Truth and its Deformities

Midwest Studies in Philosophy Volume XXXII

Midwest Studies in Philosophy: Truth and its Deformities Volume XXXII Editor by Peter A. French and Howard K. Wettstein © 2008 Wiley Periodicals, Inc. ISBN: 978-1-405-19145-6

MIDWEST STUDIES IN PHILOSOPHY EDITED BY PETER A. FRENCH HOWARD K. WETTSTEIN EDITORIAL ADVISORY BOARD: ROBERT AUDI (UNIVERSITY OF NEBRASKA) PANAYOT BUTCHVAROV (UNIVERSITY OF IOWA) DONALD DAVIDSON (UNIVERSITY OF CALIFORNIA, BERKELEY) FRED I. DRETSKE (DUKE UNIVERSITY) JOHN MARTIN FISCHER (UNIVERSITY OF CALIFORNIA, RIVERSIDE) GILBERT HARMON (PRINCETON UNIVERSITY) MICHAEL J. LOUX (UNIVERSITY OF NOTRE DAME) ALASDAIR MACINTYRE (UNIVERSITY OF NOTRE DAME) RUTH BARCAN MARCUS (YALE UNIVERSITY) JOHN R. PERRY (STANFORD UNIVERSITY) ALVIN PLANTINGA (UNIVERSITY OF NOTRE DAME) DAVID ROSENTHAL (CITY UNIVERSITY OF NEW YORK GRADUATE CENTER) STEPHEN SCHIFFER (NEW YORK UNIVERSITY) Many papers in MIDWEST STUDIES IN PHILOSOPHY are invited and all are previously unpublished. The editors will consider unsolicited manuscripts that are received by January of the year preceding the appearance of a volume. All manuscripts must be pertinent to the topic area of the volume for which they are submitted. Address manuscripts to MIDWEST STUDIES IN PHILOSOPHY, Department of Philosophy, University of California, Riverside, CA 92521.

The articles in MIDWEST STUDIES IN PHILOSOPHY are indexed in THE PHILOSOPHER’S INDEX.

Midwest Studies in Philosophy Volume XXXII Truth and its Deformities Editors Peter A. French Arizona State University Howard K. Wettstein University of California, Riverside

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MIDWEST STUDIES IN PHILOSOPHY Volume XXXII Truth and its Deformities

Truth and Meaning: In Perspective . . . . . . . . . . . . . . . . . . . . .Scott Soames

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The Whole Truth and Nothing but the Truth . . . . . . . . . . . . . Susan Haack

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Believing at Will . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Kieran Setiya

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Common Sense as Evidence: Against Revisionary Ontology and Skepticism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Thomas Kelly

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Why We Should Prefer Knowledge . . . . . . . . . . . . . . . Steven L. Reynolds

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Knowledge, Truth, and Bullshit: Reflections on Frankfurt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Erik J. Olsson

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Pragmatism on Solidarity, Bullshit, and other Deformities of Truth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cheryl Misak

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Alethic Pluralism, Logical Consequence and the Universality of Reason . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Michael P. Lynch

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Grading, Sorting, and the Sorites. . . . . . . . . . . . . . . . . . . . . . .Tim Maudlin

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Where the Paths Meet: Remarks on Truth and Paradox . . . . . . . . . . . . . . . . . . . . . . . . . . JC Beall and Michael Glanzberg

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Pointless Truth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Jonathan Kvanvig

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Indeterminate Truth . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Patrick Greenough

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Truth in Semantics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Max Kölbel

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Being and Truth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Paul Horwich

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Quine’s Ladder: Two and a Half Pages from the Philosophy of Logic. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Marian David

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Truth-definitions and Definitional Truth . . . . . . . . . . . Douglas Patterson

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Contributors

JC Beall, Department of Philosophy, University of Connecticut Marian David, Department of Philosophy, University of Notre Dame Michael Glanzberg, Department of Philosophy, University of California, Davis Patrick Greenough, Department of Philosophy, St. Andrews University Susan Haack, Distinguished Professor in the Humanities, Professor of Philosophy, Professor of Law, University of Miami Paul Horwich, Philosophy Department, New York University Thomas Kelly, Department of Philosophy, Princeton University Max Kölbel, Department of Philosophy, University of Birmingham (Logica, Universitat de Boscelona) Jonathan Kvanvig, Department of Philosophy, Baylor University Michael P. Lynch, Department of Philosophy, University of Connecticut Tim Maudlin, Department of Philosophy, Rutgers University Cheryl Misak, Department of Philosophy, University of Toronto Erik J. Olsson, Department of Philosophy, Lund University Douglas Patterson, Department of Philosophy, Kansas State University Steven L. Reynolds, Philosophy Department, Arizona State University Kieran Setiya, Department of Philosophy, University of Pittsburgh Scott Soames, School of Philosophy, University of Southern California

Peter A. French is the Lincoln Chair in Ethics and the Director of the Lincoln Center for Applied Ethics at Arizona State University. He was the Cole Chair in Ethics, Director of the Ethics Center, and Chair of the Department of Philosophy of the University of South Florida. Before that he was the Lennox Distinguished Professor of the Humanities and Professor of Philosophy at Trinity University in San Antonio, Texas. He has taught at Northern Arizona University, the University of Minnesota, and Dalhousie University, Nova Scotia. He has served as Exxon Distinguished Research Professor in the Center for the Study of Values at the University of Delaware. Dr. French has a B.A. from Gettysburg College, an M.A. from the University of Southern California, and a Ph.D. from the University of Miami. He received a Doctor of Humane Letters (L.H.D.) honorary degree from Gettysburg College in 2006. Dr. French has an international reputation in ethical and legal theory and in collective and corporate responsibility and criminal liability. He is the author of nineteen books, including The Virtues of Vengeance, Cowboy Metaphysics: Ethics and Death in Westerns, Ethics and College Sports, Corporate Ethics,

War and Border Crossings: Ethics When Cultures Clash, Responsibility Matters, Corporations in the Moral Community, The Spectrum of Responsibility, Collective and Corporate Responsibility, Corrigible Corporations and Unruly Laws, Ethics in Government, and The Scope of Morality. He is currently writing a book with the working title Our Better Angels Have Broken Wings While the Pukin Dogs Are Flying Overhead, that concludes with a memoir of his experiences at bases around the world teaching ethics to Navy and Marine chaplains who were either returning from the war in Iraq or about to be deployed there. Dr. French has lectured at locations around the world. Some of his works have been translated into Chinese, Japanese, German, Italian, French, and Spanish. Amazon.com lists 48 books credited to him as author, editor, or co-editor, published by major commercial and university presses. Dr. French is a senior editor of Midwest Studies in Philosophy. He was the editor of the Journal of Social Philosophy and general editor of the Issues in Contemporary Ethics series. He has published dozens of articles in the major philosophical and legal journals and reviews, many of which have been anthologized. He is a member of the Board of Governors and a Founding Fellow of the Arizona Academy of Science, Technology and the Arts. Howard K. Wettstein is Professor of Philosophy at the University of California, Riverside. He holds a B.A. in Philosophy from Yeshiva College, and an M.A. and Ph.D. from the City University of New York. Wettstein has published two books, The Magic Prism: An Essay in the Philosophy of Language (Oxford University Press, 2004) and Has Semantics Rested On a Mistake? and Other Essays (Stanford University Press, 1991), as well as a number of papers in the philosophy of language, one focus of his research. Another and current focus is the philosophy of religion, and he has published papers on such topics as awe, doctrine, ritual, the problem of evil, and the viability of philosophical theology. He is currently at work on a book in the philosophy of religion. He is a senior editor (with Peter French) of Midwest Studies in Philosophy, and has edited a number of other volumes including Themes From Kaplan (Oxford University Press, 1989, co-edited) and Diasporas and Exiles: Varieties of Jewish Identity (University of California Press, 2002). Truth and Its Deformities is the 32nd volume in the Midwest Studies in Philosophy series. It contains major new contributions on a range of topics related to the general theme of the volume by some of the most important philosophers writing on truth in recent years. It is an international collection of contributors working on such topics as truth and meaning, evidence and testimony, bullshit, truth and paradox, and pointless truth. The list of contributors includes Scott Soames, Susan Haack, Kieran Setiya, Tim Maudlin, Max Kölbel, Marian David, and Paul Horwich. In the tradition of Midwest Studies in Philosophy, this volume should set the terms of the debate on these topics for philosophers for some time to come.

Midwest Studies in Philosophy, XXXII (2008)

Truth and Meaning: In Perspective SCOTT SOAMES

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y topic is the attempt by Donald Davidson, and those inspired by him, to explain knowledge of meaning in terms of knowledge of truth conditions. For Davidsonians, these attempts take the form of rationales for treating theories of truth, constructed along Tarskian lines, as empirical theories of meaning. In earlier work,1 I argued that Davidson’s two main rationales—one presented in “Truth and Meaning”2 and “Radical Interpretation,”3 and the other in his “Reply to Foster”4—were unsuccessful. Here, I extend my critique to cover an ingenious recent attempt by James Higginbotham to establish Davidson’s desired result. I will argue that it, too, fails, and that the trajectory of Davidsonian failures indicates that linguistic understanding, and knowledge of meaning, require more than knowledge of that which a Davidsonian truth theory provides. I begin with a look at the historical record.

1. Scott Soames, “Truth, Meaning, and Understanding,” Philosophical Studies 65 (1992): 17–35; and Philosophical Analysis in the Twentieth Century, vol. 2 (Princeton and Oxford: Princeton University Press, 2003), chap. 12. 2. Donald Davidson, “Truth and Meaning,” Synthese 17 (1967): 304–23; reprinted in Inquiries into Truth and Interpretation (Oxford: Clarendon Press, 200l). Citations will be to the latter. 3. Donald Davidson, “Radical Interpretation,” Dialectica 27 (1973): 313–28; reprinted in Inquiries into Truth and Meaning. Citations will be to the latter. 4. Donald Davidson, “Reply to Foster,” in Truth and Meaning, ed. Gareth Evans and John McDowell (Oxford: Oxford University Press, 1976), 33–41; reprinted in Inquiries into Truth and Meaning. Citations will be to the latter. Midwest Studies in Philosophy: Truth and its Deformities Volume XXXII Editor by Peter A. French and Howard K. Wettstein © 2008 Wiley Periodicals, Inc. ISBN: 978-1-405-19145-6

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Scott Soames THE EVOLUTION OF AN IDEA: A HISTORICAL SUMMARY

When Davidson enunciated his idea, in the 1960s, that theories of meaning can be taken to be nothing more than theories of truth, it met with a warm reception. For devotees of Ordinary Language, its attraction lay in its promise of providing a theoretically respectable way of grounding claims about meaning, and distinguishing them from claims about use, that those who still placed meaning at the center of philosophy had come to recognize the need for.5 For those laboring under the Quinean legacy of skepticism about analyticity, synonymy, and meaning, the idea afoot was that extensional notions from the theory of truth and reference were respectable, whereas intensional ones from the theory of meaning were not. This was an audience to which the Davidsonian program was bound to appeal. It was one thing to claim that meaning has no special role to play in philosophy. As discomforting as this was to Ordinary Language philosophers, it was something that Quineans could live with. Much more troublesome was the idea that meaning had no place in science. It certainly did not seem that way to soldiers in the Chomskian revolution, who were busy transforming linguistics. The central work of the period, Aspects of a Theory of Syntax,6 enshrined the distinction between deep and surface structure, while championing the thought that a semantic theory of a natural language would interpret the deep structures of its sentences. To many, this brought to mind the Russellian distinction between logical and grammatical form. But what, it was wondered, is logical form, and what would it be to interpret it? Davidson laid the groundwork for answering these questions in a way that made sense to philosophers in the tradition of Russell, Tarski, Carnap, and Quine. For Davidsonians like Gilbert Harman, the logical forms of natural language sentences were their Chomskian deep structures, to interpret them was to give a truth theory for the language, and to see this as a theory of meaning was to see it as explicating what it is to understand the language.7 Though audacious, these ideas can be seen as the application of a familiar idea from philosophical logic. Since Tarski’s seminal work on truth in the 1930s, it has been commonplace to view an interpreted formal language as the result of adding a model, plus a definition of truth-in-a-model, to an uninterpreted formal system, thereby arriving at an assignment of truth conditions to every sentence.8 But if truth theories can be used in this way to endow sentences with meaning, then, surely, it seemed, they can also be used to describe the meanings of already meaningful sentences—provided, in the case of natural language, that we are clever enough to find the requisite logical forms to which to apply them. This was the technical task of the Davidsonian program. The philosophical challenge was to justify the claim that completing this task would yield a theory of meaning. 5. See chapters Parts 2–4 of Philosophical Analysis in the Twentieth Century, vol. 2. 6. Noam Chomsky, Aspects of a Theory of Syntax (Cambridge: MIT Press, 1965). 7. Gilbert Harman, “Deep Structure as Logical Form,” Synthese 21 (1970): 275–97. 8. Alfred Tarski, “The Concept of Truth in Formalized Languages,” in Logic, Semantics, and Metamathematics, 2nd ed., ed. John Corcoran (Indianapolis: Hackett, 1983), 152–78; and “On the Concept of Logical Consequence,” in Logic, Semantics, and Metamathematics, 2nd ed., ed. John Corcoran (Indianapolis: Hackett, 1983), 409–20.

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Coming up with this justification proved to be easier said than done. Consider again the use of a truth theory to endow sentences with meaning. Our announcement that we are using the theory to introduce an interpreted language contains a crucial piece of information not contained in the theory itself—namely, that certain of its theorems are to be viewed as providing paraphrases of the sentences the truth conditions of which they state. This suggests that if descriptive theories of meaning are to be put in the form of Tarskian truth theories, something beyond what they state must play a crucial role. Also, when we introduce interpreted formal languages, we typically do not have to choose which of the many theorems stating truth conditions of a single sentence provide acceptable paraphrases of it. Since potential paraphrases can often be proved to be extensionally equivalent, each is acceptable for the purposes of philosophical logic, or metamathematics. This is not true when our purpose is to give a descriptive theory of meaning. Thus, if a Tarskian truth theory is to fill the bill, it must be combined with something else that not only provides the information that meaning-giving paraphrases are sought, but also specifies which of the many potential candidates are the genuine articles. This is the heart of the justificatory problem Davidson faced. Initially, there was widespread optimism about its solution, together with widespread unclarity about what such a solution would require. The optimism was fueled by the attractiveness of the overall picture—which was seen as applying the proven advances of philosophical logic to the interpretation of natural language, without backsliding on Quine’s influential skepticism about meaning. Davidson thought that systematic knowledge of truth and reference could do all legitimate work for which we need a notion of meaning. His strategy was to embrace Quine’s rejection of analyticity, synonymy, and our ordinary notion of meaning, substituting knowledge of truth and reference for knowledge of meaning—whenever there was something genuine to be captured. Since truth and reference are scientifically legitimate, such a theory was deemed respectable. Since it could be used to explain what it is to understand a language, it fit the emerging paradigm in linguistics. In short, one can have Quine, and Chomsky too. There is no need to suppress, of course, the obvious connection between a definition of truth of the kind Tarski has shown how to construct, and the concept of meaning. It is this: the definition works by giving necessary and sufficient conditions for the truth of every sentence, and to give truth conditions is a way of giving the meaning of a sentence. To know the semantic concept of truth for a language is to know what it is for a sentence—any sentence—to be true, and this amounts, in one good sense we can give to the phrase, to understanding the language. This at any rate is my excuse for a feature of the present discussion that is apt to shock old hands; my freewheeling use of the word “meaning,” for what I call a theory of meaning has after all turned out to make no use of meanings, whether of sentences or of words. Indeed, since a Tarski-type truth definition supplies all we have asked so far of a theory of meaning, it is clear that such a theory falls comfortably within what Quine terms the “theory of reference” as distinguished from what he terms the

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Scott Soames “theory of meaning.” So much the good for what I call a theory of meaning, and so much, perhaps, against my so calling it.9

There were, however, some conceptual flies in the ointment. The grand Davidsonian-cum-Quinean theme presupposed that truth and reference can be retained, while meaning is rejected. But it is not clear that our ordinary notions of truth and reference can be separated from our ordinary notion of meaning. Having rejected meaning as unscientific in Word and Object, and implicitly called ordinary reference into question by implicating it in his indeterminacy theses, Quine finished it off in “Ontological Relativity,” calling for what was, in effect, its elimination.10 Surely, if the ordinary notion of an expression referring to a rabbit is to be eliminated, then the related notion of a predicate being true of a rabbit must also go. But this brings truth itself into play. How can one hold onto it, once one has abandoned its sister, being true of ? For Quine, the question is moot, since he was willing to trade our ordinary notions of truth and reference for Tarski’s disquotational replacements.11 In the beginning, Davidson was too. Initially, he wrongly equated the notion of truth needed in his theories of meaning with Tarski truth.12 He was also a revisionist about reference.13 He did not believe that his referential axioms stated facts about the world from which the truth conditions of sentences follow. On the contrary, these axioms had no independent content, and reflected no independent reality. Rather, they were seen as aspects of the total theory that derive their content entirely from their role in connecting theorems about the truth conditions of sentences with one another. On this picture, one derives a statement of the truth conditions of S from statements about the reference of S’s parts. The contents of these referential statements are abstracted from their role in deriving statements about the truth conditions of other sentences containing those parts. But since those other sentences contain additional words not in S, further referential axioms are required to derive theorems stating their truth conditions, thereby linking their interpretations to that of S. And so it goes, until the contents of every sentence and word are intertwined with, and dependent upon, the contents of every other sentence and word. In the end, Davidson thought, our understanding any word or sentence is conceptually dependent on our understanding of every other word and sentence—a radical version of meaning holism, akin to Quine’s own. We decided a while back not to assume that parts of sentences have meanings except in the ontologically neutral sense of making a systematic contribution 9. Davidson, “Truth and Meaning,” 24, my emphasis. 10. W. V. Quine, Word and Object (Cambridge: MIT Press, 1960); “Ontological Relativity,” in Ontological Relativity and Other Essays (New York: Columbia University Press, 1969), 26–68. 11. For discussion, see chap. 11 of Philosophical Analysis in the Twentieth Century, plus the final section of my article, “The Indeterminacy of Translation and the Inscrutability of Reference,” Canadian Journal of Philosophy 29 (1999): 321–70. 12. See Scott Soames, “What Is a Theory of Truth?” Journal of Philosophy 81 (1984): 411–29; and Understanding Truth (New York: Oxford University Press, 1999), 102–07 and 238–44. 13. See Donald Davidson, “Reality without Reference,” Dialectica 31 (1977): 247–53.

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to the meaning of the sentences in which they occur. Since postulating meanings has netted nothing, let us return to that insight. One direction in which it points is a certain holistic view of meaning. If sentences depend for their meaning on their structure, and we understand the meaning of each item in the structure only as an abstraction from the totality of sentences in which it features, then we can give the meaning of any sentence (or word) only by giving the meaning of every sentence (and word) in the language. Frege said that only in the context of a sentence does a word have meaning; in the same vein he might have added that only in the context of a language does a sentence (and therefore a word) have meaning.14 That was the grand philosophical canvas on which Davidson painted. Some of its main elements, like the idea that Tarskian truth predicates can be used for Davidson’s purposes, were just errors to be recanted.15 Other parts—like Quine’s critique of analyticity and synonymy, and his indeterminacy theses—are vulnerable to powerful objections.16 Although the Davidsonian program continues to this day, much of the original philosophical background for it has fallen away. I will not, therefore, presuppose it in what follows. Instead, I will freely substitute the ordinary notion of truth for Tarski’s; I will not assume that intensional semantic notions are illegitimate, and I will not rely on any kind of semantic holism. My question is, How, if at all, can one justify Davidson’s claim that theories of truth qualify as theories of meaning? I will approach this question with as little philosophical baggage as possible. THE PROBLEM OF JUSTIFICATION Davidson originally held that a truth theory for L qualifies as a theory of meaning, if knowledge of what it states is sufficient for understanding L. The problem was in showing that his theories satisfied the condition. How can knowledge of a truth theory be sufficient for understanding meaning, when its theorems give truth conditions of sentences only in the weak sense of pairing them with materially equivalent claims? If all I know about S is expressed by the theorem ⎡‘S’ is true iff P⎤, I can readily draw the conclusions expressed by ⎡‘S’ doesn’t mean that ~P⎤ and ⎡‘S’ doesn’t mean that Q⎤, where the claim made by Q is obviously incompatible with that made by P. But how does one move from these modest negative results to interesting positive conclusions about what S does mean? Initially, Davidson thought that compositionality gave the answer. In compositional theories, theorems stating the truth conditions of sentences are derived from axioms interpreting their parts. Thus, he reasoned, “accidentally true” statements of truth conditions, like ⎡‘Snow is white’ is true iff grass is green⎤ will not be generated without 14. Davidson, “Truth and Meaning,” 22, my emphasis. 15. See Soames, “What Is a Theory of Truth?” 422–24; and Understanding Truth, 102–07. Also, Donald Davidson, “The Structure and Content of Truth” (The Dewey Lectures 1989), Journal of Philosophy 87 (1990): 279–328. 16. See Philosophical Analysis in the Twentieth Century, chaps. 16 and 17 of vol. 1, chaps. 10 and 11 of vol. 2.

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simultaneously generating falsehoods, like ⎡‘Snow is grass’ is true iff grass is grass⎤ and ⎡‘Trees are white’ is true iff trees are green⎤. Since truth theories must be true in order to qualify as theories of meaning, Davidson believed that the problem of “accidentally true” statements of truth conditions would not arise. Instead, he thought, truth theories that are both true and compositional will end up deriving only those statements ⎡‘S’ is true iff P⎤ in which P is a close enough paraphrase of S that “nothing essential to the idea of meaning . . . [would remain] to be captured.”17 John Foster showed him to be wrong.18 Let LS be an extensional fragment of Spanish. Suppose one has a true, compositional truth theory T1 of LS that delivers a translational T-theorem—⎡‘S’ is true in LS iff P⎤ in which P means the same as S—for each sentence of LS. We now construct a new theory T2 by replacing all axioms of T1 interpreting a word, phrase, or sentence-forming construction with new axioms stating different, but extensionally equivalent, interpretations. Since T1 is both true and compositional, so is T2—despite the fact that all T-theorems of T2 may, like (1), be nontranslational. 1. ‘Mis pantelones son verdes’ is true in LS iff my pants are green and first-order arithmetic is incomplete.19 Knowledge of these theorems is not sufficient to understand LS. So, T2 cannot be a theory of meaning, even though it satisfies Davidson’s constraints. The problem remains, even if we assume constraints strong enough to rule out all but translational truth theories—defined as those that entail a translational T-theorem for each sentence of the language. Knowing what is stated by the translational truth theory T1 is no more helpful in coming to understand LS than knowing what is stated by the nontranslational T2—unless one also knows, of that which is stated by T1, that it is expressed by a translational theory. If one wrongly thinks that T1 is nontranslational, then knowledge of the truth conditions it states will not yield knowledge of meaning. Thus, knowledge of what is stated by even the best truth theories is insufficient for understanding meaning. Davidson’s response was to make the obvious minimal revision of his justificatory proposal. On the revised view, what makes a translational truth theory TT a correct theory of meaning is that knowledge of the claim made by the conjunction of its axioms, plus knowledge, of that claim, that it is made by a translational theory are, together, sufficient for understanding L.20 The idea is this: (i) Knowledge of the conjunction of axioms of TT allows one to derive a translational T-theorem for each S, and thereby to pair S with the claim expressed by a translation of S. (ii) Knowledge, of this truth-conditional knowledge, that it is expressed by a translational theory, allows one to identify the claim paired with S as the claim expressed by S. In this way, one comes to understand the language.

17. Davidson, “Truth and Meaning,” 26. 18. J. A. Foster, “Meaning and Truth Theory,” in Truth and Meaning, ed. Gareth Evans and John McDowell (Oxford: Oxford University Press, 1976), 1–32. 19. Here, and throughout, I put aside complications caused by indexicals. 20. Davidson, “Reply to Foster,” 36–37.

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However, this reasoning fails. For each sentence S, a truth theory will have infinitely many T-theorems ⎡‘S’ is true iff P⎤ among its consequences. If the theory is translational, at least one will be translational. But nothing in the theory specifies which one. Knowledge of a theory known to be translational does not allow one to separate translational from nontranslational theorems. Thus, it does not suffice for understanding the language.21 The natural response is to add a definition of canonical theorem to truth theories, picking out, for each S, a unique T-theorem as translational. However, it is doubtful that this would provide the needed justification. Once information about canonicality is added, the only role played by knowledge of the canonical truth theorem (CTT) is that of allowing one to identify a claim in which S is paired with a certain content, which is then stipulated to be the content expressed by a translation. Neither the truth of CTT, nor the fact that it states the truth conditions of S, plays any role in interpreting S. All it does is to supply a translational pairing, which could be supplied just as well in other ways. One could get the same interpretive results by replacing the truth predicate in a translational truth theory with any arbitrary predicate F whatsoever. Whether or not the resulting theory is true makes no difference. To interpret S, all one needs to know, of the canonical F-theorem, is that it links S with the content expressed by a translation of S. No one would conclude from this that translational F-theories count as theories of meaning. Why, then, suppose that translational truth theories do? So far, we have been given no answer.22 The collapse of this justificatory attempt should not be lamented. Prompted by Foster’s objection into invoking a notion paraphrase beyond anything in the truth theories themselves, we face the dilemma of appealing to a notion strong enough to overcome the objection, at the cost of robbing truth and reference of their cherished roles in explicating meaning, or of not overcoming the objection at all. If the justificatory enterprise is both to succeed, and be worth the candle, some way out of this dilemma must be found. Some believe that the answer lies in psycholinguistic speculation.23 According to them, a translational T-theory counts as a correct theory of meaning because speakers unconsciously use it to interpret sentences. On this view, canonical T-theorems are statements ⎡‘S’ is true iff P⎤ that, as a matter of psycholinguistic fact, terminate the interpretive derivations of ordinary speakers. There are several reasons to doubt this. First, it requires a robust “language of thought,” distinct from natural languages, used to state the truth conditions of natural language sentences. Presumably this system must include Mentalese counterparts of all natural-language predicates. But it is implausible to think that I have 21. See Soames, “Truth, Meaning, and Understanding.” 22. This point should not be obscured by the fact that Davidson did not, in his reply to Foster, explicitly involve the notion of a translational truth theory. Instead, he invoked the idea of a truth theory that is known to satisfy a set of controversial constraints about what meaning and interpretation are, and what it is to verify theories of such. Unless satisfaction of these constraints guarantees translationality (which it would seem it does not), knowing that they are satisfied will not be sufficient to interpret sentences, and Davidson will not have an answer to Foster. 23. Richard Larson and Gabriel Segal, Knowledge of Meaning (Cambridge: MIT Press, 1995).

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any way of linguistically representing the concept of a microwave oven other than by using the English expression. Second, such a theory simply passes the buck from explaining what it is to understand natural language to explaining what it is to understand Mentalese. Third, if natural language sentences are understood by interpreting them in antecedently understood Mentalese, then all that is required is translation from the former to the latter. Although a canonical truth theory, stated in Mentalese, could, in principle, provide this, it could not do so efficiently. The derivations of T-theorems are long and cumbersome. If all one wanted was a translation, no one would dream of using them over other, more efficient methods. Why then suppose that Nature foisted them on us? Fourth, there is no compelling psycholinguistic evidence I am aware of that supports this psychologizing of the Davidsonian project. Finally, even if, by the purest luck, it were to turn out that actual English speakers in fact used internalized Davidsonian truth theories as imagined, this would not be a semantic fact about English, but a psychological quirk about us. If a new speaker came along, who assigned all English expressions precisely the interpretations we do, but used a different method for translating into Mentalese, he would still be an English speaker. Psychologizing the Davidsonian semantic program is not a way of saving it; it is a way of killing it. HIGGINBOTHAM’S JUSTIFICATORY IDEA: A FIRST APPROXIMATION That program remains one of the active approaches in semantics today—despite the crisis created by the so far unsuccessful attempts to solve its justificatory problem. By far, the most promising suggested solution that I know of derives from James Higginbotham’s “Truth and Understanding.”24 Semantic theories, he says, should tell us what sentences, and the expressions that make them up, mean. He says: The kind of meaning that a sentence has, however, is determined by what it may be used to say, and the kind of meaning that words and phrases have is determined by their contributions to the meanings of the sentences in which they occur. It could therefore be proposed that semantic theory is charged with establishing, formally, all of the facts to the effect that so-and-so means such-and-such, or at least all such facts as come readily to the lips of native speakers, hoping in this way to clarify the nature and extent of the human capacity for language. I think that this simple answer is correct.25 He warns us, however, not to expect theorems that mention meaning. Rather, he proposes to explicate meaning in terms of truth, reference, knowledge, and 24. James Higginbotham, “Truth and Understanding,” Philosophical Studies 65 (1992): 3–16; reprinted in Mark Richard, ed., Meaning (Oxford: Blackwell, 2003). Citations are to the reprinted version. 25. Ibid., 255–56.

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understanding. It is facts involving these notions that semantic theories are expected to account for. The facts that semantics must account for comprise the context-independent features of the meaning of expressions that persons must know if they are to be competent speakers of the languages to which those features are assigned. What they must know, I suggest, consists of: facts about the reference of expressions, about what other people know and are expected to know about the reference of expressions, about what they know about what one is expected to know about the reference of expressions, and so on up. From this point of view, meaning does not reduce to reference, but knowledge of meaning reduces to norms of knowledge of reference. Such norms are iterated, because knowledge of meaning requires knowledge of what others know, including what they know about one’s own knowledge.26 He adds: As a speaker of English, you are expected, for example, to know that ‘snow is white’ is true if and only if snow is white; to know that ‘snow’ refers to snow, and that ‘is white’ is true of just the white things . . . 27 Applying his point about iteration, we may add that as a speaker of English you are also expected to know that speakers of English are expected to know: that ‘snow is white’ is true iff snow is white, that ‘snow’ refers to snow, and that ‘is white’ is true of just the white things. If, and only if, you know all such things, the idea goes, you understand English. The plausibility of this idea is illustrated by what it tells us about an earlier example. Higginbotham would say: If you know not only (i) that ‘mis pantelones son verdes’ is true in Spanish iff my pants are green, but also (ii) that necessarily, one who understands that sentence knows (i), and so on for further iterations, then you know that the sentence means that my pants are green, and not that my pants are green and arithmetic is incomplete. Repeating this for every sentence should, he suggests, be sufficient for understanding the language. In order to test this idea, as a defense of Davidson, we must make it precise. The idea is that a theory the theorems of which give the contents of linguistic norms, iterated knowledge of which is necessary and sufficient for understanding L, qualifies as a theory of meaning of L. Let C1 be a first approximation of this claim (understanding a theorem to be any logical consequence of T). C1. Any theory T satisfying (a) and (b) is an acceptable theory of meaning for L. (a) For each theorem TT of T, (i) knowledge of TT is necessary for understanding L, (ii) knowledge that knowledge of TT is necessary for 26. Ibid., 257. 27. Ibid.

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Scott Soames understanding L is necessary for understanding L, and so on for further iterations.28 (b) The knowledge specified in (a) is sufficient for understanding L.

The justificatory argument is completed by C2. C2. Translational, Davidsonian truth theories satisfy C1. WHY THIS FIRST APPROXIMATION WILL NOT DO However, C2 will not do. Many theorems of translational truth theories—both axioms and their logical consequences—fail to satisfy C1(a). Let L be a fragment of English corresponding to the first-order predicate calculus. The best candidates for theorems satisfying C1(a) are the referential axioms for names and predicates, plus those for the truth-functional connectives. However, even here the case is not clear. Suppose L does not contain any reference predicate relating words and things, any knowledge predicate relating agents and propositions, any devices for referring to expressions, any expression designating L, any understanding predicate holding between agents and languages, or any necessity operator. Such a language, though primitive, surely could be spoken—presumably as a first language. It is debatable whether an individual’s mastery of L would be sufficient to credit him or her with implicit knowledge of what its terms refer to, and what its predicates are true of. But even if it is sufficient, what of the iterations? Must a native speaker of L know that in order for anyone to understand L it is required, and hence necessary, that one know that ‘Plato’ refers to Plato and that ‘is human’ is true of o iff o is human—even though he or she may have no way of expressing the concepts that make up this alleged knowledge? It is not obvious that this is necessary. It is one thing to credit a speaker with implicit knowledge guiding his or her use of language. It is quite another to credit the speaker with implicit knowledge attributing this implicit knowledge to others. Thus, it is doubtful that the referential axioms satisfy C1(a).29 Matters get worse for Tarski’s quantificational axioms, and for his definition of truth in terms of truth relative to an assignment. Do all L-speakers who understand its quantificational sentences know these things? Do they also know that in order to speak L one must know them, and hence that every L-speaker does? Do they, still further, know that every speaker knows the previous iterated claim? It hardly seems likely. I understand L, yet I do not know that every speaker of L knows Tarski’s quantificational axioms—let alone that they know that I know the very thing I take myself not to know. These consequences of C1 and C2 are incredible. Next consider theorems that are not axioms. Let T/R be a translational theorem that specifies the truth (or reference) conditions of a sentence S (or expression E) in terms of a strict paraphrase of S (or E). Putting aside the question of whether translational theorems like this satisfy condition C1(a), we have two 28. (i) and (ii) may equivalently be put: (i) it is required, and hence necessary, that one who understands the sentences and other expressions of L (with the meanings they actually have) knows TT; (ii) it is required, and hence necessary, that one who understands the sentences and other expressions of L (with the meanings they actually have) knows (i). 29. Thanks to William Dunaway for discussion of points in the previous paragraph.

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nontranslational cases to consider. In case 1, we let TEarly be any theorem that appears on a line earlier in the derivation of T/R than the line on which TR appears. It is not plausible that TEarly must satisfy C1(a). The only grounds for thinking that it must are grounds for thinking (i) that speakers actually employ this derivation to generate T/R, which they use to interpret S, or E; (ii) that every speaker knows that other speakers do the same, and would refuse to count anyone as knowing L whose understanding of S, or E, came about in some other way; and (iii) that every speaker knows that every speaker knows this.As before, such results are incredible. Although I understand L, I do not think that I have the knowledge of other speakers, or that they have the knowledge of me, needed for the condition to be satisfied. In case 2, we let TExtra be a theorem of the truth theory that is neither translational, nor one needed to derive any translational theorem. Surely there is no reason to think that it satisfies C1(a). Note, it does not help to claim that TExtra will not count as “canonical.” Since C1 and C2 are stated in terms of simple theoremhood, their conjunction is refuted.

REFORMULATING THE IDEA Perhaps we can do better by reformulating the justificatory claim as RC1. RC1. A theory T which identifies some canonical subset SubT of its theorems, and correctly says that it satisfies (a) and (b), is an acceptable theory of meaning for L. (a) For each member TT of SubT, (i) knowledge of TT is necessary for understanding L, (ii) knowledge that knowledge of TT is necessary for understanding L is necessary for understanding L, and so on for further iterations. (b) The knowledge specified in (a) is sufficient for understanding L. RC2. Properly augmented translational theories of truth and reference satisfy RC1. This revision avoids our earlier problems by excluding some of the problematic theorems. Doing this requires adding new theoretical machinery to the truth theory defining canonical theorems, and specifying, via the empirical claim TC, the work they are supposed to do. TC The class of canonical theorems of T satisfies (a) and (b) of RC1. This expansion T+ of the truth theory T is what is claimed to be the theory of meaning for L. Davidsonian theories of truth and reference alone are not enough. Instead, the theories that genuinely explain meaning contain Davidsonian theories as parts, while making further claims about knowledge and understanding. Since questions about what counts as understanding sentences and other expressions are closely tied to questions about their meanings—over and above their truth and reference conditions—the exciting initial thought that Davidsonian theories would explicate meaning in wholly extensional terms has gone by the board.This need not be an objection. But it is a fact.

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There is, however, an objection in the wings. Suppose that both (2) and (3) are theorems of an expanded, translational truth theory T+ of a fragment L of English—as well they might. 2. ‘2 = 2 and if n = 2, there are numbers x, y, z such that xn + yn = zn, but if n > 2, there are no such numbers’ is true in L iff 2 = 2 and if n = 2, there are numbers x, y, z such that xn + yn = zn, but if n > 2, there are no such numbers. 3. ‘2 = 2 and if n = 2, there are numbers x, y, z such that xn + yn = zn, but if n > 2, there are no such numbers’ is true in L iff if n = 2, there are numbers x, y, z such that xn + yn = zn, but if n > 2, there are no such numbers. If (2) and (3) are both canonical, then it will be left unclear whether the quoted sentence means that which is expressed by the right-hand side of (2), or that which is expressed by the right-hand side of (3). If, following Higginbotham, we take what is said by an utterance of S to be a good guide to the meaning of S,then the right-hand sides of (2) and (3) will, it seems, differ in meaning—since an assertive utterance of the former will result in an assertion of the claim expressed by the first conjunct (that the number 2 = the number 2), whereas an assertive utterance of the latter will not. Given that the quoted sentence presumably does not mean both, we conclude that T+ fails to satisfy clause (b) of RC1, and, so, is false (assuming that one who does not know the meaning of the quoted sentence does not understand it). The same failure occurs, even if only (2) is counted as canonical, so long as both (2) and (3) satisfy (a) of RC1. If they do, then appeal to this condition will not determine whether what the quoted sentence means is given by the right side of (2), or the right side of (3). Thus, RC1(b) will be in the same jeopardy as before. Before, T+ claimed that (2) and (3) both satisfy RC1(a). Here, T+ says this about (2), while remaining silent about (3)—which, we are presently assuming, does satisfy the condition. Since this silence does not entail anything about the meaning of the quoted sentence, T+ is thrown into the same doubt as before. The difficulty presented by these sentences can be avoided only if we can show that although (2) satisfies RC1(a), (3) does not. But this is doubtful. To understand the quoted sentence, one must be familiar with the number 2, and know what it is to identify it with a number n—in which case the first conjunct will be superfluous, since, in that case, one cannot help knowing that 2 = 2. Thus, knowledge of (2) and (3) will go hand in hand—in which case knowledge of (3) will be necessary for understanding L, if knowledge of (2) is. Still, it might be objected, even if knowledge of (2) and (3) do necessarily go hand in hand for competent speakers, knowledge that knowledge of (2) and (3) necessarily go hand in hand might not be required for competence.All it takes for this iterated knowledge claim to fail is for there to be a misguided philosopher who—though himself a competent speaker of L who knows both (2) and (3)—doubts, and so does not know, that this must be true of all competent speakers. Given the nearly unbounded reach of such possible doubt, we cannot rule this out—which means that we cannot, in the end, be sure that (3) does satisfy condition RC1(a).

