Bondage, the Philosophical Review, 115 (4): 415-448, 2004 25 Ibid. p. 23 47 an occurrence of “y” do not. For Fine, if the sense of “semantic role” employed in SS and SD is the intrinsic sense, then, the “resolution” to the antinomy is to reject SD. SD is true only when “semantic role” is understood in the extrinsic sense. Resisting SD requires resisting SI. Resisting SI requires String Semantics. In short, his argument is this. Premise 1: 2a and 2b have the same intrinsic semantics roles. Premise 2: 3a and 3b differ in their intrinsic semantic roles. Premise 3: if premise 1 and premise 2, then, SI is false. Premise 4: if SI is false, then, String Semantics. If we can get an extrinsic semantic difference between occurrences of, “x” and “y” without an intrinsic semantic difference between the variables, then we can get premises 1 and 2. We can account for premise 2 while only positing an extrinsic semantic difference between occurrences of “x” and “y”. But if we admit premise 2 while also conceding premise 1, then, SI is false. This is premise 3. What is the reasoning behind premise 4? The idea behind it seems to be this. How do we get an intrinsic semantic difference between 3a and 3b if SI is false and “x” and “y” are not required to also differ in intrinsic semantic roles? The answer is “strings”. There is a string attaching two occurrences of “x”, in a sequence “x”, “x”. There is no string attaching “x”, “y”. String Semantics provides the strings 26 . 26 It is difficult to figure out exactly how the argument for premise 4 is supposed to go. The rules for String Semantics only allow for assigning strings that attach elements in a proposition. There is no rule for assigning constituents of a formula. Yet, in order to get an intrinsic semantic difference between 3a and 3b without an intrinsic semantic difference between “x” and “y”, we wind up having to assign strings that 48 3.2 Response to the Antinomy The antinomy argument is unsound for two reasons. Premises 1 and 4 are both problematic. Let us start with premise 4. To see the problem with it, we have to distinguish between the semantic features of a variable unrelativized to an assignment and the semantic features of it relativized to an assignment. Let us start with the semantic features of a variable relativized to an assignment. It should be uncontroversial that a variable is directly referential. Let us say that A assigns the number 1 to “x” and to “y”. So then, “x” and “y” relative to A have the same semantic content. However, according to String Semantics, since 3a has two occurrences of the same term, whereas 3a relative to A encodes a coordinated proposition, 3b relative to A does not. Strings Semantics is concerned with supporting Relational Compositionality and, when it comes to variables, it is concerned with the semantic content of a variable relative to an assignment. However, SI is only concerned with the semantic features of “x” and “y” unrelativized to an assignment. Recall the reasons for rejecting SI. The variable “x” and “y” have the same intrinsic semantic role in that they essentially range over the same domain. Yet, 3a and 3b differ in their intrinsic semantic roles in that whereas 3a relative to any assignment is false, 3b relative to some is true. The variables “x” and “y” essentially ranging over the same domain is relevant only to their semantic features attach the variables themselves. Even if it is right that we have to assign strings to constituents of a formula, how is this supposed to be a basis for the conclusion that we have to assign strings to elements of a proposition? 49 unrelativized to an assignment. Likewise, 3a and 3b differing in their semantic roles in the way Fine points out is only relevant to their semantic features unrelativized to an assignment. In other words, while String Semantics is only concerned with the semantic features of variables relative to an assignment, the reasons for rejecting SI has only to do with the semantic feature of a variable unrelativized to an assignment. The reasons for rejecting SI have nothing to do with String Semantics. The reasoning behind premise 4 demonstrates a failure to notice this. A standard, non-relational, Tarskian semantics for variables is compatible with the semantic difference between 3a and 3b that Fine notices. Why does Fine think that the reasoning for premise 4 is sound when it is not? Here is a clue. It is thus by giving up the intrinsicalist doctrine (SI), plausible as it initially appears to be, that the antinomy is to be solved. We must allow that any two variables will be semantically the same, even though pairs of identical and of distinct variables are semantically different; and we should, in general, be open to the possibility that the meaning of the expressions of a language is to be given in terms of their semantic relationships to one another. 27 Here is my diagnosis. Fine (unwittingly) slips from thinking about the semantic features of the variables unrelativized to an assignment when thinking about premise 2, premise 3 and the antecedent of premise 4 to thinking about the semantic features of the variables (the meaning of the expressions) relativized to an assignment when thinking about the 27 Ibid. p. 24 50 consequent of premise 4. Recall that Fine’s reasoning behind premise 2 is that whereas 3a is false relative to any assignment, 3b is true relative to some. He is clearly thinking here about the semantic features of these sentences unrelativized to an assignment. And, this is an important premise in the argument against SI. So, he continues to have this semantic value in mind up until the antecedent of premise 4. Then, as he prepares to draw his conclusion, he slips to thinking about the semantic features of 3a and 3b relativized to an assignment when thinking about the consequent of premise 4. The reason for the slip is, no doubt, his employment of the ill-defined notion of “semantic role” throughout argument. He wrongly assumes that a variable has one semantic role. The wider lesson here is that there is no such thing as “the semantic role” of a variable. A variable has at least two semantic roles—its unrelativized to an assignment semantic role (which we will in short time define) and its relativized to an assignment semantic role which is its semantic content relative to an assignment. Without understanding this, a proper and full understanding of the variable is not possible 28 . 28 Fine, in direct correspondence, has insisted that he is not making the mistake that I attribute to him here. That is, he is not conflating the unrelativized semantic features of a variable with its relativized semantic content. Rather, his only conclusion from the antinomy is that SI is false. In fact, he denies that the proposition encoded by 3a relative to A is coordinated despite 3a having two occurrences of “x”. Fine’s present position is that the proposition(s) encoded by 3a and 3b relative to any assignment which assigns the same object to “x” and “y” are the same. The proposition encoded by 3a, like the proposition encoded by 3b, is uncoordinated. The reason 3a is uncoordinated despite the fact that 1a is coordinated is that “variables and names are very different kinds of terms”. This however is inconsistent with Fine’s discussion on pp 115-118 of Fine (2007) (see in particular footnotes 10 and 11). Fine’s response here is puzzling. If the proposition encoded by 3a is uncoordinated despite 3a having two occurrences of “x” because it involves variables and “variables and names are very different”, then, how is the argument from the Antinomy of the Variable supposed to be an argument for String Semantics? The antinomy argument was supposed to have a bearing on whether or not we should say that the proposition encoded by 1a is coordinated. Given Fine’s response to my objection to his argument, it is hard to see how the antinomy argument is an argument for String Semantics. 51 Premise 1 is also problematic. To see this, we must distinguish between the semantic content of a variable v unrelativized to an assignment and what I call v’s “logical content”. Let us start with the notion of logical content. Notice that 2a and 2b are not logically equivalent. That is, 2a and 2b can come apart in truth-value relative to a single assignment. Let A be an assignment which assigns 1 to “x” and 0 to “y”. While 2a relative to A is true, 2b relative to A is false. This is an intrinsic semantic difference between 2a and 2b. What does the fact that 2a and 2b are not logically equivalent in this way consist in? It consists in the fact that 2a and 2b differ in logical content. The logical content of an n-place predicate F is a function from model structures to n-place properties or n-place propositional functions. The logical content of a variable is a function from assignments to values. The logical content of “x” is a function from an assignment A to the object A assigns to “x” as value. The logical content of “y” is a function from A to the object A assigns to “y”. The difference in “x”’s and “y”’s logical contents is an intrinsic semantic difference. The logical content of Fx is a function from a model structure M and assignment A to the proposition encoded by Fx relative to M and A, which is the proposition which predicates the property P that M assigns to F of the object o that A assigns to “x”. An analogous thing is true of Fy. 2a and 2b differ in logical content in that “x” and “y” differ in logical content. Contrary to SS (Semantic Sameness), “x” differs from “y” and 2a differs from 2b in their intrinsic semantic roles. 52 Fine anticipates a response like this. Under this conception of semantic value…it will be a function, which takes each assignment into the individual, which it assigns to “x”. It is, therefore, clear, if we identify semantic roles and semantic values that “x” and “y” will differ in their semantic roles…we therefore secure the semantic difference between the pairs “x, y” and “x, x” under this account of semantic role. However, we are [then] unable to account for the fact that the semantic role of the variables “x and “y” is the same in the cross-contextual case. 29 30 Fine’s objection here to identifying the semantic role of a variable with its “semantic value” or its logical content is that we will then get the result that “x” and “y” differ in their intrinsic semantic roles. But, he thinks this is unacceptable because insofar as they essentially range over the same domain, we must say that “x” and “y” have the same intrinsic semantic role. What should we say here? On the one hand, we want to say that “x” and “y” differ in their intrinsic semantic roles in that they differ in their logical contents. On the other hand, insofar as they essentially range over the same domain, we 29 Ibid. p. 11 30 Here is what he means by “cross context case”. In an initial attempt to resolve the conflict between SS and SD, Fine proposes an ambiguity in “sameness of semantic role” in terms of contexts. The variables “x” and “y” have the same semantic roles in the cross contextual sense. For example, “x” plays the same semantic role in the context of “x > 0” as “y” plays in the context of “y > 0”. Fine’s idea is that we can substitute “y” for “x” in the first context or vice versa in the second context without altering the semantic features of either context. This is just another way of supporting the idea that the variables “x” and “y” have the same intrinsic semantic role. However, “x” and “y” differ in semantic roles in the intra- contextual sense. For example, “x” and “y” play different semantic roles within the context “x > y”. Surely, replacing one of the variables for the other within this context alters the semantic features of the context. This observation supports his idea that “x” and “y” differ in their extrinsic semantic roles. 53 want to say that “x” and “y” do not differ in their intrinsic semantic roles. The answer is “both”. We can plainly see that “x” and “y” differ in their logical contents. But also, insofar as they essentially range over the same domain, they have the same semantic content unrelativized to an assignment. Let us identify the semantic content of a variable unrelativized to an assignment as the identity function on the domain. We can also identify the semantic content of an open formula like 2a unrelativized to an assignment with a propositional function. The propositional function semantically encoded by 2a is the function from an object o to the proposition that o is greater than o. Analogous things are true of “y”. Thus, “x” and “y” and 2a and 2b have the same unrelativized to an assignment semantic content. Indeed 3a and 3b differ in their unrelativized to an assignment semantic content. 3a’s unrelativized to an assignment semantic content is a function from an object o to the proposition that o is greater than o. 3b’s unrelativized to an assignment semantic content is a function from an ordered pair of objects <o, o*> to the proposition o is greater than o*. If I may be permitted to talk about the proposition encoded by a formula like 2a of a first order language, the proposition encoded by 2a relative to A which assigns 1 to “x” must be the proposition that 1 is greater than 0 31 32 . Relative to B, which assigns 2 to “x”, 31 This idea of identifying the semantic content of a variable unrelativized to an assignment was inspired by Nathan Salmon’s suggestion that the semantic content of a bound occurrence of a variable is the identity function on the domain (Salmon Nathan, A Theory of Bondage, Philosophical Review, 2006). Without getting into too much detail, here is the idea that occurred to me. What does a variable binder do to a variable when it binds it? It nullifies the assignment. So, if the semantic content of a bound occurrence of a variable is the identity function on the domain, that must be because the semantic content of a variable unrelativized to an assignment (when the assignment is nullified) is the identity function on the domain. 54 the proposition encoded by 2a is the proposition that 2 is greater 0. If the domain D is the set of natural numbers, for any n in D, if n is assigned to “x”, the proposition encoded by 2a is the proposition that n is greater than 0. The reason the semantic content of ‘x’ relative to an assignment varies as it does is that its unrelativized semantic content is the identity function on the domain of possible assignments. In giving an assignment we simply select an element from the domain over which its unrelativized content is defined. The reason “x” is able to range over the entire domain it is assigned to range over is that its semantic content is the identity function on the entire domain. Consider 4a. ∀x (x > 0) 4a is true iff everything in the domain is greater 0. The reason is that the semantic content of “x” is the identity function defined for the entire domain. The exact same thing is true of “y”. And, insofar as “x” and “y” essentially range over the same domain, they essentially have the same semantic content—the identity function on that domain. Contrary Fine, even if we admit that “x” and “y” differ in their intrinsic semantic role in that they differ in logical content, we can still account for the fact that they have 32 Indeed, standard first order logic -- developed as a means of formalizing mathematical and logical reasoning -- is not concerned with propositions or properties. Most standard applications are concerned only with assigning the proper extensions to expressions relative to model structures. Even more recent developments of intensional logics can typically afford to ignore hyperintensional distinctions. However, semantic investigations of assertive and doxastic content do not have this luxury, and so must distinguish between necessarily equivalent propositions. When formal languages of first order logic are enlisted in this enterprise, one must, therefore, go beyond what is given by standard treatments of such languages. 55 the same intrinsic semantic role in that they range over the same domain and therefore have the same semantic content unrelativized to an assignment. Fine has another objection to identifying the semantic role of a variable with its logical content. There is another, perhaps more serious, problem with this approach [identifying semantic role with logical content]. For, although it posits a difference between the variables “x” and “y” (and hence between “x”, “y” and “x”, “x”), it does nothing to account for their semantic difference. For in the last analysis, the posited difference between the semantic values for “x” and “y” simply turns on the difference between the variables “x” and “y” themselves 33 . As Fine sees it, what we need is an accounting of how 3a and 3b differ semantically in the way that they do. So, his objection to identifying logical contents with intrinsic semantics roles is that appealing to the fact that “x” and “y” differ in their logical contents cannot give us such an accounting. The reason is that two variables differ in their logical contents simply in virtue of the fact that they are distinct variables. And, the mere fact that two variables are distinct surely cannot account for a semantic difference. This objection is a bit baffling. The fact that “x” and “y” are distinct variables is exactly the reason 3a and 3b differ semantically in the way that they do. Distinct variables get their values assigned independently of one another; different occurrences of the same variable do not. Isn’t this precisely the reason 3a is false relative to any assignment 33 Ibid. p. 11 56 whereas 3b is true relative to some? There is no A such that 3a relative to A is true because two occurrences of a single variable get their value(s) assigned in “coordination”. 3b, in contrast, is true relative to an A because the variables “x” and “y” are different variables and thus get their values independently of each other. The fact that “x” and “y” are distinct and thus differ in their logical contents is precisely what explains the semantic difference between 3a and 3b 34 . Here is the reason the antinomy is not a genuine antinomy. In establishing SS, Fine is thinking about “x”’s and “y”’s semantic content unrelativized to an assignment. He is right that they do have the same semantic content unrelativized to an assignment in that they essentially range over the same domain. So, 2a and 2b encode the same propositional function. What about 3a’s and 3b’s semantic content? Are their semantic contents the same or different? They are different. The unrelativized semantic content of 3a is a function from o to the (always false) proposition that o is greater than o. The unrelativized semantic content of 3b is a function from a pair of objects o, o* to the (sometimes true) proposition that o is greater than o*. 