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Adopted from Pdflib Image Sample 1 WITH REFERENCE TO TRUTH: STI~IES IN REFERENTIAL SEMANTICS by DOUGLAS FILLMORE CANNON A.B., Harvard University 1973 SUBMITTED TO THE DEPARTMENT OF LINGUISTICS AND PHILOSOPHY IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in PHILOSOPHY at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY June 1982 <e> Douglas Fillmore Cannon 1982 The author hereby grants to M.I.T. permission to reproduce and to dis­ tribute publicly copies of this thesis document in ~hole or in part. Signature of Author__________~-.;~~~---•. ~....;;;""",,---.::l----- Certified by------------------__._1r--------- I < George Boolas Thesis Supervisor Accepted by aL~ «) ~"0 ~ilijarvis Thomson MA5~HUS~~fl~I~~~artment Graduate Committee OF TEtHNOlOSY Archives JUL 8 1982 2 WITH REFERENCE TO TRUTH: STUDIES IN REFERENTIAL SEMANTICS by DOUGLAS FILLMORE CANNON Submitted to the Department of Linguistics and Philosophy on April 8, 1982, in partial fulfillment of the requirements for the Degree of Doctor of Philosophy in Philosophy ABSTRACT In the first parts of my thesis I explore two philosophical programs in the area of referential semantics, namely, rigid designation accounts of proper names and naturalistic theories of truth. I conclude with an inquiry into the theory of truth for mathematics and its relationship to mathematical Platonism. In Part One, I confront Kripke's well-known views with Quine's pro­ posal that proper names correspond to a kind of predicate. I argue that the belief that proper names are rigid designators is unjustified and that many questions about the reference of terms in various possible worlds have no determinate answer. I take issue with Kripke's emphasis on the question, "How is the reference of names determined?", and suggest that it reflects dubious philosophical presuppositions. In Part Two, I note that Field envisions a theory of truth as a natural property to be employed in a scientific account of the nature of knowledge. I explain how his account reworks the machinery of Tarski's theory of truth, making use of putative semantic relations between names and their referents and predicates and their extensions. It thereby com­ mits itself to a natural relation of reference that underlies all language. I argue that nothing in our ordinary notion of referring provides evidence for such a relation and object to specific aspects of Field's account. Finally, I describe a conflict that appears to Benacerraf between the requirements of a semantics for the language of mathematics and those of a plausible account of mathematical knowledge. Concentrating on the seman­ tical side, I argue that no unified semantic theory should be expected. Nevertheless, an explanatory account of truth for mathematical statements is available, in the form of a theoretical definition of truth, as firs~ formulated by Tarski. I maintain that the correctness of this theory of truth is not a genuine issue in the philosophy of mathematics. In parti­ cular, the theory does not entail or even lend support to Platonism. Thesis Supervisor: George Boalos, Professor of Philosophy 3 TABLE OF CONTENTS Acknowledgments 5 ONE: SENSE ABOUT PROPER NAMES 7 I. Proper Names and Predicates 9 II. Predicates and Rigid Designation 29 III. Reference without Sense 40 TWO: FIELD'S THEORY OF TRUTH 47 I. Two Versions of Tarski's Definition 49 II. Truth for Sentence Tokens 64 III. Generality in Truth Definitions 68 THREE: TRUTH AND THE PHILOSOPHY OF MATHEMATICS 78 I. Benacerraf's Dilemma 83 II. The Logical Form of Arithmetic Sentences 93 III. The Semantics of Singular Terms in Arithmetic 104 IV. The Semantics of Quantifiers 108 v. The Call for Truth Conditions 115 VI. The Theory of Truth for Mathematical Statements 125 A. Theoretical Definitions 126 B. Tarski's Theoretical Definition of Truth 131 4 VII. Platonism and Truth 135 A. Three Aspects of Platonism 139 B. Significance and Grammaticality 141 c. Realism with Respect to Mathematical Objects 145 D. The Principle of Bivalence 149 E. The Independence of Truth from Verifiability 153 F. Explaining Away Mathematical Objects 156 Biographical Note 159 5 ACKNOWLEDGMENTS Detailed acknowledgments have rightly been judged self-indulgently autobiographical, but equally they may provide the only human interest in an otherwise dreary treatise. When ones college and graduate education spans eighteen years, one inevitably incurs a multitude of debts. I am no exception. lowe my most general philosophical orientation to w.v.o. Quine, from whom I had the privilege of learning logic not once, but twice. Richard Henson introduced me to the philosophy of language and, perhaps unwittingly, first conveyed the idea that my philosophical poten­ tial might not be flatly ordinary. David Bennett introduced me to the philosophy of mathematics, and even more to the present point, suggested that my reluctance to accord truth and falsity to mathematical statements might result from thinking