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Although this may seem all to the good, it will vindicate T+ as a theory of meaning only if we can be sure that (2) does satisfy the condition. Can we be sure of that? Consider mathematical nonfactualists who accept Fermat’s last theorem while denying that any mathematical statements are true, and so reject (2). Though I take such philosophers to be mistaken about the scope of the truth predicate, I do not doubt that they understand the sentence quoted in (2), even though they do not believe, and hence do not know, (2).30 As a result, I do not believe, and so I do not know, that knowledge of (2) is necessary for understanding L. Surely this does not mean that I am not a competent speaker, or that I do not understand the quoted sentence. Hence, our final attempt to justify Davidsonianism is unconvincing. The justificatory problem thus remains unsolved. THE DISCONNECT BETWEEN THEORY AND PRACTICE Earlier, I noted that in “Truth and Meaning,” Davidson responded to the worry that, since the theorems of his truth theories are only material biconditionals, his theories might issue in true but grotesquely nontranslational theorems like S. ‘Snow is white’ is true iff grass is green and thereby fail to count as theories of meaning. As I indicated, his response was heroic. The threatened failure of nerve may be counteracted as follows. The grotesqueness of (S) is in itself nothing against a theory of which it is a consequence, provided the theory gives the correct results for every sentence (on the basis of its structure, there being no other way). It is not easy to see how (S) could be party to such an enterprise, but if it were—if that is, (S) followed from a characterization of the predicate ‘is true’ that led to the invariable pairing of truths with truths and falsehoods with falsehoods—then there would not, I think, be anything essential to the idea of meaning that remained to be captured. What appears to the right of the biconditional in sentences of the form ‘s is true if and only if p’ when such sentences are consequences of a theory of truth plays its role in determining the meaning of s not by pretending synonymy but by adding one more brush-stroke to the picture which, taken as a whole, tells us what there is to know of the meaning of s; this stroke is added by virtue of the fact that the sentence that replaces ‘p’ is true if and only if s is.31 This refusal to appeal to an antecedently understood notion of meaning, synonymy, or translation to constrain acceptable theories of truth—or to justify taking them to be theories of meaning—was, in effect, quietly abandoned nine years later, in the 30. See Mark Richard, “Deflating Truth,” Philosophical Issues 8 (1997): 57–78 for a defense of the philosophical coherence (if not correctness) of such nonfactualists. My response is found on pp. 88–93 of that volume. For further discussion, see Scott Soames, “Understanding Deflationism,” Philosophical Perspectives 17 (2003): 369–83. 31. Davidson, “Truth and Meaning,” 26, my emphasis.

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wake of Foster’s objection. By that time, however, the original methodological refusal had become securely embedded in a procession of empirical analyses of linguistic phenomena advancing the Davidsonian program. For example, in 1968, just one year after “Truth and Meaning,” Davidson analyzed: 4a. Galileo said that the earth moves as having the structure 4b. Galileo said that: The earth moves in which ‘that’ is a demonstrative used by the speaker to refer not to what Galileo said, nor, of course, to Galileo’s utterance, but to the speaker’s utterance of ‘The earth moves.’ On this picture, the theory of truth, cum theory of meaning, issues in a theorem along the lines of (4c).32 4c. An utterance, by x, of ‘Galileo said that the earth moves,’ containing as a subpart x’s utterance u of ‘the earth moves,’ is true iff some utterance of Galileo and x’s utterance u make Galileo and x samesayers. Over the years, much has been said for and against this analysis. Although it inspired a progression of increasingly sophisticated successors, it is, I think, fair to say that no one today stands by it in its original form. The point, however, is not to rehearse its shortcomings, but to note how it fits Davidson’s admonition in “Truth and Meaning” not to construe the right-hand sides of the T-theorems of his interpretive theories as “pretending” to capture the meanings of that which appear on the left. This point is illustrated by (4c), since one can know that which is said by my utterance of (4a) without knowing anything about me, or any utterance of mine, and since what is said by my utterance u could have been true, even if u had had a different content, or if neither it, nor I, had existed. Given these intensional and hyperintensional differences, one cannot regard (4c) as translational in any interesting sense. Although this may have seemed acceptable according to the justificatory picture sketched in “Truth and Meaning,” it is not acceptable according to post-Foster attempts at justification—all of which rely, in one way or another, on translational theorems. In changing the justification of the program, Davidson, in effect, narrowed the class of empirical analyses capable of advancing it. This lesson has yet to be learned. Even though the justificatory story has changed—imposing strong constraints on canonical theorems—empirical analyses offered to advance the program often do not take these constraints seriously. A recent analysis of propositional attitudes by Richard Larson and Peter Ludlow is a case in point.33 The proposal, which is arguably the most sophisticated Davidsonian successor of the one in “On Saying That,” uses the rules for deriving T-theorems to assign annotated phrase structure trees, called “interpreted logical forms,” to sentences. For example, (5b) is the interpreted logical form assigned to (5a). 32. Donald Davidson, “On Saying That,” Synthese 19 (1968–69): 130–46. 33. Richard Larson and Peter Ludlow, “Interpreted Logical Forms,” Synthese 95 (1993): 305–56.

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5a. John speaks Spanish. 5b. 〈S, truth〉 〈NP, John〉

〈“John”, John〉

〈VP, John〉 〈V, John, Spanish〉

〈NP, Spanish〉

〈“speaks”, 〈John, Spanish〉〉

〈“Spanish” Spanish〉

These interpreted logical forms are taken to be the objects of attitude verbs. Thus, (6) is said to be true iff Mary asserts/believes (5b). 6. Mary asserts/believes that John speaks Spanish. Spelled out in words, the T-theorem interpreting (6) amounts to (7). 7. ‘Mary asserts/believes that John speaks Spanish’ is true iff Mary asserts/ believes the interpreted phrase marker whose root node is the pair 〈‘S’, truth〉, which dominates a pair of nodes 〈‘NP’, John〉 and 〈‘VP’, John〉, where 〈‘NP’, John〉 dominates 〈‘John’, John〉, and 〈‘VP’, John〉 dominates a pair of nodes 〈‘V’ 〈John, Spanish〉〉, and 〈‘NP’, Spanish〉, with the first of these nodes dominating 〈‘speaks’, 〈John, Spanish〉〉 and the second dominating 〈‘Spanish’, Spanish〉. Is (7) true? It is hard to say. Since its right-hand side is a theoretical claim we have no pretheoretic grasp of, it is not easy to judge the truth or falsity of (7), without already having accepted the theory. This is awkward, since it is by evaluating such theorems that we are supposed to test the theory itself.34 Suppose, for the sake of argument, that (7) is true. Although this would support the analysis, as a theory of truth, it would not vindicate it as a theory of meaning. Theorems like (7) do not supply paraphrases for the sentences they purport to interpret, and so do not conform to post-Foster attempts to justify the Davidsonian program. Nor, in my opinion, do they conform to any other viable justificatory approach.35 All too often, truth-theoretic analyses are offered, even though no attempts to justify their claim to be theories of meaning have been successful. Even worse, the most sophisticated empirical analyses are sometimes inconsistent with the most sophisticated of the justificatory attempts. This is not a healthy state for what purports to be an empirically viable theory of meaning to be in. WHAT IS THE ALTERNATIVE? Given the problems of both the justification and execution of the Davidsonian program, we would do well to consider an alternative. The justificatory problem 34. Elsewhere, I have made suggestions about how to extract empirically testable claims from such theorems, and hence come to a judgment about their truth or falsity. See Scott Soames, Beyond Rigidity (New York: Oxford University Press, 2002), 147–59; and “Truth and Meaning: The Role of Truth in the Semantics of Propositional Attitude Ascriptions,” in Proceedings of the 7th International Colloquium on Cognitive Science, ed. Kepa Korta and Jesus M. Larrazabal (Dordrecht: Kluwer, 2003), 21–44. 35. Larson and Ludlow appear to adopt a version of the psycholinguistic justification discussed earlier.

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arose directly from Davidson’s initial conviction that theories of meaning must not talk about meaning. Since his truth theories make no statements about what sentences mean, justifying their use as theories of meaning has always been a challenge. Theories that do state informative truths about what the sentences of a language mean are natural alternatives. By this, I do not mean theories that derive an instance of (8) for each sentence S of a language, from axioms about the parts of S. 8. ‘S’ means in L that S. To date, no one has constructed theories that do that in an illuminating way. Rather, I mean theories that recursively assign certain entities to sentences—identified as their meanings—on the basis of their semantically significant structure. The idea, which goes back to Frege and Russell, was rejected by Davidson forty-one years ago in the first few pages of “Truth and Meaning.” Up to here we have been following in Frege’s footsteps . . . But now, I would like to suggest, we have reached an impasse: the switch from reference to meaning leads to no useful account of how the meanings of sentences depend on the meanings of the words . . . that compose them. Ask, for example, for the meaning of ‘Theaetetus flies.’ A Fregean answer might go something like this: given the meaning of the name ‘Theaetetus’ as argument, the meaning of ‘flies’ yields the meaning of ‘Theaetetus flies’ as value. The vacuity of this answer is obvious. We wanted to know what the meaning of ‘Theaetetus flies’ is; it is no progress to be told that it is the meaning of ‘Theaetetus flies.’36 The contrast here between a real and pretended account will be plainer still if we ask for a theory . . . that has as consequences all sentences of the form ‘s means m’ where ‘s’ is replaced by a structural description of a sentence and ‘m’ is replaced by a singular term that refers to the meaning of that sentence; a theory, moreover, that provides an effective method for arriving at the meaning of an arbitrary sentence structurally described. Clearly some more articulate way of referring to meanings than any we have seen is essential if these criteria are to be met. [This is what he sees no prospect of. Thus he concludes] . . . Paradoxically, the one thing meanings do not seem to do is oil the wheels of a theory of meaning—at least as long as we require of such a theory that it non-trivially give the meaning of every sentence in the language. My objection to meanings in the theory of meaning is not that they are abstract or that their identity conditions are obscure, but that they have no demonstrated use.37 Davidson’s objection to meanings as entities is that they cannot be used to nontrivially give the meanings of sentences, or to play any useful role in theories of meaning. The objection, though not entirely without force, is not true. Combining the ideas of Russell and Tarski, we can recursively assign structured Russellian 36. Davidson, “Truth and Meaning,” 20–21. 37. Ibid., 21–22.

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propositions—the constituents of which are objects and properties—to all sentences of a language. Adding a theory of truth for propositions gives us a theory that specifies the truth conditions of sentences, identifies which are synonymous with which, provides a natural account of attitude ascriptions, and lays the foundation for a theory of the assertions made, and the beliefs expressed, by sincere assertive utterances. Like all empirical theories, this one is underdetermined by the data for it. However, since its claims are testable, the theory is capable of empirical confirmation or disconfirmation. But does it, one may ask, really give us the meanings of sentences? Yes and no. To take the simplest sort of example, we may suppose that it tells us the meaning of (9a) is (9b). 9a. A is larger than B. 9b. 〈the relation of being larger than, 〈a, b〉〉 If the theory is correct, then the theorem pairing it with (9b) is a true theoretical description of the meaning of (9a). However, this way of giving us the meaning of (9a) is not one that would allow us to understand it, if we did not already. One might dismiss this as unimportant, since as long as the meanings of sentences are correctly identified, the fact that they are not presented in a way suitable for language learning means only that the theory is no replacement for the language lab. Since our interest in semantic theories is theoretical, not pedagogical, this is no loss. However, there is a difficulty here that goes much deeper. What is (9b), after all, but a simple set-theoretic structure, the standard set-theoretic expansion of which is (9c)? 9c. {{the relation of being larger than}, {the relation of being larger than, {{a}, {a,b}}}} How could this structure be the meaning of anything, let alone (9a)? There is nothing in it to indicate that the relation larger than is being predicated of anything, or, if it is, what exactly it is predicated of. Does (9c) represent a as being larger than b? Does it represent b as being larger than a? Does it represent a as being larger than a? Or is (5c) not representational at all? Surely, there is nothing in this set-theoretic structure by virtue of which it represents anything as being one way rather than another. But if it is not representational, then it does not have truth conditions, in which case, it cannot be the meaning of any sentence. This, I suspect, is what lies behind Davidson’s worry about propositions, and his dismissive remarks about theories of meaning that invoke them. Since any other abstract structure that we can identify and make precise will be similarly nonrepresentational, the problem cannot be solved by selecting any such structure as the meaning of (9a). One could, of course, take propositions to be inherently and intrinsically representational, and so sui generis. However, this is a council of despair. Davidson would not accept such obscuritanism, and we should not either. If we posit structured propositions as meanings of sentences, we ought to explain what they are, and how they are able to play the roles we assign to them.38 38. The best recent attempt to do this that I know of is the illuminating discussion in Jeffrey C. King’s The Nature and Structure of Content (Oxford: Oxford University Press, 2007).

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The only way to do this is, I believe, to acknowledge that propositions are not intrinsically representational. Here is the idea. We retain the conception of propositions as structured complexes, the constituents of which are objects and properties. To say that certain constituents make up a complex is to say that, in the complex, the constituents stand in certain relations to one another. The complex is, in effect, the standing of the constituents in those relations. What these relations are depends on the specific abstract structures we take propositions to be. Which structures these are does not matter. Suffice it to say, for our purposes, that the proposition expressed by (9a) is a complex in which a, b, and the larger-than relation stand in a certain relation R. How does it come about that this entity—a’s and b’s standing in R to larger than—represents a as being larger than b? The answer rests not on anything intrinsic to R, but on the interpretation placed on R by the way that we use it. Though abstractly expressed, the idea is commonplace. Take maps, for example. On my map, the dot labeled “Los Angeles” is (roughly) two inches below and half an inch to the right of the dot labeled “San Francisco.” The standing of these dots in this spatial relation on the map represents the city Los Angeles as being (roughly) 320 miles south and eighty miles east of the city San Francisco. It does so, in part, because of the interpretation we give to the relation being two inches below and half an inch to the right of on the map. This is the kind of interpretation we give the propositional relation R, in interpreting the complex in which a and b stand in R to larger than. In both cases—the map and the proposition—our interpretation of a relation that the constituents of a structure stand in is what endows the structure with representational properties, and hence, truth conditions. A proposition, like a map, is something we interpret. This idea comes from The Tractatus.39 There, propositions are taken to be sentences that we use in a certain way. Sentences are complexes in which words and phrases stand in certain structural relations. For example, sentence (9a) is the standing of the names ‘A’ and ‘B’ in a certain grammatical relation to the predicate ‘is larger than.’ Call this relation RG. We interpret RG as predicating the larger-than relation expressed by the predicate of the objects a and b designated by its arguments, thereby bringing it about that (9a) represents a as being larger than b. At this point, it may be objected that propositions have dropped out of the picture. But they need not.We still need them to play the roles of what synonymous sentences have in common, and of what we assert and believe by uttering and accepting sentences. Synonymous sentences may differ in vocabulary, and in some aspects of superficial syntactic structure. However, if they express the same proposition, then utterances of them “say the same thing,” and express the same belief.To assert a proposition is to assertively utter, inscribe, or produce some representation that expresses it. A similar point holds for beliefs and other (nonperceptual)

39. Ludwig Wittgenstein, Tractatus Logico Philosophicus (London: Routledge and Kegan Paul, 1922). For a brief discussion of Wittgenstein’s theory of propositions (interpreted sentences), see pp. 215–16 of vol. 1 of my Philosophical Analysis in the Twentieth Century.

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propositional attitudes. To bear such an attitude toward a proposition is to bear a more basic relation to a propositional vehicle that expresses it. What, on this account, is it for an abstract structure—like (9b/c)—to count as the proposition that a is larger than b? It is for us to use the structure to predicate larger than of a and b. What is it for us to use the structure in that way? It is, very roughly, for us to use the grammatical structure of some sentence or other representation, the semantic contents of the constituents of which are a, b, and larger than, to predicate the latter of the former. In these cases, the representational properties of propositions are grounded in, and explained by, the representational properties of sentences, not the other way around. The picture is complicated by the fact that there is, I think, one kind of propositional attitude we bear to propositions that is not mediated by representations that express them. The attitude involves perception. When I see an object o as being red, I typically see both o and the color, which is a kind of property. Since perception is a form of cognition, my perceptual experience involves my predicating the color of the object. I do not, by virtue of this cognitive activity, thereby see the proposition that o is red. However, since the proposition is part of the content of my perceptual state, I do come to bear a propositional attitude toward it. What counts as my bearing this attitude toward it is simply that my perceptual experience involves the predication we use the proposition to represent. In both the perceptual and the linguistic case, the explanation of what is predicated of what in the proposition bottoms out in predication as a cognitive activity of agents—in one case, in the way agents interpret different perceived propositional constituents, in the other case in the way they interpret linguistic representatives of those constituents. Many details of this story remain to be filled in. The task of doing so has a constructive part and a foundational part. In the constructive part we use propositions as theoretical constructs in linguistic and cognitive theories, and subject those theories to empirical test. In the foundational part, we explain what propositions are, how they acquire their representational properties, and how we are related to them. Since the tasks run in tandem, advances in one need not wait on progress in the other. This, it seems to me, is the most promising alternative to the Davidsonian approach to semantics.

Midwest Studies in Philosophy, XXXII (2008)

The Whole Truth and Nothing but the Truth* SUSAN HAACK

Much truth is spoken, that more may be concealed. —Mr. Justice Darling (1879)1 The word “truth” is sometimes used as an abstract noun: so used, it refers to the concept of truth or, as some might prefer to say, to the property of being true, or to the meaning of the word “true” and its synonyms in other languages. It is also sometimes used to refer to the things that fall in the extension of this concept; i.e., to true propositions, beliefs, statements, theories, etc.2 In English we have just the one word, “truth,” to do both jobs; the distinction would be more obvious if we also had, say, “true-ness” for the first use. But the difference between the two uses is marked grammatically: in the second use, but not the first, “truth” takes the indefinite article (as in the opening sentence of Pride and Prejudice: “it is a truth universally acknowledged that a single man in possession of a good fortune must be in want of a wife”),3 and the plural form (when we speak of “the truths of arithmetic,” for example, or in the second sentence of the Declaration of Independence: “We hold these truths to be self-evident, that all men are created * © 2008 Susan Haack; appears here by permission of the author. 1. Charles J. Darling, Scintillae Juris, 3rd enlarged ed. (London: Davis and Son, 1879), 73. 2. There is a similar doubleness in the word “law”: compare “law is the will of the sovereign” and “Michigan law regarding the admissibility of expert testimony was revised in 2004.” (See fn.18 below.) 3. Jane Austen, Pride and Prejudice (1813), in The Works of Jane Austen (London: Spring Books, 1966), 171. Midwest Studies in Philosophy: Truth and its Deformities Volume XXXII Editor by Peter A. French and Howard K. Wettstein © 2008 Wiley Periodicals, Inc. ISBN: 978-1-405-19145-6

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equal . . . ”). “Falsehood” works similarly, serving both as an abstract noun referring to the concept or the property of falseness and as a common noun referring to false propositions, etc.; and, like “truth,” in the latter use it takes the plural form and, more rarely, the indefinite article. “Falsity,” however, seems to function, with rare exceptions, as an abstract noun. This dual role of the word “truth” can give rise to trouble. Some, confusing the two uses, treat “truth,” the abstract noun, as if it referred to some very special, all-important true proposition; and so speak reverently of the Truth, with a capital “T,” as in “the Truth shall set you free.” Others, finding this kind of reverence for “the Truth” disturbing, confusedly arrive at the mistaken conclusion that it is mere superstition to place any value on truth, or even that we should repudiate talk of truth altogether. Patricia Churchland, for example, writes that “the truth, whatever that is, definitely takes the hindmost”;4 Sandra Harding that “the truth—whatever that is!—will not set you free”;5 Jane Heal, that “[t]ruth is generally thought to be a Good Thing,” but this “seeming truism” is misconceived, for truth is not really an evaluative term at all;6 Stephen Stich, that “once we have a clear view of the matter, most of us will not find any value . . . in having true beliefs”;7 and Richard Rorty, that he “does not have much use for notions like ‘objective truth.’ ”8 I have tackled both these kinds of confusion elsewhere;9 here, I want to focus on yet a third kind of confusion, also encouraged by the dual use of “truth”: attributing to truth, true-ness, what are really properties of some, but not all, truths.10 There is one truth, one true-ness or truth-concept. But there are many truths, i.e., many and various true propositions, etc. Truth is not dependent on what we believe or accept; it is not relative to culture, community, theory, or individual; and it is not a matter of degree, nor is it a conglomeration of properties that might be satisfied in full or only in part. But some truths are made true by things we do, 4. Patricia Smith Churchland, “Epistemology in the Age of Neuroscience,” Journal of Philosophy 75, no. 10 (1987): 544–53, 549. 5. Sandra Harding, Whose Science? Whose Knowledge? (Ithaca, NY: Cornell University Press, 1991), xi. 6. Jane Heal, “The Disinterested Search for Truth,” Proceedings of the Aristotelian Society, 88 (1987–88): 97–108, 97. 7. Stephen P. Stich, The Fragmentation of Reason: Preface to a Pragmatic Theory of Cognitive Evaluation (Cambridge, MA: Bradford Books, MIT Press, 1990), 101. 8. Richard Rorty, Essays on Heidegger and Others (Cambridge, England: Cambridge University Press, 1991), 86. 9. See Susan Haack, Evidence and Inquiry: Towards Reconstruction in Epistemology (Oxford: Blackwell, 1993); 2nd ed. forthcoming under the title Evidence and Inquiry: A Pragmatist Reconstruction of Epistemology (Amherst, NY: Prometheus Books, 2009), chaps 8 and 9; “Confessions of an Old-Fashioned Prig,” in Manifesto of a Passionate Moderate: Unfashionable Essays (Chicago: University of Chicago Press, 1998), 7–30; “Staying for an Answer: The Untidy Process of Groping for Truth,” Times Literary Supplement, July 9, 1999: 12–14, reprinted in Susan Haack, Putting Philosophy to Work: Inquiry and Its Place in Culture (Amherst, NY: Prometheus Books, 2008), 25–36; “Engaging with the Engaged Inquirer: Response to Mark Migotti,” in Susan Haack: A Lady of Distinctions, ed. Cornelis de Waal (Amherst, NY: Prometheus Books, 2007), 277–80. 10. This diagnosis was already implicit in an earlier article of mine, “The Unity of Truth and the Plurality of Truths,” Principia 9.1–2 (2005): 87–110; reprinted in Haack, Putting Philosophy to Work (see fn. 9), 43–60. Correspondence with Steven Pethick helped me make it explicit.

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and others by what we believe; and some truths make sense only relativized to a time, a place, or a culture. Moreover, some true propositions are in some degree vague, others more precise; and some are in one way or another partial, others more complete. Truth, in short, is simple; but truths are not. Truths come in all shapes and sizes; and much of the time we traffic in the almost, the approximately, or the partially true. The goal of the first section of this article is to articulate these contrasts more carefully; the goal of the second, to explore some epistemological, rhetorical, and practical dimensions of partial truth. 1. THE TROUBLE WITH “TRUTH” AND “TRUTHS” I note for the record that “true” is used in English as a predicate not only of beliefs, theories, claims, statements, propositions, and so on, but also of persons, pictures, and so forth, which are not propositional. We speak of a “true friend,” a “true likeness,” a “true scholar,” “true love”; we describe the whale as “a true mammal” and not “a true fish”; a memorable movie title speaks of “True Grit.” These non-propositional uses are quite closely related to the propositional ones, conveying something like “real, genuine, truly (an) F”: truly a friend, truly a likeness, truly a mammal, truly a scholar, truly determined, etc. In other uses, “true” is not quite so easily assimilable to the truth of propositions; for example, when we speak of “being true to oneself,” meaning something like “acting in accordance with one’s real character and values,” or when we describe a joint or beam as being “out of true,” meaning that it is crooked, slanted, askew. But in what follows I confine myself to “true” as it applies to propositions, statements, beliefs, and such. I take for granted that truth, true-ness, is not to be identified with acceptanceas-true; for what is accepted as true may not be true, and what is true may not be accepted as such. Nor is truth to be identified with belief, or even with warranted belief; for what is believed, even what is believed on good evidence, may not be true, and what is true may not be believed. Nor is truth to be identified with knowledge; for while what is known must be true, what is true may not be known. Nor is truth to be identified with agreement; for while, if we agree that p, we agree that p is true, we may agree that p when p is not true, and we may not agree that p when p is true. And neither is truth is to be identified with sincerity, truthfulness, or candor; for while a sincere, truthful person may be disposed to speak the truth as he believes it to be, if his belief is mistaken his sincere assertion will be false. I also take for granted that the most plausible of the umpteen competing philosophical theories of truth are, in intent or in effect, generalizations of the Aristotelian insight that “to say of what is not that it is not, or of what is that it is, is true.”11 Some of these, the many variants of the correspondence theory, turn those emphatic adverbs for which we reach when we say that p is true just in case really, in fact, p, into serious metaphysics, by construing truth as a relation, structural or conventional, of propositions or statements to facts or reality. Others, such 11. Aristotle, Metaphysics, trans. W. D. Ross, Book Gamma (IV), 7, 1011b25, in The Basic Works of Aristotle, ed. Richard McKeon (New York: Random House, 1941), 749.

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as Alfred Tarski’s semantic theory, Frank Ramsey’s laconicist theory, and the many and various contemporary deflationist, minimalist, disquotationalist, prosententialist, etc., theories that are their descendants, do not require such large ontological investments. But Tarski himself doubted that his theory could be applied beyond the realm of regimented, formalized logical and mathematical languages; “the very possibility of a consistent use of the expression ‘true sentence’ which is in harmony with the laws of logic and the spirit of everyday language,” he writes, “seems to be very questionable.”12 And now that the dust has settled from the Davidson program,13 we can see that Tarski’s reservations were prescient. The most promising approach seems to be something along the lines of Ramsey’s simple statement that “a belief that p . . . is true if and only if p; for instance, a belief that Smith is either a liar or a fool is true if Smith is either a liar or a fool and not otherwise.”14 Though it was long known as the “redundancy theory” of truth, Ramsey’s account, laconic as it is, does not imply that “true” has no genuine role to play; Ramsey was well aware that, while “it is true that” is eliminable from direct truth-attributions (as when we say that it is true that Caesar crossed the Rubicon), it plays a substantial role in indirect truth-attributions (as when we say that Plato said some true things, and some false). Ramsey was also well aware that his account leaves many questions still to be answered—technical questions about the sentential quantifiers that will be needed to explain those indirect truth-attributions, and philosophical questions about representation (what it is for this to be the proposition that p) and reality (what it is for it to be the case that p). And he does not pretend to offer a criterion of truth, but acknowledges that his account leaves epistemological issues untouched. But Ramsey’s simple initial formulation will suffice for my articulation of what I mean by claiming: • that although there are many and various true propositions, there is only one truth; • that although some true propositions are about things of our making, truth is objective; • that although some true propositions make sense only understood as relative to place, time, culture, legal system, etc., truth is not relative; • that although some true propositions are vague, truth is not a matter of degree; and • that although some propositions are only partly true, truth does not decompose into parts. 12. Alfred Tarski, “The Concept of Truth in Formalized Languages” (first published in Polish in 1933), in Logic, Semantics, Metamathematics, trans. J. H. Woodger (Oxford: Clarendon Press, 1956), 152–278, 165. 13. In “A Nice Derangement of Epitaphs,” in Truth and Interpretation, ed. Ernest Lepore (Oxford: Blackwell, 1986), 433–46, Donald Davidson himself effectively acknowledged that his project of giving a Tarskian theory of meaning for natural languages had been misconceived, writing (pp. 445–46) that he had reached the conclusion that “there is no such thing as a language, not if a language is anything like what many philosophers have supposed.” 14. F. P. Ramsey, On Truth (papers from 1927–29), ed. Nicholas Rescher and Ulrich Majer (Dordrecht, The Netherlands: Kluwer, 1992), 12.

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The core principle, that a proposition is true just in case it is the proposition that p, and p, applies whatever kind of truth-capable proposition we are dealing with, whether it be a mathematical theorem or a historical conjecture, a prophecy of imminent disaster or a meteorological prediction, a proposition about literature or a proposition about law, a theory in physics or a sociological generalization, a statement about what I had for breakfast on September 11, 2001, or a prediction of who will win the next presidential election, or (assuming that propositions of ethics are truth-capable) a proposition about what actions, motives, traits of character, persons, rules, institutional arrangements, etc., are morally desirable and what undesirable.15 This, at its simplest, is what I mean by saying that, though there are many truths, many theories of truth, and many conceptions, and misconceptions, of truth, there is just one truth: that what it is for a claim to be true is the same, regardless of what the claim is about. The same simple formula, that a proposition is true just in case it is the proposition that p, and p, is enough to tell us that whether a proposition is true or is false is normally an objective matter; i.e., that it is neither necessary nor sufficient for a propositions’s being true that you, or I, or anyone, believes it. This is obvious enough where claims and theories about natural phenomena and events, which are not of our making, are concerned. But it is no less true with respect to propositions about phenomena and events that occur only under artificial circumstances created in the laboratory, even though these are of our making; for whether such a claim is true or is false is still independent of whether you, or I, or anyone, believes that it is true or believes that it is false. Nor is it any less true with respect to legal truths, even though these are made true by legislation or precedent, i.e., by things people do; or with respect to social-scientific claims and theories, even though these are about social phenomena and institutions, which are constituted in part by people’s beliefs, hopes, fears, etc. Consider, for example, the proposition that, as George Orwell puts it, “the English working class . . . are ‘branded on the tongue,’ ”16 i.e., that in England class status is closely correlated with accent. Whether this is true or is false does have something to do with whether enough people in England believe it; nevertheless, its truth-value is still independent of whether you, or I, or any individual believes that it is true or believes that it is false. Some propositions are incomplete, and hence incapable of truth or falsity, unless understood as restricted to a place, a time, or a culture. (Some might prefer to construe such supposed propositions as really only propositional functions, needing completion before they make it to the status of proposition.) A proposition to the effect that the law is thus-and-so, for example, makes sense only construed as relative to a legal system and to a time. It was once, but is no longer, 15. And similarly, mutatis mutandis, for propositions of aesthetics (and for any other class of proposition where it is a matter of dispute whether they are truth-capable). 16. Orwell wrote that “[t]he English working class, as Mr. Wyndham Lewis has put it, are ‘branded on the tongue.’ ” See George Orwell, In Front of Your Nose: The Collected Essays, Journalism, and Letters of George Orwell, vol. IV, ed. Sonia Orwell and Ian Angus (New York: Harcourt, Brace and World, 1968), 5. He is referring to Wyndham Lewis, The Vulgar Streak (Santa Barbara, CA: Black Sparrow Press, 1985), 38, where Martin speaks of “the superstition of class like a great halter around one’s neck—in which my very tongue was branded.”

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true of English law that the penalty for stealing a sheep is death;17 it has been true of Florida law since 1952, and was true of Michigan law between 1956 and 2004 (when Michigan law was changed) that the admissibility of scientific testimony is subject to the Frye Rule.18 And many social-scientific claims, similarly, have to be understood as relativized to a place and a time. To judge by the speech of news announcers and actors in the recent British television programs I see in the U.S., though it was true of England at the time I grew up that class was closely associated with accent, this is true no longer. And so on. But whether it is true or it is false that in English law in 1831 the penalty for stealing a sheep was death, or whether it is true or it is false that in England in 2008 class and accent are closely correlated, is not relative to time or place. That some truths are relative to place, time, culture, legal system, etc., does not entail that what it is to be true is similarly relative. Some truths are vague, in various ways and in varying degrees. “In varying degrees” is meant to indicate that it is less a matter of some truths being vague and others precise than of some being vaguer and others more precise: “he is tall” is vaguer than “he is significantly taller than the average Japanese male,” for example, but this in turn is vaguer than “He is six-foot-six.” To convey the real complexities, however, would require more than this simple kind of example—for what we call a language is really a great cluster of related idiolects, a vast, dense mesh of similar-enough but not quite identical patterns of usage. And any natural language is constantly shifting and changing a little here and there. Some words and phrases are regimented, become less vague, when they are adopted as specialized tools in this or that field, and others lose specificity of meaning, become vaguer, when they gain currency in popular speech or in the jargon of advertisers, etc.19 “In various ways” is meant to indicate that there are many sources of vagueness. Enthusiasts of fuzzy logic, and not a few philosophers, have been preoccupied with the vagueness that arises with predicates like “tall,” “high,” “bald,” “loud,” “reliable,” etc., that express properties that come in degrees. But other parts of speech besides predicates can be gradational: nouns like “heap,” “crowd,” or “bunch,” for example, or adverbs like “quickly,” “fairly,” “reasonably,” or “normally.” There are also vague quantifying phrases, like “a few,” or “many”—a list to 17. The law providing that a person convicted of stealing a sheep should be sentenced to death, was passed “in the Seventh and Eighth Years of the Reign of King George the Fourth.” (This, of course, was the legal reality behind the saying, “might as well be hung for a sheep as a lamb.”) The law was repealed in 1832. Statutes of the United Kingdom of Great Britain and Ireland, 2 & 3 William IV, 1832, CAP. LXIII, s. I ( July 11, 1832). 18. According to the Frye Rule (dating from Frye v. United States, 54 App.D.C. 46, 293 F. 1013 (1923)), novel scientific testimony is admissible only if the principle on which it is based is “sufficiently established to be generally accepted in the field to which it belongs.” Florida adopted this rule in Kaminski v. State, 63 So.3d 339 (1952), and continues to accept it today; Michigan adopted this rule in People v. Davis, 34 Mich.348 (1956), but dropped it in 2004, when new Michigan Rules of Evidence adopted the Daubert standard (derived from Daubert v. Merrell Dow Pharmaceuticals, Inc., 509 U.S. 579, 113 S.Ct. 2786 (1993)), according to which expert testimony, scientific or otherwise, is admissible only if it is both relevant and reliable. 19. See Susan Haack, “The Growth of Meaning and the Limits of Formalism: Pragmatist Perspectives in Science and Law,” forthcoming in English in Teorema (Spain) and in Portuguese in Revista de Filosofia UNISINOS (Brazil).

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which C. S. Peirce would have added the existential quantifier, “some”20 (which reminds me to mention that Bertrand Russell at one time described indefinite descriptions, such as “a man” in “I met a man” or “I saw a unicorn,” as ambiguous).21 And there are other kinds of indeterminacy of meaning besides the gradational. Familiar conversation fillers like “nice” or “fine,” as well as more ephemeral buzzwords like “hinky” or “funky”—which according to Jacques Barzun, “as defined by an expert, means ‘very good or beautiful; solid; cheap; smelly; or, generally, no good’ ”—owe their usefulness in part precisely to their etiolated meanings, their lack of any very specific sense; they depend, as Barzun observes, on “tone, glance, or eyebrow.”22 And then there are what Barzun calls “foam-rubber public-relations words,”23 which owe their usefulness in part to the fact that, while they retain their favorable connotations, their meanings have been stripped almost bare. Such foam-rubber PR jargon is by now ubiquitous not only in political speech (“progressive,” “change,” “democratic”), in advertising (“new,” “improved,” “scientific”), and in the jargon of real-estate salesmen (“gourmet kitchen,” “great room”), but also, as boosterism has become the order of the day there too, in the academy as well (“prestigious,” “excellence,” “distinguished,” “research-active,” “collegial”).24 It might seem that ambiguity is a matter of an expression’s having too many meanings, and is thus the very opposite of vagueness, which is a matter of an expression’s having too little meaning; but when terms with several or many meanings are used with no discrimination of sense, the effect is often hard to distinguish from vagueness. Technical terms in philosophy often suffer this fate: “realism,”25 for example, “naturalism,”26 “social epistemology,” “virtue epistemology,”27 and no doubt many others. There is also a peculiar kind of vagueness that might equally be described as “pseudo-precision,” where key terms of no very 20. C. S. Peirce, Collected Papers, ed. Charles Hartshorne, Paul Weiss, and (vols. 7 and 8) Arthur Burks (Cambridge, MA: Harvard University Press, 1931–58), 5.446, 1905. References to the Collected Papers are by volume and paragraph number. 21. Bertrand Russell, Introduction to Mathematical Philosophy (London: Allen and Unwin, 1919), chap. XVI. 22. Jacques Barzun, “What Are Mistakes and Why,” in A Word or Two Before You Go (Middletown, CT: Wesleyan University Press, 1986), 3–9, 8. Compare these uses of “funky,” which I happened upon while I was writing this article: “Chris’s cabin was funky and charming” ( James Patterson, 1st to Die [New York: Warner Books, 2001], 370); “ . . . a fashion craze that came and went quickly in the funky 1960s and 1970s, when people who should have known better snapped up clothing in loud, psychedelic colors” (Rachel Dodes and Christina Passariello, “Gasp! Polyester Is the New Name in Paris Fashion,” Wall Street Journal, March 1, 2008: A1.) 23. Jacques Barzun, A Stroll with William James (Chicago: University of Chicago Press, 1984), 223. 24. See also Susan Haack, “Preposterism and Its Consequences,” in Manifesto of a Passionate Moderate: Unfashionable Essays (Chicago: University of Chicago Press, 1998), 188–208. 25. On the many, shifting meanings of “realism,” see Susan Haack, “Realisms and Their Rivals: Recovering Our Innocence,” Facta Philosophica 4, no. 1 (2002): 67–88. 26. On the many, shifting meanings of “naturalism,” see Haack, Evidence and Inquiry (see fn. 9), chap. 6. 27. On the many, shifting meanings of “social epistemology” and “virtue epistemology,” see the foreword to the 2nd ed. of Haack, Evidence and Inquiry (see fn. 9).