34 Fine (in direct correspondence) has insisted that I have misunderstood his reason for refusing to allow the difference in logical contents between “x” and “y” to explain the semantic difference between 3a and 3b. His reason for the refusal is that the difference in logical content between “x” and “y” is due merely to the fact that “x” and “y” are distinct variables. And, that fact is merely a notational (conventional) difference. As Fine sees it, such a difference cannot possibly account for a genuine semantic difference. This response is really mysterious. If “x” and “y” differing in logical content is not a genuine semantic difference, then 3a and 3b differing in the way Fine points out that they do is not really a semantic difference either. That difference is really a difference in their logical contents. 3a’s logical content is such that it always returns a false proposition; 3b’s logical content is such that it sometimes returns a true proposition. If we go along with Fine and say that a difference in logical content is not a legitimate semantic difference, then, 3a and 3b do not differ semantically. 57 The consequences for Fine’s argument are: i Premise 1 fails if “intrinsic semantic role” is read as logical content, ii Premises 1-3 are true if “intrinsic semantic role” is read as unrelativized semantic content, but then Premise 4 fails, since the failure of SI is fully explained on a standard, Tarskian semantics of variables. The wider lesson from this entire discussion is that in order to have a complete and proper understanding of the variable, we must see that it has 3 distinct semantic roles or semantic values—its relativized to an assignment semantic content, its unrelativized to an assignment semantic content and its logical content. 3.3 Frege’s Puzzle: String Semantics versus Collapse Semantics Let us evaluate here how well String Semantics and Collapse Semantics do with respect to Frege’s Puzzle. The challenge of Frege’s Puzzle is to get a difference in epistemic (a priori/ a posteriori) status between 1a and 1b within the Millian framework. Let us start with String Semantics. In order for either semantics to meet this challenge, it must be able to yield a difference in representational content between 1a and 1b. To see why a difference in representational content is necessary, let us recall the distinction we made in chapter 2 between a proposition p and its representational content 35 . Recall Church’s theorem. We said that to believe the many formulations of the theorem is really to believe one thing—the representational content which is the theorem. Insofar as Jones 35 This distinction was originally made in Salmon, On Content, Mind 101 (404): 733-751, 1992. 58 believes the theorem, he believes each of the propositions encoded by the various formulations of it. The problem with String Semantics is that it does not yield a difference in representational content between 1a and 1b. How do we determine the representational content of the proposition encoded by 1b? First, we determine its constituents. The constituents are the ordered pair <Elton John, Elton John> plus the identity relation. Second, we determine the way in which the constituents are composed. The proposition is a predication of the relation on the ordered pair. Thus, the proposition encoded by 1b represents the world as being such that the members of the ordered pair stand in the identity relation. According to String Semantics, the proposition encoded by 1a consists of the ordered pair <Elton John, Elton John>, the identity relation and a string connecting the members of the pair. But, it is hard to see how the string can have a bearing on the representational content. The representational content is that the members of the ordered pair stand in the identity relation. Thus, 1a and 1b do not differ in representational content. Fine acknowledges this much 36 . But then, anyone who believes the representational content, that the members of the pair stand in the identity relation, ipso facto believes both propositions. Fine, unsurprisingly, denies this. It might be wondered how there can be such elusive differences in meaning (between the representational content of a proposition and what it takes to “grasp” it). But what it comes down to, in the end, is a difference in the content of semantic requirements. In 36 For details on this, see his discussion about the difference between his view and the Fregean view, p.59 (Fine 2007). 59 saying that “Cicero = Cicero” expresses the positively coordinated proposition that c = c, what I am saying is that it is a semantic requirement that the sentence signifies an identity proposition whose subject and object positions are both occupied by the object c while, in say that “Cicero = Tully” expresses the uncoordinated proposition that c = c, I am merely saying that it is a semantic requirement that it signifies an identity proposition whose subject position is occupied by c and whose object position is occupied by c…the [difference in] requirements are, therefore, capable of reflecting a genuine difference in meaning. 37 Fine’s suggestion here is that though the propositions have same representational content, there are different requirements for fully grasping them. In order to grasp the coordinated proposition, an agent must see that the object in the subject position is identical with the object in the object position; in contrast, there is no such requirement for grasping the uncoordinated proposition. In both cases the same objects are represented in the same way – as standing in the same relation. Yet, they differ in that the requirements for grasping them are different. Fine thinks that this is a basis for saying that an agent can believe one without believing the other despite a lack of difference in representational content. And, this is a basis for establishing a difference in epistemic status. Fine’s position is unstable. There are two stable positions here. One position is that the two propositions have the same representational content and therefore have the same epistemic status. The other position is that the two propositions differ in epistemic status so they differ in representational content. The third position that they have the 37 p. 59 60 same representational content yet differ in epistemic status is unstable. If the representational content is the same, then, the two propositions represent the exact same fact. Either knowing that that particular fact obtains is a priori or it is not. If it is, then, the representational content is a priori and thus both propositions are a priori. If not, then neither is. Every formulation of Church’s theorem is a priori knowable because the theorem is a priori knowable. Every formulation of Murphy’s Law is a posteriori because Murphy’s Law is a posteriori. If we say that 1a and 1b have the same representational content yet differ in epistemic status, then, we will have to distinguish between the epistemic status of a proposition and the epistemic status of its representational content. For these sometimes come apart. But, that would be absurd. Also, if the two propositions differ in epistemic status because the requirements for grasping them are different, then, the two propositions must differ in representational content. Once we grasp the representational content of a proposition, we ipso facto grasp the proposition. In order to make sense of the idea that the requirements for grasping the two propositions are different, we are forced to the position that they differ in representational content. For these reasons, String Semantics cannot be the answer to Frege’s Puzzle. Let us now turn to Collapse Semantics. On Collapse Semantics, we get the requisite difference in representational content. According to Collapse Semantics, while 1a encodes the collapsed monadic proposition that EJ is self-identical, 1b encodes the uncollapsed dyadic proposition that EJ stands in identity to RD. Notice the difference between the property of being self-identical and the property of being identical to 61 Reginald Dwight. The property of being self-identical is instantiated by every possible object. The property of being RD is uniquely instantiated. So, in grasping the proposition that EJ is self-identical, I grasp that he has a property instantiated by every possible object. In grasping the proposition that he is identical with RD, I grasp that he has this very unique property. One of these propositions is trivial; the other is not. Thus, the two propositions differ in representational content. Thus, we have a basis for saying that these differ in epistemic status. In chapter 4, I provide a detailed argument that Collapse Semantics can deliver a difference in epistemic status. 3.4 Defending Relational Compositionality In this section, the Relationist has to play some defense. Here is a reason to think that moving to Relational Compositionality is not the answer to Frege’s Puzzle. Consider 5a. Elton John is a musician 5b. Reginald Dwight is a musician 6a. Elton John is more famous than Reginald Dwight. 6b. Reginald Dwight is more famous than Elton John 38 . 38 This kind of example is due to David Lewis. 62 As we saw in chapter 2, sentences like 5a and 5b differ in cognitive value. This is perhaps a reason to think that 5a and 5b differ in the propositions they encode. This is a problem for Millianism. But, since neither 5a nor 5b has two occurrences of the same term, appealing to Relational Compositionality is of no effect. There are two Millian responses here—the right one and the wrong one. Fine’s gives the wrong one. He concedes the following about 5a and 5b. It might be thought to be an embarrassment for the relationist that he does not take there to be an intrinsic semantic difference between the sentences or the names, in this case…for does there not appear to be such a difference? There is, of course, a cognitive difference between the two sentences but it should not automatically be assumed that this requires an intrinsic semantic difference between the two sentences 39 . The problem with this response is that Fine is conceding more than the Millian is required to concede. The Millian need not concede that there is no semantic difference between 5a and 5b. They differ in logical content; a difference in logical content is a semantic difference. The logical content of a name is a function from model structures to objects. The logical content of a sentence s is a function of s’s syntax plus the logical contents of its constituent parts. 5a and 5b differ in logical content because “Elton John” and “Reginald Dwight” differ in logical content. But, for Fine, given his vision of why we must move to String Semantics, the concession is unavoidable. Note that String Semantics per se is not incompatible with saying that there is an intrinsic semantic 39 Ibid. p. 53 63 difference between 5a and 5b. But, the manner in which Fine argues for it is. For Fine, the extrinsic semantic difference between “Elton John” and “Reginald Dwight” is a primitive fact. It is not explained in terms of an intrinsic semantic difference between them. He refuses to acknowledge such a difference. Thus, he has cornered himself into position where the concession is unavoidable. This leads the Relationist to an untenable position. The Relationist provides a semantic solution to the version of Frege’s Puzzle involving 1a and 1b. So, the Relationist gives off the impression that a solution to the puzzle must be a semantic one. Yet, since he cannot seem to find a semantic difference between 5a and 5b, he says that such a difference is not necessary. Fine, unable to find a difference in the intrinsic semantic roles between 5a and 5b, concedes that such a difference is not necessary to account for a difference in cognitive value. A difference in extrinsic semantic roles is enough. Stop right there. This cannot be correct. I thought, with respect to Frege’s Puzzle, the whole point of opting for Relational Compositionality was to account for the cognitive difference between 1a and 1b in terms of a difference in their intrinsic semantic roles despite the fact that names and variables are Millian. Either a difference in intrinsic semantic roles is necessary to account for a difference in cognitive value or such a difference is not necessary. If it is, then since Relational Compositionality is unable to yield such a difference with respect to the 5a and 5b version of the puzzle, Relational Compositionality cannot be the answer to the puzzle. If it is unnecessary, then, there is no motivation for Relational Compositionality. If an extrinsic semantic difference is all that is required, then, even without identifying an intrinsic semantic difference, we can account for the cognitive 64 difference between 1a and 1b. For they differ in their extrinsic semantic roles. 1a and 1b stand in different semantic relations to 1a. Plus, it has been pointed out that 6a and 6b seem to differ in cognitive value no less than 1a and 1b 40 . However, if we refuse a difference in intrinsic semantic roles between “Elton John” and “Reginald Dwight”, then, there is no basis for saying that there is an intrinsic semantic difference between 6a and 6b. If the Relationist is forced to say that a difference in intrinsic semantic roles is not necessary to account for this difference, then, Relational Compositionality is in serious trouble. It is in need of a better defense. As I see it, the problem with Fine is in failing to recognize that the 1a and 1b version of the puzzle and the 5a and 5b version present different challenges. The challenge presented by the former is to account for a difference in epistemic status between 1a and 1b within a Millian framework. The challenge presented by 5a and 5b version is to explain the difference in cognitive value between 5a and 5b and between 6a and 6b within a Millian framework. In order to meet the challenge presented by the 1a and 1b version, it was necessary to find a difference in the representational contents between them. But, the only way to do that within the Millian framework was to abandon standard compositionality in favor of Relational Compositionality. As for the 5a and 5b and the 6a and 6b versions, I provide answers to these kinds of puzzles in chapter 2 making use of the notion of logical content. 5a and 5b differ in their cognitive value in that they differ in their logical contents. The same is true of 6a and 6b. 40 Soames makes this argument in Substitutivity, reprinted in Davidson, On Sense and Direct Reference, Blackwell Publishing, 2006 65 Chapter 4 Frege’s Puzzle and Collapse Semantics INTRODUCTION: In this chapter, I propose that we deal with Frege’s Puzzle by adopting a new kind of semantic theory—what I call, “Collapse Semantics”. A semantic theory tells us what kind of meanings the simple expressions of a language have and provides rules for calculating the meanings of the complex expressions out of which the simple expressions are constructed. On a standard semantic theory, for example, the meaning or propositional contribution or semantic content of a name like “Elton” is an object, the semantic content of a predicate like “physician” is a property, the semantic content of a predicate like “loves” is a relational property, the semantic content of a functor like “is a father of” is a function, etc. We are then given rules for calculating the meanings of complex expressions from the meanings of the simple expressions in terms of syntax. Consider 1a. Elton John is Elton John 1b. Elton John is Reginald Dwight 66 1a and 1b have the same syntax—noun phrase, transitive verb, noun phrase. In order to calculate the propositional contribution of the predicate “is Elton John”, we combine the semantic content of “is” (of identity), the identity relation, with its second relatum, the semantic content of “Elton John” which is the person Elton John. The combining yields the property of standing in the identity relation to Elton John. The semantic content of the predicate is this property. We then take this and combine it with the first relatum, the person Elton John, to get the proposition that Elton John stands in the identity relation to Elton John. 1a and 1b, since they have the same syntax, differ in the propositions they semantically encode iff “Elton John” and “Reginald Dwight” differ in their propositional contributions or semantic content. Collapse Semantics, in addition to providing rules for calculating meanings for complex expressions in terms of syntax, provides a rule for calculating meanings on the basis of the number of occurrences of a term. Collapse Semantics differs from standard semantics in that it has one additional rule. According to Collapse Semantics, 1a has two readings. The first reading is the one we can calculate strictly in terms of the rules given by standard semantics, i.e., in terms of syntax. On this reading, 1a and 1b encode the same proposition iff the names “Elton John” and “Reginald Dwight” have the same semantic content. Assuming Millianism, the view that the meaning or propositional contribution or semantic content of a name is just its referent, 1a and 1b, since they are both 2-place or dyadic, both encode the dyadic proposition that Elton John stands in identity to Elton John. However, the second reading is not something we can derive just from 1a’s syntax. Instead, we derive it from the additional rule given by Collapse 67 Semantics. Stating the rule precisely and complete is a bit cumbersome. But, roughly, the rule is this. If a sentence S has a 2-place predicate R and 2 occurrences of the same term a, then, S encodes the structurally collapsed reflexive monadic proposition that a self-R’s; if S has a 3-place predicate and 3 occurrences of a, S encodes 4 collapsed propositions--the totally collapsed 1-place monadic proposition that a R’s itself to itself and 3 partially collapsed dyadic propositions—that a R’s itself to a, that a R’s a to itself (λx [Rxax]a) and that a R’s a to itself (λx [Raxx]a), etc. So, 1a, for example, though a dyadic predication, encodes the structurally collapsed monadic reflexive proposition that Elton John is self-identical. According to Collapse Semantics, a sentence S having two or more occurrences of the same term induces a structural collapse so that on at least one of the readings of S, S encodes a structurally collapsed proposition with reflexivity. Let us turn to Frege’s Puzzle. Intuitively, 1a and 1b differ in their informational value. Call this intuition, “The Frege Intuition” or “FI”. FI is powerful. While 1a seems to be trivial and a priori, 1b seems to be non-trivial and a posteriori. So, insofar as the epistemic status (a priori/a posteriori) status of a sentence S is determined by the epistemic status of the proposition semantically encoded by S, 1a and 1b must express different propositions. However, there are very powerful reasons that support Millianism. This is the puzzle. As I see it, what the puzzle shows is that standard semantics is inadequate. Given standard semantics, we have to either reject either FI or Millianism. But, neither of these options is viable. Rejecting Millianism, as we will see, simply cannot be the answer to the puzzle. Rejecting FI, which two leading Millians, Nathan Salmon (1986) and Scott 68 Soames (2002) advocate, as we will see, cannot be the answer either. Besides, rejecting FI is an unattractive option. It saddles Millians with an uncomfortably counter-intuitive result. The purpose of this chapter is to advocate a move towards Collapse Semantics. Here is the argumentative strategy. In part I, I argue that rejecting Millianism cannot be the answer to the puzzle. In part II, I provide independent arguments for Collapse Semantics. In part III, I reconstruct the Salmon and Soames argument against FI. I then offer a rebuttal appealing to Collapse Semantics. In part IV, I offer a criterion for the a priori for singular propositions (since these are the kinds of propositions we are dealing with if names are Millian). In part V, Appealing to Collapse Semantics and the results of part IV, I argue that FI and Millianism are fully compatible. I then finish with some concluding remarks. 