truth to be something it is not. He recom- mended Alfred Tarski, as therapy. Michael Friedman taught me without visible reward. Judith Thomson not only encouraged me to take up grad­ uate studies, but found me a place as well. Patric~ Winston and the M.I.T. Artificial Intelligence Laboratory sponsored my novitiate at this Institute. Hilary Putnam supplied the general structure of these inves­ tigations in his Locke Lectures and the seminar meetings that surrounded them. As important as what he said was what [le left unsaid. And most importantly, Richard Cartwright and George Boolos provided the super­ vision, encouragement, patience, and guidance that enabled me finally to write a thesis. The one taught me how to treat of philosophy generally; the other, how to treat of philosophy of mathematics. 6 It was a particular disappointment to me that circumstances had taken Pr·ofessor Cartwright out of the country before I had been able to bring this work to its culmination, for he had listened with persistence to a great many ill-formulated ideas, prodding and cajoling me until I got them straight. No one who has not studied with him can appreciate the range and power of his philosophical way. For specific discussions in aid of the present project, I thank Rogers Albritton, Timothy Appelt, Richard Boyd, Joshua Cohen, S. Marc Cohen, Warren Goldfarb, Paul Horwich, Jeffrey Poland, Scott Soames, James Thomson, Judith Thomson, Barbara Von Eckardt, and belatedly, Joseph Bevando. For assistance with typing and manuscript preparation, I thank Rowland Cannon, Jr., Diane Harris, John Magee, Maxine Pollard, and Joan Yatteau. On a more personal level, my parents enabled me to continue this madness without incurring even more debts that I did. And Mary Ellen Sullivan and our girls have both lov=d me and bet their lives on me. My gratitude to them is most heartfelt of all. And now lowe all of these people a public exculpation for blunders and falsehoods contained herein. 7 ONE: SENSE ABOUT PROPER NAMES 8 In a thought provoking footnote to his important work, Naming and Necessity, Saul Kripke exempts from his criticism of the classical the- ory of proper names a proposal of Quine's that names correspond to a kind of predicate. Kripke claims that Quine's proposal leaves the pro- ject that he undertakes in his essay ess~ntially unchanged. I want to investigate whether that claim is true. Quine's suggestion has not been as widely noticed as have other views on naming. Perhaps many share the suspicion Kripke enunciates that the proposal is not "a substantive 1 theory of the reference of names. 1I Quine's own disclaimers reinforce that suspicion. One reason that I want to discuss Quine's proposal is that I think that it can develop enough philosophical flesh to provide a serious alternative. But perhaps a deeper reason is that I believe that considering the problems Kripke discusses with Quine's proposal in mind will undermine--to good effect--many of the analytical tools that Kripke employs in his discussion. In the first part of this paper I will explain exactly what Quine has proposed. I will contrast a narrower with a broader construal of 1 Saul A. Kripke, Naming and Necessit¥ (Cambridge, Mass.: Harvard University Press, 1980), p. 29, n. 5; originally in Semantics of Natural Language, ed~ Donald Davidson and Gilbert Harman (Dordrecht: Reidel, 1972), pp. 253-355. 9 the proposal and relate the contrast to issues about the natura of philosophical analysis. And I will criticize some of the detail of Quine's exposition. In the second part I will raise some of Kripke's questions about naming and reference on the supposition that names are predicative. After extending the notion of rigid designation in a natu­ ral way, I will try to generate doubts about certain widely accepted cases of rigid designation. Doing so will emphasize the importance that Kripke attaches to the question, "How is the reference of names deter­ mined?" In the third part I will criticize typical theoretical answers to this question and suggest that the question embodies dubious philo­ sophical presuppositions. Finally I will suggest ways of reformulating the question that would enable Quine to answer it. I• PROPER NAMES A1~D PREDICATES Russell's theory of descriptions is a well-kn.own proposal for ex­ plaining the logical form of sentences containing definite descriptions. Under the proposal such sentences are analyzed, to use the term that Russell himself used, into certain replacement sentences which exhibit their own logical structure. Russell claimed that the replacement sen­ tence in each case expresses the same proposition as the original sen­ tence, this being the standard of a correct analysis. The key feature of the proposal is that the replacement sentences contain no definite descriptions; rather, certain constructions out of the quantifiers of first-order logic and the identity relation do the work of the definite !O descriptions.
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