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determinate meaning are dressed up in mathematical or logical formalism to convey the illusion of rigor—a kind of vagueness notoriously common in the social sciences, but no less ubiquitous, it seems to me, in neo-analytic philosophy. Vagueness is usually contrasted with precision; and precision, like vagueness, is subtler than is sometimes supposed. We think first, perhaps, of the measurable, quantifiable, syntactically expressible regimentation rightly valued by mathematicians, scientists, and logicians, where gradational terms are replaced by precisely defined substitutes. But we should not forget another kind of exactness rightly valued not only by poets, playwrights, and novelists, not only by wits and devotees of the mot juste, but by everyone who respects effective prose. As Orwell reminds us in “Politics and the English Language,” “[w]hat above all is needed” for good writing “is to let the meaning choose the words, and not the other way around”:28 This is the kind of “poetic” exactness achieved by choosing the less familiar and more discriminating word or phrase over the lazily comfortable and commonplace, or by coming up with a fresh metaphor or simile rather than relying on the stale and clichéd. It is sometimes thought that vagueness is an obstacle to truth; on the contrary, however, it is actually easier to say something true if you are not too precise: compare “he’s quite tall” with “he’s six foot two-and-fifteen-sixteenths in his thickest socks,” or “New York has a large population” with “the State of New York has a population of n adults and m children under 18.” To describe a statement as “accurate,” I take it, is to say that it is precise as well as true. (This may explain why we may describe a statement as “precisely” or “exactly,” but not as “accurately,” wrong.) But though many truths are vague, truth, or true-ness, is not a matter of degree. One way of arguing for this would be to rely, again, on Ramsey’s formula. Another would be to point to certain kinds of linguistic evidence (though this has the disadvantage of a certain parochialism; ideally, one would need to explore the corresponding phenomena in several, preferably not-too-closely-related, languages). Still, in English at least, the evidence is pretty persuasive. The kinds of adverbial modifier we routinely use with predicates like “tall,” “intelligent,” or “rich,” which express properties that come in degrees—modifiers like “fairly,” “rather,” “extremely,” “unusually,” “abnormally”—cannot be used to modify “true.” We do, indeed, sometimes say that a statement is “quite true”; but in this use “quite” must be understood in the sense in which it is equivalent to “absolutely” or “perfectly,” not in the (British) sense in which it is equivalent to “fairly” or “rather.” And we sometimes say that a statement is “very true”; but this means, not that the statement is true to a high degree, but that it is not only true but also very much to the point. We also sometimes describe statements as “approximately” or “roughly” true or, more idiomatically, “roughly right.” But these locutions are evidence, not that truth is a matter of degree, but that true statements may be more or less vague. 28. George Orwell, “Politics and the English Language,” in In Front of Your Nose: The Collected Essays, Journalism, and Letters of George Orwell, vol. IV, ed. Sonia Orwell and Ian Angus (New York: Harcourt, Brace and World, 1968), 127–40, 129. See also Barzun, A Word or Two Before You Go (see fn. 22).

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“ ‘p’ is approximately true” is a useful locution; but it is dispensable in favor of the more transparent, “ ‘approximately p’ is true.”29 Again, some propositions, statements, etc., are, as we say, “not entirely true,” but only “partially” or “half” true. (I don’t believe I have ever read or heard “a third true” or “a quarter true”; but I did find John Fekete writing, in a section of his Moral Panic entitled “Half-Truths Only, Please” of “fractional truth.”)30 To describe a statement as partially true may mean either of two significantly different things: (i) that it is true in part but also false in part; or (ii) that it is true but incomplete. A statement that is partially true in sense (i) (i.e., true only in part) will also be partially true in sense (ii) (i.e., not the whole truth); but the converse implication does not hold. A statement partially true in the first sense falls short because it is not nothing but the truth; a statement partially true in the second sense falls short because it is not the whole truth. The first meaning of “partially true,” “part of ‘p’ is true,” is relatively straightforward. In the simplest case, some conjunct (or conjuncts) of a conjunctive statement is (or are) true, and another (or others) false; for example, “she was poor but she was honest” is true-in-part if she was poor but not honest, or if she was honest but not poor. In slightly less simple cases, the conjunctive character of a statement is not quite overt, but implicit in a conjunction of predicates; for example, “he is a scholar and a gentleman” is true-in-part if he is a scholar but not a gentleman, or if he is a gentleman but not a scholar. In other cases, the implicitly conjunctive character of a statement resides in an adverbial phrase; for example, we might describe “I last saw him on Christmas Day, 1974,” as true-in-part if I last saw him in 1974, but it was not Christmas Day but Christmas Eve, or I last saw him on Christmas Day, but it was 1975, not 1974. And so on. (As I suggested in Deviant Logic, partial truth in this sense could be represented by a many-valued logic satisfying Emil Post’s somewhat nonstandard matrices.)31 The second possible meaning of “ ‘p’ is partly true,” “ ‘p’ is part of the truth,” is both significantly less straightforward and significantly more interesting. After all, no statement, however comprehensive, could represent the whole truth about absolutely everything; in this sense of “partial truth,” every truth must be partial. So what, you might wonder, is going on when we ask a witness to swear that the evidence he will give will be “the truth, the whole truth and nothing but the truth”? It’s complicated; but what we ask, I take it, is not that the witness should tell the whole truth about everything, which is impossible, but that he should tell the truth as he believes it to be, without relevant omissions. The point is clearer

29. I surveyed the linguistic evidence in more detail in “Is Truth Flat or Bumpy?” in Prospects for Pragmatism, ed. D. H. Mellor (Cambridge, England: Cambridge University Press, 1980), 1–20; reprinted in Susan Haack, Deviant Logic, Fuzzy Logic: Beyond the Formalism (Chicago: University of Chicago Press, 1996), 243–58. See also Susan Haack, “Do We Need ‘Fuzzy Logic’?” International Journal of Man-Machine Studies 11 (1979): 432–45, also reprinted in Haack, Deviant Logic, Fuzzy Logic, 232–42. 30. John Fekete, Moral Panic: Biopolitics Rising (Montreal: Robert Davies Publishing, 1994; 2nd rev. ed. in 1995), 97. 31. See Haack, Deviant Logic, Fuzzy Logic (see fn. 29), 62–63 in both editions.

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when we complain that a politician didn’t tell the whole truth about the costs of putting this proposal into effect, that a philosophy department doesn’t tell the whole truth about the placement record of those who successfully complete the Ph.D., and so on. The most obvious way of telling less than the whole relevant truth is simply to omit relevant information; for example, to boast that x obtained a tenure-track position at Euphoric State32 and y a visiting position at Podunk College, but omit to mention the several recent Ph.D.s who found no job at all. Another way is to use key terms in a covertly extended sense. A 1993 survey reported that 81 percent of women in college and university dating relationships in Canada suffered sexual abuse; but Fekete argues that this alarming figure is one of those fractional truths, because the term “sexual abuse” was used so broadly that it covered everything from being raped at knife- or gun-point to unwanted flirting.33 Another way again—a disturbingly common form of dishonesty in academic writing in philosophy, and no doubt in other disciplines too—is the incomplete acknowledgment: noting that this small element of what you are saying is derived from someone else’s work, while at the same time quietly “borrowing” other ideas of theirs with no acknowledgment. This sneaky little rhetorical trick (of which I have more than once been the victim) might be described as condemnation by faint—or rather, by feint!—praise. To be sure, just what omissions constitute a failure to tell the whole (relevant) truth can be a tricky question. “About” is vague, and relevance comes in degrees. That the witness saw the defendant shoot the deceased, for example, is highly relevant to his guilt; that the witness saw the defendant in the neighborhood around the time of the crime is relevant only to a much lesser degree, and so on. Moreover, whether and if so to what degree p is relevant to q depends on matters of fact. Whether and to what degree the fact that this drug causes cancer in animals is relevant to whether it also causes cancer in humans, for example, depends on how physiologically similar the animals in question are to humans (in the relevant respects), on whether the doses were comparable given the relative size of the animal and of a human being, etc. But that some propositions are only partly true does not entail that truth, or true-ness, decomposes into component parts. A partial truth in the first sense (a proposition that is not wholly true) is, strictly speaking, just plain false. And— unless it is also partially true in the first sense, only true in part—a partial truth in the second sense (a proposition that is less than the whole relevant truth) is, strictly speaking, just plain true.34

32. David Lodge, Changing Places:A Tale of Two Campuses (1975) (Harmondsworth, Middlesex: Penguin Books, 1978). 33. Fekete, Moral Panic (see fn. 30), 60. 34. Contra F. H. Bradley, who thought that nothing short of the Whole Truth about Absolutely Everything was really-and-truly true. See F. H. Bradley, Appearance and Reality: A Metaphysical Essay (Oxford: Clarendon Press, 1895), 320–21.

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Susan Haack 2. PROBLEMS WITH PARTIAL TRUTH (AND SOME VAGARIES OF VAGUENESS)

These thoughts throw some light on worries about truth in history. Any account of a past event—a battle, say, the fall of an empire, the birth of a nation—will, inevitably, be incomplete. A report of a battle, for example, will surely tell us which side won, what the consequences of this battle were for the war and perhaps for subsequent events, perhaps how many combatants were killed and how many injured, which commanders performed notably well or notably poorly, perhaps what the weather or the terrain contributed to the result, maybe even something about this general’s insistence on taking a bath every morning no matter the circumstances, or that drummer-boy’s heroism, and so on; probably not, however, how many horses were killed or tanks destroyed, and surely not how many ants or flowers were crushed during the battle, etc. It conveys only part of the whole truth about “what really happened.” But this doesn’t mean that no historical account can be (so far as it goes) true; nor, of course, that historians should give up the aspiration to discover truths about the past. That said, however, it needs to be added that the incompleteness of a true-but-incomplete account may mislead, despite its truth. Reporting only battlefield casualties, for example, may mislead by distracting attention from the effects of disease or famine brought on the population at large, and so forth. For incomplete evidence is inherently liable to be misleading, i.e., to support a conclusion that further evidence would show to be false. The writers of detective fiction understand this well: as Spenser, Robert B. Parker’s laconic private eye, tells a witness who wants to know why he wants to know, “If I knew what was important to know and what wasn’t, I’d have this thing pretty much solved.”35 Epistemologists take it for granted: the “Gettier paradoxes” with which they were preoccupied for years exploit the potential of incomplete evidence to mislead. (In describing his hypothetical cases where, he argues, someone has justified true belief but nevertheless does not know, Edmund Gettier takes for granted that a belief can be justified in virtue of evidence that is less than complete and in fact misleading, while being true for quite other reasons.)36 Specialists in military intelligence sometimes recognize it: Donald Rumsfeld’s much-derided but true observation, that in assessing the reliability of intelligence on Iraq the government had to deal not only with the knowns, not only with the unknowns, but also with the “unknown unknowns,” for example, implicitly acknowledged the potential of incomplete evidence to mislead. For true poetic precision, however, I turn to novelist Jeffrey Lent: The truth [is] not a line from here to there, and not ever-widening circles like the rings on a sawn log, but rather trails of oscillating overlapping liquids that

35. Robert B. Parker, Walking Shadow (New York: Penguin Putnam, 1995), 100. 36. Edmund Gettier, “Is Justified True Belief Knowledge?” Analysis 23 (1963) (see fn. 9): 121–23.

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poured forth but then assumed a shape and life of their own, that circled back around in spirals and fluctuations to touch and color all truths that came out after that one.37 Precisely as Lent’s melding metaphor suggests, new evidence can throw new light on things we thought we knew:“oh, he isn’t being so distant because he’s upset with me,” we might say, when we learn that his child is seriously ill, “he’s worried about little Johnnie, poor thing”; or “oh, maybe Vioxx isn’t such a big advance in arthritis treatment as advertised,” when we learn that three cases of adverse cardiovascular effects were omitted from the published report of Merck Pharmaceutical’s first major clinical study, the VIGOR trial.38 And now I see that, after all, it is possible to connect that idiom, “out of true,” mentioned earlier but set aside, to the main thread of the discussion. “Out of true,” as I observed, means “slanted” or “askew”; and the effect of telling only part of the truth, we now see, can be to slant or to skew the audience’s perception of the larger truth that is not told. No doubt, also, it is because partial truth is apt to be misleading that “partial” means not only “incomplete,” as in the second sense of “partial truth,” but also “biased” (as in “no one on the committee was impartial— every one of them was more concerned to cover up the government’s/the company’s/the university’s malfeasance than to get to the bottom of the problem,” or “that wasn’t an impartial jury—the crime was so horrible that every one of them was bound and determined to convict from the outset, however weak the evidence might be”).39 And perhaps Lent’s metaphor helps us see how “colorable” has come to have its two near-incompatible meanings, “seemingly valid or genuine” and “intended to deceive, counterfeit.”40 Someone may offer us partial truth—telling us something true only in part, or telling us less than the whole truth—either unintentionally, or deliberately. You may innocently tell me something true only in part in the false belief that all of it is true; you may innocently fail to tell the whole truth relevant to the question at issue because you do not realize that this or that is relevant. (After all, whether p is relevant to q depends on matters of fact; and if you are ignorant of, or mistaken

37. Jeffrey Lent, After the Fall (New York: Vintage, 2000), 253–54. 38. Claire Bombadier et al., “Comparison of Upper Gastrointestinal Toxicity of Rofecoxib and Naproxen in Patients with Rheumatoid Arthritis,” New England Journal of Medicine, 343.21 (November 25, 2000): 1520–28. The public learned in 2005 that the VIGOR trial, Merck’s first large clinical trial of Vioxx, had tracked gastrointestinal effects (thought likely to be favorable to the drug) for longer than it tracked cardiovascular effects (thought likely to be unfavorable); so that adverse cardiovascular effects occurring during the study, but after it stopped tracking such effects, were not included in the published report. David Armstrong, “How the New England Journal Missed Warning Signs on Vioxx: Medical Weekly Waited Years to Report Flaws in Article that Praised Pain Drug,” Wall Street Journal, May 15, 2006: A1, A10. I tell the story in some detail in “The Integrity of Science: What It Means, Why It Matters,” Ética e Investigacão nas Ciências da Vida—Actos do 10o Seminario do Conselho Nacional de Ética para as Ciências da Vida (2006): 9–28; reprinted in Haack, Putting Philosophy to Work (see fn. 9), 103–27. 39. I should note that “partial to . . . ” means “fond of,” as in “I am partial to dark chocolate.” 40. Webster’s Ninth New Collegiate Dictionary (Springfield, MA: Merriam Webster, 1991).

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about, some of those facts, you may innocently omit part of the truth.) And vagueness, similarly, may be lazy or inadvertent, or may be deliberate. Deliberate vagueness may be benign and even essential: the provisions of a constitution, for example, must in the nature of the case be flexible enough to offer guidance for future circumstances unforeseeable at the time it is written.41 Of course, sometimes deliberately open-textured legal rules turn out to be, arguably, too easily manipulable to be as helpful as hoped: as is perhaps the case with, for example, legal tests to determine whether proffered scientific testimony is reliable,42 or whether this kind of government action constitutes an establishment of religion.43 And sometimes the intent behind deliberate vagueness is not benign; the hope is to evade awkward issues, or to mislead one’s audience. Like deliberate vagueness, deliberately partial truth is sometimes benign, both in intent and in effect. When you ask me what I think of your new dress, and—tactfully omitting to mention its unflattering style—I tell you that it’s a really nice color, I may be telling you only part of the truth in hopes of sparing your feelings. When a physician emphasizes the instances in which this treatment has been successful, and downplays its high failure rate and awful side-effects, he may be telling only part of the truth in hopes of persuading the patient to take the only chance of recovery he has, of keeping him optimistic enough not to give up and turn his face to the wall.

41. See also Susan Haack, “On Legal Pragmatism: Where Does ‘The Path of the Law’ Lead Us?” American Journal of Jurisprudence 50 (2005): 71–105; and “On Logic in the Law: Something, but not All,” Ratio Juris 20, no. 1 (2007): 1–31. 42. For example, the Frye Rule (fn. 18 above) can be made broader by narrowing the scope of the relevant field in which a novel scientific principle must be generally accepted, and narrower the broadening the scope of the field. For example, the novel scientific evidence excluded in Frye concerned the results of a primitive polygraph test the defendant had taken and passed, which the court argued was not yet generally accepted among psychologists and linguists; had the court confined the relevant community to the much smaller class of polygraph examiners, however, the upshot would have been different. In Daubert (fn. 18 above) the U.S. Supreme Court provided a flexible list of factors courts might consider in screening proffered scientific testimony for reliability; these too have proved manipulable. For example, such testimony has been deemed admissible on the grounds that it is based on work which was peer-reviewed, but also admitted despite not having been peer-reviewed; and excluded on the grounds that it is based on work that has not been peer-reviewed, but also excluded despite having been peer-reviewed. See Susan Haack, “Peer Review and Publication: Lessons for Lawyers,” Stetson Law Review 36, no. 7 (2007): 789–819, for details. 43. The test articulated in Lemon v. Kurztman, 403 U.S. 602 (1971) was that a statute is compatible with the Establishment Clause iff: (i) it has a secular legislative purpose; (ii) its primary effect is neither to advance nor to inhibit religion; and (iii) it does not foster excessive entanglement with religion. In subsequent decisions, the “entanglement” clause became a kind of Catch-22, as state actions intended to ensure that a statute did not advance religion were taken themselves to constitute “excessive entanglement.” The current understanding of the second prong of the Lemon test—first proposed by Justice O’Connor in her concurrence in Lynch v. Donnelly, 465 U.S. 668 (1984), and adopted by the majority in its ruling in County of Allegheny v. ACLU, 492 U.S. 573 (1989)—requires that the statute not convey to an objective observer that the government endorses or that it disapproves of religion. This “endorsement test” can be made stronger or weaker, obviously, depending on what exactly that hypothetical “objective observer” is assumed to know.

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Justice Darling, whom I quoted at the beginning of this article, was reflecting on the weaknesses of the testimony of lay witnesses (his opinion of the testimony of expert witnesses, by the way, was even lower). Still, in our adversarial legal system it is expected that each party will highlight the parts of the truth that best serve his side of the case, and that attorneys will craft questions to their witnesses narrowly, so that they can tell the whole truth relevant to this, very specific question without letting anything incriminating slip. The hope is that the part of the truth that one side omits will be brought to light by the other side, by the presentation of contrary witnesses, or under cross-examination, or both; which, I take it, is part of the epistemological rationale for the adversary system.44 (Sometimes, it works as hoped;45 often, I fear, it does not.)46 But I want to focus now, not on the very special case of adversarial legal procedure, but on more straightforward cases where someone deliberately tells less than the whole truth with the intention of misleading his audience to his own benefit and their disadvantage. Or perhaps I should say, I say “deliberately or quasi-deliberately,” because very often what is going on might best be described as, if not quite intentional, willful nonetheless. As Cardinal Newman observed, “[i]t is not in human nature to deceive others, for any long time, without, in a measure, deceiving ourselves.”47 When telling only the palatable or the favorable part of the truth gets to be a habit, you can easily find yourself conveniently forgetting the omitted facts, and starting to believe that this partial truth is the whole relevant truth of the matter. The distinction between someone’s being unintentionally misleading in telling us only part of the truth and his being deliberately misleading is clear enough in principle; but in practice things are not nearly so clear-cut. (The same goes for the distinction I took for granted earlier between someone’s being unintentionally vague and his being deliberately so. While in principle the 44. The celebrated evidence scholar John Wigmore famously described cross-examination as “the greatest legal engine ever invented for the discovery of truth.” See John H. Wigmore, “Cross-Examination as a Distinctive and Vital Feature of Our Law,” in Evidence (Boston: Little, Brown & Co., 1904), sec. 1367. 45. See, e.g., Blum v. Merrell Dow Pharmaceutical, 1 Pa. D. & C. 4th 634 (1998) where, evidently, the Blums’ attorney’s cross-examination revealed that the consensus in the peerreviewed scientific literature that Bendectin was harmless had been artificially created by the company itself. The case (which was eventually, in 2000, decided by the Pennsylvania Supreme Court in favor of Merrell Dow) is discussed in some detail in my “Peer Review and Publication” (see fn. 42). 46. See, e.g., Barefoot v. Estelle, 803 U.S. 880 (1983). Mr. Barefoot had been sentenced to death after two psychiatrists testified (as required by the Texas death-penalty statute) that he would be dangerous in future. The U.S. Supreme Court found that Mr. Barefoot’s constitutional rights had not been violated. Though an amicus brief from the American Psychiatric Association acknowledged that psychiatric predictions of future dangerousness were wrong two times out of three, Justice White, writing for the majority, brushed this aside, noting that Mr. Barefoot’s attorneys had the opportunity to cross-examine the prosecution’s witnesses, and to produce contrary testimony. See also Marvin Frankel, “The Search for Truth: An Umpireal View,” University of Pennsylvania Law Review 123, no. 5 (1975): 1031–59; Susan Haack, “Epistemology Legalized: Or, Truth, Justice, and the American Way,” American Journal of Jurisprudence 49 (2004): 43–61. 47. John Henry Newman, “Profession without Practice,” in Parochial Sermons (New York: D. Appleton and Co., 1843), vol. I, sermon X.

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difference is clear enough, in real life the line is often hard to draw; for conveniently self-induced fogginess is no less ubiquitous, probably, than convenient forgetting of unpalatable aspects of the truth. As I might say, echoing Newman: it is not in human nature to fudge issues to others, for any long time, without, in a measure, fudging them in one’s own mind too.) Even when someone tells only part of the truth innocently believing it to be the whole truth of the matter, we may sometimes feel that he should have been more forthcoming; not of course that he should, per impossible, have told us the relevant facts of which he was unaware, but that it would have been desirable for him to have added that he may not know everything relevant, or even everything about what facts are relevant. And even when someone deliberately, or quasideliberately, tells only part of the truth from motives of kindness or tact, we sometimes might feel that it would have been better had he been more forthcoming: perhaps, for example, that I would have been a better friend had I tactfully suggested that, while the dress was a really nice color, it was a bit too clingy for the job interview at which you were planning to wear it; or that it would have been kinder for the physician not to have raised false hope, but instead to have helped the patient come to terms with the inevitable. Deliberately or quasi-deliberately withholding part of the truth with benign intent is analogous to telling a white lie. Deliberately or quasi-deliberately withholding part of the truth in hopes of misleading your audience to your own benefit is, by my lights anyway, analogous to a plain old (black?) lie. “Analogous to,” but not “the same as”—which, I think, begins to explain why the temptation to mislead by telling others less than the whole truth, and to persuade oneself that this something-less-than-the-whole-truth is the whole truth of the matter, is so strong. The reasons for deceiving others, from simple self-interest to reluctance to be the bearer of bad news, are familiar enough. But telling less than the whole truth is very often an especially attractive way of going about deceiving others; it is psychologically easier, because perceived as morally less offensive than lying. If you tell me only part of the (relevant) truth, you can tell yourself that you have not actually lied to me. You may well mislead me; and if you omit part of the truth with the intention that I be misled, you are guilty of deception—but not of outright lying.And we tend to have much less compunction about misleading others by this apparently more defensible and subtler route than we would about lying outright. The philosophy department that reveals only part of the truth about its placement record, for example, may manage to feel absolved by the thought that it has been very careful to ensure that everything in its graduate prospectus is true.48 In just one week while I was writing this article, two articles in the Wall Street Journal caught my eye: One, noting that pharmaceutical companies are under no obligation to publish all the studies they conduct and submit to the FDA,49 reported that “the effectiveness of a dozen popular anti-depressants has been

48. This is a sanitized version of a true story painfully close to home. 49. Food and Drug Administration (the federal agency that must approve drugs and medical devices before they can be marketed in the U.S.).

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exaggerated by the selective publication of favorable results,”50 and that this has led many doctors to make inappropriate decisions about when and to which patients to prescribe such medications; the other, urging that “[t]oo often, chief executives sugarcoat the truth. That’s more dangerous than ever,” quoted James M. Kilts, former CEO of Nabisco: “[m]any times it’s the thing not said . . . that gets a CEO in trouble.”51 Indeed, deliberate and quasi-deliberate deception by partial truth seems to be absolutely ubiquitous—a good deal commoner, I suspect, than the Lie Direct—in business, in advertising, in politics, and, I am sorry to say, in the academy too. That, however, is another story for another occasion.52

50. David Armstrong and Keith J. Winstein, “Antidepressants under Scrutiny over Efficacy: Sweeping Overview Suggests Suppression of Negative Data Has Distorted View of Drugs,” Wall Street Journal, January 17, 2008: D1, D3. The quotation is from p. D1. 51. Kaja Whitehouse, “Why CEOs Need to Be Honest with Their Boards,” The Wall Street Journal, January 14, 2008: R1, R3. The quotations are from p. R1. 52. My thanks to Mark Migotti, for helpful comments on a draft; to Helen Wohl, of the University of Miami Law Library, for help in tracking down relevant materials; and to María-José Frápolli, for the talk entitled “Nothing but the Truth” that she gave at the 2007 National Colloquium on Philosophy of Language in San Leopoldo, Brazil, which gave me the idea for my title.

Midwest Studies in Philosophy, XXXII (2008)

Believing at Will KIERAN SETIYA

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lthough it is widely held that we cannot form beliefs at will, and that this reflects a metaphysical not just a psychological disability, it has not been easy to explain why this should be. The most well-known argument, due to Bernard Williams, has been decisively criticized.Aside from some remarks about perceptual belief, whose application is obviously local, his reasons appear in the following passage:1 [It] is not a contingent fact that I cannot bring it about, just like that, that I believe something, as it is a contingent fact that I cannot bring it about, just like that, that I’m blushing. Why is this? One reason is connected with the characteristic of beliefs that they aim at truth. [ . . . ] With regard to no belief could I know––or, if all this is to be done in full consciousness, even suspect–– that I had acquired it at will. But if I can acquire beliefs at will, I must know that I am able to do this; and could I know that I was capable of this feat, if with regard to every feat of this kind which I had performed I necessarily had to believe that it had not taken place? (Williams 1970, 148)

Williams’s argument has two premises. First, that if I am able to acquire beliefs at will, I must know that I am able to do so; this is presumably meant to follow from some general requirement on intentional action. Second, that I cannot at once 1. On perceptual belief, see Williams (1970, 148–49); his discussion is criticized in Bennett (1990, 94–95). Midwest Studies in Philosophy: Truth and its Deformities Volume XXXII Editor by Peter A. French and Howard K. Wettstein © 2008 Wiley Periodicals, Inc. ISBN: 978-1-405-19145-6

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believe that p and know that I have come to believe this at will. It is supposed to be a consequence of the second premise that the condition in the first cannot be met. There are standard objections. First, even if we grant the restriction on beliefs known to have been acquired at will, it seems to leave room for knowledge of the relevant ability either on general grounds or through knowledge, of beliefs I used to have, that they were acquired at will (Winters 1979, 254–55). What the principle rules out is the case in which I know that I have formed a particular belief at will while continuing to hold that belief, as when I have just completed the act of forming it. But then it ought to be enough to save the possibility of believing at will that each instance of doing so is accompanied by local amnesia, in which I forget how my belief was formed (Bennett 1990, 93). These objections grant the premises of Williams’s argument, but deny its validity. A further objection is that the second premise is false. One could know that one’s belief was acquired at will but persist in having it, and do so rationally, if one takes it now to be supported by sufficient evidence (Winters 1979, 253). A limiting case of this phenomenon occurs with beliefs that one believes to be self-fulfilling (Velleman 1989, 127–29). In this article, I explore the remains of Williams’s argument, examine one replacement, and propose a limited repair. The replacement argument appears in Pamela Hieronymi’s recent essay, “Controlling Attitudes” (2006). It is distinctive in that it is not just a revision or modification of Williams’s approach and because of its aspiration to generality. Its strategy is meant to work for intention, too, and indeed for any “commitment-constituted attitude,” showing that you cannot intend, resent, or forgive at will (Hieronymi 2006, 74, n. 49). In objecting to her argument about belief, we begin to clarify what would count as “believing at will.” That project is further pursued in section II, which distinguishes two grades of voluntary belief: forming a belief intentionally and forming it intentionally “irrespective of its truth” (Williams 1970, 148). Hieronymi’s argument is meant to exclude the former possibility. Williams’s argument is more modest, being directed against the latter. Section III presents an argument, inspired by Williams, for a qualified version of the modest impossibility claim. His principal mistake was to confuse the kind of knowledge involved in acting intentionally with knowledge of the ability to act.When we correct for this, the standard objections lapse. Section IV takes up a question prompted by the modesty of Williams’s conclusion, and mine: Should we make a virtue of possibility and go on to identify the intentional forming of belief, not “irrespective of its truth,” with the exercise of judgment? Against Descartes, on one interpretation, and against some recent work on truth as the aim of belief, I urge that we should not. I After rehearsing one of the standard lines against Williams––the claim that one could systematically forget the origin of one’s intentionally formed beliefs (see Hieronymi 2006, 46–47, following Bennett 1990, 93)––Pamela Hieronymi argues, in “Controlling Attitudes,” that we cannot believe or intend at will. In the case of belief, her explanation rests on four premises:

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Kieran Setiya 1. Belief is answerable to the truth of the proposition believed. 2. Believing at will would have to involve a mediating intention, by whose execution the belief is formed. 3. This intention would not be answerable to the truth of the relevant belief. 4. Intention is answerable to the same considerations as its object.

“Answerability” is a matter of subjection to standards of justification or warrant: belief is answerable to the truth in that, by nature, its justification rests on meeting standards of consistency and evidential support that have to do with truth (Hieronymi 2006, 49–50). By contrast, if one could believe at will, one could execute an intention to believe that p that would be answerable not to the truth, but to standards of practical justification, turning on such things as the benefits and costs, or moral virtues, of having that belief. In the ordinary case, however, “both the intention [to act] and the action are answerable to the same set of reasons” (Hieronymi 2006, 61): the justification for intending to f and the justification for doing it go hand in hand. It follows that the intention to believe that p both is and is not answerable to the truth of the corresponding proposition. It is a paradoxical intention. While there may be room to induce the belief that p within oneself by managerial activity––hypnosis, conditioning, searching for plausible evidence that will seem to support the desired belief––one cannot form the belief that p by executing the intention to believe. A peculiar feature of this argument is that its explicit topic is the intention to believe that p, not the intention to form that belief. This way of framing things ignores a metaphysical contrast that is essential to action theory, between states, like being tall, and things that can be finished or completed and in that sense done. This distinction corresponds to the grammatical notion of perfective aspect. States cannot be, so to speak, perfectively instantiated; they cannot be done.2 To say that someone was tall, or believed that p, is not to say that they completed a performance of being tall, or believing that p, as one might complete a performance of walking and thus have walked. It is merely to describe their prior and perhaps enduring condition. By contrast, to say that someone digested their food, or grew to be tall is to describe a completed happening of digestion or growth. The distinction is exhaustive: what can be instantiated by an object can be instantiated perfectively, like walking, digesting, and growing; or it is a state, like believing, desiring, and being tall. The fact that believing is a state gives Hieronymi’s argument a specious plausibility. For the basic object of intention is never a state, but always something that can be done, the sort of thing of which we can ask why someone did it and evaluate his reasons. Although it makes sense to say, for instance, that I intend to be a philosopher when I grow up, this can be true only if I intend to do something that I think will make me a philosopher––to become one, 2. Here I draw on Michael Thompson’s (forthcoming) “Naïve Action Theory”; cf. Comrie (1976, 48–51). Why not give equal attention to the progressive? States cannot be perfectively or progressively instantiated: One cannot be in the process of believing that p as one can be in the process of walking home. This is true, but it may not be specific to states: think of apparently instantaneous actions like starting and stopping, for which the progressive has no ordinary use, but which can nevertheless be done.

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or to work in a philosophy department, or to do philosophy, or to bring one of these things about. Intending is the kind of state that motivates one to do what can be done and guides it to completion.3 Since believing cannot be done, in the perfective sense, it cannot be the basic object of intention. One cannot simply intend to believe that p. Rather, when A intends to believe that p, he intends to form the belief that p or to bring about his own possession of that belief. In the latter case, he would not count as believing at will, even if he acted on his intention. He would simply manage himself in a way that is calculated to produce the belief, which is evidently possible. Believing at will in the disputed sense requires one to form the belief that p intentionally; the forming of belief must itself be an instance of intentional action. What happens when Hieronymi’s argument is adapted to this point? We have to replace premise (1) with this: 1*. The forming of belief is answerable to the truth of the belief that is being formed. And now it is a striking feature of the argument that, if it works, it shows not only that one cannot form a belief at will, but that one cannot so much as intend to do so. It follows from the modified premises that the intention to form the belief that p would be answerable to the truth of that belief, and that it would not. Nothing could satisfy these conflicting conditions; so there can be no such intention. The strength of this conclusion is disturbing. Even if it is impossible to form a belief intentionally, someone might intend to form a given belief, if only in ignorance. This point is especially clear when we think of future plans, as when I intend to form the belief that p next month and have yet to reflect on how.The problem, if there is one, lies in acting on this intention, not in having the intention to begin with. Hieronymi’s argument proves too much. Something has gone wrong. There are two ways to diagnose the error, short of engaging with the more general framework of answerability and the normative conceptions of intention and belief on which the argument rests.4 First, we might object to premise 3. Even if the intention to form the belief that p is answerable to practical reasons, why can’t those reasons coincide in the particular case with being answerable to the truth of that belief? Why not conclude that beliefs can be formed intentionally, but that the practical reasons for doing so are always truth-related? That issue will be taken up below, in section IV. More radically, we might object to the assumption, tacitly made throughout, that the object of intention––in this case, forming a belief––can only be subject to one sort of justification. Why not say instead that, in forming a belief intentionally, one is subject to both epistemic and practical 3. See Reasons without Rationalism (Setiya 2007, 31–32); the sense of guidance may differ for basic and nonbasic action, but in this context the details can be ignored. 4. According to Hieronymi (2006, 50), intention and belief are “commitment-constituted”: “to believe that p is to be committed to p as true––to take p to be true in a way that leaves one answerable to certain questions and criticisms.” Against the claim of constitution, one would think that I am answerable to those questions precisely because I believe that p, a state of mind that explains, and therefore cannot be identified with, my normative vulnerability. Similar doubts apply to the normative constitution of intending and other attitudes.

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assessment? One’s action is answerable to reasons of both kinds, both practically and epistemically answerable, and there is at least provisional room for a belief to be formed in a way that is epistemically justified but practically irrational, or the reverse. Unless we can explain why it cannot be subject to plural standards of justification, we cannot rule out the intentional forming of belief. What follows instead is that the intention to form that belief is itself to be assessed in both epistemic and practical terms or, more plausibly, that the equation of premise 4––that intention is answerable to the same considerations as its object––holds only for the latter. One’s decision to f is practically justified if and only if one would be practically justified in doing f.5 But one’s decision may be justified in that sense even if it is a decision to do something badly “in its own terms”: to fall short of the standards of excellence that apply to doing f, as the particular kind of action it is. I may deliberately lose to my child at noughts and crosses by playing ineptly, or decide to sabotage the theft by leaving my fingerprints on the safe. In each case, I am practically justified in doing a bad job. So far, there is nothing to stop us from conceiving of intentional belief-formation in just the same way, as a kind of action one can perform badly in its own terms, and deliberately so––that is, without regard for standards of epistemic justification––but for good practical reasons. The upshot is that Hieronymi’s argument fails to demonstrate the impossibility of believing at will, even of forming a belief intentionally “irrespective of its truth.” The failure is instructive in forcing us to distinguish the state of believing from the process of forming a belief. What purports to be intentional in believing at will is belief-formation. Believing is not itself a possible action because it cannot be done, in the perfective sense; but this is irrelevant to the claim of impossibility with which we are concerned. We are left with no clear picture of the content of that claim, or of satisfactory grounds on which it might be held. II Begin with the need for clarification: What is it that we mean to rule out when we deny that it is possible to form a belief at will? Presumably not the possibility of wishful thinking, which in its simplest form consists in the motivation of belief by anxious desire.6 This is perfectly commonplace, if regrettable, a kind of beliefformation that is epistemically irrational, functioning to dispel anxiety or to bring satisfaction, and in which we do not knowingly engage. Believing at will may depend upon our capacity for wishful thought, but it takes the more specific form of intentional action: To believe at will is, at the very least, to form a belief intentionally. A further condition is often imposed on believing at will, that it must involve the forming of belief in basic intentional action, not by taking further means. This is what Jonathan Bennett (1990, 88–90) has in mind when he insists on the 5. Even this is controversial. It might be denied by those who accept the possibility of “intending at will,” so that the reasons for intending to f and the reasons for doing it come apart, as perhaps in Kavka’s (1983) “The Toxin Puzzle.” Hieronymi (2006, 63–64) rejects this possibility, but her argument against it depends on the assumption presently in dispute. 6. See Johnston (1988, 67–74).

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“motivational immediacy” of voluntary belief. As Hieronymi (2006, 48–49) points out, however, the proposed restriction is puzzling. Nonbasic actions like building a house are no less intentional or voluntary than such putative basic actions as clenching one’s fist. Why should we limit our attention to the latter? What prompts the condition is a desire to leave room for the deliberate production of beliefs by what I earlier called “managerial activity”: hypnosis, conditioning, searching for plausible evidence that will seem to support the desired belief. Like wishful thinking, these activities are commonplace; unlike it, they are also intentional. Even so, they do not amount to believing at will. Those who insist that a belief formed at will must be formed without taking further means do so in order to set these possibilities aside; for in basic action, the relation between intention and performance seems “direct” in a way that it is not in the selfmanagement of belief. There is, however, no need to make this restriction in order to explain why managing oneself or one’s situation so as to produce a belief is not a form of believing at will. It is a necessary truth about nonbasic action that if one does A by doing B, doing B is a constitutive not productive means to doing A: It is an instance of doing A or a part of the process of doing A, not just a prior cause that makes it happen.7 That is why, although I can cause myself to blush by dropping my trousers in public, I do not count as blushing intentionally, not even as a nonbasic action, when I do so. Dropping my trousers is not an instance of blushing, nor is it part of that process; it is merely something that prompts it to occur. Likewise, hypnosis may be a means of producing a belief, but is not itself an instance or a part of belief-formation, even when I do it to myself. The same is true of conditioning and of the search for plausible evidence. No matter how efficiently I take such means, my belief is merely a product of intentional action; I do not form the belief intentionally, and so I do not count as believing at will. It follows from the principle above that to form a belief intentionally one must do so as a basic intentional action or by taking constitutive means, such as wishful thinking or inference (which are instances of belief-formation) or becoming more confident (which is part of it). We do not have to restrict our attention to basic action in order to explain why self-manipulation does not count. It is tempting to stop here, with a simple equation: Believing at will is forming a belief intentionally, not just by taking productive means. That is a perfectly legitimate way to use the words and a minimal condition on what falls under them. Thus, if it is impossible to form a belief intentionally, as a completely general matter, it is impossible to believe at will. That is what the most ambitious arguments, like Hieronymi’s, purport to show. Intentional belief-formation is, we might say, the first grade of voluntary belief. There is room for doubt, however, that the target of our puzzlement is so generous. When Williams denies that it is possible to believe at will, his discussion is qualified. Consider the following remarks, dropped from the presentation of his central argument above: 7. Throughout this paragraph, I rely on judgments about when doing A is an instance or a part of doing B, and when it is not. A proper treatment of the contrast between constitutive and productive means would have to say more about the basis of such claims. In doing so, it would pass from the topic of intentional action, in particular, to the nature and unity of events, as such.