4.1 Why rejecting Millianism cannot be the answer to Frege’s Puzzle Here are reasons to think that rejecting Millianism cannot be the answer to Frege’s Puzzle. Consider 2a. Ketchup is ketchup 2b. Ketchup is catsup 41 41 This example is from Salmon, Nathan, How to Become a Millian Heir, Nous, 1989 69 Intuitively, 2a and 2b differ in their informational value. While 2a is trivial and a priori, 2b is non-trivial and a posteriori. Let us call this intuition, “the Frege Intuition*” or “FI*”. It seems that anyone who insists on FI must also insist on FI*. So then, 2a and 2b must express different propositions. And, anyone who rejects Millianism because of FI, for parallel reasons, must reject Mill* because of FI*. Mill*: “ketchup” and “catsup” are synonymous. However, rejecting Mill* is decidedly unattractive. No doubt, “ketchup” and “catsup” are perfectly synonymous. So, they cannot differ in meaning. The point here is that rejecting Millianism because of FI does not get us very far. Of course, one can “bite the bullet”, so to speak, and nonetheless reject Mill*. But, this is kind of move betrays shortsightedness. Consider 3a. No one doubts that everyone believes that all medical doctors are medical doctors. 3b. No one doubts that everyone believes that all medical doctors are physicians. 42 Intuitively, while 3a is true, 3b is false. Surely, someone doubts that everyone believes that all medical doctors are physicians. However, just as surely, no one doubts that everyone believes that all medical doctors are medical doctors. Let us call the intuition that 3a and 3b differ in truth-value, “The Mates Intuiton” or “MI”. Anyone who insists on FI and FI* must also insist on MI 43 44 . Insofar as the objects of the attitudes are 42 This example is from Benson Mates, Synonymity, UC Publications in Philosophy, 25:210-226. Reprinted in Semantics and the Philosophy of Language, L. Linsky, ed. (Champaign: University of Illinois Press, 2952), 111-136 (1950) 70 propositions, the embedded propositions, the proposition that all medical doctors are medical doctors and the proposition that all medical doctors are physicians must be distinct. But, surely, no one wants to deny that the terms “medical doctor” and “physician” are synonymous. They are both synonymous with “a person licensed to practice medicine”. The strategy of rejecting Millianism and Mill* because of FI and FI* respectively naturally leads to denying this because of MI. Thus, rejecting Millianism because of Frege’s Puzzle is not a viable option. 4.2 Collapse Semantics Before I provide independent argumentation for Collapse Semantics, it should be pointed out that positing structural collapse is not unique to Collapse Semantics. Collapse Semantics is unique in that it posits reflexivity and structural collapse for sentences with two or more occurrences of the same term. The name “Collapse Semantics” is a bit misleading. A non-misleading name would have been, “Multiple Occurrence Collapse Semantics”. For Collapse Semantics is not unique in positing structural collapse in 43 It should be noted that Salmon and Soames reject FI, FI* and MI. See their joint introduction to their Propositions and Attitudes, Oxford Press, 1988 and Soames’s Substitutivity, reprinted in On Sense and Direct Reference, p.327, Davidson, Matthew, 2007, McGraw Hill. So, they are consistent. Consistency demands that anyone who rejects one should reject all of them. Anyone who accepts one of them should accept all of them. Consistency demands of any Fregean who insists on FI to also insist on MI. 44 It should be noted that Alonzo Church, a devoted Fregean, who wholeheartedly accepted FI and FI*, rejected MI. See his, Intensional isomorphism and identity of belief, Philosophical Studies, Volume 5, Number 5, p.65-73, 1954. Church’s position is unstable. What supports FI and FI* is intuition. What supports MI is intuition. Church recognizes that “physician” and “medical doctor” are perfectly synonymous. So, he feels compelled to reject MI and then explain away the intuition behind MI. Church therefore cannot credibly criticize the Millian who does the exact same thing with FI. He cannot object to the Millian by simply insisting on FI. 71 general. Soames (1994), for instance, who rejects (multiple occurrence) Collapse Semantics, argues for structural collapse and reflexivity for sentences with anaphora like 4a 45 . 4a. Elton loves his mother. 4b. Elton loves Reginald’s mother There is a very natural reading of 4a where it predicates the property of being a self- mother lover to Elton. “Elton is a good boy. Like every good boy, Elton loves his mother”. In order to get this reading, the occurrence of “his” must be anaphoric behaving like a bound variable. But bound by what? Its antecedent is a name, so it cannot be that. There is no quantifier, so it cannot be that. Soames’s suggestion is that the binder must be an abstraction operator, the operator being introduced by the anaphoric relationship. We grasp reflexivity in this reading. Soames provides an accounting. On Soamesian Semantics, 4a’s lambda expansion is, “λx [Lx(m(x))] a”. 4a, though a dyadic predication, encodes a structurally collapsed monadic proposition with reflexivity. While 4a and 4b have the same structure, on one of the readings of 4a, their lambda expansions are structurally distinct 46 . 45 Soames, Scott, Attitudes and Anaphora, Philosophical Perspectives, 8, Logic and Language, p. 251-272, 1994 46 This provides a satisfying explanation for why 4a and 4b differ in informational value. Suppose I know that Jones believes that everyone, no matter how wretched, loves his or her own mother. So then, with asking Jones about Elton in particular, I know that Jones believes the proposition encoded by 4a. However, 72 Here is the first argument for Collapse Semantics in particular. Consider 5a. I love my mother 5b. He loves my mother There is a very natural reading of 5a where it encodes the proposition that I love my own mother. “I’m a good boy. Like every good boy, I love my mother”. So, we get structural collapse and reflexivity. It encodes the proposition that I am an own mother lover. In contrast, 5b, accompanied by a demonstration of a picture of me, encodes the dyadic proposition that I stand in the love relation to my (DK’s) mother. In order to account for the reflexivity in 5a, we must have binding and an abstractor. So, 5a’s expansion is, “λx [Lx(m(x))] I”. 5b, since it does not have two occurrences of the same term, does not have binding or an abstractor. This is precisely how it should be because we do not pick up any reflexivity when we grasp 5b. The only explanation for why 5a encodes the structurally collapsed proposition but 5b does not that I can see is that while 5a contains two occurrences of the same term, 5b does not 47 . if I do not know that Elton is the same person as Reginald, without more information about Jones, I do not know that Jones believes the proposition encoded by 4b. 47 If we accept Soames’s analysis of 4a and anaphora, then, the analysis of 5a, on Collapse Semantics, must be something like this. The second occurrence of “I”, i.e., “my” in 5a is acting like a bound variable instead of a referring term. It, like the occurrence of “his” in 4a, is essentially a bound variable. Also, the relationship between two occurrences of the same term is essentially an anaphoric relationship. Just as the anaphoric relationship in 4a induces an abstractor, the relationship between two occurrences of the same term in 5a induces an abstraction operator. 73 Here is the second argument. Consider 6a. ∀x (Lxx) 6b. ∀x (Lxa) Notice that we can derive 7 from 6a or 6b by universal instantiation. 7. Laa The importance of this can only be appreciated if we are allowed to think about the propositions encoded by 6a and 6b. Indeed, standard first order logic -- developed as a means of formalizing mathematical and logical reasoning -- is not concerned with propositions or properties. It is only concerned with assigning the proper extensions to expressions relative to model structures. However, when formal languages of first order logic are enlisted in the investigation of doxastic and assertive contents, we must go beyond what is given by standard treatments of such languages. Insofar as we want to understand what it is that Jones believes when he believes that everyone loves himself, we must able to identify the proposition encoded by 6a. The proposition encoded by 6a is that everyone loves him or herself. The proposition encoded by 6b is that everyone loves a. So then, insofar as 7 is an instantiation of 6a and 6b, 7 encodes both the proposition that a loves himself and the proposition that a stands in the love relation to a. This suggest that 7 encodes both the dyadic proposition that a loves a and the monadic 74 proposition that a loves himself, just as Collapse Semantics predicts. In general, when we have a universal claim that everything has property F, then, any instantiation of that claim is a claim about some particular object o, that o has F. Here is a third argument. Suppose Jones wishes to make the point that his band of friends is not as close as they could be. The reason is that each of them, Tom, Dick and Harry is really selfish. He sits them down and starts getting really preachy, “Tom only cares about Tom, Dick only cares about Dick and Harry only cares about Harry”…“hey guys, we can’t have a true fraternity if each man only cares about himself”. The inference to the universal claim that each man only cares about himself is a natural one. One plausible explanation for this is that one of the readings of, “Tom only cares about Tom”, is that Tom only cares about himself. The fourth argument is this. The thought that a sentence like 1a encodes the monadic proposition is almost irresistible. Consider Kripke and Salmon. Kripke: …Am I myself necessarily self-identical? Someone might argue that in some situations which we can imagine I would not even have existed, and therefore the statement “Saul Kripke is Saul Kripke” would have been false, or it would not be the case that I was self- identical. Perhaps, it would have been neither true nor false, in such a world, to say that Saul Kripke is self-identical. 48 48 Kripke, Saul, Identity and Necessity, p. 219, reprinted in Metaphysics, Michael Loux, 2001. Kripke maintains that a sentence like 1a only encodes the collapsed monadic proposition. 75 Salmon: Direct-reference theory is saddled with serious philosophical problems. One set of problems concerns identifications. If direct-reference theory is correct, then a statement like “Mark Twain is Samuel Clemens” simply says about Mark Twain that he is himself. So the sentence would mean the same thing as, “Mark Twain is Mark Twain”. 49 Very often when speakers consider a sentence like 1a, with two occurrences of the same term, the mind immediately grasps reflexivity. Admittedly, this is a bit of a conjecture. But, I have a strong sense that it is true 50 . When Jones assertively utters 1a, it is very natural to report him as having asserted the collapsed monadic proposition. The report most certainly feels accurate. Now, if speakers are uniformly grasping the monadic proposition when considering 1a and the assertion reports seem natural and accurate, then, it is really hard to see the motivation for denying Collapse Semantics. The predicate “is” (of identity), for instance, can be thought of as denoting a two- place function from objects o and o* to the true iff o and o* stand in identity. 49 Salmon, Nathan, A Father’s Message, in the preface of Metaphysics, Mathematics, and Meaning, Philosophical Papers, Oxford Press, 2005. For Salmon, this is just a momentary lapse. He and Soames have been adamant that a sentence like 1a only encodes the dyadic proposition. But, this is precisely my point. Even someone who adamantly opposes Collapse Semantics, like Salmon, finds himself identifying the proposition encoded by a sentence like 1a as the collapsed reflexive proposition. 50 This is anecdotal, so it must be taken for what it is worth. In my experience, people who reject Millainism usually say something like the following, “come on, are you saying that Hesperus is Phosphorus says the same things as Hesperus is Hesperus? No, Hesperus is Phosphorus does not simply say that Hesperus is self-identical”. Diehard Millians respond, “I don’t think it is that implausible”. I have even heard Millians say, “I don’t care how counterintuitive that seems. It’s still true”. The point here is that Millians and non-Millians alike seem to pick up on the monadic reading of 1a. 76 Equivalently, we can think of the predicate as denoting a function from an object o* to the function from an object o to the true iff o stands in identity to o*. Using lambda, we can think of this function as λy [λx [x = y] z] u. By function application, the denotation of the predicate is a is the function λy [λx [x = y] z] a. By lambda elimination, we get λx [x = a] z. On standard semantics, for any term t, regardless of whether t is an occurrence of the same term as a or not, t = a can only be expanded as λx [x = a] t. So, the only lambda expansion of 1a is 1a-LE-2. 1a-LE-2. λx [x = EJ] EJ On Collapse Semantics, if t is an occurrence of the same term as a, then, t = a can also be expanded as λx [x = x] t. If the Collapse Semanticists is granted creative license for this one move, I believe Frege’s Puzzle can be solved. On Collapse Semantics, 1a can be expanded as 1a-LE-1 and 1a-LE-2. 1a-LE-1. λx [x = x] EJ 1a-LE-2. λx [x = EJ] EJ 4.3 The Salmon and Soames argument against “The Frege Intuition” 77 I will first present the Salmon and Soames or NS-SS argument that contrary FI, 1b, like 1a, is a priori. Second, I will make a conjecture about it. Third, I will give my rebuttal to it. The NS-SS argument Here is Salmon: It is precisely the seemingly trivial premise that a = b is informative whereas a = a is not informative that should be challenged, and a proper appreciation for the distinction between semantically encoded and pragmatically imparted information points the way…with a sharp distinction between semantically encoded information and pragmatically imparted information kept in mind, it is not in the least bit obvious, as Frege’s puzzle maintains, that a = b is, whereas a = a is not, informative in the relevant sense 51 . To be sure, a = b sounds informative…but that is pragmatically imparted information, and presumably not semantically encoded information. It is by no means clear that the sentence a = b, stripped naked of its pragmatic impartations and with only its properly semantic information content left, is any more informative in the relevant sense than a = a …these two sentences may very well encode the same piece of information. I believe they do 52 . 51 The relevant sense here is that they do not differ in semantically encoded information. Their pragmatically imparted information may differ but their semantically encoded information does not. Thus, in the sense that their semantically encoded information is the same, the semantically encoded information of one is informative iff the other is. 52 Salmon, 1986 78 Soames: If names don’t have descriptive semantic content, then it would seem that their only semantic contents are their referents. From this it follows that co-referential names have the same content. If we add a plausible principle of compositionality 53 , we are led to the view that sentences differing only in the substitution of one of those names for another must have the same semantic content, and so must semantically express the same proposition…if a and b are proper names and the sentence a = b is true, then it semantically expresses the same proposition as the sentence a = a. But then, since the proposition expressed by a = a is surely knowable a priori, so is the proposition expressed by a = b. 54 Salmon and Soames are essentially giving the same argument. They want us to make a sharp distinction between two kinds of information imparted by an assertive utterance of a sentence s--the information semantically encoded by s and the information pragmatically imparted by an assertive utterance of s. To see the difference between these, consider 1b. For Soames, an assertive utterance of 1b can, depending on the shared beliefs between a speaker and her audience about the person named “Elton John” and the person named “Reginald Dwight”, express various pragmatically enriched propositions or assertive contents. Suppose I am the speaker and my buddy Bobby is the speakee, and Bobby and I share the belief about the person we refer to as “Elton John”, that he is super stylish, flamboyant, a spectacular song-writer and performer; also, we 53 Though a principle of compositionality is distinct from a theory of semantics, for our purposes, we can understand the principle of compositionality Soames has in mind as roughly the same thing as standard semantics. 54 Soames, (2002) 79 share the belief about the guy we refer to as “Reginald Dwight”, that he is drab, dull, a no-talent, etc. Given that this shared belief is in the background, I can utter 1b to express, among other things, the singular proposition about Elton John, the super stylish, flamboyant, super star, songwriter and performer, that he is identical with Reginald Dwight, the drab, dull, bore. The information pragmatically imparted by an assertive utterance of a sentence s is any part of the pragmatically enriched proposition, which is not included in s’s semantic content. For Soames, the information semantically encoded by a sentence s is that which is common to all potential assertive utterances of s. Soames’s idea is that if we take all the assertive contents of all the potential assertive utterances of s, s’s semantic content would be the “common denominator”, i.e., that which all the assertive contents have in common. The idea then is that the elements common to all of the assertive contents of 1b are Elton John, the identity relation and Elton John. So then, the semantic content of 1b is the bare singular proposition about Elton John that he stands in identity to Reginald Dwight. It is not at all clear that this proposition is any different than the proposition expressed by 1a. For Salmon and Soames, the two propositions are the same. Thus, 1a is a priori iff 1b is. The argument in a nutshell: P1: The proposition expressed by 1a and 1b are the same. (Millianism plus standard semantics) 80 P2: The proposition expressed by 1a is a priori (obvious) C: The proposition expressed by 1b is a priori (Leibniz’s Law) A Conjecture: Before I offer my rebuttal to the argument, I will make a conjecture about it. The conclusion to the argument is startling. Moreover, I believe it is false. Why then does the argument appear to go through? My conjecture is that when we evaluate the argument, we (unwittingly) slip back and forth from the monadic and dyadic propositions encoded by 1a. We saw that even Salmon, who scrupulously maintains the distinction, slips on occasion. It is very easy to be enticed by the NS-SS argument even if it turns out to be inconclusive or even unsound. When we think of premise 1, we identify the proposition semantically encoded by 1b as the dyadic proposition. We then notice that 1a and 1b have the same syntax and we calculate that they have to encode the same proposition. So, premise 1 goes through. 