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Kieran Setiya If I could acquire a belief at will, I could acquire it whether it was true or not; moreover I would know that I could acquire it whether it was true or not. If in full consciousness I could acquire a “belief” irrespective of its truth, it is unclear that before the event I could seriously think of it as a belief, i.e., as something purporting to represent reality. At the very least, there must be a restriction on what is the case after the event; since I could not then, in full consciousness, regard this as a belief of mine, i.e., something I take to be true, and also know that I acquired it at will. (Williams 1970, 148)

One can interpret the opening conditional as a mistaken inference, from the fact that believing at will is forming a belief intentionally to the conclusion that we can do so without regard for its truth.8 That ignores the possibility of views that allow for intentional belief-formation so long as it is epistemically constrained, as when it is performed on the basis of grounds one takes to be sufficient evidence. (See the discussion in section IV.) Alternatively, and more plausibly, one can read the conditional as a stipulation about what is to count as “believing at will”: not just intentional belief-formation, but forming a belief intentionally “irrespective of its truth.” That is the second grade of voluntary belief. To simplify terms, I will distinguish forming a belief intentionally (the first grade) from believing at will (the second) and define the latter more carefully as follows: To believe at will is to form the belief that p by intentional action, believing throughout that, if one were to form that belief or to become more confident that p intentionally, one’s degree of confidence or belief would not be epistemically justified. Here the idea of forming a belief intentionally “irrespective of its truth” is generalized from outright belief to degrees of confidence and understood to require the belief that one’s attitude to the proposition of that p would not be epistemically justified if it were intentionally formed. The question is local: In the circumstance at hand, would a belief or greater confidence in that particular proposition, formed in that way, be epistemically justified? My answer may be “yes” for one proposition in one circumstance, but “no” for another. We can see the force of the requirement by examining what it fails to count as believing at will. There are three possibilities.9 Someone might believe that he already has sufficient evidence on which to form the belief that p and that his belief would be justified, at least so long as it is formed in the right way. Those who conceive of judgment as forming a belief intentionally under the guise of evidence will think of this as the typical case. Alternatively, one might believe that the belief that p would be justified if one were to form it intentionally, because new evidence

8. For something like this move, see Alston (1988, 261). 9. For the sake of simplicity, I describe these possibilities in terms of belief alone; exactly parallel remarks would apply to the process of becoming more confident that p.

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would then exist. This evidence might be supplied by the belief itself, as when I believe that confidence in my own success would make success more probable, or by the intention to form the belief that p, if I am somehow convinced of a correlation between having that intention and the fact that p. In none of these cases is a belief formed “irrespective of its truth” since the subject expects his belief to be supported by sufficient evidence, and so to be epistemically justified. Finally, the definition does not count as believing at will someone who neither accepts nor denies that his belief that p would be justified if it were intentionally formed. This omission is harder to motivate. Should we say of the agnostic or uncertain agent that in forming a belief intentionally he forms it “irrespective of its truth”? Not in forming it against what he thinks the evidence will support, though he does not form it in accord with such a belief. His action occupies an intermediate grade, stronger than intentional belief-formation, but weaker than believing at will, as it was defined above. In what follows, I set this possibility aside, not because it is insignificant, but because it would complicate an already qualified argument in ways that I am unable to address. III Despite the objections, Williams’s argument hints at an obstacle that stands in the way of any attempt to believe at will. He states the obstacle, mistakenly, as the claim that one cannot know, of any belief, that it was acquired at will. The standard reply is that one can do so perfectly well if one takes that belief now to be supported by sufficient evidence; it does not matter what one thinks about its origins.10 What this reply concedes is that there is an epistemic constraint on belief, of roughly this shape: It is impossible to believe that p or to be confident that p while believing that this degree of confidence or belief is not epistemically justified.11 Unfortunately, I do not know how to explain exactly why this condition holds, or how to prove that it does. One argument for the epistemic constraint is that, without it, we cannot account for the impossibility of believing at will; a fragment of that argument appears in this article. In any case, the basic thought is that part of what it is to believe that p––part of what distinguishes believing from other attitudes that might inform behavior, like assuming something, taking it for granted, or accepting it in a context––is the disposition to defend one’s attitude in epistemic terms, as for instance by appeal to evidence that p. Properly characterized, this disposition is inconsistent with believing that one’s attitude is not epistemically justified, which is therefore inconsistent with the belief that p. Apparent violations of this principle are better understood as cases in which one has a nagging thought or a tendency to act as if p, even though one does not believe it.

10. See Winters (1979, 253) and Velleman (1989, 127–29). 11. See Hampshire (1975, 79, 86–87), and compare Winters (1979, 246–47).

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This comes out when we ask someone,“Why do you think that?” If I deny that I am epistemically justified in believing that p, the proper response is to say “I don’t really believe that p, I just can’t get that possibility out of my head” or “I can’t help lapsing back into my old ways.” Similar points apply to being confident that p, where this confidence falls short of belief, though the details here are even harder to sort out. Whatever its precise explanation, the epistemic constraint on confidence and belief restricts the scope of believing at will. If I know that I have formed the belief that p at will, it follows by the definition in section II that I believe that my belief would be unjustified if it were formed in that way. Only a failure of attention or logical confusion could save me from realizing that my belief that p is therefore not epistemically justified, and so permit me to have that belief in light of the epistemic constraint. Such failures and confusions are no doubt possible, and to that extent so is believing at will––though Williams seems right to insist that, if one manages it in this way, one does not do so “in full consciousness.” That phrase is a useful shorthand for the kind of attention and logical clarity that ensure the trivial inference from “My belief that p was formed intentionally” and “My belief that p would not be justified if it were formed intentionally” to the conclusion that my belief is not epistemically justified. The remaining question is whether one could form a belief at will without failure of attention or logical confusion, because one does so without knowing that one’s belief has been intentionally formed. Think of Jonathan Bennett’s “Credamites”: Credam is a community each of whose members can be immediately induced to acquire beliefs. It doesn’t happen often, because they don’t often think: “I don’t believe that P, but it would be good if I did.” Still, such thoughts come to them occasionally, and on some of those occasions the person succumbs to temptation and wills himself to have the desired belief. [ . . . ] When a Credamite gets a belief in this way, he forgets that this is how he came by it. (Bennett 1990, 93) So long as the forgetting is sufficiently prompt that the origins of the belief are forgotten by the time it is formed, the Credamites will never find themselves in the predicament just described. When they form a belief at will, they will be in no position to infer that this belief is not epistemically justified. This possibility goes deeper than the other objections to Williams’s argument: it identifies a condition that must be met by any instance of believing at will that takes place “in full consciousness.” As the previous paragraph showed, in order to believe at will without failure of attention or logical confusion, one must be unaware that one’s belief has been intentionally formed. What explains the impossibility of forming a belief at will “in full consciousness” is that this demand for ignorance cannot be met; it runs up against the nature of intentional action. This is not because one cannot f intentionally without knowing that one is able to f, as Williams claimed. What we need instead is a more direct connection between knowledge and intentional action, something closer to

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Anscombe’s (1963) idea of “practical knowledge.”12 In the ordinary case, what I do intentionally, I do knowingly; I can identify what I am doing as one of my intentional actions. Thus, if I have no idea that I am shaking my head as I listen to a visiting speaker, or I fail to recognize this as an expression of my will rather than a reflex or involuntary movement, I am not doing so intentionally. The implication here is qualified, not only because the beliefs involved will sometimes fail to count as knowledge, as for instance when knowledge of ability is absent, but because there are cases in which an agent acts intentionally in doing f not only without knowledge of what he is doing, but without the belief that he is doing it.As Donald Davidson observed,“[a] man may be making ten carbon copies as he writes, and this may be intentional; yet he may not know that he is; all he knows is that he is trying” (Davidson 1971, 50; see also Davidson 1978, 91–94). The carbon-copier need not even believe that he is making ten copies, since he doubts that the pressure will go through so many times. As I have argued elsewhere, however, the challenge posed by such examples is limited (Setiya 2007, 24–25). Although the carbon-copier does not believe that he is making ten copies, he is doing so by performing other intentional actions of which he is aware. For instance, he believes that he is pressing on the article as hard as he can, and that this is the means by which he hopes to make the copies, even if he is not sure that he will succeed. We can incorporate this amendment as follows: If A is doing f intentionally, he believes that he is doing so, or else he is doing f by performing some other intentional action, in which he does believe.13 Consider, in light of this principle, a specific attempt to form a belief at will, as when a more optimistic Alice undertakes the White Queen’s challenge to believe that she is “just one hundred and one [years], five months and a day.”14 According to our earlier definition of believing at will, Alice must form the belief that the White Queen is a hundred and one by intentional action, believing throughout that if she were to form that belief or to become more confident of it intentionally, her confidence or belief would not be epistemically justified. Now, in the sense that matters to us, forming the belief that p just is becoming sufficiently confident that p.15 Barring logical confusion, one cannot believe that one is forming the belief that p, in this sense, without believing that one is becoming more 12. See also Hampshire (1959, 95, 102). 13. On the explanation of this requirement, see pt. 1 of Reasons without Rationalism (Setiya 2007). In “Practical Knowledge” (Setiya, forthcoming), I discuss the epistemology of knowledge in intentional action, and consider how the principle in the text might be further qualified so as to deal with partial belief. It would introduce too many complications to address these issues here. 14. The example is taken from Carroll (1896, 183–84), where Alice denies that she is able to form the relevant belief: “Can’t you?” the Queen said in a pitying tone. “Try again: draw a long breath and shut your eyes.” Alice laughed. “There’s no use trying,” she said “one can’t believe impossible things.” 15. See Bennett (1990, 90–92). Our topic is credence or degree of belief, not acceptance in a context or for the sake of practical reasoning. For this distinction, see Bratman (1992).

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confident that p; one cannot want to form the belief that p without wanting to become more confident that p; and one cannot form the belief that p intentionally without intentionally becoming more confident that p. It follows that, in forming her belief, and barring logical confusion, Alice is intentionally becoming more confident that the White Queen is a hundred and one. She must be doing so as a basic intentional action or by taking constitutive means, which she thinks of as ways of becoming more confident. Given the principle of practical knowledge, above, she must believe, in doing so, that she is becoming more confident that the White Queen is a hundred and one, by intentional action. It follows in turn, again barring logical confusion, that Alice believes that she has become more confident of this intentionally. For “becoming more confident that p” is, in linguistic terms, an atelic progressive, like “walking” or “singing”; its application logically implies the application of the corresponding perfective.16 If A is walking, he has walked. If he is singing, he sang. And if he is becoming more confident that p, he has become more confident. Barring logical confusion, Alice therefore finds herself in the quandary with which this section began. She believes that she has intentionally become more confident that the White Queen is a hundred and one, and that if it were gained intentionally, her confidence would not be epistemically justified. How can she help but see, then, that her confidence is not justified, and so violate the epistemic constraint on confidence and belief? Only through inattention or logical confusion can Alice become more confident that the White Queen is a hundred and one, and thus succeed in forming that belief at will. The principles behind this argument are completely general: the definition of believing at will, the epistemic constraint on confidence and belief, and the qualified thesis of practical knowledge: To believe at will is to form the belief that p by intentional action, believing throughout that, if one were to form that belief or to become more confident that p intentionally, one’s degree of confidence or belief would not be epistemically justified. It is impossible to believe that p or to be confident that p while believing that this degree of confidence or belief is not epistemically justified. If A is doing f intentionally, he believes that he is doing so, or else he is doing f by performing some other intentional action, in which he does believe. Since forming the belief that p just is becoming sufficiently confident that p, where “becoming more confident” is an atelic progressive, the requirement of practical knowledge in forming a belief intentionally cannot be met, without logical confusion, unless one believes that one has intentionally become more confident that p. The epistemic constraint implies that one cannot do this, without failure of atten16. A classic discussion is Comrie (1976, 44–45); for a more recent philosophical treatment, see Szabó (2004, 44–50, esp. at 47). The contrast is with telic progressives like “walking home” and “singing the Marseillaise,” which can apply at a time even though the corresponding perfective does not and never will obtain.

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tion or logical confusion, if one satisfies the definition of believing at will; for one is in a position to infer, quite trivially, that one’s degree of confidence that p is epistemically unjustified. It follows that one cannot believe at will “in full consciousness”: One must at some point fail to attend to one’s beliefs or fail to accept their logical consequences. The argument of the last two paragraphs assumes that, if someone forms the belief that p intentionally, they are at some point intentionally forming that belief. It turns on the application of the progressive. One might object that this ignores the possibility of instantaneous belief-formation, an intentional change of state that has no duration at all, so that it is never true to say that its subject is forming the relevant belief.17 But the argument still applies. The only way to make sense of practical knowledge for such nondurative action is to assume that, upon doing it, the agent knows what he has done. Or, more carefully: he believes that he has f-ed, or else he did so by performing some other intentional action, in whose performance he does believe. It remains true that, in forming the belief that p intentionally, without logical confusion, one must believe that one has intentionally become more confident that p. And in a case of believing at will, this will be in tension with the epistemic constraint on confidence and belief.18 Although Williams was wrong to state this constraint as he did, and to focus on knowledge of ability rather than practical knowledge, his conclusion was basically right. The impossibility of believing at will “in full consciousness” rests on the fact that doing something intentionally is doing it knowingly, at least in the qualified sense that one must believe that one is doing it as an intentional action or that one is taking further means. This is what prevents the Credamites from forgetting what they have done, given the kind of action belief-formation would have to be: either nondurative or a process of becoming more confident. Believing at will without failure of attention or logical confusion would require a lapse of self-knowledge, an ignorance of what one is doing intentionally that conflicts with its being intentional. That is the sense in which, and the extent to which, it is impossible to believe at will. IV This modest result says nothing about the possibility of forming a belief intentionally when one does not believe that, if one were to form it in that way, one’s belief would be epistemically unjustified. It thus says nothing against the conception of judgment as intentional action. On this conception, to judge that p is, inter alia, to form the belief that p intentionally for reasons that one takes as evidence that p. 17. See Comrie (1976, 41–44) on the idea of a “punctual situation.” 18. It would simplify the argument of this section if we could assume, in general, that upon doing f intentionally, one believes that one has done it, or else one did it by doing other things in whose performance one does believe. The present remarks would then apply to any case of intentional belief-formation. But is that assumption true? Might there be a case of basic intentional action in which one is unable to keep track of one’s progress and thus unable to know when one is done––like closing one’s hand behind one’s back while under anesthetic?

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Understood in this way, judgment is distinct from mere “change in view,” which can happen without intentional involvement, from ordinary intentional actions of investigation and inquiry––looking and listening, asking someone else, performing an experiment, examining arguments––and from the state or condition of believing that p on the ground that q. It is supposed to be a matter of doing something, forming a belief, as an intentional action. One attraction of this picture, however the details are worked out, is that it offers to supply a sense in which we can be active rather than passive in our beliefs. It also promises a partial account of self-knowledge: We know what we are coming to believe in making a judgment in just the way that we know what we are doing in doing it intentionally. The epistemology of “practical knowledge” may have puzzles of its own, being “knowledge without observation” (Anscombe 1963, 13–15) and perhaps without inference (Hampshire 1959: 70).19 But if judgment is intentional belief-formation, solving these puzzles will account for more than knowledge of one’s overt behavior; it will begin to explain what is distinctive about self-knowledge of belief. Despite all this, I doubt that judgment is well conceived as intentional action––though not because there is some further incoherence left unfathomed by the argument of section III. Instead, the problems turn on asking how the act of judgment is intentionally performed. Is the assessment of evidence on which a judgment is based explicit or not? There are difficulties either way. Suppose, first, that the act of judgment is based on an explicitly positive assessment of the evidence that p. Presumably, this belief about the weight of evidence need not itself be the product of judgment, or we would face a vicious regress. This concession is awkward: Sophisticated epistemic thoughts arise from consideration of evidence without our intentional involvement, which then issues in the plain belief that p. Surely judgment is no less involved in the former than the latter. But even if we set the awkwardness aside, there is the fact that a sufficiently strong assessment of the evidence that p entails belief and therefore leaves no room for a further act of judgment. If I think that the evidence proves that p, I therein believe that p; there is nothing more for me to do.20 What is needed here is a belief about the evidence that does not entail belief in what the evidence supports, as perhaps the belief that it is conclusive without amounting to proof, or that it is merely sufficient. In the first case, I take the evidence to require the belief that p; in the second, I take it to permit that belief. Again, there are difficulties either way. It is only in pathological cases, ones of epistemic akrasia, that surveying some evidence that we take to require the belief that p leaves us unconvinced––without the relevant belief.21 There is, ordinarily, no temporal gap between recognizing the conclusive force of evidence and believing the conclusion. No act of judgment 19. For further discussion, see “Practical Knowledge” (Setiya, forthcoming). 20. Something similar may hold for thoughts about epistemic likelihood in relation to confidence or degree of belief. For a conception of epistemic modals congenial to this, see Yalcin (2007, forthcoming). 21. If epistemic akrasia is strictly impossible, the argument of this paragraph could be simplified accordingly. See, for instance, Hurley (1989, 130–35). Note, however, that Hurley’s argument is directed against the possibility of believing against what one regards as the balance of evidence for a reason, not against the possibility of doing so simpliciter.

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remains to be performed. What is more, when we do find ourselves in this predicament, afflicted by epistemic akrasia, we do not have the power to form the recalcitrant belief simply by intentional action. As a matter of psychological fact, our failures of reason are not so tractable; they cannot be resolved at will. What about the other possibility, in which we are so far unconvinced by evidence we take to permit but not require the belief that p? Here it would be an epistemic error to form the belief that p intentionally, even if one could. To do so is to let one’s intention to form the belief that p tip the epistemic balance, even when it is quite irrelevant to the truth of that belief.22 Conceived as intentional action, the exercise of judgment in cases of mere permission would be epistemically irrational. What follows from these remarks? Only that we need a different account of the way in which judgment is epistemically constrained, one in which it is performed directly on the basis of considerations that constitute the relevant putative evidence, not through a prior belief about what the evidence weighs. We need an account of what it is to treat such considerations as evidence, tacitly or implicitly, when one intentionally forms a belief. In the most elaborate recent defense of judgment as intentional action, by Nishi Shah and David Velleman (2005), this account is meant to be derived from the doctrine that belief “aims at truth.” The story builds on an earlier article by Shah (2003), “How Truth Governs Belief,” at the heart of which we find the following argument: In forming a belief intentionally, one conceives what one intends to form as a belief. This is to conceive it as a cognitive attitude that is correct if and only if its object is a true proposition. In acknowledging this standard of correctness, one accepts the prescription to believe that p if only if is true that p as governing one’s belief-formation. It follows that, in forming the belief that p intentionally, one activates a disposition to be moved by, and only by, considerations one regards as relevant to the truth of that proposition.23 Like Hieronymi, Shah and Velleman rely on a normative conception of belief. They take it as analytic that the belief that p is correct if and only if it is true that p. This is something one understands in applying the concept of belief. What is more, the judgment of correctness for belief conforms to a strict motivational internalism. In conceiving what one intends to form as a belief, one accepts the prescription to form it if and only if its object is true; one intends to form a true belief. This might be queried. After all, in cases of clear-eyed akrasia, we seem to judge that it would 22. See White (2005, 447–49). One can accept this point while resisting White’s consequent argument against the possibility of mere epistemic permission. As with the previous note, ruling out this possibility would only simplify the argument in the text. 23. This is not a direct quotation but an attempt to paraphrase the line of reasoning in Shah (2003, 467–70). A similar argument appears in Shah and Velleman (2005, 501, 505, 519), but with a further step, through the activity of “affirmation” (Shah and Velleman 2005, 503–5), which is distinct from but productive of belief. This revision is problematic. As Shah and Velleman (2005, 503) admit, it makes the transition from judgment to belief “ineffable,” as though it were merely a contingent fact that in judging that p one forms the belief that p. The view in the text removes the mystery: judgment is intentional belief-formation.

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be correct to f without intending to do it. Is there something special about correct belief?24 But our present concern is more mundane. How to make sense of beliefformation governed by the intention to believe the truth, and (allegedly) therefore governed by one’s tacit assessment of the evidence? There is an obvious objection: Reasoning cannot aim at issuing in an acceptance of p if and only if that acceptance would be correct in virtue of p’s being true, because pursuit of that aim would entail first ascertaining whether p is true; and ascertaining whether p is true would entail arriving at a belief with respect to p, as an intermediate step in deliberating whether to believe it. (Shah and Velleman 2005, 519–20) We cannot be required to form the belief that p as a precursor to judging that p, if judgment is intentional belief-formation. The solution, according to Shah and Velleman (2005, 520), is that judgment “cannot aim at truth directly [ . . . ] one cannot aim in the first instance at accepting p if and only if it is true; one must aim at following some truth-conducive method that will lead to its acceptance.” But this is ambiguous. Are we to picture the indirection of judgment as a matter of taking further means, which are designed to issue in true belief? One tries to find supporting evidence, on the basis of which one will come to believe that p if and only if it is true that p. Such truth-conducive means will usually take a more specific form: looking and listening, asking someone else, performing an experiment, examining arguments. But since these means are productive, not constitutive, of belief-formation, they are not ways in which one can form the belief that p intentionally, even as a nonbasic action.25 What we have described is not the mental act of judgment, but epistemically benevolent selfmanagement. It is good to acknowledge this possibility and its importance in our epistemic lives, but wrong to think that, in doing so, we are describing the capacity to judge.26 It follows that the indirection of judgment must be explained in some other way. Perhaps it lies in the fact that judgment is performed for what we might call “indirect reasons.” One does not judge that p on the ground that p, having already formed that belief. Instead, one adverts to facts that one takes, implicitly, as evidence that p. In a simple case, I judge that p on the grounds that q and that if q, p. The problem is that, if I am to form the belief that p intentionally as a way of forming a true belief about the question whether p, forming that belief must present itself to me as an appropriate means. Unless I conclude, on the grounds that q and that if q, p, that forming the belief that p would be forming a true belief, this will not be so. And since the latter proposition is factive, drawing that conclusion 24. For Shah and Velleman (2005, 510–11), the answer to this question lies in a form of “expressivism” about correctness for belief. 25. See the beginning of section II. 26. A further objection: If judgment is taking productive means to belief-formation, and its deployment of the concept of belief requires that one intend to believe the truth, we leave no room for the deliberate induction of false beliefs by productive means. What about hypnosis and conditioning?

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amounts to having already formed the belief that p. We are back with the original difficulty.27 As things stand, then, we have failed to arrive at a plausible model of judgment as forming a belief intentionally on the basis of putative evidence, whether the assessment of evidence is explicit or not. Perhaps there is some other way to make sense of this: The present discussion cannot claim to be exhaustive. But it suggests a moral drawn by Gilbert Ryle, in The Concept of Mind: We must distinguish clearly between the sense in which we say that someone is engaged in thinking something out [and] the sense in which we say that so and so is what he thinks [ . . . ] In the former sense we are talking about work in which a person is at times and for periods engaged. In the latter sense we are talking about the products of such work. The importance of drawing this distinction is that the prevalent fashion is to describe the work of thinking things out in terms borrowed from descriptions of the results reached. We hear stories of people doing such things as judging, abstracting, subsuming, deducing, inducing, predicating, as if these were recordable operations actually executed by particular people at particular stages of their ponderings. [ . . . The] words “judgement,” “deduction,” “abstraction,” and the rest properly belong to the classification of the products of pondering and are misrendered when they are taken as denoting acts of which pondering consists. (Ryle 1949, chap. IX, sec. 2) On the one hand, there are the ordinary intentional actions––looking and listening, asking someone else, performing an experiment, examining arguments––that constitute inquiry. And on the other hand, there are the products of inquiry, which are states like judgment, knowledge, and belief. We cannot form a belief intentionally “irrespective of its truth.” And even when we care about truth and evidence, there is no act of judgment, in which a belief is formed.28

27. For similar reflections, see Müller (1992, 177–78)––though he persists in thinking of judgment as “intended to be true” (Müller 1992, 176): judgment is “purposeful and intentional but not performed for a reason” (Müller 1992, 179). It is hard to know what to make of this. Why not say instead that judgment is purposive, in that it is somehow aimed at truth, but not intentional or the execution of one’s intention to believe the truth, precisely because it is not performed by taking means to that end? One alternative here is to think of making a judgment as intentionally forming-a-belief-about-the-question-whether-p though not intentionally forming the belief that p or the belief that not-p, as one might intentionally pick a straw without intentionally picking any particular one. It is hard to imagine, however, what constitutive means we could take to this oddly indeterminate act, and the proposal in any case forgoes the primary virtues of conceiving judgment as intentional action. It no longer explains what is active about my attitude to p when I make the corresponding judgment, or how I know what I am coming to believe. Instead, we get a view on which it is possible to make a judgment whether p while having no idea which judgment one has made. 28. For comments on earlier versions of this material, I am grateful to Cian Dorr, Marah Gubar, Peter Railton, Nishi Shah, to audiences at the Universities of Minnesota, Michigan and Ohio State, and especially to Matt Boyle and Evgenia Mylonaki.

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Alston, W. 1988. “The Deontological Conception of Epistemic Justification.” Philosophical Perspective 2: 115–52. Anscombe, G. E. M. 1963. Intention, 2nd ed. Oxford: Basil Blackwell. Bennett, J. 1990. “Why Is Belief Involuntary?” Analysis 50: 87–107. Bratman, M. 1992. “Practical Reasoning and Acceptance in a Context.” Mind 101: 1–15. Carroll, L. 1896. “Through the Looking-Glass and What Alice Found There.” In The Complete Works of Lewis Carroll, ed. A. Woollcott, 121–249. New York: Modern Library, 1936. Comrie, B. 1976. Aspect. Cambridge: Cambridge University Press. Davidson, D. 1971. “Agency.” Reprinted in his Essays on Actions and Events, 43–61. Oxford: Oxford University Press, 1980. ———. 1978. “Intending.” Reprinted in his Essays on Actions and Events, 83–102. Oxford: Oxford University Press, 1980. Hampshire, S. 1959. Thought and Action. Notre Dame, IN: University of Notre Dame Press. ———. 1975. Freedom of the Individual. Princeton, NJ: Princeton University Press. Hieronymi, P. 2006. “Controlling Attitudes.” Pacific Philosophical Quarterly 87: 45–74. Hurley, S. 1989. Natural Reasons. Oxford: Oxford University Press. Johnston, M. 1988. “Self-Deception and the Nature of Mind.” In Perspectives on Self-Deception, eds. B. McLaughlin and A. Rorty, 63–91. Berkeley: University of California Press. Kavka, G. 1983. “The Toxin Puzzle.” Analysis 43: 33–36. Müller, A. 1992. “Mental Teleology.” Proceedings of the Aristotelian Society 92: 161–83. Ryle, G. 1949. The Concept of Mind. London: Hutchinson. Setiya, K. 2007. Reasons without Rationalism. Princeton, NJ: Princeton University Press. ———. Forthcoming. “Practical Knowledge.” Ethics 118. Shah, N. 2003. “How Truth Governs Belief.” Philosophical Review 112: 447–82. ———, and Velleman, J. D. 2005. “Doxastic Deliberation.” Philosophical Review 114: 497–534. Szabó, Z. G. 2004. “On the Progressive and the Perfective.” Noûs 38: 29–59. Thompson, M. Forthcoming. “Naïve Action Theory.” In his Life and Action, Cambridge, MA: Harvard University Press. Velleman, J. D. 1989. Practical Reflection. Princeton, NJ: Princeton University Press. White, R. 2005. “Epistemic Permissiveness.” Philosophical Perspectives 19: 445–59. Williams, B. 1970. “Deciding to Believe.” In Problems of the Self, 136–51. Cambridge, England: Cambridge University Press, 1981. Winters, B. 1979. “Believing at Will.” Journal of Philosophy 76: 243–56. Yalcin, S. 2007. “Epistemic Modals.” Mind 116: 983–1026. ———. Forthcoming. “Nonfactualism about Epistemic Modality.” In Epistemic Modality, eds. A. Egan and B. Weatherson. Oxford: Oxford University Press.

Midwest Studies in Philosophy, XXXII (2008)

Common Sense as Evidence: Against Revisionary Ontology and Skepticism THOMAS KELLY

I How far might philosophy succeed in undermining our ordinary, common sense views about what there is or what we know? Some philosophers suggest: not very far. Thus, according to David Lewis: One comes to philosophy already endowed with a stock of opinions. It is not the business of philosophy either to undermine or justify these preexisting opinions to any great extent, but only to try to discover ways of expanding them into an orderly system. (Lewis 1973, 88) Compare Kit Fine: In this age of post-Moorean modesty, many of us are inclined to doubt that philosophy is in possession of arguments that might genuinely serve to undermine what we ordinarily believe. It may perhaps be conceded that the arguments of the skeptic appear to be utterly compelling; but the Mooreans among us will hold that the very plausibility of our ordinary beliefs is reason enough for supposing that there must be something wrong in the skeptic’s arguments, even if we are unable to say what it is. In so far then, as the pretensions of philosophy to provide a world view rest upon its claims to be in possession of the epistemological high ground, those pretensions had better be given up. (Fine 2001, 2) Midwest Studies in Philosophy: Truth and its Deformities Volume XXXII Editor by Peter A. French and Howard K. Wettstein © 2008 Wiley Periodicals, Inc. ISBN: 978-1-405-19145-6

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Many others are less modest about the possibilities for philosophy. Thus, van Inwagen (1990) and Merricks (2001) champion metaphysical theories from which it follows that the world contains no inanimate macroscopic objects: no tables or chairs, no mountains or islands. Dorr (2002), Horgan and Potrc (2000), and Unger (1979a,b,c) embrace the same conclusions but hold, more radically still, that there are no human beings either. Turning from metaphysics to epistemology, Unger (1975) maintains that we know literally nothing at all. If any such theory is correct, then the answer to the question posed above is: very far indeed. The question at issue is not the psychological one of how far philosophy might succeed in leading us to actually abandon our ordinary views about what there is or what we know. Perhaps given certain facts about my psychology, there are some common sense convictions that I would simply never give up no matter how powerful the arguments against them are. Rather, the question is how far philosophy might succeed in making it rational to abandon our ordinary common sense views. Even if there is no psychological possibility of our abandoning certain views, this does not, I assume, suffice to show that those views could not be rationally undermined by philosophy. Once the psychological question has been set carefully to one side, why so much as suspect that there are any substantial limits here, at least in principle? Consider two reasons for dismissing out of hand the suggestion that philosophy is limited in its ability to overturn common sense. First, what passes for “common sense” is not something which stays fixed. It is a commonplace that things which are utterly taken for granted by people in one historical epoch or cultural milieu—the very kinds of things which “everyone knows”—are widely taken to be false by people in others. (Stock examples include beliefs about the shape of the earth and about the relative intelligence of members of different races.) But if today’s common sense is tomorrow’s outmoded dogma, isn’t the suggestion that philosophy is limited in its ability to overturn common sense one which can be taken seriously only by someone with an insufficiently historical sensibility? However, while we should not underestimate the extent to which what passes for common sense changes, we should not overestimate the extent to which it does either. Consider the kinds of propositions with which G. E. Moore (1925) is concerned in his “A Defence of Common Sense”—for example, the proposition that a significant number of people have lived on the surface of the earth. Or consider the most extreme consequences of the most radically revisionary theories in contemporary metaphysics and epistemology, such as those enumerated above. Whatever their ultimate epistemic status, the convictions targeted by such theories are hardly local dogmas. Even if much of what passes for common sense is relative to time and place, there is, it seems, a Hard Core that is not relative in this way. Consider a second reason for dismissing out of hand the suggestion that philosophy is limited in its ability to overturn common sense: the extent to which natural science has apparently succeeded in doing so. Again, it is a commonplace that certain natural sciences—notably, modern physics—have overturned some of our most fundamental prescientific convictions about the nature of reality. (Here I simply assume that our best scientific theories should be interpreted realistically;

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if some other interpretation is assumed, then so much the worse for the objection.) We do not suppose that folk physics stands fast in the face of the Special Theory of Relativity. But if science can undermine our pretheoretical, common sense views in extremely radical ways, what reason is there to think that systematic theorizing in philosophical ontology and epistemology cannot do the same? In fact, the impressive ability of the natural sciences to undermine fundamental common sense convictions is weak evidence that philosophy occupies a similar position. As a comparative matter, common sense is more vulnerable to being undermined by science than by philosophy.1 The Special Theory of Relativity, revisionary consequences and all, deserves more credence than even the most sophisticated systematic theories in contemporary ontology. Among other salient facts, the Special Theory of Relativity is generally accepted by the relevant scientific authorities, while as a rule no systematic ontological theory commands anything approaching such acceptance among those with the best claim to possessing the relevant kind of philosophical expertise. More generally, it is reasonable for us to think that the epistemic conditions which prevail in the most progressive and advanced sciences are superior to those which prevail in contemporary metaphysics and epistemology.2 Thus, common sense is more vulnerable to being overturned by theories which emerge from those sciences than by systematic theories in metaphysics and epistemology, for the simple reason that the former typically deserve greater credence than the latter. We need not rest much weight on this last consideration, however. For there is, I think, a deeper and more interesting reason why science is better positioned to challenge common sense, a reason which does not depend on what are perhaps relatively contingent facts about the current conditions prevailing in philosophy and the natural sciences. Consider a Williamsonian world: a possible world in which We Do Better.3 In this world, the intellectual standards that are generally observed in the philosophical community greatly exceed those that are generally observed in our own. Claims and counterclaims are invariably articulated with the utmost precision and clarity; the phenomenon of philosophers “talking past one another” is an unfamiliar one. As a rule, arguments are put forward in maximally rigorous form. Authors devote painstaking care to the task of making explicit any relevant background assumptions that their readers might not share.As a result of these and other practices, the philosophical community regularly achieves a kind of consensus which in our world is attained only by mathematics and certain natural sciences. In time, it becomes reasonable to think of philosophy as a genuinely and straightforwardly progressive discipline, one which achieves stable and lasting results that can be safely taken for granted and built upon by later philosophers. 1. Cf. Anil Gupta (2006) and William Lycan (2001). According to Gupta, “Any theory that would wage war against commonsense had better come loaded with some powerful ammunition. Philosophy is incapable of providing such ammunition. Empirical sciences are a better source” (p. 178). According to Lycan, “Science can correct common sense; metaphysics and philosophical ‘intuition’ can only throw spitballs” (p. 41). 2. Much of the case for this is laid out in clear and compelling form by Kornblith (forthcoming). 3. Cf. Williamson (2006), “Must Do Better.” The heuristic device of the Williamsonian world was suggested by Alex Byrne.

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Even in this possible world, there are, I think, principled reasons to suppose that common sense has more to fear from science than from philosophy. Consider first the tools with which the philosopher might challenge common sense. First, she might offer arguments which target various common sense beliefs. More constructively, she might offer a systematic theory, together with reasons for accepting that theory, which entail that the relevant propositions are false. However, how it is rational for us to respond to a given argument or theory is not something which is entirely independent of what we believe. As Moore and many since have emphasized, the more credible the proposition targeted by a given argument, the less credible it is that the argument is sound. Even in what would seem to be the best case for the revisionary-minded philosopher—a case in which she presents us with a transparently valid argument which proceeds from premises that we accept— there is no guarantee of success, for it might be that the rational response to the argument (or at least, a rational response to the argument) is to relinquish belief in the conjunction of the argument’s premises, now that we see where they lead. Analogous points apply in the case of a novel theory.Even if each of the propositions which make up the theory is highly plausible on its face, the overall credibility of the theory depends on the credibility of its consequences. By the time we reach the point of considering theories which entail that there are no people—or even, more modestly, that there are no planes, trains, or automobiles—it is at least somewhat difficult to see how appreciating such consequences does not drag the overall credibility of the theory below the relevant threshold. It is, at the very least, not completely clear how a change in our view of the world as radical as the kind envisaged might be rational, given that at the end of the day the philosopher can only present us with arguments and theories, and how it is rational for us to respond to those arguments and theories is not something which is wholly independent of our beliefs. In contrast, there is a much more straightforward mechanism by which a scientific theory that seems surely false by our present lights can nevertheless come to be rationally accepted: namely, by making surprising predictions that are independently verified. Here the standard Bayesian framework is illuminating. Even if one’s current credence in some scientific hypothesis is arbitrarily close to zero, its conditional probability on such-and-such an observation might be quite high. (One is simply extremely confident that the relevant observation will not be made.) When, contrary to all expectations, the relevant observation is made—a fact which can be ascertained in the absence of any prior commitment to or even sympathy for the theory—the theory is dramatically confirmed. Such is the great epistemic value of successful predictions that are surprising relative to one’s prior view of the world. In such cases, it is experience which prompts a dramatic and radical change in one’s views. Moreover, and crucially, it is a radical change which can be represented and understood as rational from the perspective of one’s prior beliefs. The general remarks about philosophy and empirical science offered in the previous three paragraphs are relative banalities. In the present context, I take their cumulative upshot to be the following: There is simply no mechanism analogous to successful prediction by which a speculative theory in philosophical ontology or epistemology which is extremely unlikely on one’s current beliefs can be dramatically confirmed. (It is not, after all, as though van Inwagen’s account of

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composition, from which it follows that there are no chairs, would be dramatically confirmed by our waking up tomorrow and finding ourselves with not enough places to sit.) It is a familiar fact that experience bears much less directly on systematic theories in speculative ontology and epistemology than on theories in the empirical sciences (to the extent that experience is taken to be relevant to the former at all). While this ensures that theories in speculative ontology and epistemology are relatively invulnerable to being disconfirmed by observation, it also ensures that they are largely cut off from being confirmed by observation. This last disadvantage is especially significant in cases in which the philosophical theories in question are extremely unlikely to be true relative to our original beliefs. For it ensures that such theories cannot bootstrap their way into rational acceptance via the paradigmatic route taken by many currently accepted scientific theories which were once extremely unlikely relative to our view of the world. For this reason, the extent to which science succeeds in overturning common sense is an unreliable measure of the extent to which philosophy is able to do so. “In general, common sense is more vulnerable to being undermined by science than by philosophy”—does such a claim betray commitment to a view about the distinction between science and philosophy which is untenable in our broadly Quinean, post-positivist era? No such commitment is incurred. Let it be conceded that philosophy is continuous with empirical science, that the boundary between the two is vague when not a matter of convention, and that there are numerous issues with respect to which the question “Is that a philosophical or scientific issue?” is not a good one either to ask or to attempt to answer. All of that is consistent with the plain fact that some philosophical theories are not science. The metaphysical systems of the British idealists which Moore opposed on behalf of common sense are paradigms of things that are philosophy and not science. The same is true of the metaphysical theories of a van Inwagen, a Merricks, or a Horgan, and the kinds of considerations and arguments offered by radical skeptics from Sextus Empiricus to Unger. Among philosophers who would describe themselves as following some particular method, that of “reflective equilibrium” (Goodman 1953; Rawls 1972) would perhaps be at least as popular a choice as any other. According to the method of reflective equilibrium, justification consists in achieving a stable coherence in one’s overall view, a coherence achieved through a process of mutual adjustment among considered judgments at different levels of generality. Gilbert Harman, one of the most persistent4 and epistemologically sophisticated defenders of the method, offers the following characterization: We correct our considered intuitions about particular cases by making them more coherent with our considered general principles and we correct our general principles by making them more coherent with our judgments about particular cases. We make progress by adjusting our views to each other, pursuing the ideal of reaching a set of particular opinions and general views that are in complete accord with each other. The method is conservative in 4. See Harman (1986, 1994, 1999, 2003, 2004). But for some recent coauthored doubts, see Harman and Kulkarni (2007, 13–19).

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Critics, however, have frequently taken the apparently conservative character of the method as a good reason to reject it.5 Of course, the method of reflective equilibrium is, at worst, conservative and not reactionary. The method allows, indeed dictates, changes in one’s current views (at least, provided that one’s views are not already in perfect reflective equilibrium). Moreover, in particular cases, the changes dictated might constitute nonaccidental improvements in the accuracy of one’s overall view. Thus, inaccurate judgments about particular cases can be brought closer to the truth via the normative pull exerted by more accurate judgments about general principles; conversely, inaccurate judgments about principles can be improved via the normative pull of accurate judgments about cases. Of course, if one’s initial views are sufficiently off the mark, then pursuing reflective equilibrium is unlikely to result in an overall view with impressive accuracy. In particular, if both one’s judgments about particular cases and about principles are sufficiently far from the truth, then there is no reason to suppose that successfully achieving reflective equilibrium from such a misguided starting point will be worth much. But what if the truth is in fact radically different from what we ordinarily think? Hence the “conservatism” worry, that privileging one’s prephilosophical beliefs in the way that seems to be recommended by the method of reflective equilibrium would preclude one from arriving at the truth in a case in which those beliefs are sufficiently wide of the mark. I myself do not advocate the method of reflective equilibrium. On the picture of philosophical method that I draw upon below, paradigmatic evidence for or against some philosophical theory consists, not of our considered judgments or intuitions,but rather pieces of knowledge that we possess.As we will see,this account is less susceptible to the charge that it is unduly conservative. Yet even as applied to the method of reflective equilibrium, the charge of conservatism must be put with extreme care if it is not to miss the mark entirely. The charge cannot simply be that, if our prephilosophical beliefs are sufficiently mistaken, then even perfect application of the method of reflective equilibrium will fail to lead us to the truth.That much is correct, but it is dubious that any plausible philosophical methodology lacks the feature in question. Indeed, we should be positively suspicious of any account of philosophical method which is advertised to us as lacking that feature.The discovery of deep truths in metaphysics and epistemology, we can safely assume, is no mean feat even in relatively favorable circumstances.A case in which our prephilosophical beliefs about what there is or what we know are in fact radically in error is a case in which we are maximally ill-positioned to find such truths. It is one in which we sit down to play the exceedingly difficult games of metaphysics and epistemology having been dealt a particularly bad hand. If these are indeed our circumstances, it would be a mistake to assume that an adequate philosophical method ought to provide us with a rational path out of the darkness and into the light. 5. See, among many others, Singer (1974), Stitch (1983), and Copp (1985). A recent attempt to defend the use of reflective equilibrium in moral and political philosophy against the charge that the method is overly conservative is Scanlon (2002), see especially pp. 145–51.

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To make things more concrete, suppose that those revisionary metaphysicians who claim that the world contains no inanimate macroscopic objects are in fact correct. It is tempting to assume that, if the revisionary metaphysicians are correct, then there must be some way for us to discover that they are correct via sufficient philosophical reflection—where such discovery would involve our rationally traversing some path that leads from where we are now to the surprising truth. But to the extent that a change in view inspired by philosophy is a reasonable one, it can be represented as the product of reasoning, reasoning which proceeds from premises. (In contrast, a rational change in view about my present surroundings might not be the product of reasoning but rather direct observation.) In order for such a philosophy-inspired change in view to be reasonable, it is of course not enough that the premises from which the reasoning proceeds are in fact true; what is required is that they are reasonably believed to be true. In a case in which the deep truths of metaphysics and epistemology are radically inconsistent with our prephilosophical beliefs, there is no reason to suppose that even an ideally conducted philosophical inquiry would provide some way of getting from Here to There. Certainly, we do not hold our best scientific methods to the analogous standard. That is, we would reject the suggestion that it is a condition of adequacy on some empirical method that it provides a way of rationally arriving at truths about its target domain even in the worst cases for its application. In a world in which the empirical evidence which we have to go on is consistently misleading or unrepresentative—either because of the malevolent chicanery of an evil demon, or through simple long-run bad luck—the impeccable application of our best scientific methods will not only fail to deliver the truth but lead us further and further astray. We do not think that this is a good objection to those methods. Moreover, if we did fall into thinking of it as a condition of adequacy on a scientific procedure that it leads us to the truth even in various worst case scenarios, this would inevitably lead us to a badly distorted conception of scientific method. Similarly, by insisting that an adequate philosophical method would allow us to rationally arrive at the truth even when applied in various worst case scenarios, we risk distorting our conception of philosophical method. II Consider two philosophers, the first a revisionary metaphysician, the second a radical skeptic. The revisionary metaphysician champions an ontological view from which it follows that the world contains no inanimate macroscopic objects. For his part, the skeptic champions an epistemological view from which it follows that we know nothing about the external world. In response to the revisionary metaphysician, the Moorean might say the following: As you yourself admit, it is a consequence of your theory that there are no wooden tables, twenty dollar bills, or tropical islands. But in fact, there are such things. Therefore, your theory is false.

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And similarly, in response to the skeptic: As you yourself admit, it is a consequence of your theory that we do not know whether it has ever rained in New Jersey, whether cows are sometimes slaughtered for food, or whether people sometimes die of cancer. But in fact, we do know these things. Therefore, your theory is false. Of course, in responding to a particular theory in this way, the Moorean is not thereby committed to claiming that the theory in question is devoid of philosophical interest. Indeed, he might very well be of the opinion that there are important insights to be gained from carefully studying it. But the Moorean will insist that, with respect to what would seem to be the crucial question of whether the theory is true or false, he has already said all that needs saying. To go beyond this by attempting to provide additional reasons for thinking that the theory is false, or reasons which meet some further condition, is at best to engage in a kind of methodological supererogation. At worst, it is simply piling on. What, if anything, is wrong with these Moorean responses? Of the many philosophers who would agree that there is something wrong, let us distinguish two groups. On the one hand, there are the revisionary metaphysicians and the skeptics, philosophers who actually hold the views that the Moorean so unceremoniously dismisses. I take it that such a philosopher has something quite straightforward to say about what is wrong with a Moorean response to her theory: namely, that when the Moorean responds in his characteristic way, he speaks falsely. That is, a philosopher who holds a substantive ontological view according to which there are no wooden tables will think that, when the Moorean cites this as a false consequence of the theory, it is the Moorean who is guilty of asserting what is false. A second group of philosophers who take a dim view of such Moorean responses consists of those whom I will call Moderates. Moderates are so-called because they have something in common with both the Moorean and those who espouse the theories that the Moorean targets. On the one hand, the Moderate resembles the Moorean in that she too believes both that there are wooden tables, and that this something that we know. Moreover, inasmuch as the Moderate, like all parties to the dispute, acknowledges that these putative facts are inconsistent with the philosophical theories in question, the Moderate will presumably agree, again with the Moorean, that the philosophical theories are themselves false. On the other hand, the Moderate will agree with the revisionary metaphysician and the skeptic that there is something deeply inadequate or objectionable about the Moorean dismissal of their theories. So, for example, the Moderate will hold that it is illegitimate for the Moorean to simply treat the fact that some metaphysical theory entails that there are no wooden tables as a good reason for rejecting that theory. Of course, inasmuch as at the end of the day the Moderate will agree that there are wooden tables, the problem with the Moorean response cannot be that in offering that response the Moorean says something that is false. Still, the Moderate will insist that the Moorean is mistaken in holding that we can justifiably conclude that the philosophical theory is false by reasoning in his characteristic way. We might then put the difference between the revisionary metaphy-

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sician and the Moderate as follows: While both maintain that the Moorean response is inadequate, the Moderate holds that the response is procedurally inadequate, while the revisionary metaphysician holds that it is substantively inadequate. Of course, the revisionary metaphysician might very well hold that, in addition to being substantively inadequate, the Moorean response is objectionable on purely procedural grounds as well. But the Moderate will hold that the response is procedurally, although not substantively, inadequate. In terms of sheer numbers, perhaps relatively few philosophers hold metaphysical or epistemological views from which it follows that there are no wooden tables, or that there are none so far as we know. But many would hold that there is something deeply objectionable about dismissing such theories on Moorean grounds. Indeed, perhaps most philosophers—or at least, a significant plurality—are best classified as Moderates. As someone with broadly Moorean sympathies, I am interested in how we should understand the dialectic between the Moorean and those who hold radically revisionary theories in metaphysics and epistemology. But for the most part, my concern in what follows will be with the dialectic between the Moorean and the Moderate. My primary aim will be to put as much pressure as possible on the Moderate by suggesting that there is a certain methodological tension in agreeing with the Moorean in matters of substance while condemning his procedure. III What then is wrong with the Moorean, according to the Moderate? Traditionally, perhaps the most common charge against the Moorean is that he is guilty of begging the question.6 Here I want to begin by taking up a closely related charge, but one which seems to me to be in some respects even more fundamental: namely, that in proceeding in his characteristic way, the Moorean is guilty of dogmatism.7 6. On begging the question, see, e.g., Sinnott-Armstrong (1999). Recently, there has been a strong resurgence of interest in Moore’s response to the epistemological skeptic. In particular, the status of his famed “proof of an external world”—“Here is one hand; Here is another; Therefore, the external world exists”—has been vigorously debated. (For a sampling, see Wright 2002, 2003, 2004; Davies 1998, 2000, 2003, 2004; Pryor 2004, as well as the relevant essays in Nuccetelli and Seay 2008.) Even when this debate is not explicitly conducted in terms of whether Moore’s argument “begs the question” but rather whether it exhibits “transmission-failure,” it is clear that traditional concerns involving the former are often central to what is at issue. My own view is that questions about the status of Moore’s proof and questions about the status of the Moorean response under consideration here are distinct. In particular, one might consistently maintain both that (i) Moore’s “proof of an external world” fails as such, inasmuch as it could not deliver the knowledge that there is an external world to someone who previously lacked that knowledge, and (ii) the kind of Moorean reasoning under consideration here can deliver knowledge that some revisionary metaphysical theory is false. Indeed, I am inclined to think that this combination of views is where the truth lies. 7. In what follows, I will employ the term “dogmatism” and its cognates so that they function as terms of negative epistemic appraisal. Thus, to call someone a dogmatist in my sense is ipso facto to criticize that person. I believe that this is a common usage in contemporary Western culture, but it is not the only one. For example, “dogmatic” does not function as a term of criticism as it used by either the Catholic Church or James Pryor (2000).

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The Moorean treats the fact that a novel philosophical theory is inconsistent with certain of his prephilosophical, common sense opinions as a sufficient condition for rejecting that theory. Isn’t this a practice which can accurately be described as dogmatic? Indeed, one might think that the kind of dogmatism which the Moorean seems to manifest is antithetical to the ideal of philosophical inquiry itself. Socrates inaugurated the Western philosophical tradition when he championed a compelling ideal of open-minded intellectual inquiry. Above all else, what is required is a willingness to “follow the argument where it leads.” One must be open to the possibility that inquiry will lead to conclusions that appear strange or even absurd when judged from the perspective of the opinions which one held at the beginning of the inquiry. The crucial first step to engaging in any such inquiry, Socrates held, was to appreciate the extent of one’s own ignorance; in order to have any chance of discovering the truth, one must recognize (or at least, be open to the possibility) that one does not possess the truth already. Of course, a broadly similar theme was forcefully articulated by Descartes at the outset of modern philosophy. Consider the picture of philosophical inquiry presented in the Meditations. In order to engage in such inquiry properly, the meditator must consciously and actively distance himself from his prephilosophical opinions. After all, many of these opinions have the status of mere prejudices, having been uncritically inherited in one’s youth.8 It is only when such prephilosophical opinions have been, if not literally discarded, at least bracketed, that philosophical inquiry can be responsibly conducted. Once an opinion has been independently substantiated in the course of the inquiry, it can be employed as a basis for further reasoning; prior to such substantiation, however, it would be illegitimate to allow that opinion to influence the conclusions which one reaches.To do otherwise would be to allow the inquiry to be biased or tainted from the outset. From such a vantage point, the Moorean’s readiness to dismiss philosophical theories on the basis of their inconsistency with his common sense opinions seems positively unphilosophical—which, in the present context, I take to be equivalent to the charge that the Moorean is a dogmatist. How might the Moorean answer this charge? I believe that the Moorean response to the skeptic and the revisionary metaphysician is best understood as a

8. “Some years ago I was struck by the large number of falsehoods that I had accepted as true in my childhood, and by the highly doubtful nature of the whole edifice that I had subsequently based on them. I realized that it was necessary, once in the course of my life, to demolish everything completely and start again right from the foundations . . . ” (AT VII 17, the opening words of the First Meditation.) Compare the following passage from the Discourse on Method: But regarding the opinions to which I had hitherto given credence, I thought that I could not do better than undertake to get rid of them, all at one go, in order to replace them afterwards with better ones, or with the same ones once I had squared them with the standards of reason. I firmly believe that in this way I would succeed in conducting my life much better than if I built only upon old foundations and relied only upon principles that I had accepted in my youth without ever examining whether they were true. (AT VI 13–14)

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particularly radical rejection of the broadly Cartesian9 picture of philosophical inquiry sketched above, together with an alternative account of how such inquiry should proceed. To be clear, I do not mean to suggest that anyone who presses the charge of dogmatism against the Moorean is herself committed to some particular conception of how philosophical inquiry should be conducted. However, for heuristic purposes, it will be helpful to begin by examining how the Moorean might attempt to parry the charge when it is made by a proponent of Cartesian philosophical inquiry; we will then consider how that defense might be extended when the same charge is made from other quarters. In contrast to the proponent of Cartesian philosophical inquiry, the Moorean should be understood as someone with an alternative view about the proper starting points for philosophical inquiry, a view closer to those associated with such twentieth-century philosophers as C. S. Peirce and W. V. Quine. In particular, the Moorean will insist that before beginning philosophical inquiry, we already possess a significant amount of relevant knowledge, and that we are entitled to utilize and draw upon this knowledge in the course of our philosophical theorizing. Thus, the Moorean will insist that before engaging in ontology, we already know a great deal about what exists and what does not, and that we are entitled to bring such knowledge to bear in constructing and evaluating ontological theories. Similarly, the Moorean will insist that, before engaging in epistemology, we already know a great deal about what is known and what is not, and that we are entitled to bring such higher-order knowledge to bear in constructing and evaluating epistemological theories. Indeed, the Moorean should go further than this and insist on the following point: When one engages in philosophical inquiry, not only is one entitled to bring to bear any relevant knowledge which one already possesses, but one is obligated to do so, on pain of irrationality. As a general matter, when one knows something that bears on a question that one is concerned to answer, it is not rational to simply decline to take that information into account in arriving at a view. But what holds for questions in general holds also for the special cases of questions in ontology and in epistemology. Thus, for the Moorean, the Cartesian model of philosophical inquiry is not some kind of intellectual ideal which we should strive to approximate as best we can; on the contrary, treating the Cartesian model as a normative ideal is a recipe for irrationality. Of course, ever since Descartes wrote, it has been fashionable for later and lesser philosophers to accuse him of making some large-scale mistake (or at least, of encouraging others to make some large-scale mistake by the example of his own practice, even if he did not commit the mistake himself) that sets modern philosophy off on the wrong foot. Too often, it is left unclear exactly what sin Descartes is supposed to have committed, or encourages us to commit. Since I am a philosopher who satisfies the aforementioned description, I want to be quite clear about what 9. In writing of a “broadly Cartesian picture of philosophical inquiry” (rather than, e.g., “Descartes’s picture of philosophical inquiry”), I mean to distance myself from the suggestion that the methodology in question was Descartes’ own, either in theory or in practice, as opposed to one which is naturally suggested by certain famous passages in prominent Cartesian texts. The stronger attribution is one which I lack the scholarly competence to make.

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I think is wrong with a Cartesian model of philosophical inquiry. My suggestion is this: If one adopts a Cartesian model of philosophical inquiry as a normative ideal, one will be led to violate a fundamental norm of theoretical rationality: namely, the requirement of total evidence. What is the requirement of total evidence? While there are subtle issues about how exactly the relevant principle should be formulated, the basic idea is simple and straightforward: To the extent that what it is reasonable for one to believe depends on the evidence which one possesses, what is relevant is one’s total evidence, as opposed to some proper subset of one’s total evidence.10 Thus, imagine that Holmes is attempting to determine the identity of the person who committed a certain crime. As a result of his investigative efforts to this point, he has uncovered a number of facts that bear on the question. Some of this evidence points to Colonel Mustard, some points to Professor Plum, some to the Reverend Green. According to the requirement of total evidence, in arriving at a view about who committed the crime, it is rationally incumbent upon Holmes to take into account all of this evidence, as opposed to some proper subset of it. Perhaps the evidence possessed by Holmes which suggests that Mustard committed the crime is substantial enough that it has the following property: If Holmes possessed only this evidence, he would be fully justified in concluding that Mustard did it on that basis. Still, it does not follow that Holmes is justified in concluding that Mustard committed the crime as things stand. For it might be unreasonable to so conclude, once all of the evidence that Holmes possesses is taken into account. The requirement of total evidence is not itself controversial. Rather, controversy enters when it is applied in conjunction with a substantive view about what counts as evidence.11 According to Williamson (2000), one’s total evidence consists of all and only those propositions that one knows. That is: KNOWLEDGE: E is a part of S’s evidence if and only if E is a proposition that S knows. This account, like all others that have been proposed, is controversial. Among other things, it is inconsistent with the venerable and still popular idea that at least some of one’s evidence consists of experiences that one undergoes.12 Let us work with the much weaker, although still nontrivial idea that one’s knowing that some proposition is true is a sufficient (even if not necessary) condition for the inclusion of that proposition among one’s total evidence. That is: KNOWLEDGE*: If E is a proposition that S knows, then E is a part of S’s evidence. 10. Notice that the formulation in the text does not entail the controversial view that what it is reasonable to believe is entirely determined by one’s total evidence (“Evidentialism,” in the terminology of proponents Conee and Feldman [2004]). Perhaps other factors are also relevant. A classic discussion of the requirement of total evidence is Hempel (1960). I discuss some of the aforementioned subtleties of formulation in Kelly (forthcoming a). 11. For critical overviews of some of the relevant issues, see Kelly (2006, forthcoming b). 12. For discussion of this issue, see Williamson (2000, 197–99) and Kelly (2006).

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Although not wholly uncontroversial, KNOWLEDGE* would be accepted by many, including many who would balk at accepting the significantly stronger KNOWLEDGE.13 When KNOWLEDGE* is taken in conjunction with the requirement of total evidence, the upshot is the following: If one knows something that is relevant to a question that one is attempting to answer, one should take that information into account in arriving at a view. I believe that this claim is true. Indeed, I believe that it borders on the platitudinous. Although we will consider a challenge below, its initial plausibility is surely enough to justify examining where it leads when applied to the present case. How does following a Cartesian model of philosophical inquiry tend to lead to violations of the requirement of total evidence? Suppose that, at the outset of inquiry, one sets aside or brackets one’s prephilosophical, common sense opinions, perhaps on the grounds that many of these opinions have the status of mere prejudices. I take this to mean, at a minimum, that one’s prephilosophical opinions will not be allowed to influence what conclusions one draws upon philosophical reflection, at least until they receive independent substantiation in the course of that inquiry. However, if some of one’s prephilosophical opinions have the status of knowledge, then they should be taken into account from the get-go. To decline to do so is tantamount to deliberately ignoring relevant evidence. The same holds for somewhat more modest proposals associated with Descartes, for example, that one should set aside all of one’s prephilosophical beliefs except for those which are completely certain and indubitable or those which do not admit of the slightest doubt.14 If some of one’s prephilosophical opinions have the status of knowledge but are not completely certain and indubitable in Descartes’s sense, then following a norm of “take into account only those opinions which are completely certain and indubitable” will lead one to ignore those propositions. On the assumption that known propositions qualify as evidence, consistently following such a norm will lead one to ignore relevant evidence. Compare: Perhaps Holmes’ total evidence makes it reasonable for him to conclude that Plum committed the crime, inasmuch as various things that he knows strongly suggest this conclusion. However, once all 13. Notice that, on the assumption that knowing entails justifiably believing, KNOWLEDGE* would be accepted by a philosopher who holds any of the following theses: If S justifiably believes that E, then E is part of S’s evidence. If S has justification for the belief that E, then E is part of S’s evidence (regardless of whether S actually believes E or not). If S believes that E, then E is part of S’s evidence. Moreover, KNOWLEDGE* is perfectly consistent with the decidedly un-Williamsonian views that one’s evidence includes one’s experiences and/or other items that are not themselves propositions. 14. “Reason now leads me to think that I should hold back my assent from opinions which are not completely certain and indubitable just as carefully as I do from those which are patently false” (AT VII 18); “Anything which admits of the slightest doubt I will set aside just as if I had found it to be wholly false” (AT VII 24).

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of the propositions that are not completely certain and indubitable have been bracketed, there is no guarantee that what remains will still support this conclusion; perhaps the evidential rump suggests that Mustard or Green committed the crime instead. If Holmes concludes that Green committed the murder because that is what is most likely relative to the set of propositions that are completely certain and indubitable, he is guilty of violating the requirement of total evidence. Descartes feared that giving substantial weight to one’s common sense, prephilosophical opinions would lead to a stifling intellectual conservatism. As noted above, many critics of the method of reflective equilibrium reject it for exactly this reason. The Cartesian concern is that opinions which have the status of prejudices would in effect be given veto power over novel theories. Does the present picture pave the way for this? The objection behind the question would perhaps be telling against an account on which any prephilosophical opinion that one holds is included among one’s total evidence. However, the present suggestion is not that any prephilosophical opinion that one holds is part of one’s total evidence; rather, the suggestion is that any prephilosophical opinion that one knows is included. Mere prejudices are not knowledge. While it would indeed be dogmatic to reject a philosophical theory because it is inconsistent with some prejudice that one holds, this has no tendency to show that it is dogmatic to reject a philosophical theory because it is inconsistent with something that one knows. Of course, in particular cases, it might be arbitrarily difficult to determine whether one genuinely knows or is in the grip of some prejudice. For someone sufficiently in the grip of a prejudice, it might feel, from the inside, just as though he knows—a familiar and unfortunate fact. Although undeniable, it is a poor reason to conclude that someone who rejects a theory on the basis of its inconsistency with genuine knowledge is dogmatic in the same way that someone who rejects the theory on the basis of its inconsistency with his prejudices is. Of course, things would be otherwise if it were impossible for us to identify genuine instances of knowledge from the inside, or if we were so inept at doing so that successful identifications were rare occurrences. But there is no reason to suppose that either of these situations is ours. Our eminent fallibility in identifying genuine instances of knowledge from the inside (in particular, we sometimes falsely believe that we know) is not a good reason to suppose that such identifications are either impossible or rare. I know that you know cows are sometimes slaughtered for food, and if I know this about you then I am surely in a position to know the same about myself. At any rate, this is the kind of thing which would be denied only by someone who was already committed to a fairly radical form of skepticism.That is: Only someone who is already committed to a fairly radical form of skepticism, prior to engaging in philosophy, should find the Cartesian starting point an attractive one for conducting metaphysical and epistemological inquiry. Incidentally, here we can note one very special case in which Cartesian inquiry is, at least arguably, an appropriate methodology. Suppose that one came to the theory of knowledge with literally no prior knowledge of what is known and what is not known. (That is, suppose that one lacked any higher order knowledge.) Or suppose—what is perhaps more difficult to imagine—one came to ontology with no knowledge of what exists and what does not exist. In these cases, the

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Cartesian procedure is arguably appropriate, perhaps even uniquely appropriate. Of course, we should not expect someone who literally knows nothing about what is known and what is not to make much progress in theorizing about knowledge. It is only because we already know (that is, know prior to engaging in philosophical reflection) a great deal about what is known and what is not, that we have much hope for making genuine progress in the theory of knowledge. Similarly, whatever hope we have for making genuine progress in ontology would seem to be contingent on our coming to the philosophical table knowing quite a bit about what there is and what there isn’t. In short, the prospects for making genuine progress in metaphysics and epistemology depend on our not occupying the very position in which Cartesian philosophical inquiry might be an appropriate methodology. Here then are two opposite ways of falling into unreasonableness. First, one might overestimate one’s knowledge: One takes oneself to know things that one does not in fact know. When one overestimates one’s own knowledge, one will tend to rule out theories which should not be ruled out: One rules out some theory on the grounds that it is inconsistent with something that one knows, but it is false that one knows anything with which the theory is inconsistent. This phenomenon is an utterly familiar one; it is the characteristic error of the dogmatist. It is this phenomenon, I take it, with which Socrates and Descartes were justifiably concerned, and the concern underwrites some of their most distinctive methodological emphases. Alternatively, one might underestimate one’s knowledge. In terms of sheer relative frequency, the error of underestimating what one knows is undoubtedly committed far less often than the error of overestimating what one knows. Large numbers of books have been written by psychology professors carefully documenting our tendency to systematically overestimate our knowledge in various domains;15 in marked contrast, no such books have been written about the opposite tendency. Indeed, it might very well be that, apart from unusually diffident individuals, the most common contexts in which people significantly underestimate the extent of their knowledge are explicitly philosophical ones.16 It is neither surprising nor unjustifiable that philosophers have been more concerned with our propensity to overestimate our knowledge than with the possibility that we will underestimate it. After all, not only is the former error committed with far greater frequency, but it is also the characteristic error of the dogmatist, and on some accounts the struggle against dogmatism is the very raison d’être of the philosophical enterprise.17 Nevertheless, notwithstanding the scant 15. An engaging overview of much of this literature is Gilovich (1991). 16. Apposite here is the fact, frequently remarked upon by those who teach beginning students of philosophy, that such students often exhibit great enthusiasm for disowning any knowledge at all when presented with even quite crude skeptical considerations. Of course, a certain variety of contextualist about knowledge—one who holds that it is relatively easy to raise the ordinary standards for knowing—will see this phenomenon as a supporting datum. 17. Notice also that the venerable “KK principle”—according to which knowing that p entails knowing that one knows that p—would seem to rule out the very possibility of underestimating one’s knowledge altogether, on conceptual grounds. This principle—enshrined as an axiom of epistemic logic in Hintikka (1962)—is currently out of favor, and rightly so in my judgment. Nevertheless, historically speaking, a significant number of philosophers have found something

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attention that it has received from philosophers, underestimating what one knows is a genuine error. Moreover, it too is an error which, on those occasions when it is committed, tends to issue in unreasonableness. If one underestimates what one knows, one will tend to draw unreasonable conclusions in virtue of ignoring or not giving due weight to relevant facts of which one is aware. One knows something that is relevant to the inquiry in which one is engaged, but one proceeds as though one does not; one is thus at risk of drawing conclusions that one would not draw if one took into account all of the relevant information that one possesses. This is the characteristic error of the philosopher who engages in Cartesian inquiry about knowledge, or about what there is, when she possesses some relevant knowledge about what there is, or what we know, before philosophical inquiry begins. Of course, as noted above, the Moderate who accuses the Moorean of dogmatism need not accept a Cartesian picture of philosophical inquiry. Still, the Moorean will press the point against the Moderate: Once the Cartesian picture has been safely set aside, and any pretense of conducting philosophical inquiry in a way uninfluenced by prephilosophical opinion has been explicitly disavowed, why shouldn’t we treat the fact that there are wooden tables as a good reason to reject those theories with which it is inconsistent? On the face of it, the Moderate would not seem to be in a strong position to resist the suggestion. After all, she too believes that there are wooden tables, and that we know that there are. (Again, contrast the apparently dialectically stronger position of someone who would deny these things on the basis of accepting some revisionary philosophical theory.) Given this, how can the Moderate criticize the Moorean for appealing to what is in fact common ground between them? Indeed, why doesn’t the Moderate’s refusal to follow the Moorean amount to a violation of the requirement of total evidence by the Moderate’s own lights? Some possibilities: First Response: Common sense counts for something, but not for as much as the Moorean thinks. The Moderate might claim that while the Moorean is correct in holding that the fact that a theory entails there are no wooden tables counts against that theory, the Moorean’s mistake is to hold that it counts decisively against that theory. According to this line of thought, while the consequence in question is a non-negligible cost of the theory, that cost is not necessarily prohibitive; rather, it needs to be weighed as one consideration among others which bear on the ultimate acceptability of the theory. (Indeed, the revisionary metaphysician might very well say the same thing.) Especially in view of our acknowledged propensity to overestimate what we know, it would be unwise to treat this consequence as a sufficient reason to dismiss the theory. Notoriously, arbitrarily high subjective confidence is no guarantee of truth; even here, it is at least possible that intuitive about it. Note that the KK principle is quite close to the conclusion that it is impossible to genuinely underestimate one’s knowledge: If one knows that p is true, then one knows that one knows that p is true, and thus (presumably) does not falsely believe that one does not know that p, nor even lack the true belief that one knows that p. This is false but not obviously so. The closest analogous principle that would rule out the possibility of overestimating one’s knowledge would perhaps be this: If one believes that one knows that p, then one knows that p. This principle, of course, has no appeal at all.

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we are wrong. And if we are wrong about the existence of wooden tables, then a theory which is incompatible with their existence might be true. In short, the Moderate might claim that the Moorean’s mistake is to treat what is in fact merely disconfirming evidence as though it were falsifying evidence. While this reply seems sensible enough, the significance of the concession should not be underestimated. Again, the envisaged Moderate allows that inconsistency with the existence of wooden tables is a non-negligible cost of the theory, but denies that this cost is prohibitive. However, it is not as though the Moorean case hangs on some particular proposition or small number of propositions, as opposed to countless others with which the theory is also inconsistent. (In this respect, contrast a theory which entails that there are no inanimate macroscopic objects with another theory which idiosyncratically entails the falsity of some particular common sense belief but otherwise leaves our ordinary view of things more or less unmolested.) If the Moderate concedes that there are wooden tables is evidence against the theory, he should also be prepared to concede that countless other propositions which enjoy similar epistemic standing will also count as evidence against it. In short, once it is allowed that this proposition counts as nonnegligible evidence against the revisionary metaphysical theory, it is hard to avoid the conclusion that the theory is massively disconfirmed when the countless other propositions of common sense which both the Moorean and the Moderate will take to have similar status are taken into account. The Moderate might object to this simple line of thought on the grounds that it betrays a naïve understanding of the marginal value of further evidence. It is a truism of confirmation theory that the probative value of a given body of evidence depends on its diversity. Thus, “All emeralds are green” is better confirmed by a sample of emeralds that have been found in wide variety of circumstances than by a sample of equal size which is made up entirely of emeralds excavated from the same mine. Similarly, how strongly a body of unfavorable evidence disconfirms a given theory often depends on its diversity. The Moderate might attempt to make use of these uncontroversial facts in the present context. Even if the fact that a theory is inconsistent with some common sense proposition is a non-negligible cost of that theory, it does not follow that inconsistency with similar common sense propositions should be counted as additional non-negligible costs. For example, even if it is allowed that it is a significant cost of a theory that it entails that there are no twenty dollar bills, it would surely be a mistake to count it as a further non-negligible cost that the same theory entails that there are no ten dollar bills. (It is not within the power of the United States Treasury to drag down the credibility of the theory by printing more denominations.) Once the theory has been properly penalized for the former consequence, the latter consequence has little if any tendency to further disconfirm it; it is in effect redundant evidence. Thus, the Moderate will insist that, when the Moorean suggests that the revisionary metaphysical theory is massively disconfirmed by common sense if it is disconfirmed by common sense at all, the Moorean is guilty of failing to discount for the diminishing marginal value of further evidence of the same kind. This reply assumes, falsely, that the evidence afforded by “common sense” is of some particular kind or type. But consider just how much of our view of the

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world is contradicted by a theory according to which there are no inanimate macroscopic objects. The contents of the relevant beliefs concern extremely diverse subject matters. Moreover, the routes by which we arrive at these beliefs are themselves extremely diverse: It is not, after all, as though they are all the deliverances of some single faculty, “Common Sense.” By any ordinary standards for evidential diversity, the evidence afforded by common sense (assuming, as the Moderate will allow, that many such propositions are known) manifests a great deal of diversity, in virtue of being heterogeneous with respect to both content and origin. (Something which is in practice likely to be missed when the fact that a theory “has counterintuive consequences” or “conflicts with common sense” is entered as a single cost in the philosophical ledger.) Given that the Moderate is not himself a revisionist about the extent of our knowledge of what there is, it seems that he should view the revisionary philosophical theory as disconfirmed by a body of evidence which is impressive with respect to its diversity as well as its sheer size. Undoubtedly, much more could be said about this issue. But let us return to the conflict between the revisionary theory and the particular common sense proposition that there are wooden tables. Again, the envisaged Moderate does not deny that there are wooden tables, or that we know that there are, or that this proposition disconfirms the theory to some extent; what he does deny is that it falsifies the theory. However, it is problematic for the Moderate to treat the proposition that there are wooden tables as genuine evidence which disconfirms yet fails to falsify the revisionary theory given that the two are logically inconsistent. Compare: When I know that a student performed poorly on a particular assignment, it is unproblematic for me to treat this fact as genuine evidence that disconfirms, but fails to falsify, the claim that he is a good student. On the other hand, it is problematic for me to treat the same known fact as genuine evidence that nevertheless fails to falsify the claim that the student performs well on every assignment, given the inconsistency between the two. But the case with which we are concerned is analogous to the latter, not the former. Of course, an account of uncertain evidence (e.g., Jeffrey 1965) will allow a proposition which is logically inconsistent with a theory to count as evidence which disconfirms but does not falsify that theory. Why can’t the Moderate simply appeal to such an account in this context? The difficulty is that the Moderate thinks that we know that there are wooden tables. Given this, and given the recognized inconsistency between the existence of wooden tables and the revisionary theory, it is obscure why we are not entitled to conclude that the theory is false on that basis. At a minimum, the Moderate would seem committed to denying the attractive and widely held principle of single premise closure: roughly, the principle that if one knows that p, and one recognizes that p entails q, then one is in a position to know that q. Many will find this cost prohibitive.18 18. For defenses of closure, see, e.g., Hawthorne (2005), Feldman (1995), and Vogel (1990). For the case against, see especially Dretske (2005a,b). Notice that here is another juncture at which the revisionary metaphysician seems to occupy a stronger dialectical position than the Moderate. Inasmuch as the revisionary metaphysician thinks that it is false that there are wooden tables, he will a fortiori deny that we know that there are; he therefore faces no pressure to give up closure. Moreover, by adopting a Jeffrey-style picture of uncertain evidence, the Moderate can, if he so

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Second Response: Even those who know can be dogmatists. The Moderate might remind the Moorean that, even if one genuinely knows that p, this does not give one a license to dismiss any considerations which tell against p which might emerge in the future (Harman 1973; Kripke, 1971). Consider the story of the FAIR COIN. You hand me what is in fact a fair coin. For amusement, I flip the coin over and over, keeping careful track of whether it lands “heads” or “tails” on each toss. After n tosses, the ratio of head to tails is well within the range that one would expect, on the assumption that the coin is fair. Given that n is large enough, then (let us assume) I know that the coin is fair. Call this time t1. FAIR COIN (continued). Seeking further amusement, I continue flipping the coin. It lands heads on toss n + 1, and on toss n + 2 . . . and on each of the next m tosses after time t1. It is vastly improbable that a coin that is fair would land heads m consecutive times. Indeed, given the overall ratio of heads to tails among the n + m tosses, it is very improbable that the coin is fair. Thus, after the m tosses, I no longer know that the coin is fair, for it is unreasonable to think that the coin is fair given my evidence. Imagine, however, that back at time t1, I engage in the following piece of reasoning. From the known proposition that the coin is fair, I validly infer that any evidence which suggests that the coin is not fair is misleading evidence. Thus, when I subsequently observe the long run of heads, I dismiss that evidence on the grounds that it must be misleading and confidently retain my belief that the coin is fair. Uncontroversially, my proceeding in this way is dogmatic and unreasonable. The general moral: Even if one genuinely knows, this does not guarantee that one’s later dismissal of that which conflicts with one’s knowledge is not dogmatic. The Moderate might seize on this moral as grist for his mill. For the Moderate wishes to credit the Moorean (as well as herself) with the knowledge that, for example, there are wooden tables while nevertheless denying that it is legitimate for the Moorean to simply dismiss revisionary metaphysical theories on the basis of such knowledge. Thus, the Moderate might claim that the dogmatism exhibited by the Moorean on behalf of common sense is akin to the dogmatism that I exhibit in the story of FAIR COIN. However, the attempted assimilation proceeds too quickly. Consider again my behavior in FAIR COIN. Although it is clear enough that my behavior is unreasonable, it is far from obvious why it is unreasonable. After all, given that I know that the coin is fair at time t1, then, by the very plausible closure principle chooses, unproblematically treat the proposition that there are wooden tables as evidence which disconfirms but fails to falsify his theory. He can thus accommodate the intuition that it is at least some evidence against his theory that it entails the nonexistence of wooden tables, while insisting that acceptance of the theory is nevertheless the rational course once all of the relevant evidence is taken into account.