1a and 1b have the same syntax and so must encode the same proposition. Then, we move to premise 2 and (unwittingly) slip from considering the dyadic proposition to considering the monadic proposition. As mentioned before, considering the monadic proposition when considering 1a is almost irresistible. The fact that the monadic proposition is a priori is of course obvious. So, premise 2 goes through. Then, one gets the startling result that 1b is a priori. My conjecture is that even if Salmon and Soames do not make the mistake I suggest, many who accept their argument do. 81 Rebuttal If we identify the proposition semantically encoded by 1a as the monadic proposition, then, premise 1 is false If we identify the proposition semantically encoded by 1a as the monadic proposition, then premise 1 is false. The property of being self-identical is universally instantiated. The property of being identical with Elton John/Reginald Dwight is not. Thus, these are distinct properties. Thus, the monadic and dyadic propositions are distinct 55 . Insofar as the proposition semantically encoded by 1a is the dyadic proposition, the proposition semantically encoded by 1a and the proposition semantically encoded by 1b are distinct. If we identify the proposition semantically encoded by 1a as the dyadic proposition, then, premise 2 is inconclusive. Salmon and Soames reject Collapse Semantics and so identify the proposition semantically encoded by 1a as the uncollapsed dyadic proposition for both premises. So, premise 1 goes through with no problem. But, premise 2 is no longer obvious. Without argumentation, it is inconclusive. 55 It should be noted that not everyone accepts that the monadic and dyadic propositions are distinct. Kripke, for instance, denies it. As he sees it, accepting the difference between the two invites some unwelcome results. 82 3 reasons to think that without argumentation, premise 2 is inconclusive There are 3 reasons to think that without argumentation, premise 2 is inconclusive. The first has to do with FI. If we identify the proposition semantically encoded by 1a as the dyadic proposition, then, since the proposition semantically encoded by 1b is the dyadic proposition, if we presume FI, we should presume that the dyadic proposition is a posteriori. In other words, the presumption is against premise 2. So, without argumentation, we cannot accept it. The second is that the a priori is not a species of the analytic 56 . A sentence s of language L is analytic if s is true simply as a consequence of the stipulated rules of L or true simply in virtue of meaning. 1a is analytic regardless of whether we understand the proposition semantically encoded by it as the monadic proposition or the dyadic proposition. However, that does not guarantee that any proposition encoded by it is a priori. To see this, consider 8a. Dthat [the author of Naming and Necessity] is the author of Naming and Necessity if there is a unique author of the book. 8b. Saul Kripke is the author of Naming and Necessity if there is a unique author of the book. 56 I lifted this point from Soames, chapter 4, Reference and Description, Princeton Press, 2005 83 9a. I am here now—relative to context—C1 <SK, CUNY 57 , 12pm-12.8.07, @> 9b. Saul Kripke is at CUNY at 12pm-12.8.07 in @. As far as I am aware, both Salmon and Soames acknowledge that indexicals are directly referential and that “dthat” is a device for direct reference 58 59 . Dthat [the ϕ] relative to a context C directly refers to the ϕ at the time and world of C. A context is a 4-tuple consisting of an agent, a time, a location and a world. Thus, the proposition semantically encoded by 8a relative to a C where SK is the author of the book and the proposition semantically encoded by 8b are the same. Likewise, the proposition semantically encoded by 9a relative to C1-<SK, CUNY, 12pm-12.8.07, @] and the proposition semantically encoded by 9b are the same. So, 9a is a priori iff 9b is. Surely, the proposition semantically encoded by 8b is a posteriori. Thus, 8a is a posteriori. An analogous thing can be said about 9a. 60 Thus, 8a and 9a are both a posteriori. Why then 57 “CUNY” is an acronym for “The City University of New York”. 58 Kaplan does not include “that” in the formal system of demonstratives. Instead, he has “dthat” serve as it surrogate. The main reason for doing so is that “that” often takes an accompanying demonstration, a physical gesture of some kind, for a referent to be determined. The referent and semantic content of “that” relative to a context is the object demonstrated by an accompanying demonstration. But, from a practical standpoint, there is no way of simulating a physical gesture in a formal language. Moving from “that” to “dthat” allows us to get around this problem. “Dthat” is much more flexible than “that”. Instead of insisting on a physical gesture as an accompanying demonstration, a singular term, like a definite description, e.g., the author of Naming and Necessity can serve as the accompanying demonstration. 59 To say that “dthat” is a device for direct reference is to say that if we take any singular term t, dthat [t] relative to a context C directly refers to the object picked out by t at the time and world of C as content. 60 For Salmon and Soames, there is much at stake in maintaining that 8a and 9a are a posteriori rather than a priori. Given that 8b is clearly a posteriori, if it turns out that 8a is a priori then 8a and 8b would differ in epistemic status despite the fact the propositions semantically encoded by them are the same. But then, since the proposition encoded by 8b is clearly contingent, 8a would be contingent a priori. Roughly then, though 8a’s modal status is derived from the modal status of the proposition it semantically encodes, 8a’s epistemic status is not derived from the epistemic status of the proposition semantically encoded by it. 84 do they seem to be a priori? The reason must be that 8a and 9a are “analytic”--true simply in virtue of the rules governing the Logic of Demonstratives. The only contexts allowed in a model structure of the Logic of Demonstratives are what Kaplan calls “proper contexts”. A context C is proper iff the agent of the context, is in the location of the context at the time of the context in the world of the context. Also, 9a, when evaluated at the world and time of a context, must be true. Anyone who understands the rule of the logic to which the language belongs can see that 8a and 9a have to be true. What this shows is that the a priori is not a species of the analytic. The fact that 1a is analytic does not guarantee that the proposition semantically encoded by it is a priori. Thus, the dyadic proposition needs to establish its a priori credentials on its own, so to speak, independent of its association with 1a. For this, independent argumentation for premise 2 is needed. Without one, premise 2 is inconclusive. The third reason is that while we can properly judge that the monadic proposition is true by reason alone, we cannot do the same with the dyadic proposition. 1a can establish its a priori credentials on its own. It does not need to appeal to its association to 1a. The monadic proposition is the predication of the property of being self-identical to Elton John. Reason has something to say about predications involving this property. The property is very non-discriminating. Reason says that any object, actual or merely possible, must have this property. An object has this property not because of anything Instead 8a’s epistemic status comes directly from itself. Is 8a the kind of sentence which expresses a truth regardless of what the world is like? If yes, 8a is a priori, if no, not. In sum, 8a’s epistemic and modal statuses come from two different sources. This then is a basis for saying that there is no single thing (the proposition) which is both contingent and a priori. Thus, the significance of the Kripkean divide between the necessary and the a priori is minimized. This is something both Salmon and Soames are loath to accept. 85 special about that object. That is why when the proposition semantically encoded by 1a is identified as the monadic proposition premise 2 goes through without argumentation. But, the dyadic proposition is a different matter. It predicates identity with Reginald Dwight to Elton John. This property is not universally instantiated. Instead, it is a very discriminating property. It is instantiated by at most one object—Elton John. Any object other than Elton John lacks it, even his molecule for molecule twin. The fact that Elton John has it is a non-trivial and “metaphysical” fact about him. For this reason, it is hard to see how reason alone can decide whether the dyadic proposition is true. Some (a posteriori) information about the metaphysical facts is necessary. Reason seems to allow us to not believe the dyadic proposition and to even disbelieve it. If I were to meet Elton John, very easily I might not believe that he is the “real” Elton John. I might suspect that he is merely a molecule for molecule twin and even believe that he is not Elton John. Independent of its association with 1a, we have no reason to even suspect that the dyadic proposition is a priori. For these reasons, without argumentation, we should resist premise 2. NS-SS argument for premise 2 Let us consider an NS-SS argument for the claim that the dyadic proposition is indeed a priori. For NS-SS, the proposition semantically encoded by 1b is a priori because it is true and therefore the same proposition as the one encoded by 1a. Why is this a reason to think that it is a priori? There are two possible answers to this. The first is that if the 86 proposition encoded by 1b is also encoded by a sentence like 1a, then, it is encoded by at least one transparently true sentence. Anyone who understands 1a can see that it must be true. So, any proposition encoded by it is a priori. Though, no doubt, there are many who take NS-SS to be arguing in this manner, they do not argue in this fashion. They both recognize that the propositions encoded by 8b and 9b are a posteriori despite being encoded by 8a and 9a, respectively. Also, they both see that for virtually any singular proposition p, we can construct a sentence s (using the term “dthat”), where s is transparently true and s encodes p iff p is true 61 . To see this, consider the proposition encoded by 10b. 10a. Michael Jordan wore the number “23” for the Chicago Bulls, if anybody did. 10b. Dthat [the last man to wear “23” for the Chicago Bulls] wore the number “23” for the Chicago Bulls, if anybody did. The proposition encoded by 10a is a true singular proposition. If we can construct a transparently true sentence which encodes it, then for any true singular proposition p, we can construct one for p. As we know, 10b encodes the same proposition as the one encoded by 10a. But, surely, the result that every true singular proposition is a priori is intolerable. This answer is a non-starter. 61 Though this observation is original with me in the sense that I did not get it from anyone else, as it turns out, Soames has already made it in at least two places—in his Age of Meaning and in his Reference and Description. 87 The second possibility is that any such proposition is a proposition about the content of the subject term, “that it is it”. So, insofar as the proposition encoded by 1b is also encoded by 1a, it is the singular proposition about Elton John, that he is him. And, any such proposition must be a priori. This is the argument Salmon and Soames endorse. What is special about the dyadic proposition being characterizable as, “the proposition about Elton John, that he is him”? The answer is that any such characterization reveals in a transparent way that the “two” members of the proposition stand in the identity relation. That is, the proposition can be characterized in a way which reveals its truth in a transparent way. Thus, it is a priori. Salmon proposes a slightly different but related way of thinking about this idea 62 . Consider the formula, “λx [λy, z [y = z] x, x] EJ”. The proposition encoded by this formula is the predication of “the reflexive property of standing in self-identity to EJ”. The functor, “λx [λy, z [y = z] x, x]” encodes the propositional function from an object o to the dyadic self-identity proposition that o stands in the identity relation to o. If we give Elton John to this function, we get back the uncollapsed dyadic self-identity proposition that Elton John stands in the identity relation to Elton John. As we can see, this function always returns a true proposition. Understanding the function is enough to know that this is so. Since the dyadic proposition is true, we know that it is the value of this function applied to some argument. In other words, since the dyadic proposition is true, it is 62 This alternative way of thinking about his and Soames’s position was proposed to me by Salmon in direct correspondence. 88 characterizable as the value of a function which we know always returns a value which is true. Thus, since the dyadic proposition is true, it is a priori knowable. My Rebuttal Does the fact that the dyadic proposition can be characterized as the value of a function f, where understanding f is enough to know that it always returns a value which is true, enough to establish that it is a priori? There are reasons to doubt that it is. Consider function f*; f* is a function whose domain is the set of physicians D. f* is defined for all and only the members of D. It takes us from an object o from D, to the singular proposition that o is a physician. We can see that just by understanding the function, any of its values must be true. Suppose Jones is a physician. So then, we know that the proposition that Jones is a physician is the value of this function. That is, it is characterizable as the value of a function, where understanding that function is enough to know that it always returns a value which is true. However, we should not therefore be tempted to say that the singular proposition that Jones is a physician is a priori. It clearly is not. The wider lesson here is that genuine cases of the a priori cannot just be manufactured. Kaplan’s “dthat” operator is an example. Indeed it is true that understanding how “dthat” works is enough to know that dthat [the ϕ] is ϕ must be true. Introducing a name n by a description D is another example. We can introduce n to be the name of whatever satisfies the D. And, understanding how a stipulation like this 89 works is enough to know that the proposition that n is D must be true. But, these are not genuine cases of the a priori. Likewise, constructing a function which always returns a true proposition is not a way to manufacture genuine cases of the a priori. For these reasons, I remain skeptical of premise 2 of the NS-SS argument. I conclude that the argument is inconclusive. 4.4 A criterion for the a priori for singular propositions Let us recall Kripke’s epistemic argument against descriptivism 63 . Consider 11a. George Washington is the first American president 11b. The first American President is the first American President The description most people associate with the name “George Washington” is the “The first American President”. So, if the name were synonymous with any description, it would be synonymous with this one. And, 11a and 11b would encode the same proposition. So, one of them would be a priori iff the other is. The proposition encode by 11b is a priori. But, the proposition encoded by 11a is not. The upshot is that “George Washington” is not synonymous with, “The first American President” or any other description. So, there is no description associated with the name. Millians, 63 See Kripke, Saul, (1980), for all the arguments, including the epistemic argument, against descriptivism. 90 Salmon, Soames, et al, draw the further lesson that the meaning of “George Washington” is therefore just its referent. The question I am interested in here is why the proposition encoded by 11b is a posteriori? My proposed answer to this question has two parts. The first part is that a concrete object like George Washington is indefinable, unanalyzable. The best we can do in terms of a definition is to demonstrate George Washington and give an ostensive definition. To be George Washington is to be that guy, to have “thatness” (demonstrating George Washington) 64 . Even if we suppose that being a homo sapien is an essential property of George Washington, it is no part of his definition. One reason is that being a homo sapien is also an essential property of Abraham Lincoln. Another reason is that if it were part of his definition, the proposition that George Washington is a homo sapien would be a priori. But, it is not. Though necessary if true, the proposition is posteriori. The second part to the answer is that the property of being the first American President is a non-trivial monadic property. Definition of a monadic trivial property: A monadic property F is trivial iff for any object o, applying ~F to o leads to incoherence. 64 In contrast to a concrete object like George Washington, an abstract object like the number 2 can be defined set-theoretically, perhaps. Following Frege and Russell, we can think of it as the class of all sets with exactly 2 members. We can (perhaps) provide a set-theoretic analysis of the natural numbers in this way. But, no analogous analysis can be given for a concrete object like George Washington. 91 Take proposition that o is a man and not a man for some arbitrary o. This is incoherent. Thus, the monadic property of being a man or not a man and the monadic property of being such that if a man then a man are trivial. Take the proposition that o is an unlicensed physician. This is incoherent. Thus, monadic property of being licensed or a physician is trivial. For a proper criterion of the a priori for singular propositions with concrete, indefinable, unanalyzable objects as constituents, we first need a definition of the a priori. Definition of the a priori: A proposition p is a priori iff p can be justified by reason alone. The criterion is this. For any singular proposition p with a concrete object o as a constituent and a monadic property F, o is F is a priori iff F is trivial. Since o is concrete and therefore indefinable, the property has to do all of the work, so to speak. The property has to be such that we can judge by reason alone that any object has to have it. The proposition that Elton John is a man or not a man is a priori. The reason is that this property is trivial. For an arbitrary o, o is a man or not a man is a priori. Likewise, the proposition that Elton John is licensed or a physician is a priori. We can know that it is true simply by grasping the concepts. The proposition encoded by 11a’s a posteriori status can best be explained if we assume Millianism. 11a encodes the singular proposition about George Washington, that he is the first American President. George Washington is a concrete object and the property of being the first American President is non-trivial. Likewise, the reason the proposition that George Washinton is a homo sapien 92 is necessary but a posteriori is that the property of being a homo sapien is non-trivial. In general, on my suggestion, the reason the Kripkean necessary a posteriori is possible is that some monadic properties, e.g., being a homo sapien, not being made of ice, etc., are essential to anything which has them. Yet, they are non-trivial. Here is the recipe for the necessary a posteriori. First, take an indefinable, unanalyzable object o. Second, take a non-trivial essential property F. Predicate the property of the object—o is F. You are guaranteed a proposition which is necessary a posteriori if true 65 . 4.5 Argument that “Elton John is Reginald Dwight” is a posteriori I contend that while the property of being self-identical is trivial, the property of being identical with Reginald Dwight, though essential, is non-trivial. Surely, the property of being identical with Reginald Dwight is non-trivial. The claim that o is not identical with Reginald Dwight, for some arbitrary o, is perfectly coherent. Thus, though it is necessary if true, the dyadic proposition is only knowable a posteriori. The claim that Elton John, stands in identity to Reginald Dwight depends for its truth on a metaphysical fact—whether or not Elton John has the property of standing in identity to Reginald Dwight. The dyadic proposition is metaphysically non-trivial. In contrast, the property 65 Indeed Kripke’s examples of the necessary a posteriori include not only monadic properties but also n- place properties, where n > 1. For example, the claim that a particular table is “made of” ice is necessary a posteriori if true. But with this two-place property, we fill in the relevant argument spots so that we get a monadic property, i.e., the property of being made of ice. Then we take this property and ask whether or not it is trivial. 93 of being self-identical is trivial. Thus, while 1a is trivial and a priori, 1b is non-trivial and a posteriori. This concludes my argument that FI and Millianism are fully compatible. Conclusion Frege’s Puzzle has been a particularly intractable puzzle. The reason, I believe, is an uncritical adherence to standard semantics. From that framework, a satisfactory solution to the puzzle is impossible. The options are to either reject FI or reject Millianism. In part I, we saw that rejecting Millianism is not a viable option. In part V, we saw that the dyadic proposition is a posteriori. So, contrary Salmon and Soames, if we hold onto standard semantics and reject FI, we have to reject FI by accepting that 1a and 1b are both a posteriori not that they are both a priori. But, the position that 1a is a posteriori is simply unacceptable. It is only by moving to Collapse Semantics do we get any kind of compelling solution to the puzzle. Also, Collapse Semantics provides an attractive solution to the “ketchup”/”catsup” puzzle and Mates’s puzzle. On Collapse Semantics, 2a and 2b encode different propositions. 2a encodes two propositions, one of which is the proposition that the property of being ketchup is self co-extensional, whereas 2b only encodes the proposition that the property of being ketchup and the property of being catsup are co-extensional. The former is clearly a priori, and a compelling argument can be made that the latter is a posteriori. As for Mates’s puzzle, the collapsed reading of 3a is that no one doubts that everyone believes that the property of being a medical doctor is 94 self co-extensional. That has got to be true. Surely, everyone believes that. And, surely, no one doubts that everyone believes that. In contrast, 3b encodes the uncollapsed proposition that no one doubts that everyone believes that the property of being a medical doctor and the property of being a physician are co-extensional. It is probably not true that everyone believes that. I am not sure whether I myself doubt it. But, surely, someone doubts it. So, 3b is not true. For all of the reasons stated in this chapter, I believe the case for moving towards Collapse Semantics is compelling. 95 Chapter 5 Modifying “Belief” and Partial Definition I do two things in this chapter. First, I make the case that the central lesson of Kripke’s puzzle is that our ordinary concept of belief needs to be modified. There are two principles by which we determine whether a particular agent A believes a particular proposition p or does not. The principle by which we determine whether an A believes p, let us call, “Disquotation-Belief” or “DB”. The principle by which we determine whether an A does not believe p, let us call, “Disquotation-Non-Belief” or “DNB”. I believe that our ordinary concept of belief commits us to both DB and DNB. However, DB and DNB are together inconsistent with a particular undeniable fact about language 66 and some innocuous stipulations. That is, with DB, DNB, an undeniable fact about language and some innocuous stipulations, we can derive a contradiction. Thus, I believe that our ordinary concept of belief must be modified. An interesting foil to my position is Nathan Salmon’s 67 . Salmon too recognizes that we must give up at least one of DB and DNB. But, for him, the lesson is not that we must give up our ordinary concept of belief. As he sees it, the ordinary concept of belief does not commit us to both. It commits us to DB; it 66 The undeniable fact is that some expressions in our language are non-transparent or opaque. The notion of transparency will be defined later in the chapter. 67 Salmon’s views about the puzzle can be found in Salmon, Nathan, Notes on a Puzzle About Belief, in Saul Kripke, edited by Alan Berger, (forthcoming) 96 does not commit us to DNB. So, the central lesson of the puzzle is that we must reject DNB. The second is to propose a modified concept of belief. I suggest a concept whereby the predicate “belief” is only partially defined. The partially defined conception of belief yields the double benefit of preventing us from being able to generate a contradiction while also allowing us to hold onto those features we intuitively think of as being essential to any acceptable concept of belief. Indeed we cannot accept both DB and DNB. But, with the partial definition conception, we are not forced give either up either. We can reject that either is false 68 . The chapter has two parts—1 and 2. Part 1 is devoted to showing that our ordinary concept of belief needs to be modified. Part 1 has subparts. In 1A, I present a potentially lethal problem for Millianism, what is known as “the problem of opacity”. In 1B, I present Kripke’s Puzzle as a way of showing that opacity is not a problem specific to Millianism. Rather, opacity reveals a problem with our ordinary concept of belief. In 1C, I consider two arguments for the Salmon position that there is asymmetry between DB and DNB and that DNB is false. These arguments are resisted. I then give an argument that the Salmon’s position cannot be correct. Saying that DNB is false has unwanted consequences. In 1D, I argue that our ordinary concept of belief needs to be modified. Part 2 is devoted to proposing and defending the partial definition conception. 68 The notion of a partially defined predicate was originally suggested by Scott Soames, Understanding Truth, chapter 6, Oxford Press 1999. As Soames conceives of the notion, we can find ourselves in a situation where we must reject that an n-place predicate applies to an n-tuple and reject that the predicate does not apply. 97 In 2A, I propose a partial definition of conception of “belief”. In 2B, I consider possible objections to this conception. Then, I offer replies. In 2C, I propose a semantics for belief ascriptions based on the new definition. In 2D, I present a different version of Kripke’s Puzzle. Then, I apply the partial definition conception of belief to deal with that version as well. 5.1 Modifying Belief 5.1A Opacity Let us see why opacity seems to be a problem specific to Millianism. Consider 1a. Elton John is a famous musician 1b. Reginald Dwight is a famous musician According to Millianism, the view that the propositional contribution or semantic content of a name is just its referent, “Elton John” and “Reginald Dwight” have the same semantic content. So, given any reasonable principle of compositionality 69 , 1a and 1b semantically encode the same proposition. 69 It does not matter whether we adopt Standard Compositionality or Relational Compositionality 98 However, there are very powerful reasons to think that 1a and 1b encode different propositions. Consider the principle DB. DB: For any agent A and any sentence s of any language L, if A is a normal user of s and A has sufficiently deliberated and the circumstances are normal, then, if A is disposed to internally assent to the unique proposition A takes to be semantically encoded by s, then A believes the proposition encoded by s. Let us say that an agent A is a normal user of a sentence s of a language L iff A takes s to mean in L what s in fact means in L. Insofar as Jones is a normal user of 1a, he takes it to semantically encode what it in fact encodes. So, in considering whether he takes himself to believe 1a expresses a truth, he primarily considers whether he takes himself to believe the proposition which is in fact encoded by it. Let us say that he has sufficiently deliberated about whether he takes himself to believe a particular proposition p or not iff he will never find himself in a position where he has to change his mind because of a lack of deliberation. Here is an example to illustrate what I have in mind. Suppose Jones runs into Carol at time t but he cannot quite remember her name. At t*, he misremembers that her name is “Susan”. So, at t*, he takes himself to believe that her name is “Susan”. So, at*, he is disposed to internally assent to the claim that Carol’s name is “Susan”. But then, suddenly, at t** he correctly remembers that her name is “Carol” and not “Susan”. Since he was able to recall Carol’s name at t**, he must have known it at t*. So then, he must have believed at t* that her name was “Carol”. This is perhaps reason to doubt that he really believed at t* that “Susan” was her name even though he was disposed to internally assent to the claim that it was. Let us say that the reason he took himself to 99 believe at t* that her name was “Susan” is that he did not sufficiently deliberate on the matter. To say the circumstances are normal is to say that there is no “funny business”, e.g., there is no evil demon manipulating Jones’s mind so that he is disposed to internally assent to p and take himself to believe p iff he does not believe p. When we understand DB in the intended way, it is hard to see how it can fail. Let us say that Jones is a huge EJ fan. He has been to numerous concerts, bought every CD, has posters of him plastered all over his room, etc. He loves EJ for his lavishness and flamboyance. But, mostly, he loves him for his music. If asked, no doubt, he will insist that he believes that that the guy he identifies with “EJ” is a musician. Jones, who is a normal user of 1a, after sufficient deliberation, under normal circumstances, is disposed to internally assent to what he takes to be encoded by 1a. Thus, by DB, he believes the proposition encoded by 1a. Let us take stock at this point. By DB, the stipulation that Jones is a normal user of 1a, the stipulation that he has sufficiently deliberated, plus the stipulation that the circumstances under which he is disposed to internally assent to the proposition he takes to be encoded by 1a is normal, we derived the result that Jones believes the proposition encoded by 1a. Now, consider the principle DNB. DNB: For any agent A and any sentence s of any language L, if A is a normal user of s and A is confident that A is a normal user of s and A is not apprehensive and A has sufficiently deliberated and the circumstances are normal, then, if A is disposed to internally withhold assent to the unique proposition that A takes to be encoded by s, then, A does not believes the proposition encoded by s. 100 Notice that DNB has two provisos not present in DB. The first proviso is that A be confident that A is a normal user. The reason for this proviso is that A may be disposed to withhold assent to the proposition that A takes to be encoded by s not because A takes herself to not believe it. Rather, A might withhold assent to it because A is not confident that s really encodes what A takes it to encode. To illustrate what I have in mind, consider one of Stephen Rieber’s examples. 70 Mary is a normal user of the synonymous pair of words “bet” and “wager”. Both of these mean, staking something of value on an uncertain event 71 ; so, she takes the two terms to have this meaning. However, she is not confident that she is a normal user of both terms. So, she is disposed to withhold assent to the claim that the two terms are synonymous. We definitely do not want to therefore conclude that she does not believe that the two terms are synonymous. This proviso is meant to exclude these kinds of false negative results. The second proviso is that she is not apprehensive. It might turn out that the reason she is disposed to withhold assent is that she is simply overly cautious. She is crippled by extreme caution. The second proviso is meant to preclude this possibility. The provisos are supposed to preclude an agent A from being disposed to internally withhold assent to a proposition p for any reason other than that A takes herself to not believe p. When DNB is understood in the intended way, it is difficult to doubt. 70 Stephen Rieber, Understanding Synonyms without Knowing that they are Synonymous, Analysis 52, p. 224-228, 1992 71 This definition is from dictionary.com. 101 As it happens, Jones has a next-door neighbor who is unusually modest and low key. All Jones knows about him is that his name is “RD”. RD likes to keep things very low key when he is within the confines of his own neighborhood. He keeps things so low key that Jones could never guess that he is the musician he loves and identifies as “EJ”. Jones has absolutely no reason to believe that his neighbor is a musician. Jones, who is a normal user of 1b, confident that he is a normal user of 1b, not apprehensive, after sufficient deliberation, under normal circumstances, is disposed to internally withhold assent to what he takes to be encoded by 1b. The reason he is disposed to withhold assent is that he does not take himself to believe it. So, by DNB, he does not believe the proposition encoded by 1a. Let us again take stock. DNB, plus the stipulation that Jones is a normal user of 1b, plus the stipulation that he is confident that he is a normal user, plus the stipulation that he is not apprehensive, plus the stipulation that he has sufficiently deliberated, plus the stipulation that the circumstances are normal gives us the result that Jones does not believe the proposition encoded by 1b. As we can see, our stipulations do not commit us to saying that Jones is in any way irrational. Thus, if we assume Millianism, we can conclude that Jones believes the proposition encoded by 1a and that he does not believe it. This is the problem of opacity. The problem poses a serious challenge to Millianism. 102 5.1B Kripke’s Puzzle Here is Kripke’s Puzzle 72 . Consider Pierre a normal monolingual French speaker who lives in France and is a normal user of 2a. 2a. Londres est jolie 2b. London is pretty On the basis of what he has heard about the city he identifies as “Londres”, he is strongly inclined to think that it is pretty. Pierre, who is a normal user of 2a, after sufficient deliberation, under normal circumstances, is disposed to internally assent to what he takes to be semantically encoded by it. Thus, by DB, Pierre believes the proposition encoded by 2a. As it happens, he later moves to a particularly unattractive part of London with fairly uneducated inhabitants. His neighbors do not speak any French, so he has to learn English by “direct method”, without using any translation from French to English or vice versa. He picks up the word “London” and some other words sufficient to make him a normal user of 2b. He would never guess that the city he now inhabits and identifies as, “London” is the city he adores and identifies as “Londres”. He does not think the city he now inhabits is pretty at all. So, Pierre, a normal user of 2b, confident that he is a normal 72 Kripke, Saul, A Puzzle about Belief, In Meaning and Use, edited by A. Margalit. Dordrecht and Boston: Reidel. 103 user, not apprehensive, after sufficient deliberation, under normal circumstances, is disposed to internally withhold assent to what he takes to be encoded by it. So, by DNB, he does not believe the proposition encoded by 2b. Thus, we get the result that Pierre believes the proposition encoded by 2a and does not believe the proposition encoded by 2b. But, surely, “Londres” and “London” are literal translations of one another, i.e., have the same semantic content. And, the same is true of the predicates “est jolie” and “is pretty”. 