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mentioned previously,19 I can also know that any evidence which suggests otherwise is misleading evidence. But if I know that any evidence which suggests otherwise is misleading, why am I not rationally entitled to ignore such evidence when I subsequently encounter it? This is Saul Kripke’s “dogmatism paradox,” a genuine philosophical puzzle.20 I take the essential solution to the puzzle to have been provided by Harman (1973). In broad outline, that solution runs as follows. Even though I know that the coin is fair at time t1, once I am exposed to evidence which strongly suggests that the coin is biased toward heads, I no longer know that the coin is fair. And if I no longer know that the coin is fair, then I no longer know that any evidence which suggests otherwise is misleading. So there is no single time at which I both know that the coin is fair and possess the evidence which suggests that it is not. Acquiring the counterevidence undermines my prior knowledge that the coin is fair, and thus, any legitimate basis for inferring that the counterevidence is misleading. If, contrary to fact, I somehow retained my knowledge that the coin is fair even after acquiring the counterevidence, then I would be in a position to reasonably conclude that that counterevidence is misleading. One virtue of Harman’s analysis is that it accounts for cases in which one is rationally entitled to dismiss counterevidence as misleading on the grounds that it is inconsistent with what one knows. Consider, for example, the following TRUE STORY. I live with my family at 76 Alexander Street. On a fairly regular basis, we receive mail for a person named “Frederick Jacobs” at this address; none of us has ever met a person with that name. This mail provides genuine evidence that someone named Frederick Jacobs lives at 76 Alexander Street.(Consider:when a passerby on the street,curious about who lives at this address, opens our mailbox and finds mail addressed to Jacobs, this increases the credibility of the relevant proposition for the passerby.) Nevertheless, on the basis of my knowledge that only members of my family live at 76 Alexander Street and that Jacobs is not a member of my family, I reasonably conclude that this evidence is misleading and dismiss it without further ado.21 Why isn’t my behavior in TRUE STORY dogmatic, given that the seemingly parallel behavior that I exhibit in FAIR COIN is dogmatic? Answer: Because even after I acquire the evidence which suggests that Jacobs lives at 76 Alexander Street, I still know that Jacobs does not live there. And, given that I know that Jacobs does not live at 76 Alexander Street, I am in a position to reasonably conclude that any evidence which suggests that he does is misleading. Thus, the phenomenon associated with Kripke’s dogmatism paradox turns out to be much less useful for the Moderate’s purposes than might have initially 19. Again, the principle in question is that if S knows p, and S recognizes that p entails q, then S is in a position to know q. 20. Kripke, “On Two Paradoxes of Knowledge” (unpublished lecture delivered to the Cambridge Moral Sciences Club).The first published discussion of the paradox is Harman (1973:148–49). 21. Although all of the details of the example are nonfictional, the inspiration for using them in this way is due to Crispin Wright (2004).

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appeared. Again, the Moderate wants to credit the Moorean—and himself—with knowledge of such common sense propositions as there are wooden tables but deny that this provides a legitimate basis for concluding that revisionary metaphysical theories inconsistent with such propositions are false. The kinds of cases discussed in connection with the dogmatism paradox seem to perfectly illustrate the possibility of manifesting dogmatism on behalf of genuine knowledge (as opposed to mere prejudice, unjustified belief, etc.). However, upon closer inspection, the cases in question do not provide examples in which someone who genuinely knows is guilty of dogmatism. Rather, the cases are yet further examples in which someone who fails to know behaves dogmatically on behalf of what she fails to know—a behavior which the Moorean, no less than the Moderate, is free to condemn. So long as the Moderate grants that we know that there are wooden tables, it is obscure why it would be impermissible to reason from that piece of knowledge to the falsity of the revisionary theory. The next response speaks to this issue directly. Third Response: Appealing to common sense is dialectically inappropriate. Even if one genuinely knows that p, there might nevertheless be contexts in which it would be inappropriate to cite p as evidence. To borrow a trivial example from Williamson (2000): In a context in which the truth of p is up for discussion— imagine that participants in a conversation are actively offering and assessing evidence for and against p—it would be inappropriate to cite p itself as evidence, even if one happens to know that p is true.The Moderate might claim that when the Moorean offers there are wooden tables and other common sense propositions as decisive evidence against the revisionary metaphysical theory in a context in which the truth of that theory is under discussion, he makes the same mistake as someone who offers p as conclusive evidence in favor of p in a context in which the truth of p is what is at issue. Such a thought has considerable plausibility. Recall the Moorean’s original response to the revisionary metaphysician: As you yourself admit, it is a consequence of your theory that there are no wooden tables, twenty dollar bills, or tropical islands. But in fact, there are such things. Therefore, your theory is false. Undoubtedly, one of the things that makes this response seem so unsatisfying and improper is that it is explicitly addressed to the revisionary metaphysician. Surely it is inappropriate to cite these consequences as sufficient reason to reject the theory to the revisionary metaphysician himself, for he is well aware of the consequences yet holds the theory still. Here the familiar concern that the Moorean is begging the question enters most directly. Of course, unlike the revisionary metaphysician, the Moderate will agree that the relevant consequences are false: that there are wooden tables is common ground between the Moderate and the Moorean, in a way that it is not common ground between either of them and the revisionary metaphysician. Can the Moorean appeal to the common sense propositions as evidence in conversations with the Moderate, so long as those conversations take place behind the revisionary metaphysician’s back? But the Moderate

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might claim that the literal presence—or even existence—of the revisionary metaphysician is immaterial. Rather, the Moderate might claim that the dialectical impropriety of citing the common sense propositions against a hypothetical proponent of the revisionary theory entails straightaway that those propositions provide an insufficient basis for rejecting the theory itself. In making this last claim, the Moderate assumes the truth of the dialectical conception of evidence (cf. Williamson 2007, chap. 8). According to the dialectical conception of evidence, one possesses genuine evidence against some theory only if one possesses evidence that it would be appropriate to offer as such in the context of dialectical engagement with a proponent of that theory. However, we have good reasons to reject the dialectical conception of evidence. One can have good evidence that some claim is true (or false) even if one has no potentially persuasive evidence, or evidence that it would be dialectically appropriate to cite as such. As Williamson emphasizes, acceptance of the dialectical conception of evidence would immediately hand a cheap and sweeping victory to the crudest and least sophisticated of skeptics. Thus, against a skeptic who simply insisted without argument that nothing is evidence for anything else, anything that one might offer as evidence would fail to qualify as such when judged by the dialectical standard. If meeting the dialectical standard was necessary for something to count as genuine evidence, one would have no genuine evidence at all when in the presence of such a skeptic. But surely this is incorrect. One can have genuine evidence, that is, evidence which tends to justify one’s beliefs, even when one has no evidence that it would be dialectically appropriate to offer.22 Thus, even though it would be dialectically inappropriate to cite the relevant common sense propositions to the revisionary metaphysician, it does not follow that they do not provide the Moorean—or the Moderate—with decisive evidence against the revisionary metaphysician’s theory. Indeed, given that the Moorean and the Moderate know the relevant propositions, they would be positively remiss if they failed to take them into account in making up their own minds about the revisionary metaphysician’s theory. Still, there is at least this much to be said against the Moorean response: It is a dialectically inappropriate response to the revisionary metaphysician. In particular, given that it is clear that the Moorean considerations have no chance of persuading the revisionary metaphysician, the appropriate course when dialectically engaged with such a person is to seek new considerations which might inspire conviction rather than simply reciting the Moorean considerations. (Again, the mistake committed by the envisaged Moderate is to suppose that it follows from this that the Moorean considerations do not themselves provide sufficient grounds for rejecting the revisionary theory.) What should we make of this? Consider two cases. In the first case, a proponent of a theory with various radically revisionary consequences presents the theory in a public lecture; the revisionary consequences are enumerated on a handout distributed in advance of the lecture, in a section entitled “Some Surprising Consequences of My Theory.”The dialectical effect of this is to preempt certain objections, or at least, to limit what can 22. On the dangers of not recognizing the distinction in question, see also Pryor (2004).

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be claimed for them in the way of decisiveness. If, in the question-and-answer session immediately following the talk, a member of the audience said “Here are some decisive reasons for thinking that your theory is false”—and proceeded to assert the negations of propositions drawn from the list, her behavior would be considered not only rude but also in gross violation of the norms which govern the relevant practice. Of course, it would be respectable for the questioner to offer reasons for retaining belief in the common sense propositions in the face of the theory. But in that case, the common sense propositions have already ceased to function as evidence: One is expected to argue to the common sense propositions rather than from them. In the second case, the proponent of the theory is initially unaware of the radically revisionary consequences of his theory (suppose that they are unobvious). Rather, the consequences are first pointed out by a member of the audience in the question-and-answer session. The questioner claims that the considerations which she has brought to general attention suffice to refute the theory on offer; many of those present agree with her assessment, although (unsurprisingly) the speaker does not. Here there is no suggestion that the norms of dialectical combat have been violated. Indeed, the questioner would seem to have engaged in the relevant practice in an exemplary manner. Whatever the exact content of the relevant norms, it is at least somewhat curious that a practice governed by them should be thought to be a good way of arriving at the truth. (Things would be much more straightforward if the real point of the practice was, say, convincing the speaker that he is wrong. In that case, it would obviously be pointless to treat consequences that the speaker either embraces or is prepared to live with as noteworthy objections. By helpfully including the list entitled “Some Surprising Consequences of My Theory,” the theorist considerately prevents us from wasting our time by identifying in advance considerations which will bring us no further toward our goal.) Compare another context in which evidence and arguments are highly valued, yet apparently relevant evidence is routinely set aside in accordance with well-established norms: formal legal proceedings. Legal rules of evidence impose restrictions on the admissibility of relevant evidence. Despite the ostensible importance of their arriving at a true view about the issue before the court, jurors are not supposed to reach a verdict on the basis of all of the relevant evidence which could in principle be made available to them, but rather on the basis of some subset of that evidence: namely, that subset which satisfies the relevant standards of admissibility. Here, however, it is understood that the underlying rationales for such rules are typically nonepistemic. That is, the ultimate rationale for setting aside apparently relevant evidence usually derives from the system’s interest in promoting or protecting values other than truth or knowledge about the case at hand.23 Thus, genuine evidence that the defendant is 23. Usually, but not always. Thus, a judge might set aside a certain piece of evidence which genuinely suggests that the defendant is guilty on the grounds that, given the kind of evidence that it is, jurors are likely to exaggerate its probative force. Here, interestingly, relevant evidence is set aside in order to promote a purely epistemic end: The judge insists that the jurors base their judgments on what is an objectively impoverished body of evidence compared to the one which could be made available to them, on the grounds that they are likely to respond unreasonably to the superior body of evidence.

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guilty which has been seized by illegal means might be declared inadmissible so as not to reward past or encourage future illegal behavior on the part of the police. If the only value in view was that of determining whether the suspect was innocent or guilty, it would be unreasonable to set this evidence aside. It is much more difficult to justify setting aside what seems to be plainly relevant evidence when one’s overriding concern is to figure out what to believe, or, more generally, when one is in a context in which non-truth-related concerns figure less prominently. Indeed, it seems that given the norms which govern dialectical inquiry, we should be extremely skeptical of the idea that the conclusions which emerge from such inquiry are likely to be true when participants differ radically in their substantive views. In general, one of the primary attractions of engaging in inquiry with others is the prospect that, by doing so, one will end up with an improved body of evidence on which to base one’s own opinions. Suppose that you and I are eager to believe the truth about some question. Perhaps each of us knows something relevant that the other does not know. In that case, pooling our evidence provides a way of arriving at a richer body of evidence than either one of us would otherwise have enjoyed. Ideally then, the evidence which we possess after comparing notes would at least approximate the union of the evidence that each of us originally possessed. However, in a case in which you and I come to the dialectical table with radically different views, there will be relatively little common ground from which to proceed. If both of us scrupulously observe the norms suggested by the dialectical conception—for example, “Do not treat as evidence anything which the other would not accept as such”—very little will be treated as evidence indeed. The evidence which passes the relevant test will approximate, not the union of the evidence which is originally available to both of us, but rather the intersection of that evidence. But of course, there is no reason to suppose that the view which is best supported by this evidential rump is likely to be true. In terms of the particular case with which we are concerned: One can, of course, ask what it is reasonable to believe on the propositions that are genuine common ground between the Moorean and the revisionary metaphysician. But neither the Moorean nor the revisionary metaphysician should think that there is any particular reason to think that that view is likely to be true. Nor, for that matter, should the Moderate. And it is for this reason that it is a methodological mistake for the Moderate to set aside or even discount the Moorean considerations when he decides what to believe. Not only should the Moderate not condemn the Moorean’s practice, he should adopt it as his own.24 24. This article is part of an ongoing, if somewhat slow-moving, campaign on behalf of common sense; an initial foray was Kelly (2005). While the general lines of thought advanced here have been under development for some time, the recent work of Timothy Williamson (especially Williamson 2007) has been a significant influence, a fact which will be apparent to anyone familiar with that work. In addition to the several footnotes in the text, I want to explicitly acknowledge the extent of that influence while adding the disclaimer that I have no particular reason to think that he would be sympathetic to some of the more far-reaching purposes to which I put shared views here. For helpful feedback on earlier versions of the article, I am grateful to Paul Benacerraf, John Collins, Elizabeth Harman, Martin Lin, Sarah McGrath, Jill North, Ted Sider, Bas van Fraassen, and participants in a Spring 2008 graduate seminar at Princeton that I cotaught with van Fraassen.

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REFERENCES Conee, Earl, and Feldman, Richard. 2004. Evidentialism: Essays in Epistemology. Oxford: Oxford University Press. Copp, David. 1985. “Considered Judgments and Justification: Conservatism in Moral Theory.” In Morality, Reason, and Truth, ed. David Copp and Michael Zimmerman, 141–69. Totowa, NJ: Rowman and Allenheld. Davies, Martin. 1998. “Externalism, Architecturalism, and Epistemic Warrant.” In Knowing Our Own Minds: Essays in Self-Knowledge, ed. Crispin Wright, Michael Smith, and Cynthia Macdonald, 321–61. Oxford: Oxford University Press. ———. 2000. “Externalism and Armchair Knowledge.” In New Essays on the A Priori, ed. Paul Boghossian and Christopher Peacocke, 384–414. Oxford: Oxford University Press. ———. 2003.“The Problem of Armchair Knowledge.” In New Essays on Semantic Externalism and Self-Knowledge, ed. Susana Nuccetelli, 23–55. Cambridge, MA: MIT Press. ———. 2004. “Epistemic Entitlement, Warrant Transmission, and Easy Knowledge.” Aristotelian Society Supplement 78: 213–45. Descartes, René. Discourse on the Method of Rightly Conducting One’s Reason and Seeking the Truth in the Sciences. Many editions. ———. Meditations on First Philosophy. Many editions. Dorr, Cian. 2002. “The Simplicity of Everything” (Princeton University doctoral dissertation). Dretske, Fred. 2005a. “The Case Against Closure.” In Contemporary Debates in Epistemology, ed. Mathias Steup and Ernest Sosa, 13–26. Malden, MA: Blackwell Publishers. ———. 2005b. “Reply to Hawthorne.” In Contemporary Debates in Epistemology, ed. Mathias Steup and Ernest Sosa, 43–46. Malden, MA: Blackwell Publishers. Feldman, Richard. 1995. “In Defence of Closure.” Philosophical Quarterly 45(181): 487–94. Fine, Kit. 2001. “The Question of Realism.” The Philosophers’ Imprint 1(1): 1–30. Gilovich, Thomas. 1991. How We Know What Isn’t So. New York: Free Press. Goodman, Nelson. 1953. Fact, Fiction, and Forecast. Cambridge, MA: Harvard University Press. Gupta, Anil. 2006. Empiricism and Experience. Oxford: Oxford University Press. Harman, Gilbert. 1973. Thought. Princeton, NJ: Princeton University Press. ———. 1986. Change in View. Cambridge, MA: The MIT Press. ———. 1994. “Epistemology and the Diet Revolution.” In Philosophy in Mind, ed. Michaelis Michael and John O’Leary-Hawthorne, 203–14. Dordrecht, The Netherlands: Kluwer Academic Publishers. ———. 1999. Reasoning, Meaning, and Mind. Oxford: Oxford University Press. ———. 2003. “Skepticism and Foundations.” In The Skeptics: Contemporary Essays, ed. Steven Luper, 1–11. Aldershot, England: Ashgate. ———. 2004. “Three Trends in Moral and Political Philosophy.” Value Inquiry 37 (3): 415–25. ———. and Kulkarni, Sanjeev. 2007. Reliable Reasoning: Induction and Statistical Learning Theory. Cambridge: MIT Press. Hawthorne, John. 2005. “The Case for Closure.” In Contemporary Debates in Epistemology, ed. Mathias Steup and Ernest Sosa, 26–43. Malden, MA: Blackwell Publishers. Hempel, Carl. 1960. “Inductive Inconsistencies.” Synthese 12: 439–69. Reprinted in Hempel, Carl. 1965. Aspects of Scientific Explanation and Other Essays in the Philosophy of Science. New York: Free Press. Hintikka, Jaakko. 1962. Knowledge and Belief. Ithaca, NY: Cornell University Press. Horgan, Terence, and Potrc, M. 2000. “Blobjectivism and Indirect Correspondence.” Facta Philosophica 2: 249–70. Jeffrey, Richard. 1965. The Logic of Decision. New York: McGraw-Hill. Kelly, Thomas. 2005. “Moorean Facts and Belief Revision, or Can the Skeptic Win?” In Philosophical Perspectives, vol.19: Epistemology, ed. John Hawthorne, 179–209. Malden, MA: Blackwell Publishers. ———. 2006. “Evidence.” In The Stanford Encyclopedia of Philosophy, ed. Edward Zalta. Retrieved March 1, 2008 from http://plato.stanford.edu/entries/evidence.

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———. Forthcoming a. “Disagreement, Dogmatism, and Belief Polarization.” The Journal of Philosophy. ———. Forthcoming b. “Evidence: Fundamental Concepts and the Phenomenal Conception.” In Philosophy Compass, ed. Brian Weatherson and Tamar Gendler Szabo. Kornblith, Hilary. Forthcoming. “Belief in the Face of Controversy.” In Disagreement, ed. Richard Feldman and Ted Warfield. Oxford: Oxford University Press. Kripke, Saul. 1971. “On Two Paradoxes of Knowledge” (unpublished lecture delivered to the Cambridge Moral Sciences Club). Lewis, David. 1973. Counterfactuals. Cambridge, MA: Harvard University Press. Lycan, William. 2001. “Moore Against the New Skeptics.” Philosophical Studies 103(1): 35– 53. Merricks, Trenton. 2001. Objects and Persons. Oxford: Oxford University Press. Moore, G. E. 1925. “A Defence of Common Sense.” In Contemporary British Philosophy, 2nd series, ed. J. Muirhead, 192–233. London: George Allen & Unwin. Nuccetelli, Susan, and Seay, Gary, eds. 2008. Themes from G.E. Moore: New Essays in Epistemology and Ethics. Oxford: Oxford University Press. Pryor, James. 2000. “The Skeptic and the Dogmatist.” Nous 34: 517–49. ———. 2004. “What’s Wrong with Moore’s Argument?” Philosophical Issues 14: 349–78. Rawls, John. 1972. A Theory of Justice. Cambridge, MA: Belnkap. Scanlon, Thomas. 2002. “Rawls on Justification.” In The Cambridge Companion to Rawls, ed. Samuel Freeman, 139–67. Cambridge, England: Cambridge University Press. Singer, Peter. 1974. “Sidgwick and Reflective Equilibrium.” Monist 58: 490–517. Sinnott-Armstrong, Walter. 1999. “Begging the Question.” Australasian Journal of Philosophy 77: 174–91. Stitch, Stephen. 1983. The Fragmentation of Reason. Cambridge, MA: MIT Press. Unger, Peter. 1975. Ignorance: A Case for Skepticism. Oxford: Oxford University Press. ———. 1979a. “There Are No Ordinary Things.” Synthese 41: 117–54. Reprinted in Unger, Peter. 2006. Philosophical Papers, vol. 2. Oxford: Oxford University Press. ———. 1979b. “I Do Not Exist.” In Perception and Identity, eds. G. F. MacDonald, 235–51. London: Macmillan. Reprinted In Unger, Peter. 2006. Philosophical Papers, vol. 2. Oxford: Oxford University Press. ———. 1979c.“Why There Are No People.” Midwest Studies in Philosophy IV: 177–222. Reprinted in Unger, Peter. 2006. Philosophical Papers, vol. 2. Oxford: Oxford University Press. van Inwagen, Peter. 1990. Material Beings. Ithaca, NY: Cornell University Press. Vogel, Jonathan. 1990. “Are There Counterexamples to the Closure Principle?” In Doubting: Contemporary Perspectives on Skepticism, ed. Michael Roth and Glenn Ross, 13–27. Norwell, MA: Kluwer. Williamson, Timothy. 2000. Knowledge and Its Limits. Oxford: Oxford University Press. ———. 2006. “Must Do Better.” In Truth and Realism, ed. Patrick Greenough and Michael Lynch, 177–87. Oxford: Oxford University Press. ———. 2007. The Philosophy of Philosophy. Oxford: Blackwell. Wright, Crispin. 2002. “(Anti)skeptics Simple and Subtle: Moore and McDowell.” Philosophy and Phenomenological Research 65: 330–48. ———. 2003. “Some Reflections on the Acquisition of Warrant by Inference.” In New Essays on Semantic Externalism and Self-knowledge, ed. Susan Nuccetelli, 57–77. Cambridge, MA: MIT Press. ———. 2004. “Wittgensteinian Certainties.” In Wittgenstein and Scepticism, ed. Denis McManus, 22–54. Oxford: Routledge.

Midwest Studies in Philosophy, XXXII (2008)

Why We Should Prefer Knowledge STEVEN L. REYNOLDS

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will discuss Plato’s question from the Meno: Why should we prefer knowledge that p over mere true belief that p? My answer will be quite un-Platonic. We do and should prefer knowledge mostly to obtain the approval of others. Plato discusses the question using the example of knowing that a road leads to Larissa as opposed to merely having a true opinion that it does (Meno 97a–98d) and suggests that we should prefer knowledge because it is “tied down” by reasons, and so is not likely to run away.1 It is not clear, however, as a matter of psychological fact, that nonknowledgeable true opinion is generally less lasting than knowledge. For we tend to forget the grounds of our beliefs even where they have grounds, and we are not likely then to hold the mere opinions more tentatively. Still, the claim is apparently that the guide for action that consists in knowledge is more reliably available than the guide that consists in the corresponding true belief that is not knowledge. So knowledge is primarily an instrumental good. It is valuable because it enables us to obtain other goods, such as satisfying our desire to go to or avoid Larissa, and it is better than mere true belief because it is likely to persist longer and so guide more successful actions.

1. As historical claim, this (and further attributions to Plato below) is of course lacking in nuance and not based on any genuine understanding of the historical and philosophical background relevant to Plato’s views on the topic. I include it against the advice of Tom Blackson, because I think it is useful as a schematic position (or caricature) against which to contrast the view of epistemic value that I mainly want to propose here. Midwest Studies in Philosophy: Truth and its Deformities Volume XXXII Editor by Peter A. French and Howard K. Wettstein © 2008 Wiley Periodicals, Inc. ISBN: 978-1-405-19145-6

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It seems to me that there are two important innovations from Plato’s Meno2 answer in the recent literature.3 One is that it is allowed that we may desire truth for its own sake, rather than merely as a guide to successful action. The other is that we may look back for a source of value. It is not merely that we shall benefit more in other ways, now or in the future, from having knowledge than we would from having mere true belief, as Plato suggests. There is something that is good-making in the way that we have come to hold the truth, if we thereby come to know it instead of merely truly believe it. For reasons to be explained below, I think the recent discussion still retains too many of Plato’s preconceptions about how to approach such questions of value, but let us first take a closer look at how the recent answers improve on Plato’s. The first main difference is that recent discussions allow that we may want the truth for its own sake, apart from any other goals having the truth may help us achieve. It is suggested that we seek knowledge because seeking knowledge is the most reliable or effective way to obtain true beliefs, and obtaining true beliefs is our main cognitive goal (BonJour 1985, 1998; David 2001; Horwich 2006; Williams 1978). That suggestion, at least understood in the most natural, reliabilist way of taking it, runs into a problem made vivid by Linda Zagzebski, which motivates much of the recent discussion and particularly its strategy of looking backward for good-making features (Zagzebski 2003a, 13–15). If the choice is between a true belief that p and knowledge that p, it seems we still prefer knowledge to true belief, even if assured (by some means that does not amount to giving us knowledge of it) that it will be a true belief. Perhaps God tells us that in the near future she will give us either a true belief or knowledge of the same content, where the proposition to be believed or known is not presently indicated, and we can now choose which to have. Suppose God also assures us that there will be no extraneous net cost or benefit to either choice. It seems that we would still choose knowing over merely having true belief, if thus assured that other things really were equal. But why should we choose knowledge, on the view that it is valuable mainly as a distinguishable, reliable route to truth, since choosing knowledge in this specific case will not make it any more likely that we will have a true belief? If it will be true in either case, we shall have all of the benefits of a true belief whether or not it also counts as knowledge. In Zagzebski’s analogy, once we have a good cup of coffee, why should we value it more for having come from a reliable coffee maker? What we want in the particular case is, by hypothesis, good coffee, or a true belief, so once we have it there is no reason to care about how we got it. This problem is sometimes 2. I specify the Meno, because in the Republic (358e) Plato lists knowing as one of the things we desire for its own sake as well as for what comes from it. 3. I will only be considering the discussions that accept Plato’s assumption that knowledge is and should be preferred to mere true belief, but of course there are important recent contributions that deny that claim. Jonathan Kvanvig holds that it is really understanding that we (should) value and that we are under the misapprehension that knowledge should be valued only because of its normally close association with understanding (Kvanvig 2003). A different way to support the denial of the presuppositions of Plato’s question is Crispin Sartwell’s spirited defense of the claim that knowledge just is true belief (Sartwell 1991, 1992).

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called “the swamping problem” apparently because the goodness of the result, good coffee, or true belief (the only relevant thing we desire for its own sake), “swamps” any difference in value due to the source. The most common response has been that knowledge is better than mere true belief because it has good-making historical qualities. Having true belief from a source that yields knowledge may be a virtuous cognitive action (Sosa 1997, 2003, 2007; Zagzebski 1996, 2003a,b), or to the believer’s credit (Greco 2003; Riggs 2002). In Sosa’s analogy, a shot released by a skilled archer is rightly valued more highly than one released by a lucky archer, even if both strike the center of the target (Sosa 2007, 77ff.). The true belief that counts as knowledge is valued not merely because it happens to be true, but also because it is true as a result of the exercise of cognitive virtues or epistemic skills. It has been suggested that these answers cannot be quite right because knowledge is often not the result of skills or virtues and also not an achievement or to our credit. Jennifer Lackey alleges a counterexample: One might accept the testimony of the first person one meets in Chicago regarding the way to the Sears Tower, and thereby come to know it (Lackey 2007). This is not an achievement or to the believer’s credit (she holds), yet it still counts as knowledge and as such is to be valued over mere true belief. So the historical explanation of value that cites cognitive virtues or achievement cannot account for this case. But is it really so clear that there are no cognitive skills presumed in the background of this story? If the receiver of the testimony would accept it even if it came from a manifestly deranged or deceitful person, then we might be reluctant to grant that she knows, even if the person from whom she received the testimony is not deceitful or deranged. So it is apparently assumed as background for the story that there is no reason in the testifier’s observable demeanor or circumstances to doubt her testimony, and that the inquirer has the requisite skills and inclinations to recognize circumstances undermining her testimonial justification were they to occur. Such background assumptions may make the knowledge so obtained seem more of an achievement, just because it will yield knowledge only to a person who has these further epistemic skills, over and above the mere ability to understand what was said in testimony. A different example may make Lackey’s point more forcefully: It is easy to know that the sky is clear, if one has normal vision and is standing outdoors at the time. But where is the achievement in opening one’s eyes? I do not find entirely convincing even the claim that this last example is a counterexample. The world class archer who makes an easy shot is still shooting skillfully, even if it is the sort of shot a much less skilled archer could also reliably make. Small achievements are still achievements, and I rather think that there is more skill even in the most ordinary perceptual judgments than Lackey allows (Reynolds 1991). So I think there is something right about the suggestion that knowledge is due to cognitive virtues or skills. It does constitute an achievement.4 The suggestion I will make can be construed as a further specification of these proposals. But they 4. This is not intended to minimize differences in the proposals. I am taking a long focus on them, since I think they all suffer from a similar problem.

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are not complete explanations of the value of knowledge, since they invite the question why we should so value what leads up to knowledge. Why should we regard this particular way of coming to believe as due to a skill or a virtue or as constituting an achievement or to our credit? If the answer is only that the skill, virtue, etc., reliably leads us to true beliefs, then it seems we have not escaped Zagzebski’s swamping problem. One might hope that skills or virtues are recognizable as such on their own, apart from their leading to such valued outcomes as knowledge (so that they can explain the additional value of knowledge rather than presuppose it), and that they are valued independently of their immediate outcomes, so that epistemic skills (etc.) could be a source of epistemic value independent of the value of true belief and thus avoid the swamping problem. But it is not so clear that we can recognize skills as such apart from their results. For example, not every cultivated way of acting or set of habits constitutes a skill or a virtue, even if it is rather difficult to learn. There are tricks one can do with a piece of cotton lint that are every bit as difficult as the achievements of archery, but we do not value them and do not think that we should. We have a number of reasons to value archery over tricks with lint. One is that there is in our society an established set of games or competitions for archers, with widely acknowledged standards, where archers can demonstrate their skills and be rewarded for outstanding achievement. A second (and not really independent) reason to value archery is that those who succeed in archery competitions, or in more informal ways demonstrate skill in archery, are praised by others.There are no competitions and no praises for autistic children who spend hours doing tricks with lint. But again that invites the question why we have competitions in archery and why we praise it. There is an obvious answer to that question. It is not found in the amount by which the intrinsic value of arrows suddenly occupying the centers of targets exceeds that of bits of lint drifting through the air in just the way the autistic child finds so fascinating, but rather in the history of archery. Archery was once of great benefit in hunting and warfare, while lint floating never has had such uses. Keeping one’s family fed and protecting them from aggression once made the skills of archery of great practical value. Archery no longer has those uses to any significant extent in our society, but its history helps explain why we now have the archery competitions and the cultural practice of praising skillful archers. Plato’s approach to questions of value discourages us from considering such cultural explanations however. If we are asked what value there is in that arrow now quivering in the center of a target over and above the value of a bit of lint floating in just that way, where both are the result of hundreds of hours of concentrated practice, we are not likely to consider the more remote history of the activities. It is tacitly assumed in the way the Meno question about knowledge is framed that the difference in value will be present and discernible in any case in which we (should) desire knowledge in preference to true (or true justified) belief, such as the case in which we desire to know which road leads to Larissa. So one considers the differences that are salient in those particular cases, seeking some good possessed by the knower over and above the good possessed by the mere true

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believer that that is the way to Larissa, a good that would explain why it is reasonable to prefer knowledge. If an apparent difference in the specific cases does not seem valuable enough to outweigh the additional (small) costs of inquiry, it is concluded that it is not the relevant difference. Another philosophically interesting case where I think a larger view is likely to be illuminating is the mysteriously high value of original visual art over exact copies.5 I have in mind here the value of the work from the master’s hand, as opposed to an attempted exact copy of a given piece, not the distinction between the highly original type of artistic work and the merely derivative (but not copied) work. If we value oil paintings, say, mainly for their aesthetic effects on the viewer, and a good copy is good precisely because it looks just like the original, and hence will have the same visual effects on the viewer, just as a viewer, then it is hard to see why we should value a particular original painting so much more than an excellent copy of it. Attempts to explain the value of the original in terms of actual aesthetically relevant defects of the existing copies only emphasize the general problem: that a really good copy should apparently be just as valuable as the original, but, mysteriously, isn’t. If we consider the society-wide practice of such valuing however, a plausible rationale for praising the original work over even perfect copies is not hard to see. Suppose that our society desires to encourage the production of new art, perhaps for the sake of producing new kinds of aesthetic experience. (There may well be other aims too. The point is not to give a complete account of our reasons in this case—no doubt they are complex—but just to point out that one plausible possible reason is likely to be overlooked on Plato’s way of approaching the issue.) One way to do that is to praise original art for being original and not a copy. An artist will then reliably earn that sort of praise for her own productions only by making new art, not by copying others’ works. The praise given would thus encourage artists to try to do something new, not merely to reproduce the old, no matter how esteemed the old art is for any of its features that would be reproduced in a good copy. Although the praise of art as “the original” may thus have as its main purpose or function changing the behavior of those engaged in producing art, it will also naturally affect those who purchase an original work from its previous owners, so that original works will have a higher value in the market than mere copies, however exact. I suggest that it is (in part) the practice of praising particular pieces of art in this way that produces our feelings that only the original piece is truly valuable, rather than the antecedent value of being the original piece that motivates our praise of it. That is not to say that just any praise will lead us to value that which is praised, of course, but praise that has some significant motivation and is widely and consistently offered will tend to produce an attitude of valuing. If we, as society, praise original art in order to encourage new art, that explains the practice of such valuing, not an individual case. Considering a single “clear case” obscures our reasons for preferring originals in general, because it focuses our attention on differences pertinent to that case, instead of its character 5. Thanks to Peter French and Peter de Marneffe for helpful and knowledgeable discussion of this issue.

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as an instance of the practice. There is a plausible partial explanation of the practice—our collective desire to encourage with our praise the production of new works of art—but that explanation would not be suggested by any salient difference between, say, Rembrandt’s Night Watch and its best copies. I think that the nature of the value of knowledge is similarly overlooked when we follow Plato’s method and consider only ourselves in a given case and ask why we should prefer to know, rather than merely truly believe, in that specific case. But before turning to a cultural explanation of the value of knowledge, I would like to say a few words about praise and criticism, or expressions of approval and disapproval. It seems to me that many philosophers, especially those who do not work in value theory generally, tend to grossly underestimate the influence of the approval or disapproval of others in our daily conduct. We like to imagine ourselves to be free spirits and independent thinkers, and some of us are, in some respects, some of the time. But we are also, like the rest of humanity, constantly evaluating ourselves and others according to standards that are enforced mainly by the approval and disapproval of other people, which we may see in a disapproving look or in an indirect implication of someone’s remarks or which, perhaps more often, we infer that they will have toward us from their remarks about absent third parties. Where we do not see particular evidence of their evaluations of our own conduct, we nevertheless constantly expect them to be silently evaluating us, as indeed we are constantly evaluating their conduct, in various standard and expected ways. To cite some obvious but usually overlooked examples, our standards of grammar, appropriateness in topics of conversation, physical distance from conversational partners, gestures, tone of voice, where to look and when, and the rhythms of conversation that indicate when to make a remark without interrupting, are all taught and motivated by the sometimes visible approval and disapproval of others. This becomes painfully apparent in the social difficulties of high functioning autistic persons, who often strongly desire to obtain the approval of others, but are able to recognize only its plainest manifestations, and so are apt to get all of these matters wrong in what seem to the rest of us to be obvious ways, oblivious to the reactions of the people with whom they are trying to converse.6 These examples also illustrate how approval and disapproval may play an important role in teaching us basic skills which we may then exercise with perhaps only the very occasional reminder (e.g., the uncomfortable look and backing away when we stand a little too close to someone). 6. I speak from personal experience. My son Andrew, who is eighteen at the time of this writing, has high functioning autism. After much patient coaching he has reached the stage at which people with whom he tries to make small talk merely wonder why his parents never tried to teach him manners. Lack of awareness of the unspoken approving or disapproving reactions of others is likely to be only one contributing factor (but it is a very obvious one) in the difficulties persons with autism have in learning these skills, since they are also relatively uninterested in imitating others and they often have cognitive or perceptual difficulties that interfere with matters of timing. For more on the difficulties of persons with autism and methods effective in remediating those problems, see Koegel and Koegel (2006). A good review essay of the recent general psychological literature on praise and motivation is Henderlong and Lepper (2002).

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It is held by a number of recent philosophers that knowledge is the norm of assertion, that is, if we assert that p, when we do not know that p, then we are properly subject to criticism.7 That suggests part of the view that I want to defend— that we value knowledge because others require that we know what we assert, at least to the extent of disapproving of us, if they think that we do not know that p when we assert that p. Since so much of our life is social, and requires frequently making assertions in conversation, that would give us a reason to value knowledge for anything that we might expect to assert. But it does not yet explain satisfactorily why we value knowledge. For it invites the question why knowledge should be the norm of assertion. Why should we value knowledge in assertions, over the expression, say, of true beliefs or justified true beliefs? Williamson suggests that no reason can be given for why knowledge is the norm of assertion, because what makes or constitutes a speech act an act of assertion is that it is subject to the norm of knowledge (Williamson 2000, 266–69). As he notes, that raises the question why we have decided to transmit information in the form of assertions, constituted by the norm of knowledge, rather than, say, qu-assertions, which have a norm of true belief. Qu-assertions that p are subject to criticism if made by those who lack true belief that p, but they are not subject to criticism if made by those who do not have knowledge that p, so long as they have true belief that p. In answer to this question he suggests that we can only transmit knowledge through our assertions if we know what we assert. A requirement of knowledge discharges our responsibility to epistemically ensure the truth of the content asserted. It is not clear, however, that we have such a responsibility, apart from the norm of knowledge itself. To say that I am responsible for ensuring the truth of what I say, where the truth can be ensured only by knowing, seems to be only a variant way of claiming that knowledge is required for assertion. In previously published work I have argued that the function of saying that people know is in part to express approval of the corresponding actual or potential testimony, rather than approval of assertions more generally (Reynolds 2002). In seeking to testify only in ways that will merit this approval we comply with public standards for testimony and thus, in the long run, improve the average quality of our testimony, making it more likely to be helpful to the recipients. Those who accept testimony offered by those who are trying to comply with a requirement of knowledge are more likely to be successful in their actions or projects than they would be if they relied instead on testimony offered by those who do not attempt to comply with such a requirement. Testimony may be roughly characterized as that subclass of assertions that are offered as informative, with the expectation or purported expectation that the recipients of the testimony will take the speaker’s word for it. The main reason for shifting to talk of testimony instead of assertion more generally is that we often

7. Among those who have defended the view that knowledge is the norm of assertion recently are Peter Unger (1975, 250–71), Timothy Williamson (1996, 2000), Keith DeRose (2002), John Hawthorne (2004), and Jason Stanley (2005).