2a encodes the proposition that London is pretty; 2b encodes the proposition that London is pretty. The “two” propositions are really one. So, Pierre believes the proposition encoded by 2a, and he does not believe it. This is the puzzle. What the puzzle shows is that opacity is not a problem specific to Millianism. The culprit must be DB or DNB or both. 5.1C Salmon and Disquotation As Salmon see it, the culprit is DNB. For him, DB and NDB are not on par. While DB is sure, NDB is not. In this section, I reconstruct two arguments on Salmon’s behalf. I then provide rebuttals to each. Then, I give an argument against the Salmon position. Here is the first argument for the Salmon position 73 . We are familiar with positive tests where passing a certain condition warrants a positive conclusion, even though failing to pass that condition does not warrant a negative conclusion. For instance, if we 73 Salmon does not give this particular argument in his paper. But, this is the kind of argument I suspect he has in mind. 104 discover a proof that a formula F of a first order logic is valid, then, the positive conclusion that F is a theorem is sufficiently warranted. Putting forward a proof that F is valid is a way of showing that it is a theorem. In contrast, failing to put forward a proof for F is not a way of showing that it is not a theorem. Even if we do not discover such a proof, drawing the conclusion that F is not a theorem would not be sufficiently warranted. In the same way, DB provides a positive test--if an agent A meets a certain requirement, A passes the test, so of speak. And, we are sufficiently warranted in concluding that A believes the relevant proposition p. Failing to pass the test of course does not sufficiently warrant the conclusion that A does not believe p. The analogy here is inapt. DNB provides a positive test for a negative result not a negative test for a negative result. Here is what I mean. Suppose Peter cannot make up his mind about whether Mary truly loves him. He thinks, at time t, “yes, she truly loves me…I can see it in her eyes.” At t, he is disposed to internally assent to the claim that Mary truly loves me. But, at t*, he thinks, “no…in my heart, I don’t really believe that…how could she have done those things to me”. At t**, he thinks, “of course, she does”. At t***, he thinks, “I’m kidding myself…I don’t think that”. Back and forth, he waffles in this manner. So, Peter has no steady disposition with respect to the claim that Mary truly loves him. DNB would be providing a negative test for a negative result if it stated that we could therefore conclude that Peter does not believe that Mary truly loves him. In that case, we could not accept DNB. However, DNB does not state that if A fails to be disposed to internally assent to p, A does not believe p. Rather, it states that if A is 105 disposed, after sufficient deliberation, to internally withhold assent to p, A does not believe p. DNB demands some kind of steady disposition. One might worry at this point about Pierre and whether he has a steady disposition with respect to the proposition encoded by 2a. Does he have a steady disposition to internally assent to it? One can be tempted to answer “no”. For, he is disposed to withhold assent to and not disposed to internally assent to it whenever it is presented to him as the proposition semantically encoded by 2b. For analogous reasons, it seems we must say that he is not steadily disposed to withhold assent to it either. I believe the opposite is true. In contrast to Peter who has no steady disposition, Pierre has two. When the proposition is presented to Pierre as the proposition semantically encoded by 2a, he is steadily disposed to internally assent. When it is presented to him as the proposition semantically encoded by 2b, he is steadily disposed to internally withhold assent. It is important to notice that DNB is a positive test for a negative result. We are, of course, familiar with positive tests for negative results, e.g., if there is a counter-model to F, then, F is not a theorem. Indeed, putting forward a counter-model to F is a way of demonstrating that F is not a theorem. And, of course, failing to find a counter-model does not show that F is a theorem. Just as negative tests for negative results are oftentimes unsound, negative tests for positive results are oftentimes unsound. So, finding a proof and finding a counter-model are on par, so of speak. A situation analogous to the one Pierre is in with respect to the proposition encoded by 2a is one in which we have a proof and a counter-model to a formula F. In such a situation, it would 106 be exceedingly unsatisfying to just conclude that F is therefore a theorem. That would be to just plain ignore the fact that there was a counter-model. The second argument for the Salmon position that DB and DNB are not on par is that there is an intuitive difference between the Belief Principle and the Non-Belief Principle. BP: For any agent A and proposition p, if A fully grasps p, then, A being disposed to internally assent to p after sufficient deliberation, under normal circumstances, is a way of A believing p. NBP: For any agent A and proposition p, if A fully grasps p, then, A being disposed to internally withhold assent to p after sufficient deliberation, under normal circumstances, is a way of A not believing p. The idea behind BP is that there is no “metaphysical gap” between A giving inner assent to p and A believing p, provided that A fully grasps p, has sufficiently deliberated on it and the circumstances are normal. For A to be disposed to internally assent to p is for A to believe p. For Salmon, BP is more strongly supported by intuition than NBP. So, ultimately, intuition favors BP over NBP 74 . On careful reflection, we should see that there is no basis for positing such an intuitive difference between BP and NBP. What is the intuitive appeal of BP? It must be that there is no intermediary step between A’s being disposed to internally assent to p and A believing p. There is nothing that needs to be added to A’s being disposed to internally assent to p to make it the case that A believes p. A’s being disposed to internally assent 74 Salmon, in conversation, has expressed to me that his case indeed rests on what he takes to be an intuitive difference BP and NBP. 107 is sufficient. A’s believing p consists in A’s mind doing something when p is presented to it. It consists in A’s mind assenting to p when p is presented to it. What makes it the case that I believe that 2 + 2 = 4? It must be that my mind is disposed to internally assent to it whenever it comes before my mind 75 . Let us call the intuition that there is no intermediary step between A’s being disposed to internally assent to p and A’s believing p, “the Cartesian Intuition”. But, if the Cartesian intuition is the intuition behind BP, then, BP and NBP are on par. For the Cartesian intuition supports NBP in exactly the same way. Surely, there is nothing that needs to be added to the fact that my mind is disposed to reject the proposition that 2 + 2 = 5 76 whenever it is presented to me to make it the case that I do not believe it. My not believing it consists in the fact my mind is disposed in this way. If the intuition behind BP is the Cartesian intuition, then, since the Cartesian intuition supports NBP in exactly the way it supports BP, BP and NBP are intuitively on par. That is, they are equally supported by intuition. Here is an argument against the Salmon position that there is an asymmetry between DB and DNB. Given that he rejects DNB as providing the correct test for non- belief, by default, the test he accepts for non-belief must be the one provided by a bi- conditional variation on DB, what we will call “Strengthened Disquotation-Belief” or “SDB”. 75 I believe that if A is disposed to internally assent to the proposition that 2 + 2 = 4 in at least one way in which is presented to A, then, rationality demands that A be disposed to internally assent to it no matter how it is presented to him. Here is a challenge. Come up with a way of presenting the proposition to an A who believes it such that A grasps the proposition but is disposed to withhold assent. 76 What I said about the proposition that 2 + 2 = 4 goes for this as well. 108 SDB: A believes a proposition p iff there is some way of presenting p to A such that, after sufficient deliberation and under normal circumstances, A is disposed to internally assent to p when presented in that way. Notice that SDB provides two tests. It provides a positive test for a positive result. If A is disposed to internally assent to p when p is presented to him some way or other, then, A believe p. But, it also provides a negative test for a negative result. If A fails to be disposed to internally assent to p when p is presented to A in some way or other, A does not believe p. But, as previously pointed out, negative tests are not on par with positive tests. Failing to find a proof for F does not show that F is not a theorem. To see that SDB is unsound, let us return to the example where Peter is waffling about whether he believes Mary truly loves him. At no point does he have a steady disposition. Thus, by SDB, we get the result that Peter does not believe it. But, that is something we should reject. He is undecided. We might say that there simply isn’t a fact as to whether he believes it. We cannot say he believes it; we cannot say that he does not. There is a very important difference between not believing something and suspending judgment about that thing. If we accept SDB, this distinction is lost. Since the Salmon position commits us to SDB, we must reject it. 109 5.1D Modifying “Belief” I argue here that our ordinary concept of belief must to be modified. The argument is the following. Premise 1: Our ordinary concept of belief commits us to both DB and DNB. Premise 2: Our commitment to both DB and DNB commits us to all expressions being transparent. Premise 3: If our ordinary concept of belief commits us to all expressions being transparent, then, if some expressions are non-transparent, then, our ordinary concept of belief must be modified. C: Our ordinary concept of belief must be modified. Given the Cartesian intuition behind DB and NDB, premise 1 is very difficult to resist. Given how we ordinarily think about belief, neither DB nor NSB can be resisted. No doubt, our ordinary concept of belief commits us to DB. And, since DB and DNB are on par, our ordinary concept of belief commits us to both. In order to evaluate premise 2, we need to know what a transparent expressions is. Here is the definition. Definition of transparency: For any expression e, e is transparent iff for any e*, if e and e* are synonymous then it is not possible for a normal user A of e and e*, who is confident that she is a normal user of both and not apprehensive, to rationally withhold judgment about whether e and e* are synonymous. 110 Consider the synonymous pair of words, “bet” and “wager”. Again, they both mean, staking something of value on an uncertain event. I claim that these terms are transparent. If Jones is a normal user of both and he is confident that he is, then, he knows that they both mean, staking something of value on an uncertain event. He sees that there is no difference in meaning at all, and he is confident that he sees this. As far as he can confidently see, they are perfectly synonymous. In order to rationally withhold internal assent to the claim that they are synonymous, he needs some reason for withholding. There are 3 potential reasons. The first is that he notices some difference in their meanings. But, that is ruled out by the fact that he is a normal user of both. The reason he has to notice a difference in meaning to be justified in withholding assent is that “bet” and “wager” are non-Twin Earthable. “Bet” means the same here on Earth as it does on Twin Earth. The reason is that “bet’s meaning is unaffected by changes in non-linguistic external facts in the environment. Given that Earth and Twin-Earth differ only in non-linguistic external facts, “bet” as used on Earth and “bet” as used on Twin Earth are synonymous. “Bet”, as used on Earth, means, staking something of value on an uncertain event; “bet”, as used on Twin Earth, means, staking something of value on an uncertain event. In order to be justified in suspending judgment about whether “bet” as used here on Earth has the same meaning as “bet” as used on Twin Earth, an agent has to notice some kind of difference in meaning between them. If he notices no difference in meaning, it must be because there is no difference in meaning. The very same things are true of “wager”. Thus, in order to be justified in suspending judgment about whether “bet” and “wager” are synonymous, an 111 agent has to haves some reason to suspect a difference in meaning between them. The second possible reason is that he has doubts about whether he is a normal user. But, that is ruled out by the fact that he is confident that he is a normal user. The third is that he is apprehensive. The reason he suspends judgment is the need for extreme caution. That is ruled out by the fact that he is not apprehensive. So, all of these potential reasons are ruled out. So then, rationality demands that he not internally withhold assent. An agent, who is a normal user of 3a and 3b, who is confident that she is a normal user, who is not apprehensive, cannot rationally withhold judgment about whether 3a and 3b are synonymous and thus co-extensional. Rationality demands that she make a judgment one way or the other. 3a. Betting on sporting events can lead to financial ruin. 3b. Wagering on sporting evens can lead to financial ruin. If Jones, a normal user of 3a, confident that he is a normal user of 3a, after sufficient deliberation, under normal circumstances is disposed to internally assent to what he takes to be semantically encoded by 3a, then, by DB, he believes the proposition encoded by it. This plus his being a normal user of 3b, plus his being confident of this fact, plus the fact that he is no apprehensive, plus his being fully rational, precludes him from also being disposed to internally withhold assent to what he takes to be semantically encoded by 3b. He is going to be disposed to internally assent to what he takes to be encoded by 3a iff he is disposed to assent to what he takes to be encoded by 3b. Thus, the occasion to invoke 112 DNB cannot arise. Likewise, if DNB were to be invoked, then, the occasion to invoke DB could not arise. Thus, DB and DNB never come into conflict. They would never be invoked together for a single agent and two synonymous sentences. They are thus perfectly consistent and sure principles. For this reason, our commitment to both DB and DNB counts on all expressions being transparent in this way. Let us now turn to premise 3. An expression e is non-transparent iff e is not transparent. In addition to the example of “Londres” and “London”, let us consider the natural kind terms “water” and ”agua”. Suppose Luis learns in school while growing up Tijuana, Mexico that the thing he calls “agua” is not an element but a compound. Its molecular structure is two parts hydrogen and one part Oxygen or H2O. He later moves to San Diego and “learns” from his extremely under-qualified science teacher that the stuff he calls “water” is not a compound but an element. Unfortunately, Luis gives credence to this teacher. So, Luis, a normal user of “agua” and “water”, rationally and with sufficient warrant believes that “agua” and “water” differ extensionally. He is a normal user of “agua” in that he takes it to mean water; he is a normal user of “water” in that he takes it to mean water. He is confident that he is a normal user of both. He has been using those terms his whole life to pick out water. His belief is sufficiently justified in that he has it on “good” authority that the two kinds of stuff are different. Thus, his belief that they differ extensionally is fully rational. Thus, he has reason to doubt that they are synonymous. Even though he is a normal user of both and he is confident that he is a normal user and he is not apprehensive in any way, he can rationally withhold judgment on whether “water” and “agua” are co-extensional. 113 The explanation for how he can be justified in believing that the two terms differ extensionally despite not seeing a difference in meaning between them is that “water” is Twin-Earthable. “Water”, as used here on Earth, has a different meaning from “water, as used on Twin-Earth. “Water”’s meaning can vary with variances in non-linguistic external facts. Typically, the kind of properties an agent A associates with “water” are things like being the stuff filling the lakes, the ultimate thirst quencher, the stuff which falls from the sky, etc. By hypothesis, A’s twin makes the same associations. Thus, “water” can differ in meaning without an agent noticing a difference. Whatever is going through A’s mind when he is thinking about “water” as used on Earth is the thing going through Twin-A’s mind when he is thinking about “water” as used on Twin-Earth. So, surely, an agent can be justified in believing that “agua”, as used here on Earth and “water” as used on Twin Earth differ extensionally even if A does not notice a difference in meaning between them. So then, A can be justified in believing that “agua” as used on Earth and “water” as used on Earth differ extensionally even without noticing a difference in meaning. Even if A does not notice a difference in meaning, there might still be! Thus, the synonymous pair “agua” and “water” are non-transparent. As we can see, the fact that “water” and “agua”, “London” and “Londres”, “Tiger” and “El Tigre”, etc. are non-transparent is going to lead to trouble. DB and DNB are going to be simultaneously invoked for Luis and “el agua es un elemento” and Luis and “Water is an element” 77 respectively. If our ordinary concept of belief commits us to 77 Just so we are not under the misapprehension that non-transparent/opaque terms are not restricted to proper names and natural kind terms, consider Nathan Salmon’s example of “ketchup”/ “catsup”. Jones 114 DB and DNB, but there are non-transparent expressions, then, our ordinary concept of belief needs to be modified. Therefore, our ordinary concept of belief needs to be modified. 5.2 Partial Definition 5.2A “Belief” and Partial Definition My proposed new definition of the predicate “belief” is one in which it is only partially defined. (PD) Partial Definition of “belief” 78 : For any agent A and sentence s, if A is a normal user of s and confident that A is a normal user of s and not apprehensive and has sufficiently deliberated and the circumstances are normal, then, if A is disposed to internally assent what A takes to be encoded by s at time t and A and is not also disposed to internally withhold assent to it at t then A believes the proposition encoded by s at t; if A, under the same conditions, is disposed to withhold assent to it at t and A is not also disposed to internally assent to it at t, A does not believe the proposition encoded by s at t 79 . visits the United States and notices that the Americans use the stuff he calls “ketchup” as a breakfast condiment for their eggs, sausages, etc. And then, he notices that they use the stuff he calls “catsup” as a lunch condiment for their hamburgers, fries, etc. As far as he can tell, the “two” stuff look, smell, taste, feel, etc. exactly the same. But, in all of his travels, he has never encountered a civilization that uses the same stuff as a breakfast condiment and as a lunch condiment. He thinks, “That would just be barbaric”. So, he believes that the “two” kinds of stuff are different. Notice that insofar as he has tasted, felt, smelt, seen, etc. ketchup, qua the stuff he calls “ketchup”, he is a normal user of “ketchup”. Jones has no problem picking the stuff he calls “ketchup”. If anyone is a normal user of the term, he is. The same is true for “catsup”. So, he is certainly a normal user of both terms. Given his extensive travels experiencing different civilizations and their practices with condiments, he is certainly justified in his belief. So, his belief that they differ extensionally is fully rational. 