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make assertions in philosophy or while discussing sports or politics (etc.) that do not express our knowledge, and yet it seems that we are not to be criticized for so doing.8 However, when we testify—expecting others to accept what we say—it seems we are expected to know and will be justly criticized if we do not. There are a number of points to bear in mind about the thesis that attributions of knowledge function as expressions of approval of testimony. I think these points are obvious on a little reflection on the notion of the function of an artifact, such as a word like “knows.” But it seems they are easy to overlook in our anxiety to spot the flaw quickly, an estimable ambition perhaps, but too much admired in our philosophical culture. First, to say that “know” functions to express approval of testimony is not to say that that is its only use, nor that every ordinary competent utterance containing “know” serves to express such approval. A carpenter’s hammer may still have the function of driving nails even if most owners of such a tool more often use it for other purposes. Nor does my thesis imply that testimony given with knowledge may not still be legitimately subject to all sorts of other criticisms (e.g., as tactless, pointless, or harmful in a thousand other ways). It does not imply that nonknowledgeable testimony is in fact always so criticized, nor that it should be. Nor does it imply that we may not sometimes excuse people, to whom it appears that they have knowledge, for testifying, even though they do not really know (e.g., the protagonists of the Gettier stories). The occasional criticism or praise of third parties that we hear (“She said it was so, but she couldn’t have known”) may sufficiently remind us of the requirement of knowledge for testimony, so that we rarely need to hear overt approval or disapproval of our own testimony. It is the approval we mainly desire, not the expression of that approval. That is why it is consistent with my thesis that, once past early childhood, we are only occasionally told that we know or do not know something. These various points should sufficiently indicate why the simplest sorts of surveys of the usage of “know” (e.g., compiling randomly selected utterances of “know” to determine what percentages are used as expressions of approval) are far too simplistic to be useful tests of my thesis. It is an empirical thesis however, and so should in principle be open to empirical testing. My point here is not to discourage attempts to think of ways to bring it to an adequate empirical test, but just to warn against the simplest sorts of empirical testing, and especially against that “test,” irresistible to philosophers because it is apparently available from one’s armchair, of trying to recall whether the ways one has recently heard “know” used seem to count intuitively as praise. I think similar observations indicate why the claim that knowledgeable testimony tends to be more helpful than nonknowledgeable testimony is not put in doubt by the citation of fairly significant classes of exceptions, such as the white lies 8. Williamson allows for such cases as inconsequential breaches of the normal rule for assertion, and cites as a parallel breaches of grammar in animated conversation (Williamson 2000, 258–60). The cases do not seem to be fully parallel however. We would regard the grammatical oddities as breaches of grammar, even though we might think it obstructive of the purposes of conversation to point them out. But I think we are not similarly inclined to admit a fault if it is pointed out to us that we do not really know that p where we have just asserted that p in a discussion.

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that spare our vanity, or the alleged benefits of acquiring a high opinion of our own abilities through the flattery of, say, our students and friends. It is no accident that proverbs discourage us from taking compliments as testimony: “a compliment is to be inhaled, not swallowed.” It is a large and difficult empirical question whether having a norm of knowledge in fact makes testimony more beneficial to us, not in every case, but on the whole. However, surely it is very plausible that it does. Turning then from some initial objections to reasons in favor of the view: One reason to hold that “know” functions to express approval of testimony is that it neatly explains why knowledge is the norm of testimony. The word “know” (or its ancient counterparts) was developed for the purpose of indicating acceptable testimony. Another reason to hold that “know” functions as praise for testimony is that this view explains all of the main features of our concept of knowledge. It thus improves on Bernard Williams’ project. He tried to explain the justification and “something for Gettier” features of knowledge on the assumption that we have a goal of true belief, arguing that seeking the other features of knowledge would be the most reliable way to obtain true belief (Williams 1978, 37–45). He assumed that we desire some features of knowledge in order to explain why we would desire the other features, and so explained some aspects of our concept of knowledge in terms of its other aspects. But as I have argued elsewhere, and shall now briefly summarize, the hypothesis that we use “knows” as an expression of approval for acceptable testimony explains why we have a concept in common use that has all of the features of our concept of knowledge. When a term for praising testimony, say “gnows,” was introduced, it would presumably have been used to praise testimony that seemed to people to have been helpful in their projects, such as finding people or things.9 If Sam told Sally that there were wild onions on the other side of a certain hill, and Sally consequently walked over the hill looking for onions and failed to find any, she might then have criticized what Sam told her as not “gnown.” If she did find the onions, however, she might have expressed her approval of Sam’s testimony by saying he “gnew” there were onions over the hill. She might have done that whether or not 9. This resembles Edward Craig’s argument that our ancestors developed the concept of knowledge and words to express it in order to indicate approved sources of information (Craig 1990). Craig assumes that our ancestors would have been seeking true belief whether p (so far resembling Bernard Williams’ idealized inquirer), and considers how they might recognize informants who are likely, through testifying, to give them true belief whether p. Those informants would be designated as knowing whether p. I begin instead with the assumption that our ancestors would create a term with which to praise those who gave helpful testimony, not assuming that they would have any antecedent desire for true beliefs. The stories of how the concept of knowledge would develop from these different starting points are quite different. For example, Craig suggests that our ancestors would seek confidence in their informants as more likely to induce belief in their testimony in those who hear that confidently expressed testimony (Craig 1990, 12–13). (See the text for my alternative.) But the main difference between my view and Craig’s is that I focus on the role of attributions of knowledge as encouraging better testimony in the future, while Craig focuses on their conveying information to aid in locating good testimony now. I do not suppose that either of us would have to deny that the area the other focuses on is also an important aspect of our use of “know.”

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she possessed concepts of truth or belief. Those concepts would not have been necessary for her to judge whether Sam’s testimony helped or hindered her project of gathering onions. In time people would notice that someone who had just come from over the hill tended to give helpful testimony about what could be found there, and that those who had not recently been there were less likely to give such helpful testimony. Users of “gnow” would thus gradually come to apply it to those who had a certain kind of history—a history of certain kinds of perception, received testimony, and so on—even in advance of soliciting or acting on their testimony. If our ancestors disagreed with the testimony someone had given, they would expect that testimony to be unhelpful (to others at least, since of course they would not act on it themselves), and so would criticize it as not gnown, and also eventually (because of the disagreement) as not true. Perhaps on observing cases of apparently confident testimony that had not been helpful, although the testifiers were willing to act on it themselves, they would come to regard those testifiers as having been in states that governed their actions in the way that received testimony sometimes does, but that did not amount to having gnowledge, that is, as having mere beliefs.10 Our ancestors would have recognized that some persons seem to themselves to gnow, but because of errors or omissions in their awareness of their own relevant history or circumstances (as in the Gettier stories), they would not have the sort of history that was required for really gnowing. Those persons might be said to be “justified” in what they testified or would testify (because it reasonably seemed to them that they knew, and so that they were obeying the requirement), but to lack knowledge. If someone seemed to themselves to lack knowledge, but testified anyway, they would be blamed for flouting the norm of testimony, even if it happened that they really gnew. So our ancestors would gradually develop a concept of justification, or at least a practice of refraining from criticizing those who seemed to themselves to know, and they would come to regard justification, or seeming to the subject to know, as a requirement for gnowledge. They would also recognize an absence of belief by the subject as strong but fallible evidence that the appropriate history for gnowledge was lacking. So they would probably come to require belief for gnowledge too. My view thus apparently explains all of the standard requirements of our concept of knowledge—truth, belief, justification, and something for Gettier—without merely assuming an antecedently existing desire for any of them.11 I do not of course deny that two of these features are more 10. I am of course echoing Wilfrid Sellars’ myth of Jones, which explains how our ancestors might have acquired a concept of belief from observations of the testimony and related actions of others. I have extended it to a myth on which it would be natural to expect “knows” to express a more fundamental concept than “believes,” as Williamson holds (Sellars 1997 [1956], 102–7; Williamson 2000, 41–48). 11. For further details and attempts to answer some objections, see Reynolds (2002, 149–58). Some recent accounts of knowledge omit the justification condition, replacing it with reliabilist conditions. But they usually allow that there is at least an appearance that justification is a requirement for knowledge. So explaining that appearance would be a point in favor of my view even on these accounts of knowledge. Does my view amount to adopting a kind of “attitudinal theory” of knowledge, perhaps even a kind of noncognitivism or nonfactualism about knowledge, as in Field (1998)? I do not think I am committed to any such view. My idea is that the function of “know” to indicate approval of testimony, and the fact that only certain kinds of testimony have

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important than the others: If the testimony is not true, or is not believed, it will not be helpful, though it may still be helpful in the absence of the history required for being knowledge, provided it is in fact true.12 Another reason to prefer the view that in using “know” our society encourages better testimony, rather than true belief as such, is that testimony is more under our voluntary control than is belief. We can change our testifying behavior in order to avoid the disapproval of being thought not to know what we have testified, or to obtain the corresponding approval of being thought to know, but it is not so clear that we could thus change our believing in order to avoid the disapproval or obtain the approval (Reynolds 2007). The view that we say people know in order to encourage better testimony, and discourage substandard testimony, thus suggests a cultural explanation why we value knowledge. Our ancestors found that the sorts of features that now constitute our concept of knowledge that p, when possessed by the testifier, tended to produce helpful testimony that p. So they came to approve of testimony by those who had those features and to express that approval using the ancient equivalent of “know.” Knowledgeable testimony had been found to be helpful and nonknowledgeable testimony had been found to be less helpful, on the average and in the long run. Since people approve of our testimony when we speak with knowledge, and disapprove of it when we do not, and since we want to obtain or at least merit the approval, and avoid the disapproval, that gives us a reason to prefer to know whatever we might have occasion to testify. The function of our practice of classifying people as knowing continues to be achieved, although its history has been forgotten and its function is not clearly understood. We value knowledge over true belief because of the persisting practice of approving only of knowledgeable testimony. My personal preferences do in fact conform to the social practice, because I have been trained to have such a preference by hearing people talk approvingly of knowledge, and disapprovingly of those who testify without it. Even if I do not consciously want such praise (but I do), it has produced in me a preference for knowledge. We are aware that others approve or disapprove of our testimony depending on whether it is knowledgeable, and this motivates us to try to know. That is not to say that we are conscious of wanting to merit the approval when the question is raised whether we prefer knowledge to true belief in a given case. We certainly do not, as individuals, share the larger social goal of improving testimony. It may seem to us that we just prefer knowledge to true belief, even though no further reason for the preference comes to mind. I have such a preference because, social animal that I am, I have always desired the approval of others, and given our existing institution of approving knowledge, I naturally responded to

tended to be helpful in the past, has led to a fairly definite informational content for the term “know” as we now use it. Given that it has that content now, it is an ordinary factual question whether one knows in any particular case, subject to the usual allowances for vagueness, reasonable contextual variation in standards, and the like. 12. Thanks to Bernie Kobes for emphasizing to me the importance of acknowledging the greater importance of truth among the requirements of helpful testimony.

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that approval by developing a preference for it. I do not, however, need to be aware of this in order to be thus influenced in preferring knowledge. But that may seem not to answer Plato’s question about the value of knowledge. So far we have only heard a causal story about how our society, and I qua member of that society, have in fact come to prefer knowledge that p to true belief that p. But now that I am reflecting on that preference, I may still ask Plato’s normative question, whether I should continue to so prefer it. There does seem to be on this view a sense in which I should want knowledge, although it is perhaps not the “should” of rationality, but rather a “should” that indicates healthy or proper psychological functioning. If I did not prefer knowledge that could only be due to a serious defect in my education or in my psychology, so that either I was not properly socialized into this important cultural practice of ours, or I was pathologically indifferent to the praise and criticism that would have produced such a preference. If I were indifferent to the approval and disapproval of my fellows generally, I would very likely be even more incapable of being trained into my part in a human community than are persons with autism. A failure to learn what counted as knowledge, even if not accompanied by a general indifference to the approval or disapproval of others, would still be a very serious social handicap. Someone who had no desire to determine whether he knew in offering testimony would often give offense and perhaps in time effectively become a social outcast. I am not thinking merely of the incautious retailer of interesting gossip, but of someone who would routinely tell others the time of day, or the presence of Sally in the next room, or the way to the restroom, regardless of whether he thought he knew. Since I could fail to prefer knowledge only by having some fairly serious psychological or social defects, it seems I should prefer knowledge to true belief. But it may still be said that this account of why we value knowledge over mere true belief is not really an answer to the very specific Platonic question. The real question about our preference for knowledge is: Why should I, as a matter of self-interested rationality, in this case, prefer knowledge over true belief? Plato did not ask why I should want to be responsive to social influences so that I will prefer it. He asked for a reason why it is better for me to have knowledge in the particular case. But instead of answering that question I have only given a naturalistic story about how we have come to regard it as better to know, and perhaps a functional account of why it is better for us that we should be the sorts of beings who would thus respond to our training by preferring knowledge. It seems to me, however, that the sort of answer I have just given is not so very far from some familiar Platonic themes. The psychological defects that would make me capable of considering the question without having any effective prior preference for knowledge seem to me to be something like the damaged soul that, according to Plato, results from doing the wrong thing, especially if one frequently “gets away with it.”13 That is, they are serious mental deficiencies, although they are 13. Republic, 444c–d. I think the epistemic question is easier to answer than the corresponding moral question because it asks only why we should normally prefer knowledge over true belief, when other things are roughly equal. What makes the question why it is best to do what is morally

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not internal conflicts of the sort that Plato claimed would occur in those who act unjustly. Someone who could choose not to care for knowledge until shown a personal advantage in each particular case would be very close to someone who just did not care. But suppose the choice whether to care was only to be offered to me once, and there was no reason to think that making it either way would significantly affect my psychology in social situations generally, or even my future sensitivity to the requirement of knowledge for testimony in particular. Would there be any reason we could give to prefer knowledge then, to someone whose antecedently inculcated preference for knowledge was thus temporarily and otherwise harmlessly suspended? Suppose furthermore that I temporarily did not desire to merit the praise of other people, or even desire my own self-approval as knowing—my lack of a preference for knowledge also includes a complete but temporary lack of concern whether I am to be praised or criticized in this regard. In such a case I concede that I do not think there would be any self-interested reason for me to prefer knowledge to true belief. But is there any reason to think that only in such a case are we focusing on the genuine value of knowledge over true belief? We might worry in some other sorts of cases that our society may have inculcated in us preferences that we would be better off without, that we have come to hold “false values.” That might suggest that only an individualist thought experiment of Plato’s sort, one that prescinds from society’s influences, could yield correct assessments of values. But the idea that the only way to find the true value of anything whatever is to make oneself consider it from a radically individualistic point of view, such as we are now trying to do, seems wildly off the mark. There is no reason at all to think that there is anything false about our preference for knowledge, just because it has been partly created by our enculturation. Suppose, as we have been speculating, that knowledge would not seem preferable to an otherwise rational person some of whose important human qualities were on holiday. Why should that indicate anything disturbing about our own healthy preference for knowledge? There is one last related problem for this view about the value of knowledge that I would like to briefly address. It is that my view may seem to posit an odd sort of creation of value. It is natural to think that when we praise something we are reporting that it is good. We cannot make it good just by praising it, like the (fictitious) teacher of small children who is always chirping “Good job!” no matter how the children perform. My account apparently says that we have created a feeling that knowledgeable testimony is good by praising such testimony, and have thereby produced a preference for knowledge where it did not exist before. The good of knowledge is as it were created by our practice of approving it. Perhaps some of us will not mind that very much. Some of the things that we value, such as having a powerful serve in tennis, seem to be created by fairly arbitrary decisions about how the game is to be played and so about what the right harder, and a Platonic answer to it harder to defend, is that we seem to be required to prefer doing what is right even when prudential considerations appear to strongly favor a morally wrong course.

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players’ aims within the game will be. Merely saying something is good does not make it so, but coordinating our actions and attitudes with others to value some things and disvalue others, as we do in creating a game, may have the consequence that something previously neutral becomes really good. I think, however, that that is not quite what is going on in the case of knowledge. Even on my view it is not arbitrary that we came to praise knowledge, and so to value it over another quality such as mere true belief. There is a good in this system of social control of testimony, a good for our society in the improvement of the average quality of testimony, which motivated the cultural evolution of our way of praising testimony until it became the current practice we have of requiring people to know that p if they testify that p. It was as much a process of discovery of the good of knowing for testimony, and a process of educating ourselves and others to seek that good, as it was the creation of our preference for it. So the reason we prefer knowledge and should prefer it is that we have been taught to prefer it by our awareness, over many years, that others approve of it. We constantly judge our own actual and potential testimony by this standard. Although we also want knowledge for ourselves for many diverse personal reasons, the main social purpose of classifying ourselves and others as knowing, or not knowing, is to encourage compliance with standards for testimony that benefit all of us in myriad ways. Having been open to that encouragement over the years, and so preferring knowledge now, is a good thing for each of us. To sum up then: Why should I prefer to know that this is the way to Larissa over merely truly believing that it is? I find I just do prefer knowledge, as it were for its own sake. But from a larger perspective it seems that I should prefer it, because given the social practice of approving of testimony only if given with knowledge, I could fail to prefer knowledge, when other things seem to me to be equal, only by having the sorts of serious social or psychological defects that would make me unresponsive to the approval of others. Finally, the social practice that produces this particular preference is good for all of us because it improves the average quality of our testimony, which results in greater success in our projects generally. We do and should prefer knowledge in order to obtain the approval of others.14 REFERENCES BonJour, Laurence. 1985. The Structure of Empirical Knowledge. Cambridge, MA: Harvard University Press. BonJour, Laurence. 1998. In Defense of Pure Reason: A Rationalist Account of A Priori Justification. Cambridge, England: Cambridge University Press. Craig, Edward. 1990. Knowledge and the State of Nature. Oxford: Oxford University Press. David, Marian. 2001. “Truth as the Epistemic Goal.” In Knowledge Truth and Duty: Essays on Epistemic Justification, Responsibility and Virtue, ed. Matthias Steup, 151–69. Oxford: Oxford University Press. DeRose, Keith. 2002. “Assertion, Knowledge, and Context.” The Philosophical Review 111(2): 167–203. 14. Thanks to my colleagues Brad Armendt, Tom Blackson, Peter French, Bernie Kobes, and Peter de Marneffe for many helpful comments on an earlier draft of this article.

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Field, Hartry. 1998. “Epistemological Nonfactualism and the Prioricity of Logic.” Philosophical Studies 92(1–2): 1–24. Greco, John. 2003. “Knowledge as Credit for True Belief.” In Intellectual Virtue: Perspectives from Ethics and Epistemology, ed. Michael DePaul and Linda Zagzebski, 111–34. Oxford: Clarendon Press. Hawthorne, John. 2004. Knowledge and Lotteries. Oxford: Oxford University Press. Henderlong, Jennifer, and Lepper, Mark R. 2002. “The Effects of Praise on Children’s Intrinsic Motivation: A Review and Synthesis.” Psychological Bulletin 128(5): 774–95. Horwich, Paul. 2006. “The Value of Truth.” Nous 40(2): 347–60. Koegel, Robert L., and Koegel, Lynn K. 2006. Pivotal Response Treatments for Autism: Communication, Social, and Academic Development. Baltimore, MD: Brookes Publishing Company. Kvanvig, Jonathan L. 2003. The Value of Knowledge and the Pursuit of Understanding. Cambridge, England: Cambridge University Press. Lackey, Jennifer. 2007. “Norms of Assertion.” Nous 41(4): 594–626. Reynolds, Steven L. 1991. “Knowing How to Believe with Justification.” Philosophical Studies 64(3): 273–92. ———. 2002. “Testimony, Knowledge, and Epistemic Goals.” Philosophical Studies 110: 139–61. ———. 2007. “Against the Goal of True Belief.” Presented at the APA Eastern Division Colloquium: Truth and Belief, December 28, 2007. Riggs, Wayne D. 2002. “Beyond Truth and Falsehood: The Real Value of Knowing That P.” Philosophical Studies 107 (1): 87–108. Sartwell, Crispin. 1991. “Knowledge Is True Belief.” American Philosophical Quarterly 28(2): 157–65. ———. 1992. “Why Knowledge Is Merely True Belief.” Journal of Philosophy 89(4): 167–80. Sellars, Wilfrid. 1997. Empiricism and the Philosophy of Mind. Cambridge, MA: Harvard University Press. Originally published in Herbert Feigl and Michael Scriven, eds. Minnesota Studies in the Philosophy of Science, vol. 1 (1956). Minneapolis: University of Minnesota Press. Sosa, Ernest. 1997. “Reflective Knowledge in the Best Circles.” Journal of Philosophy 94: 410–30. ———. 2003. “The Place of Truth in Epistemology.” In Intellectual Virtue: Perspectives from Ethics and Epistemology, ed. Michael DePaul and Linda Zagzebski, 111–34. Oxford: Clarendon Press. Sosa, Ernest. 2007. A Virtue Epistemology: Apt Belief and Reflective Knowledge, volume I. Oxford: Clarendon Press. Stanley, Jason. 2005. Knowledge and Practical Interests. Oxford: Oxford University Press. Unger, Peter. 1975. Ignorance: A Case for Scepticism. Oxford: Clarendon Press. Williams, Bernard. 1978. Descartes: The Project of Pure Enquiry. New York: Penguin Books. Williamson, Timothy. 1996. “Knowing and Asserting.” Philosophical Review 105(4): 489–523. ———. 2000. Knowledge and Its Limits. Oxford: Oxford University Press. Zagzebski, Linda. 1996. Virtues of the Mind: An Inquiry into the Nature of Virtue and the Ethical Foundations of Knowledge. Cambridge, England: Cambridge University Press. Zagzebski, Linda. 2003a. “Intellectual Motivation and the Good of Truth.” In Intellectual Virtue: Perspectives from Ethics and Epistemology, ed. Michael DePaul and Linda Zagzebski, 135–54. Oxford: Clarendon Press. ———. 2003b. “The Search for the Source of Epistemic Good.” Metaphilosophy 34(1/2): 12–28.

Midwest Studies in Philosophy, XXXII (2008)

Knowledge, Truth, and Bullshit: Reflections on Frankfurt ERIK J. OLSSON

1. FRANKFURT’S MENO CHALLENGE In his book On Truth (2006; hereafter OT), Frankfurt argues—against postmodernism and other relativist philosophies—that there is an objective distinction to be drawn between the true and the false, and that the truth plays an essential role in our lives. Even those who present themselves as denying the tenability of the distinction must agree that this denial is a position that they truly endorse (OT, 9). They must agree that the statement expressing their rejection of the distinction truly and accurately describes their attitude toward it, which makes the relativistic stance ultimately incoherent. We need, then, to acknowledge as genuine a distinction between what is true and what is false. But why, exactly, is truth so important to us? Frankfurt’s basic answer amounts to an appeal to the instrumental value of truth in our daily affairs. It is surely extremely helpful to know the truth about what to eat and what not to eat, how to raise our children, where to live, and many other mundane matters (OT, 34–35). Truth, then, “often possesses very considerable practical utility” (OT, 15). On a larger scale, engineers building, say, a bridge rely heavily on true assessments of various important parameters, such as the durability of construction materials (OT, 22). Moreover, they must ascertain, with reliable accuracy, both the obstacles that are inherent to the implementation of construction plans and the resources that are available for coping with those obstacles. Successful engineering depends therefore quite obviously on its practitioners being closely in touch with an objective reality that is independent of any particular point of view. The same could be Midwest Studies in Philosophy: Truth and its Deformities Volume XXXII Editor by Peter A. French and Howard K. Wettstein © 2008 Wiley Periodicals, Inc. ISBN: 978-1-405-19145-6

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said of architects and physicians whom we would not consult unless we believed them capable of forming objectively true statements in their respective areas of expertise. There is in all these contexts a clear difference between getting things right and getting them wrong and therefore a clear difference between true and false. Although the level of subjectivity is greater when it comes to historical analyses and to social commentaries, there are even in these fields important limits to the interpretations that can reasonably be imposed on the phenomena. “There is,” as Frankfurt puts it, “a dimension of reality into which even the boldest—or the laziest—indulgence of subjectivity cannot dare to intrude” (OT, 24). Truth, Frankfurt observes, is important even in moral matters. This is so even if we concede that evaluative judgments themselves lack truth value. The reason is that whether we endorse such a judgment or not will depend on factual statements that do have truth values. Thus, we may come to endorse an evaluative judgment of a person’s moral character on the basis of statements describing that person’s behavior in concrete cases. Those statements can be true or false, and they need to be true in order for our endorsement to be reasonable. Generally, we take things to be good or bad because of certain beliefs we have about those things. Thus, we may hold one thing to be good because we believe it will increase our wealth or make us happier. If, upon closer examination, those beliefs turn out to be false, we tend to withdraw our initial positive sentiment toward the thing in question. Because of the great practical usefulness of truth, we even have reason— Frankfurt thinks—to “love” it. Love is here construed, following Spinoza, as “joy with the accompanying idea of an external cause” (OT, 39), where by “joy” is meant “that passion by which the . . . [individual] passes to a greater perfection” (OT, 41). If, in other words, a person experiencing joy in this sense identifies an object externally causing this passion, then, Spinoza believes, the person is rightly said to love that object. Now, truth, Spinoza and Frankfurt agree, is indispensable in enabling us to stay alive, to understand ourselves, and to live fully in accord with our nature (OT, 47). Once we recognize this, we must therefore love truth. Frankfurt concludes that “[p]ractically all of us do love truth, whether or not we are aware that we do” (OT, 48).1 Frankfurt’s discussion of the value of truth does not end here, but I believe nonetheless that this short summary contains the most important components of his view. It also hints at what epistemologists will perceive as a shortcoming of Frankfurt’s presentation: the failure to distinguish clearly between the value of truth and the value of knowing the truth. Frankfurt moves effortlessly from the one to the other. Thus, he observes that people “need to know the truth about what to eat and what not to eat” etc. (OT, 35), an observation that is used to support the

1. Frankfurt also believes that deception is quite common, especially in the form of bullshit, of which “[e]ach of us contributes his share” (On Bullshit, 1). But how can this be if all of us indeed love truth? Frankfurt’s answer, I presume, is that we are not (always) aware of our love for truth. Alternatively, one may speculate, truth may not be the only thing we love, and sometimes when our interests collide the truth is sacrificed. I return to Frankfurt’s discussion of bullshit in the second part of this essay.

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claim that they “require truths to negotiate their way effectively through the thicket of hazards and opportunities that all people invariably confront in going about their daily lives” (OT, 34–35). Once the common distinction is drawn between truth in general, that is, true belief, and truth that qualifies as knowledge, the question arises whether it is the former or the latter that has instrumental significance. Is true belief in general instrumentally valuable, even if the belief in question falls short of knowledge, or is it knowledge only that has practical worth? The answer, I submit, is that true belief in general has instrumental value. It is not necessary for a true belief to be valuable in this sense that it qualifies as knowledge. Suppose, to take Plato’s example in his dialogue Meno, that you wish to embark on a journey to Larissa without having any idea of what direction to take. Now you encounter a trustworthy-looking, but in fact unreliable, guide who happens to give you correct information on the matter. Having listened to her, you form a true belief concerning the location of Larissa. Surely you are better off now, practically speaking, than you were before you consulted the guide. It is instrumentally better for you to possess true information as to the location of Larissa even if in fact you do not know that information to be correct. Similarly, our engineer is better off having a true belief concerning the robustness of a given building material than having no or false information, even if her true belief fails to qualify as knowledge. For suppose that our engineer is handed a measurement instrument which happens to be somewhat unreliable but which nonetheless gives a correct reading in this particular case. Surely, this will leave our engineer in a better position, practically speaking, than she was before the measurements were conducted. It is instrumentally better for her to possess true information as to the robustness of the material than to be ignorant or in error, even if she cannot be said to know that this information is true. It seems correct to say, then, that true belief in general is instrumentally valuable, not just true belief that is known to be true. We have reason, then, to love truth in general, not just to love knowledge, at least if we accept the Spinoza-Frankfurt definition of love. But these remarks only serve to raise another, considerably more delicate and contentious, issue: Given that true belief in general is valuable, how can it be shown that knowledge is even more precious? Ever since Plato, philosophers have thought that knowledge represents the most perfect grasp of reality that a person can ever hope to attain. Knowledge is more valuable than things which fall short of knowledge. Something can fall short of knowledge in many different ways, for example, because it is simply false or not firmly held. Moreover, a true belief can fail to qualify as knowledge due to the less than reliable way in which it was acquired. Maybe Frankfurt need not provide a solution to the so-called Meno problem—the problem of accounting for the distinct value of knowledge—for his limited purposes of defending the importance of truth to a more general audience. But epistemologically more sophisticated readers are likely to remain unsatisfied with the present state of affairs. What should a solution to the Meno problem look like in order to be congruent with Frankfurt’s theory of the value of truth? One possibility would be to find a value other than instrumental value that knowledge has in greater degree

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than true belief in general. From a systematic perspective, however, it would be more satisfactory to learn that knowledge has more of the same value. Hence, from Frankfurt’s point of view the first alternative to consider is certainly the option that knowledge is instrumentally more valuable than true belief in general. 2. RELIABILIST SOLUTIONS Although there has been a lot of work on the Meno problem in recent years,2 the idea that knowledge is more valuable than true belief in an instrumental sense is not one that currently enjoys great popularity. Indeed, Jonathan Kvanvig rejects it already in the first chapter of his influential 2003 book The Value of Knowledge and the Pursuit of Understanding.3 Why are philosophers skeptical to the idea of the extra value of knowledge being instrumental in kind? Many have been persuaded by the proposed counterexamples that surface in the literature, starting with Plato and his Larissa example. The latter is intended to show that whatever surplus value knowledge may have which true belief in general lacks, that value cannot be instrumental. For there is, Plato claims, no practical difference between knowing the way to Larissa and merely having a true belief to that effect. In both cases, you are likely to reach your destination, the likelihood being also the same. A further obstacle to giving a Frankfurt style solution to the Meno problem is that, while Frankfurt is reasonably explicit when it comes to the nature of truth and of bullshit, he never clarifies his use of the term knowledge. There are, nonetheless, reasons to believe that he would not object to a reliabilist construal of that concept. At one point, he stresses the importance for engineering that technological assessments are made with “reliable accuracy” (OT, 22), and later he shows appreciation of having a view that is not only true but also “reliably grounded in the relevant facts” (OT, 77). These quotations, to be sure, do not strictly speaking commit Frankfurt to a reliabilist definition of knowledge, but they do show that reliability is a notion to which he attaches some importance. In the following, knowledge will be taken in the (process) reliabilist sense of “true belief acquired through a reliable process.”4 Unfortunately, counterexamples similar in spirit to the Larissa example have been leveled directly against the reliabilist construal of knowledge. Thus, Linda Zagzebski (2003) has argued that just as a good cup of espresso does not get any better because it was reliable produced, so too a true belief does not become more valuable due to the fact that it was obtained through a reliable process. Examples of this kind have convinced most epistemologists working on the Meno problem 2. See, for example, Jones (1997), Swinburne (1998), Riggs (2002), Zagzebski (2003), Kvanvig (2003), and Sosa (2003). For a recent overview, see Pritchard (2007). 3. For a critical discussion, see Olsson (2007). 4. Epistemologists will normally insist on an anti-Gettier clause in any definition of knowledge. Since the Gettier problem plays no role in this paper, I have chosen to simplify matters by not including an anti-Gettier clause in the analysis of knowledge. Classic formulations of the reliabilist position can be found in Goldman (1976, 1986).

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that reliabilist knowledge is no more valuable, instrumentally or otherwise, than true belief in general. Nevertheless, there are strong reasons to believe that epistemologists have generally overestimated the force of Zagzebski’s espresso analogy. It is a correct observation that, if the goodness of the espresso has been confirmed, the further information that it was reliably produced does not make it taste any better. By the same token, if a belief is already assumed true, the further information that it was reliably produced does not make that belief “more true.” But this argument assumes that the only virtue of reliable acquisition is that such acquisition indicates the quality (flavor or truth, as the case may be) of the thing produced. As we shall now see, this assumption is simply false.5,6 If a reliable coffee machine produces good espresso for you today, it can normally produce a good espresso for you tomorrow. The reason is that the coffee machine will normally be at your disposal tomorrow too; and, being reliable, it will probably produce one more good espresso. By the same token, if you have acquired a true belief that the road to the left leads to Larissa, then usually this same method will be available to you the next time around; and, being reliable, it will once again guide you correctly to your destination. There is more to reliable acquisition than meets the eye. The fact that a thing was reliably produced does not only indicate the quality of that thing; it also indicates that more things of the same quality can be produced in the future. Reliabilist knowledge will tend to multiply. Having it increases the probability of getting more of the same. Unreliably acquired true belief, by contrast, does not share this feature to the same extent. If your true belief that Larissa is to the right was acquired through an in fact unreliable method, there will be an increased tendency for that same method, being unreliable, to lead, upon reemployment, to a false belief. Hence, the probability of your attaining further true beliefs is greater conditional on your possessing knowledge than conditional on your possessing a true belief in general. Obviously, the extent to which the possession of knowledge raises the probability of future true beliefs depends on a number of empirical regularities. One is that people rarely face unique problems. Once you encounter a problem of a certain type, you are likely to encounter a problem of the same type at some later point. Problems that arise just once in a lifetime are few in number. If you are going to Larissa, the question of what is the best turn to take will probably occur more than once. Moreover, if a particular method solves a problem once, this same method is usually available to you the next time around. If you have an on-board GPS computer, you can use the navigation system to solve the problem of what 5. For a critical discussion of the espresso analogy, see Olsson (2007). 6. The account of the value of reliabilist knowledge that follows was first proposed in Goldman and Olsson (in press). In that paper, which was written in 2006, it is referred to as “the conditional probability solution” and figures as one of two rather different suggestions for how to come to grips with the Meno problem. Parts of the present approach can be found in different places in the literature, for example, in Armstrong (1973) in his reply to an objection raised by Deutscher. Williamson (2000, pp. 100–102), presents a similar theory focusing exclusively on the special case of beliefs with temporally related contents.

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road to take at the first crossroads. Unless the GPS system is stolen shortly thereafter—in most neighborhoods a rare event—this same method is also available to you when the same question is raised at the next crossroads. A further empirical fact is that, if you have used a given method before and the result has been unobjectionable, you are likely to use it again, if available, on similar occasions. Having invoked the navigation system once without any apparent problems, you have no reason to believe that it should not work again. Hence, you decide to rely on it also at the second crossroads. Finally, if a given method is reliable in one situation, it is likely to be reliable in other similar situations as well. I will refer to these four empirical conditions as nonuniqueness, cross-temporal access, learning, and generality respectively. To see even more clearly what roles these regularities play, suppose S knows that p. By the reliabilist definition of knowledge, there is a reliable method M that was invoked by S so as to produce S’s belief that p. By nonuniqueness, it is likely that the same type of problem will arise again for S in the future. By cross-temporal access, the method M is likely to be available to S when this happens. By the learning assumption, S is likely to make use of M again on that occasion. By generality, M is likely to be reliable for solving that similar future problem as well. Since M is reliable, this new application of M is likely to result in a new true belief. Thus, the fact that S has knowledge on a given occasion makes it to some extent likely that S will acquire further true beliefs in the future. The degree to which S’s knowledge has this value depends on how likely it is that this will happen. This, in turn, depends on the degree to which the assumptions of nonuniqueness, cross-temporal access, learning, and generality are satisfied in a given case. Clearly, no corresponding conclusion is forthcoming for unreliably produced true belief. While nonuniqueness and cross-temporal access are usually satisfied quite independently of whether or not the method used is reliable, there is less reason to believe that an unreliable method that yields a correct belief on its first occasion of use will also yield a correct belief on the second occasion. This blocks the step from the availability of the method on the second occasion to the likely production of true belief on that occasion. If we combine this account with Frankfurt’s observation that truth has instrumental value, it follows that knowledge is even more valuable. For a state of knowledge has instrumental value in virtue of being a state of true belief. In addition, knowledge makes further states of true belief (and, indeed, knowledge) more likely. Knowledge is, in that sense, instrumentally more valuable than true belief in general. My second point is that knowledge is particularly stable.7 A true belief that qualifies as knowledge will tend to stay put and will not so easily go away. As Williamson (2000) notes, stability of true belief is of practical importance in the carrying out of complex actions over time. Frankfurt’s example of engineers planning and building a bridge illustrates the point. It is crucial that the assessments upon which the engineering decisions are based will not change in the construction process. The thesis that true beliefs that are stable promote successful action to a 7. The stability theory was proposed in Olsson (2007).

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greater degree than true beliefs in general—what I call the Stability Action Thesis (SAT)—is firmly supported by pre-systematic judgment and will not be further argued for. However, it also needs to be established that reliable acquisition promotes stability. I call this the Reliability Stability Thesis (RST). Together RST and SAT imply the Reliability Action Thesis: Reliabilist knowledge promotes successful practical action over time. It remains to justify RST, the thesis that reliable acquisition of true belief is conducive to stability. The main part of the justification amounts to showing that, if one is using an actually unreliable method to acquire a given belief, the unreliability will tend to be detected in due time. Once the method has proven to be unreliable, beliefs that were acquired through that method will tend to be withdrawn. By contrast, the chance that doubt will be shed on an actually reliable process is lower, and it is therefore less likely that beliefs arrived at through such a method are later discarded. In order to make this likely, appeal will be made again to some empirical background assumptions.We will need all the assumptions that were invoked in the previous argument: nonuniqueness, cross-temporal access, learning, and generality. It will be assumed, in addition, that, while our inquirers may sometimes succumb to wishful thinking and other less reliable paths to belief, most of their belief acquisition processes are in fact reliable. This will be expressed by saying that they are overall reliable. According to the assumption of basic reliability, the inquirer has at her disposal some method that is basic in the sense that it can be used to resolve conflicting verdicts. Visual perception is a good example of a method that is basic in this sense: In cases of dissonant beliefs, we can often resolve the issue by stepping forward and taking a closer look. Furthermore, inquirers will be supposed to be track-keepers in the sense that they keep a record of where they got their beliefs from. According to a further assumption, inquirers view their beliefs as corrigible, meaning that they typically do not stick to their beliefs no matter what. More precisely, an inquirer who finds a given belief false is likely to question the reliability of the method by means of which that belief was formed. Moreover, once a given belief-acquisition method is classified as dubious by the inquirer, all beliefs that were obtained solely or mainly through the use of that method are also, to some extent, in doubt. Together these conditions express a sense in which an inquirer’s cognitive faculties are in good order.8 Why, then, should there be a tendency for reliably acquired (true) beliefs to be stable? Equivalently, why should there be a tendency for unreliably acquired (true) beliefs to be discarded? Consider the following sequence of events: (i) S acquires a true belief that p through method M in response to problem P. (ii) S faces a problem of the same type as P in the future (nonuniqueness) 8. Cf. Williamson (2000, p. 79). Maybe some of these assumptions can be weakened. I would welcome an inquiry into this matter, but I do not intend to pursue such an inquiry myself at this point. It suffices for my present purposes to show that, given some reasonably realistic assumptions, true beliefs that are reliably acquired will tend to be more stable than true beliefs in general.