78 The “PD” stands for “Partial Definition”. 79 For detailed discussion on the notion of partial definition, see Soames (1999). 115 Notice that this definition is a set of two conditionals not a single bi-conditional. And, Pierre does not satisfy the antecedent of either of the two conditionals with respect to 3a and 3b, thus, we cannot say that he believes the proposition encoded by 2a, nor can we say that he does not believe it. There is no fact of the matter as to whether he does; there is no fact as to whether he does not. It is simply undefined. Here then are the requisite modifications of DB and SDB. PD-DB: For any agent A and any sentence s of any language L, if A is a normal user of s and A is confident that A is a normal user and A is not apprehensive and A has sufficiently deliberated and the circumstances are normal, then, if A is disposed to internally assent to the proposition A takes to be encoded by s at time t and is not also disposed to internally withhold assent to it, at t, then, A believes the proposition encoded by s at t. PD-DNB: For any agent A and any sentence s of any language L, if A is a normal user of s, A is confident that A is a normal user of s, A is not apprehensive, and A has sufficiently deliberated and the circumstances are normal, then, if A is disposed to internally withhold assent to the proposition A takes to be encoded by s at t and A is not also disposed to internally assent to it at t, then, A does not believe the proposition encoded by s at t. Indeed we have to reject that DB and SDB are both true. We cannot say that every instance of these two principles is true for the reason we have just gone over. But, on the partial definition conception of belief, we can also reject that either DB or SDB is false. We can reject that any instance of them is false. In the case of Pierre and the proposition encoded by 2a, even though we have to reject that he believes it, we cannot say that it follows that DB is false. In the same way, even though we have to reject that he does not believe it, we cannot say that it follows that DNB is false. There simply is no fact. And, 116 if there is no fact, we cannot accept that they are false. The only way a predication of an n-place predicate to an n-tuple can be false is if there is a fact as to whether the predicate applies or not. Accepting PD-DB and PD-DNB as replacements for DB and DNB allows us to retain the essential elements of our ordinary conception of belief. An essential element to any acceptable conception of belief is that I will never find myself in a position where I have to accept that one of my judgments about what I believe or do not believe is false. 5.2B Responding to Objections to Partial Definition Let us consider two possible objections to the PD conception of “belief” here. The first is that if we accept the PD conception of “belief” and conclude that there is no fact as to whether Pierre believes the proposition encoded by 2a, then, it seems we cannot account for some of Pierre’s behavior and behavioral dispositions. For instance, he is disposed to exclaim, “tres belle” 80 whenever he thinks about London, qua the city he calls “Londres”. He sometimes finds himself exclaiming out loud, “Londres est jolie…Je croix que Londres est jolie…tres belle 81 ”. He is wistful and longs to visit that city. He is saving up money for that momentous trip. Given these facts, it seems we must say that there is a fact as to whether Pierre believes the proposition encoded by 2a. It seems he does. Also, when he thinks about London, qua the city he calls “London”, he feels a slight repulsion 80 This should be translated, “very beautiful”. 81 This should be translated “I believe that London is pretty”. 117 and even dread. He complains about the appearance of the city incessantly. If no one will listen to his complaints, he resorts to complaining to himself, “how unsightly…uuggh”. He is disposed to respond with vehemence, when asked whether he believes the city is pretty, “are you kidding…oh god, no”. So, there seems to be a fact as to whether he believes the proposition encoded by 2a. He does not. I have two responses to this objection. But, in order to give these responses, we need to introduce the notion of a ghuise. Definition of “ghuise”: For any agent A, object o and property f, f belongs to a ghuise under which A thinks of o at time t iff A is disposed to internally assent to the proposition that o is f at t. And, for any two such properties f1 and f2, f1 and f2 belong to the same ghuise under which A thinks of o at t iff at t, A is disposed to internally assent to the proposition that f1 and f2 are co-instantiated by o 82 . Notice that ghuises are sets of properties. And, it can turn out that a single object o appears to A under two different ghuises. And, it would not be surprising if many of the properties in one of the ghuises under which A thinks of o are incompatible with many of the properties in the other. Given that Pierre is disposed to internally assent to the proposition encoded by 2a and disposed to withhold assent to it, we can be sure that the city London appears to Pierre under has at least two different ghuises. The property of being pretty belongs to one ghuise; it does not belong to the other. 82 I believe this notion of a ghuise is Salmon’s notion of a guise. But, Salmon, in his Frege’s Puzzle, never defines “guise”. If Salmon agrees that my notion of a ghuise is his notion of a guise, then, in defining “ghuise”, I provide a definition of “guise” and simply borrow his notion. If he insists that the two notions are different, then, I appeal here to a novel notion. 118 The properties of being a male, able to bend steel, able to fly, a fighter for truth justice and the American way, called “Superman”, a reporter for the Daily Planet, mild mannered, named “Clark Kent”, etc. all belong to some ghuise or other under which Lois Lane thinks about Superman. In the comic book story, the properties of being able to bend steel, able to fly, a fighter for truth, justice and the American way, called “Superman”, not called “Clark Kent”, not a reporter for the Daily Planet, not mild mannered, etc. belong to one ghuise under which Lois thinks about him. Call this the “Superman” ghuise. The properties of being mild mannered, a reporter for the Daily Planet, named “Clark Kent”, not named “Superman”, not able to fly, not able to bend steel, etc. belong to a different ghuise under which she thinks about him 83 . Call this the “Clark Kent” ghuise. She thinks of Superman under these two distinct and incompatible ghuises. And, while the “Superman” ghuise has the property of being able to fly as a member, the “Clark Kent” ghuise does not. That is why she is disposed to internally assent to what she takes to be encoded by 4a while also being disposed to internally withhold assent to what she takes to be encoded by 4b. 4a. Superman can fly 4b. Clark Kent can fly 83 Some incompatible properties can belong to a single ghuise. For instance, the property of being identical to Superman and the property of not being identical to Clark Kent belong to both the “Superman” ghuise and the “Clark Kent” ghuise. The reason for this is that Superman is a constituent of the properties and thus the properties can appear under different ghuises. 119 My first response is that insofar Lois is disposed to assent to what she takes to be encoded by 4a, she is disposed to assent to it when she thinks of it under the “Superman” ghuise. So then, we can be sure that she is also disposed to assent to a huge set of general propositions, i.e., non singular propositions, e.g., that the guy named “Superman” can fly, that the guy who bends steel and fights for truth justice and the American way can fly, etc. She is disposed to internally assent to these and is not disposed to withhold assent to these general propositions. Thus, by the PD definition of “belief”, she believes all of these general propositions. Also, insofar as she is disposed to withhold assent to what she takes to be encoded by 4b under the “Clark Kent” ghuise, she is also going to be disposed to withhold assent to the proposition that the guy named “Clark Kent” can fly, that the bi-speckled, mild mannered reporter for the Daily Planet can fly, etc. She is disposed to withhold assent to these and not counter-disposed, thus, she does not believe these. Thus, we can give an accounting of all of her behavior and dispositions to behave in terms of the general propositions she believes and does not believe. When Lois hears “Superman”, she looks to the heavens because she believes, that the guy named “Superman” can fly. When she hears “Clark Kent”, she never looks up because she does not believe that the guy named “Clark Kent” can fly. Mutatis Mutandis, we can give a full accounting of all of Pierre’s behavior and dispositions to behave. The second response is that there is an important distinction we have to keep in mind. There is an important difference between A not believing p and rejecting that A believes p. If Pierre does not believe the proposition encoded by 2a, then, why is he saving money and why does he keep blurting out how pretty London is, etc.? There is no 120 acceptable answer to these questions. In contrast, if A merely rejects that A believes p, we are not committed to accepting that he does not believe it. We can reject that as well. This explains why he behaves and is disposed to behave in the way that he does and is. Since we also reject that he believes it, we can also explain his other set of behaviors and dispositions to behave. He tells anyone who will listen how he does not believe that London is pretty. The only way to account for all of his behavior and dispositions to behave is by rejecting both that he believes the proposition encoded by 2a and that he does not believe it. We can only do that with the PD definition. The second objection to the PD conception of “belief” is this. Suppose Superman has just rescued Lois in midair. She’s been pushed from the top of some building and is plunging to her death when Superman comes to her rescue. So, Lois is in Superman’s arms while they are flying through the air. It seems pretty clear that she has a de re belief about Superman--that he can fly. She believes of him, that he can fly. She thinks to herself, “thank God he can fly” as she is clutching onto him for dear life. My response here is to make a distinction between not having a de re belief and rejecting that one has a de re belief. Intuitively, we don’t want to say that Pierre does not have a de re belief. That clearly seems incorrect. Intuition is going to be able to decide between cases where we are having a de re belief and cases where we are not having one. In the example of Lois in Superman’s arms, it is pretty clear that she is having one as opposed to not having one. However, those are not the only choices. Intuition cannot discriminate between cases where we are having a de re belief from cases where we merely have to reject that we are not having one. Given that Lois is in Superman’s arms, 121 intuition tells us that either she is having a de re belief or we must reject that she is not having a de re belief. Let us stipulate that at the moment she is in Superman’s arms, she is disposed to internally withhold assent to the proposition she takes to be encoded by 4b. She thinks, “Clark only wishes he could do what Superman can do”. In this case, we don’t want to just say that Lois believes the proposition encoded by 4a. That would be to ignore one of her dispositions. Rather, we are inclined to say that we must reject both that she believes it and that she does not believe it. This is precisely the result the PD definition of “belief” yields. 5.2C Semantics for Partial Definition Here is the PD semantics for belief ascriptions for singular propositions: A believes p if ∃x [x is an actual ghuise under which A thinks about p & ∀y (y is an actual ghuise under which A thinks about p  A is disposed to internally assent to p under y)] or if ∃x [x is a potential ghuise under which A thinks about p & ∀y (y is a potential ghuise under which A thinks about p  A is disposed to internally assent to p under y)]. Any singular proposition an agent considers has to be presented to her under some ghuise or other. For any proposition p that A has already considered, there is some actual ghuise under which A has considered p. In that case, if A is disposed to internally assent to p under every ghuise under which p appears to A, then, A believes p. There is an actual ghuise under which Lois 122 considers the proposition encoded by 4a. If she is disposed to internally assent to it under every actual ghuise she thinks about it, then she believes it. There is no actual ghuise under which she considers the proposition that Batman is a man. But, perhaps, she believes it. She believes if she is disposed to internally assent to it under any potential ghuise. A does not believe p if ∃x [x is an actual ghuise under which A thinks about p & ∀y (y is an actual ghuise under which A thinks about p  A is disposed to internally withhold assent to p under y) or ∃x [x is a potential ghuise under which A thinks about p & ∀y (y is a potential ghuise under which A thinks about p  A is disposed to internally withhold assent to p under y). 5.2D 2 nd Version of Kripke Puzzle Here is one more version of Kripke’s Puzzle. In addition to being disposed to internally withhold assent to what he takes to be encoded by 2b, he is disposed to internally assent to what he takes to be encoded by its negation 2c. 2c. London is not pretty. Thus, by DB, Pierre believes the proposition encoded by 2c. So, by DB, he believes the proposition encoded by 2a, and he believes the proposition encoded by 2c. The proposition encoded by 2c is the negation of the proposition encoded by 2a. Thus, he has 123 contradictory beliefs. Yet, he is fully rational. But, here is a principle which is difficult to deny. Rationality Constraint on Belief (RCB): An agent A cannot have contradictory beliefs if A is rational. RCB is difficult to resist. However, by RCB, we can derive a contradiction. Pierre has contradictory beliefs but he is rational. By RCB, since he has contradictory beliefs, he is not rational. This is version #2 of Kripke’s Puzzle. My proposed resolution is this. Consider the Rationality Constraint on Assent or RCA. RCA: For any agent A and sentence Fa, if A recognizes that ~Fa is the negation of Fa, then, if A is disposed to give internal assent to the proposition encoded by ~Fa when it is presented to A by ~Fa, then, rationality demands that A be disposed to internally withhold assent from the proposition encoded by Fa when it is presented to A by Fa. RCA seems to me to be unassailable 84 . So, insofar as Pierre is disposed to assent to what he takes to be encoded by 2c, he is disposed to withhold assent to what he takes to be encoded by 2b. Thus, by DNB, he does not believe the proposition encoded by 2b. So, we are back to the first version of the puzzle. Pierre believes the proposition encoded by 2a; he does not believe it. Thus, we move to the PD conception of “belief”. By the PD 84 Kripke’s Peter and Paderewski case is not a counter-example to RCA. The problem with Peter is that he did not recognize that “Paderewski is not a musician” is the negation of “Paderewski is a musician”. If he did, no doubt, his pattern of assent would have rendered him irrational. 124 conception, we do not have to accept that he believes the proposition encoded by 2a. We do not have to accept that he believes the proposition encoded by 2c. Thus, given that he is rational, we do not have to accept that he has contradictory beliefs. Let us recount what we have learned here. 1. Our ordinary concept of belief commits us to DB and DNB. However, DB and DNB are incompatible. Thus, our ordinary concept of belief is incoherent. 2. There are two kinds of expressions—transparent and non- transparent. And, this fact is ultimately responsible for why we accept both DB and DNB despite their being inconsistent. 3. With the PD conception of belief, we can have a coherent concept of belief without rejecting any of the elements we think are essential to a correct conception of belief. 125 References Church, Alonzo, Intensional isomorphism and identity of belief, Philosophical Studies, 1954 Frege, Gottlob, On Sense and Reference, reprinted in On Sense and Direct Reference, Davidson, Matthew, Mc-Graw-Hill, 2007. Fine, Kit, The Role of Variables, Journal of Philosophy, 2003 --Semantic Relationism, Blackwell, 2007 Kaplan, David, Demonstratives and Afterthoughts in Themes From Kaplan (Almog, et al., eds.), Oxford 1989 --Logic of Demonstratives, Journal of Philosophical Logic, 1978 --Words, The Aristotelian Society, Supplementary Volume, LXIV (1990) Kazmi, Ali, Reference, Structure and Content, (unpublished) Kripke, Saul, A Puzzle about Belief, In Meaning and Use, edited by A. Margalit. Dordrecht and Boston: Reidel, (1979) --Identity and Necessity", In Identity and Individuation, edited by M. K. Munitz, New York University Press, 1971 --Naming and Necessity, Harvard Press 1980 Mates, Benson, Synonymity, UC Publications in Philosophy, 25:210-226. Reprinted in Semantics and the Philosophy of Language, L. Linsky, ed. (Champaign: University of Illinois Press, 2952), 1954 Mill, John Stuart, A System of Logic, 1843, reprinted in, On Sense and Direct Reference, edited by Davidson, Matthew, 2007 Rieber, Stephen, Understanding Synonyms without Knowing that they are Synonymous, Analysis, 1992 126 Russell, Bertrand, On Denoting, reprinted in On Sense and Direct Reference, Davidson, Matthew, Mc-Graw-Hill, 2007 --Knowledge by Acquaintance and Knowledge by Description (1917), in Mysticism and Logic, paperback edition. Garden City, NY: Doubleday, 1957 Salmon, Nathan, A Theory of Bondage, Philosophical Review, 2006 --Frege’s Puzzle, Ridgeview, Atascadero, California (1986) --Demonstrating and Necessity, Philosophical Review, 2002 --How to become a Millian Heir, Nous, 1989 --Lambda in Sentences with Designators: An Ode to Complex Predication, Journal of Philosophy, Forthcoming. --Notes on a Puzzle About Belief, in Saul Kripke, edited by Berger, Alan, (forthcoming) --On Content, Mind, Vol.101, No.404, 1992 --Propositions and Attitudes, Oxford Press, 1988 (co-edited with Scott Soames) Soames, Scott, Attitudes and Anaphora, Philosophical Perspectives, 8, Logic and Language, 1994 --Beyond Rigidity: The Unfinished Semantic Agenda of 'Naming and Necessity', Oxford University Press, 2002. --Philosophical Analysis in the Twentieth Century, Volumes 1 and 2, Princeton University Press, 2003 --Propositions and Attitudes, Oxford University Press, 1988 (co-edited with Nathan Salmon). --Reference and Description: The Case against Two-Dimensionalism, Princeton University Press, 2005. --Substitutivity, reprinted in On Sense and Direct Reference, edited by Davidson, Matthew, McGraw Hill Companies, 2007 --Understanding Truth, Oxford University Press, 1999.

Abstract (if available)

Abstract Although the problem in the philosophy of language known as “Frege’s Puzzle” is well known, it is not well known that 3 different, but related, puzzles have all been identified as “Frege’s Puzzle”. Each puzzle poses its own unique challenge to Millianism, the view that the meaning or propositional contribution or semantic content of a name is just its referent. It is argued here that every Millian solution to “Frege’s Puzzle” that has been proffered hitherto fails to solve it. The reason for failure is that no single solution can be a solution to all 3 puzzles. No single size fits all.

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Creator Kwon, Daniel (author)

Core Title Lessons From Frege's Puzzle

School College of Letters, Arts and Sciences

Degree Doctor of Philosophy

Degree Program Philosophy

Publication Date 08/10/2010

Defense Date 06/18/2010

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag cognitive significance,disquotation,Frege's Puzzle,guises,Kripke's Puzzle,millianism,OAI-PMH Harvest,relational semantics

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Soames, Scott (committee chair), Guerzoni, Elena (committee member), Salmon, Nathan (committee member), Schroeder, Mark (committee member)

Creator Email dkwon@usc.edu,dkwon3420@gmail.com

Permanent Link (DOI) https://doi.org/10.25549/usctheses-m3373

Unique identifier UC1461036

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Document Type Dissertation

Rights Kwon, Daniel

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