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S still has access to method M (cross-temporal access) S uses M again (learning) S now acquires a false belief, say that q S becomes aware of a conflict between q and the verdict of one of her reliable methods (overall reliability) The falsity of q is confirmed by some basic reliable method, such as visual perception at short distance (basic reliability) S gives up her belief that q and considers M to be unreliable (corrigibility) S notes that her (true) belief that p was also acquired through M (track-keeping) S gives up her (true) belief that p (corrigibility)

Given the assumption of generality of reliable methods, stating that a method that is reliable now will probably continue to be so in the future, this unfortunate sequence of events is more likely if M is unreliable than it is if M is reliable. Why? Because step 5—the acquisition of a false belief—is more likely if M is unreliable. The other steps are, we may reasonably assume, equally likely for reliable and unreliable methods. Combining this result with our previous observation that a true belief that is stable over time will tend to be more useful in action, we may conclude that (reliabilist) knowledge is instrumentally more valuable than a true belief in general. Let us apply this abstract piece of reasoning to Frankfurt’s engineering example. Suppose that our engineer is confronted with the problem of assessing the robustness of a given piece of building material. Her method for assessing the robustness is using a certain measurement device. Using this device, she comes to the conclusion that the degree of robustness equals x, for some number x. The next day, the engineer faces the similar problem of assessing the robustness of some other material. Having the measurement device still at her disposal, she decides to use it again. Unbeknown to the engineer, however, the device misrepresents the robustness of the new material, yielding a robustness value y much higher than the actual value. As a result, the engineer forms a false belief to the effect that the robustness of the new material equals y when in fact it is much lower. The construction work now proceeds on the basis of an overestimated robustness value for the second material which is used, so our story goes, in one of the critical parts of a new bridge. A few days later, that part of the bridge breaks down before our engineer’s very eyes. She now becomes aware of a conflict between her previous measurement and the confirmed fragility of the material leading to her giving up her belief in the robustness of the second material and reconsidering the reliability of the measurement device. It now occurs to our engineer that she applied the same device also on the first material. Accordingly, she concludes that this measurement cannot either be taken at face value, although it is in fact correct.The claim was that an episode like this one, terminating in the loss of a true belief, is more likely to unfold if the method used is unreliable as opposed to reliable. I believe that there is a further, albeit more indirect, way in which these approaches to the Meno problem are congenial to Frankfurt’s thinking on the

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value of truth. Frankfurt insists, as we saw, that truth is instrumentally valuable and that we should therefore be truth seekers as well as truth tellers.Yet he is, of course, well aware that in special circumstances it might be better not to know or tell the truth. To take one of his own examples, “a lie may divert us from embarking upon a course of action that we find tempting but that would in fact lead to our doing ourselves more harm than good” (OT, 75–76). To be sure, it would have been better if we could have been thus diverted without any recourse to lying, but it would be unrealistic to suppose this always to be possible. The course of action having the greatest practical value all things considered may be one that involves not telling the truth. Does this mean that truth is, after all, an overrated concept? No. What it means, Frankfurt must agree, is that all that can reasonably be said is that truth is normally instrumentally valuable. That truth is normally instrumentally valuable means that the inference from “This is true” to “This is valuable” is a defeasible one in the following sense: We may infer the latter from the former, provided that we do not possess further information to the effect that the circumstances are special in ways that would undermine the conclusion. The situation is exactly analogous when it comes to the value of knowledge. Knowledge is distinctively valuable value in all normal cases.There is a defeasible inference to be drawn from “This is knowledge” to “This is distinctively valuable”. The conclusion can be withdrawn should new evidence emerge suggesting the violation of one or more of the empirical regularities previously alluded to. The situation should be considered relevantly special if it was a one-shot case, so that the reliable method could not be reemployed, or if the inquirer considers herself incorrigible, to take just two examples. 3. FRANKFURT’S PUZZLE ABOUT BULLSHIT Acknowledging an objective distinction between truth and falsity, Frankfurt believes, as we saw, that having true beliefs is important mainly for practical reasons. This is so not only for individual inquirers, but also for society as a whole: Civilizations have never gotten along healthily, and cannot get along healthily, without large quantities of reliable factual information. They also cannot flourish if they are beset with troublesome infections for mistaken beliefs. To establish and to sustain an advanced culture, we need to avoid being debilitated either by error or by ignorance. We need to know—and, of course we must also understand how to make productive use of—a great many truths. (OT, 34–35) The use of the first person plural indicates that Frankfurt is thinking of knowledge that is shared by the members of the society. Yet there is also deception, one form of which is the central concern of Frankfurt’s On Bullshit (2005, hereafter OB). In the book, Frankfurt contrasts bullshit not only with truth telling but also with lying, one of his conclusions being that the truth teller and the liar are more closely related than either is to the

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bullshitter. The reason is that, while both the truth teller and the liar react, in their own different ways, to the truth, the bullshitter is generally unconcerned with the way things really are: Someone who lies and someone who tells the truth are playing on opposite sides, so to speak, in the same game. Each responds to the facts as he understands them, although the response of the one is guided by the authority of the truth, while the response of the other defies that authority and refuses to meet its demands. The bullshitter ignores these demands altogether. He does not reject the authority of truth, as the liar does, and oppose himself to it. He pays no attention to it at all. (OB, 60–61) Indeed, being thus unconcerned with the truth is, in Frankfurt’s view, the very essence of bullshit (OB, 33–34). What is worst, then, bullshitting or lying? Frankfurt thinks that the former is more seriously harmful, at least in the long run: Both in lying and in telling the truth people are guided by their beliefs concerning the way things are. These guide them as they endeavor either to describe the world correctly or to describe it deceitfully. For this reason, telling lies does not tend to unfit a person for telling the truth in the same way that bullshitting tends to. Through excessive indulgence in the latter activity, which involves making assertions without paying attention to anything except what it suits one to say, a person’s normal habit of attending to the ways things are may become attenuated or lost. (OB, 60) The bullshitter, Frankfurt speculates, gradually becomes a victim of her own humbug: By allowing her reporting to be systematically influenced by ulterior motives she gradually becomes unreliable in her private believing, which makes her unfit to tell the truth. At any rate, the activity of lying, by contrast, is conceptually impossible in the absence of a genuine concern for the truth. By definition, a person cannot lie without believing that there is a truth that is elsewhere to be found. There is no reason to believe, therefore, that lying should corrupt its practitioner’s epistemic character in a way similar to how bullshitting allegedly does. For this reason, “bullshit is a greater enemy of truth than lies are” (OB, 61). For essentially the same reason why bullshitting is harmful to the individual, “bullshitting constitutes a more insidious threat than lying does to the conduct of civilized society” (OT, 4–5). Consequently, “whatever benefits and rewards it may sometimes be possible to attain by bullshitting, by dissembling, or through sheer mendacity, societies cannot afford to tolerate anyone or anything that fosters a slovenly indifference to the distinction between true and false” (OT, 33). For “[i]f people were generally dishonest and untrustworthy, the very possibility of productive social life would be threatened” (OT, 69). Now we cannot help observing—Frankfurt thinks—that our society happens to be one in which deception, in all its shapes and forms, is extremely common:

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After all, the amount of lying and misrepresentation of all kinds that actually goes on in the world (of which the immeasurable flood of bullshit is itself no more than a fractional part) is enormous . . . (OT, 71–72). As Frankfurt sees it, then, the “extraordinary prevalence and persistence of bullshit in our culture” (OT, 4) is a fact that cannot be so easily dismissed. And yet, it is also an undeniable fact that our Western society is an advanced culture that is in many ways prospering—materially as well as culturally and intellectually. But if so, it follows from what we have said before that our society must be characterized by its members knowing collectively a great many truths. So apparently, it is possible after all for the members of a society to share knowledge of many truths in spite of the fact that that very society is also being massively infected by various forms of deception. But how can this be? After all, we have just learned that widespread deception and bullshit constitute a serious threat to our common quest for truth. A schematic summary of this train of thought might be useful at this point: (i) A society must in order to prosper be founded on large quantities of truths that are generally known by its members. (ii) Massive amounts of bullshit and deception, more generally, preclude large quantities of truths from being generally known. (iii) Our society is seriously infected with bullshit and deception. (iv) Hence, in our society at most only a few truths can be generally known (by (ii) and (iii)). (v) Hence, our society does not prosper (by (i) and (iv)). (vi) But our society does prosper. (vii) Contradiction (by (v) and (vi)). Let us agree to call the problem to which this piece of reasoning gives rise “Frankfurt’s Puzzle.” Frankfurt is not insensitive to the fact that he has reasoned himself into a corner: We are all aware that our society perennially sustains enormous infusions— some deliberate, some merely incidental—of bullshit, lies, and other forms of misrepresentation and deceit. It is apparent, however, that this burden has somehow failed—at least, so far—to cripple our civilization. (OT, 7) Postmodernists and relativists in general could happily take Frankfurt’s puzzle as a reductio of the view that truth is at all important. Unsurprisingly, that reaction to the puzzle is passionately dismissed in On Truth: Some people may perhaps take this complacently to show that truth is not so important after all, and that there is no particularly strong reason for us to care about it. In my view, that would be a deplorable mistake. (OT, 6–7)

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Instead Frankfurt proposes to avoid the paradox by, in effect, restricting the scope of the second premise. Bullshit prohibits the truth from being known, unless, that is, people are generally good at detecting signs of fraud: We can successfully find our way through an environment of falsehood and fraud, as long as we can reasonably count on our own ability to discriminate reliably between instances in which people are misrepresenting things to us and instances in which they are dealing with us straight. (OT, 72) In other words, Frankfurt’s answer to the question of how a thriving society is possible despite extensive bullshitting is that we—its members—are, or must be, generally good at detecting signs of deception. This optimistic proposal, however, is apparently withdrawn one page later (OT, 73): To be sure, we are rather easily fooled. Moreover, we know this to be the case. So it is not very easy for us to acquire and sustain a secure and justifiable trust in our ability to spot attempts at deception. For this reason, social intercourse would indeed be severely burdened by a widespread and wanton disrespect for truth. If we are rather easily fooled and know this to be the case, we cannot after all to any great extent discriminate reliably between instances in which people are misrepresenting things to us instances in which they are dealing with us straight. In the end, therefore, Frankfurt provides no compelling explanation of how our society can prosper and at the same time be an arena for widespread deception and fraud, leaving us with no compelling solution to the puzzle that he has framed. Is there any other solution to Frankfurt’s puzzle? One assumption I will not question is that our Western society is indeed flourishing. It is certainly characterized by immense artistic and intellectual activity, modern science being among its most striking achievements. But what about the claim that a thriving society needs to be founded on truths that are generally known? To be sure, examples of prospering societies founded on bullshit and lies do not come readily to mind, but one may still question the claim that the truths have to be known by all or even most members for the society in question to prosper. Perhaps it is sufficient for that purpose that there is an enlightened minority of people firmly in tune with the facts of the matter, especially if they are in political power. In many Western countries, those occupying higher offices are generally either knowledgeable themselves or, more importantly, have access to expert groups that are.9 The fact that there exist simultaneously various subcultures—scientologists, astrologists, religious sects, and so on—the members of which entertain beliefs that are in serious error does not threaten the prospects of material and intellectual wealth so long as those groups are small enough not to influence general elections. 9. I believe this to be true of most of the old European democracies. The U.S. under George W. Bush is a more complex case.

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The contention that our society is subject to extensive bullshitting could also be questioned, especially if it is taken to imply that the misinformation is evenly distributed. In reality, some areas of social life are more affected than others. The Internet is known not only for housing massive amounts of valuable data but also for providing a venue for dishonesty and sham. Science, by contrast, though by no means immune to fraud, contains mechanisms that at least seriously reduce its vulnerability in this regard. Finally, there may be other reasons than those tentatively put forward by Frankfurt for dismissing the thought that widespread deceptive activity necessarily undermines the prospect of society converging on the truth. In the next section I will consider recent work in social epistemology suggesting that a society may thus converge even if only a fraction of its members are successful truth seekers and truth tellers, none of whom is capable of detecting signs of deception. 4. A SOCIAL EPISTEMOLOGY PERSPECTIVE The problem of finding conditions under which the beliefs of the members of society converge on one and the same opinion has attracted attention in social epistemology. While a lot of work has been done in this area over the years,10 the special case troubling Frankfurt—concerning the prospects of a communal convergence on the truth in an environment of extensive bullshitting—has, to my knowledge, been investigated only recently. A directly relevant work is Hegselmann and Krause’s 2006 paper “Truth and Cognitive Division of Labour: First Steps towards a Computer Aided Social Epistemology,” which assesses the chances for the truth to be found and broadly accepted under conditions of what the author refer to as “cognitive division of labor” combined with a social process in which information is exchanged between the individual inquirers. By cognitive labor is meant that only some individuals are successful truth seekers as well as truth tellers. The rest are unreliable in the way they form beliefs, which makes them also, in Frankfurt’s words, unfit for telling the truth. Being unreliable as informants, they are bullshitters in one sense of that word, even though they are not necessarily intentionally bullshitting. The social process consists in a mutual exchange of opinions between all individuals, truth seekers or not. H&K study this setting both mathematically and by means of computer simulations using an iterative procedure. Fortunately, we need not go into much of the mathematical details. It suffices, for our philosophical purposes, to get a reasonably firm grasp of the main ideas and the results that follow. One assumption is that each individual starts out with a certain opinion that is taken to be arbitrarily chosen. For definiteness, we may think of it as a real number between zero and one representing some quantity that is being assessed, for example, the robustness 10. The best-known work in philosophy is probably Keith Lehrer and Carl G. Wagner’s Rational Consensus in Science and Society from 1981. More recent work include Galam and Moscovici (1991), Friedkin and Johnsen (1990), Nowak et al. (1990), Deffuant et al. (2000), SznajdWeron and Sznajd (2000), Stauffer (2004), and Lorenz (2005).

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factor in our previous engineering example. The opinions are then assumed to be made public for all to see upon which each individual updates his or her opinion based on the opinions of the others. At this point it is assumed, not unrealistically, that a given individual takes into account only the other opinions that are, from her point of view, not too exotic. In other words, a given individual bases her new opinion on (1) her own old opinion; and (2) those opinions that are within a certain distance e from her own old opinion, where the number e is referred to as the “confidence level.” To be specific, the individual suspends judgment, as it were, between these views by taking on a new view corresponding to their average value. How does truth enter into the picture? H&K assume that there is a true opinion, T, in the space of possible opinions that may be capable of “attracting” individuals in the sense that they have a tendency to approach it, perhaps because they are using rational argumentation, reasonable thinking, sound experimental procedures et cetera. Thus, H&K—wisely, I believe—choose to abstract from the qualitative nature of the methods of inquiry, focusing instead on their quantitative reliability. There is in this model an objective as well as a social component determining the opinion of a given individual. Objectivity is, as we just saw, captured by the degree to which a given individual is attracted to the truth. The social component amounts to specifying how much weight the individual assigns to the opinions of her “peers.” It is helpful to take a quick look at the main equation to which these considerations give rise: ( HK ) x i ( t + 1) = α i T + ( 1 − α i ) fi ( x ( t )) , with 1 ≤ i ≤ n

where xi(t + 1) is the new opinion of the i:th individual, ai the degree to which that individual is attracted to the truth and 1 - ai the degree to which her opinion is socially determined. Setting ai > 0 means that the i:th individual is to some extent attracted to the truth. Setting ai = 0 means that there is no direct connect between her opinion and the truth but that her new opinion is rather the mere product of her own previous one and the opinions of her peers. Cognitive division of labor, in H&K’s sense, results when only some individuals have ai > 0. H&K take care to point out that none of this should be taken to imply any conscious deliberative activity on the part of the individuals. In that sense, the equation assumes a reliabilist-externalist as opposed to an internalist perspective on inquiry. Setting ai = 0 turns the i:th individual into a kind of bullshitter, albeit one that is sensitive to social facts. Although the behavior of such an individual reflects a lack of concern with truth, she still adapts her own opinion to the views of her peers. An asocial bullshitter may be obtained as a special case by setting the confidence level equal to 0, meaning that she judges her own old belief to be the sole opinion worthy of serious consideration. Applying Peirce’s Method of Tenacity,11 an asocial bullshitter will simply stick to her own arbitrarily chosen initial position come what may.

11. See Peirce (1877).

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H&K proceed to conduct their computer simulations with amusing and occasionally unexpected results. Let us start with the case where none of the individuals is a truth seeker, and where the confidence level of each individual is fairly low so that only a few other opinions are taken into account. In other words, each individual is essentially applying the Method of Tenacity just alluded to. What will happen when the main equation is used repeatedly to update the opinions of the individuals is that a number of clusters are eventually formed consisting of individuals sharing the same opinion, each cluster being out of reach of, and hence incapable of influencing, the others. The convergence of one of those clusters on the truth will of course be a purely random affair. H&R describe the result of their simulations as “an eternal plurality of divergent views.” (Fortunately, they choose not to draw any parallels to philosophical inquiry; that would have been discouraging.) Suppose we assume, to take the other extreme, that all individuals are truth seekers in the sense of being attracted to the truth, if ever so slightly, and that circumstances are otherwise the same. Then what will happen is that there will be the same initial tendency for clusters to be formed, but these clusters will now, as the updating process continues, gradually approach the truth (and hence also each other), though they may not get to there in finite time. These extreme scenarios still do not represent a case of cognitive division of labor. For such a case to arise some individuals have to be truth seekers and others not. The perhaps most important question, for our purposes, is whether or not many individuals have to be truth seekers in order for society as a whole to converge on the truth. Interestingly, the answer to this question is in the negative. H&K provide an example where fifty percent of the individuals are slightly attracted to the truth and where all others are social bullshitters. The result after some initial clustering is that the social exchange process finally leads to a consensus that is at least fairly close to the truth. This consensus includes the bullshitters who will, because of their social nature, become indirectly connected to the truth through the information they receive from reliable peers.12 Surprisingly, the position of the truth turns out to be of significance for this result. If the truth happens to be a more moderate position, this will increase the likelihood of communal convergence on the truth. If it happens to be an extreme position, the truth seekers will still converge on it, and so will some of the bullshitters whose views were not too distant from the truth to begin with. Nevertheless, there will be an increased tendency for more distant bullshitters to form their own cluster far away from the truth. The result will be a split society where a minority of bullshitters have been left behind by the informed majority. Another unexpected result is that as truth seekers get better at their craft the chances of a communal convergence on the truth is reduced rather than—as one might have thought—increased. The effect is in fact easily explained. As the truth seekers become more attracted to the truth they will tend to approach the truth 12. In their example, H&K have made the individuals slightly more social compared with their previous simulation by raising the confidence level just a bit, thus extending the range of other opinions that are taken into account when a given individual forms a new opinion.

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more quickly. This also means that the likelihood decreases that they will influence a given social bullshitter. The effect will be a polarized society with a majority converging on the truth and one or more minorities approaching opinions distant from the truth. This will be so even if the truth happens to be a moderate view. The situation can be improved upon by making the bullshitters more social, that is, by raising the confidence level of the individuals so that more opinions are seriously considered. Just as a fisherman can increase his chances of catching a fish by increasing the size of his net, so too a bullshitter can increase his chances of connecting to a truth seeker by extending the range of views that he takes into account in forming his new opinion. What drives many of these results is the fact that a bullshitter, while by definition lacking any direct connection to the truth, may become indirectly connected to it through a social exchange process. In our case, the social process dictates (1) that one should pay attention at least to views sufficiently similar to one’s own; and (2) that one should “average” in the case of disagreement. These two social principles combine into the dictum to average in the face of peer disagreement. As H&K are the first to admit, their model can be criticized from a number of perspectives as being simplistic and unrealistic. It assumed, for instance, that all individuals have access to the current opinions of all the others. What if the social exchange process has a network structure involving primarily local informational exchange? Moreover, averaging over the views of one’s peers makes clear sense only in settings where the task is to assess the value of a quantitative variable. In many other contexts averaging has no clear meaning. Even when averaging does make sense, there are other ways of taking the views of one’s peers into account, for example by taking the median value rather than the average value. Another potential shortcoming of the model is that it does not accommodate the distinction between unreliable beliefs and unreliable reports. H&K assume that once an individual is reliable in her belief formation, she is also reliable in her reporting. The typical case of bullshitting would rather be one in which a reliable inquirer decides to report in an irresponsible and unreliable manner. Frankfurt’s corruption of character hypothesis, which we encountered in section 3, makes sense only on the more complex model. Only on that model can the fact that you consistently decide to report unreliably gradually lower your reliability as a believer. But I strongly suspect that the main philosophical point that can be extracted from H&K’s work is still valid: There may be informational exchange process which, combined with the social pressure to average among peers, compensates for the fact that a part of the population lacks direct contact with reality by ensuring that that part nevertheless enjoys an indirect access to the way things are via the beliefs and reports of reliable peers, whose views they are forced to take into account. None of this assumes any special ability on the part of the individual inquirers to detect signs of fraud. Pace Frankfurt, communal convergence on the truth does not require that “we can reasonably count on out own ability to discriminate reliably between instances in which people are misrepresenting things to use and instances in which they are dealing with us straight” (OT, 72).13 13. I wish to thank Mikael Janvid and Stefan Schubert for their comments on an earlier draft.

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Armstrong, D. M. 1973. Belief, Truth and Knowledge. Cambridge, England: Cambridge University Press. Deffuant, G., Neau, D., Amblard, F., and Wesibuch, G. 2000. “Mixing Beliefs Among Interacting Agents.” Advances in Complex Systems 3: 87–98. Frankfurt, H. G. 2005. On Bullshit. Princeton, NJ: Princeton University Press. ———. 2006. On Truth. New York: Alfred A. Knopf. Friedkin, N. E., and Johnsen, E. C. 1990. “Social Influence and Opinions.” Journal of Mathematical Sociology 15: 193–206. Galam, S., and Moscovici, S. 1991. “Towards a Theory of Collective Phenomena: Consensus and Attitude Changes in Groups.” European Journal of Social Psychology 21: 49–74. Goldman, A. I. 1976. “Discrimination and Perceptual Knowledge.” The Journal of Philosophy 73: 771–91. ———. 1986. Epistemology and Cognition. Cambridge, MA: Harvard University Press. Goldman, A. I., and Olsson, E. J. (in press). “Reliabilism and the Value of Knowledge.” In Epistemic Value, ed. Pritchard, D. et al. Oxford: Oxford University Press. Hegselmann, R., and Krause, U. 2006. “Truth and Cognitive Division of Labour: First Steps Towards a Computer Aided Social Epistemology.” Journal of Artificial Societies and Social Simulation 9 (3). Jones, W. E. 1997. “Why Do We Value Knowledge?” American Philosophical Quarterly 34, No. 4, October: 423–39. Kvanvig, J. L. 2003. The Value of Knowledge and The Pursuit Of Understanding. New York: Cambridge University Press. Lehrer, K., and Wagner, C. G. 1981. Rational Consensus in Science and Society. Dordrecht: Reidel. Lorenz, J. 2005. “A Stabilization Theorem for Dynamics of Continuous Opinions.” Physica A 335(1): 219–23. Nowak, A., Szamrez, J., and Latane, B. 1990. “From Private Attitude to Public Opinion: Dynamic Theory of Social Impact.” Psychological Review 97: 362–76. Olsson, E. J. 2007. “Reliabilism, Stability, and the Value of Knowledge.” American Philosophical Quarterly 44(4): 343–55. Peirce, C. S. 1877. “The Fixation of Belief.” Reprinted in Philosophical Writings of Peirce, ed. Buchler, J., 5–22. Dover: New York, 1955. Pritchard, D. 2007. “Recent Work on Epistemic Value.” American Philosophical Quarterly 44: 85–110. Riggs, W. D. 2002. “Reliability and the Value of Knowledge.” Philosophy and Phenomenological Research 44: 79–96. Sosa, E. 2003. “The Place of Truth in Epistemology.” In Intellectual Virtue: Perspectives from Ethics and Epistemology, ed. M. DePaul and L. Zagzebski, 155–179. Oxford: Oxford University Press. Stauffer, D. 2004. “Difficulty for Consensus in simultaneous Opinion Formation of Sznajd Model.” Journal of Mathematical Sociology 28: 25–33. Swinburne, R. 1998. Providence and the Problem of Evil. Oxford: Oxford University Press. Sznajd-Weron, K., and Sznajd, J. 2000. “Opinion Evolution in Closed Community.” International Journal of Modern Physics C 11: 1157–66. Williamson, T. 2000. Knowledge and Its Limits. Oxford: Oxford University Press. Zagzebski, L. 2003. “The Search for The Source of Epistemic Good.” Metaphilosophy 35(1/2): 13–28.

Midwest Studies in Philosophy, XXXII (2008)

Pragmatism on Solidarity, Bullshit, and other Deformities of Truth CHERYL MISAK

1. INTRODUCTION The pragmatist offers an account of truth on which truth is linked to human inquiry. The received view in analytic philosophy is that it fails quite dismally. The received view is that pragmatism fails to latch on to the concept of truth, speaking rather of some deformed version of it. The pragmatist, that is, delivers not an account of truth, but an account of warranted assertibility, agreement within a community, rational belief, or some such thing. While these phenomena might be of great interest to epistemologists and to ordinary human beings, they are not of much interest to analytic truth theorists. The received view is nicely captured by Paul Horwich. He thinks that “truth has a certain purity.” Hence, our understanding of it must be kept independent of the ideas of verification, success, and the like (1990, 12). His deflationist view has it that there is nothing more to the notion of truth than the infinite instances of the schema: “ ‘p’ is true if and only if p.” Since the whole point of pragmatism is to link the concept of truth to human inquiry (to verification, success, and the like), the pragmatist and the analytic truth theorist would seem to be in permanent and irreconcilable tension. In what follows, I shall suggest that this is not the most helpful way of understanding the relationship between contemporary deflationist views of truth and pragmatism. The founder of pragmatism, Charles Sanders Peirce, was a resolutely analytic philosopher, who never tired of chiding his good friend William James and the other Harvard philosophers about their poor training in formal logic Midwest Studies in Philosophy: Truth and its Deformities Volume XXXII Editor by Peter A. French and Howard K. Wettstein © 2008 Wiley Periodicals, Inc. ISBN: 978-1-405-19145-6

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and their lack of rigorous thinking. It might well be that the theories of truth offered by James and his follower Richard Rorty1 are best described as theories not of truth but of something else. But when we look at Peirce’s theory of truth, we shall see that he was sensitive to the kind of point that Horwich makes about the purity of the concept of truth. And we shall see that he offered the makings of an argument about how to close the gap between the deflationism and pragmatism. Once I show how pragmatism need not offer a theory of a deformity of truth, I will shift my focus to the question of how the pragmatist might think about some phenomena that become prominent when one thinks about the deformities of truth—lying and the recently popular topic of bullshitting. We will see that in managing the issues that arise here, Peircean pragmatism again has distinct advantages over Jamesian/Rortyian pragmatism. 2. THE JAMESIAN/RORTYIAN PRAGMATIST ACCOUNT OF TRUTH A debate has raged within pragmatism, from its very inception in the mid 1880s through to today, about how best to conceive of truth.2 On one side of the divide we have William James, John Dewey, and Richard Rorty who take truth to be connected to the products of actual human inquiry. These pragmatists think of truth as roughly what works for us ( James); what it is found to be warranted (Dewey); or what is agreed upon among members of our community (Rorty). Here is James: Any idea upon which we can ride . . . any idea that will carry us prosperously from any one part of our experience to any other part, linking things satisfactorily, working securely, simplifying, saving labor, is . . . true instrumentally. (1907/1949, 58) “Satisfactorily,” for James, “means more satisfactorily to ourselves, and individuals will emphasize their points of satisfaction differently.To a certain degree, therefore, everything here is plastic” (1907/1949, 61). James tends to put forward this view as a view of truth itself—as what we would now call a reductive definition of truth. Truth is an idea upon which we can ride; it is what satisfies us. Horwich’s kind of argument about the purity of truth arose very early in the history of pragmatism. Paul Carus in his 1911 Truth on Trial argues that James replaces the belief in the stability of truth, in its persistence and eternality with a more elastic kind of truth which can change with the fashions and makes it possible 1. Rorty says that his narratives about pragmatism “tend to center around James’s version (or, at least, certain selected versions out of the many that James casually tossed off) of the pragmatic theory of truth” (Rorty 1995, 71). 2. What follows is a potted history. For a more nuanced, supported, and careful account, see Misak (in press) and Misak (forthcoming). Were I to bring Dewey fully into this picture, I would align him with Rorty, in linking not truth, but its stand-in (warranted assertibility) to the actual products of inquiry.

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that we need no longer trouble about inconsistencies; for what is true to one need no longer be true to others, and the truth of to-day may the real now, and yet it may become the error of the to-morrow. (1911, 110) The point, of course, is that this more elastic kind of truth is not truth at all. G. E. Moore and Bertrand Russell3 leveled similar objections against James. It is an anathema, they point out, to think that truth, like usefulness, is a property that may come and go. It is an anathema to think that a belief, which might be held at many different times, may be true at some of those times and false at others. Whatever property James is identifying, it is not the property of truth. These are good objections. And they have stuck to pragmatism ever since they were made, despite the fact that James may be the lone pragmatist who identifies truth with what works.4 At times Rorty can be found saying with James that truth just is solidarity or what is agreed upon in the community. His more considered view is that we need to abandon the idea of truth; that is, more often than not, he takes a non-Jamesian approach to what it is that he is identifying. He holds that the account on offer from the pragmatist is not an account of truth at all, since an account of truth, as it is usually conceived, is not possible. We need to cease thinking of the mind as a great mirror which holds representations of the world. Once we abandon this account of truth, we will want to focus on beliefs that serve us well. What we aim at is not truth, but solidarity or what our peers will let us get away with saying (1979, 176). That is, in the gap left when one gives up on a theory of truth, Rorty offers an account of the best we human inquirers can do. We cannot get the truth, but we can get what works for us, what is warranted, or what we agree upon. We can get solidarity. The way that Rorty gets to this conclusion is by examining our practices of inquiry. What he finds is that the concept of what he calls Capital-T Truth plays no role in inquiry whatsoever. He concludes that philosophers should stop trying to think about the idea of truth: Truth is “not the sort of thing one should expect to have an interesting philosophical theory about” (1982, xiii). The yearning for an unconditional, impossible, indefinable, sublime thing like truth comes at the price of “irrelevance to practice” (2000, 2). Inquirers simply do not aim at that sort of thing. Since there is no practical difference between aiming to hold True beliefs and aiming to hold beliefs that will stand up in our community, it makes no sense to speak of Truth as a goal of inquiry. The inquirer can not try to compare her beliefs with reality—she can only try to live up to her epistemic responsibilities or the standards of her epistemic community. Rorty, that is, seems to agree with the purity theorist that pragmatism is not a theory of truth, but a theory of something else. Indeed, Rorty eventually came to the view that the purity theorist was right in thinking that the deflationary theory 3. See Russell and Moore in Olin (1992). 4. Even here one will find many James scholars and James himself arguing that he did not intend to make this identification. See, for instance, James (1909/1914: xv, 180).

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was uninteresting enough and that it captured all that we could say about truth. But not many deflationists have gone on to agree with him that once the deflationary view is accepted, we must see our inquiry and deliberations aiming only at agreement with our peers. That continues to strike a wrong note for the analytic truth theorist. 3. THE PEIRCEAN ACCOUNT OF TRUTH On the other side of the debate over the heart and soul of pragmatism, we have the founder of pragmatism, Charles Peirce and his contemporary followers.5 This kind of pragmatist rejects theories of truth which unlink truth from inquiry, but is nonetheless committed to doing justice to the very idea of truth and to the objective dimension of human inquiry. The focus is on the fact that those engaged in deliberation and investigation take themselves to be aiming at the truth—at getting things right, at avoiding mistakes, and at improving their beliefs and theories. Truth is not linked to the actual products of human inquiry, but rather, to the products of human inquiry, were they to be the best they could be, opening up some distance between what is justified now and what would really be justified. Peirce argues that a true belief would be “indefeasible”; or would not be improved upon; or would never lead to disappointment; or would stand up to all the evidence and argument, no matter how far we were to pursue our inquiries. Although he is often taken to have held that a true belief is one that is fated to be believed at the end of inquiry, he on the whole tries to stay away from the unhelpful idea of the final end of inquiry and he never goes anywhere near the unhelpful ideas of perfect evidence and ideal inquiry. He starts off with the thought that we must look to the consequences of a concept like truth in order to fully understand it: We must not begin by talking of pure ideas—vagabond thoughts that tramp the public roads without any human habitation—but must begin with men and their conversation. (CP 8.1126) This is the pragmatic maxim. It asserts that in order to have a complete grasp of a concept, we must connect it to that with which we have “dealings” (CP 5.416). It is critical to see that in Peirce’s hands, the pragmatic maxim is not a semantic principle about the very meaning of our concepts. That is, it is not designed to capture a full account of meaning. He argued that the maxim captures an important aspect of what it is to understand something. Not only does one have to know how to give an analytic definition of a concept and know how to pick out instances of it, but one has to know what to expect if beliefs involving the concept are true or false. If a belief has no consequences—if there is nothing we would 5. See Putnam (1981), Stout (2007), Fine (2007), and Misak (1991/2004). 6. References to Peirce’s Collected Papers are in standard form: volume number, followed by paragraph number. MSx refers to the Peirce Papers, with X being the manuscript number. For full textual evidence that the following account of the pragmatic maxim is indeed Peirce’s view, see Misak (1991/2004): chap. 1.

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expect would be different if it were true or false—then it lacks a dimension we would have had to get right were we to fully understand it. Without that dimension, it is empty or useless for inquiry and deliberation. So Peirce thought that the pragmatic aspect of understanding is a rather important one, while being very clear that it is not the be-all-and-end-all. He says, with respect to the difference between analytic definition and pragmatism: I believe I made my own opinion quite clear to any attentive Reader, that the pragmaticistic grade of clearness could no more supersede the Definitiary or Analytic grade than this latter grade could supersede the first. That is to say, if the Maxim of Pragmaticism be acknowledged, although Definition can no longer be regarded as the supreme mode of clear Apprehension; yet it retains all the absolute importance it ever had, still remaining indispensable to all Exact Reasoning. (MS 647, p. 2) This is in 1910, after he has decided that others (mostly James) have abused his “bantling ‘pragmatism’ ” so severely that he is going to kiss it goodbye and introduce “the word ‘pragmaticism,’ which is ugly enough to be safe from kidnappers” (CP 5.414). When the pragmatic maxim is turned on the concept of truth, the upshot is an aversion to “transcendental” accounts of truth, such as the correspondence theory, on which a true belief is one that corresponds to, or gets right, or mirrors the believer-independent world (CP 5.572). Such accounts of truth are examples of those “vagabond thoughts.” They make truth the subject of empty metaphysics. The very idea of the believer-independent world, and the items within it to which beliefs or sentences might correspond, seem graspable only if we could somehow step outside of our corpus of belief, our practices, or that with which we have dealings. That is, this concept of truth is missing the dimension that makes it suitable for practice and inquiry. Peirce is perfectly happy with it as a “nominal” or “formal” definition, useful only to those who have never encountered the word before.7 If we want a more robust or full account of truth, we need to have an account of the role the concept plays in practical endeavors. We need to provide a pragmatic elucidation of the concept of truth as well as an analytic definition of it.8 So, anticipating recent moves in debates about truth, Peirce was very careful to stay away from a reductive definition of truth: He did not want to define truth as that which satisfies our aims in inquiry. A dispute about definition, he says, is usually a “profitless discussion” (CP 8.100) or a “folly” as Donald Davidson (1996) has said. David Wiggins sees Peirce’s point perfectly:9 7. MS 283, p. 39. 8. Of course, the issue will be whether Peirce’s pragmatic elucidation is compatible with his analytic definition. But since Peirce thinks that the latter has such limited use (it is useful only to those who need an introduction to the concept), it is clear that he will argue that the pragmatic elucidation is the thing we should be concerned with. 9. Sellars (1962, 29) seems to have seen it as well.

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To elucidate truth in its relations with the notion of inquiry, for instance, as the pragmatist does, need not . . . represent any concession at all to the idea that truth is itself an “epistemic notion.” (2002, 318) When a concept is, as Wiggins (2002, 316) puts it, “already fundamental to human thought and long since possessed of an autonomous interest,” it is pointless to try to define it. Rather, we ought to attempt to get leverage on the concept, or a fix on it, by exploring its connections with practice. This is the insight at the very heart of pragmatism. So the Peircean pragmatist is committed to thinking that our concept of truth can be illuminated by looking at the practices which are bound up with the concept of truth—inquiry, belief, assertion, and the like. Once we see, for instance, that truth and assertion are intimately connected—once we see that to assert that p is true is to assert p—we can look to our practices of assertion to see what commitments they entail. What Peirce finds when he looks at the linkages between truth and our practices of assertion is that the concept of truth is bound up with the concepts of reasons, evidence, experience, and inquiry. As Wiggins (2004) again so nicely puts it, hard on the heels of the thought that truth is internally related to assertion comes the thought that truth is also internally related to inquiry, reasons, evidence, and standards of good belief. If we unpack the commitments we incur when we assert, we find that we have imported all these notions. When we assert that p, we assert that p does and would continue to stand up to the reasons and evidence. Hence, when Peirce engages in the task that led to Rorty’s abandoning the concept of truth, he gets a very different result.When Peirce tries to get leverage on the concept of truth by examining its role in inquiry, he finds first that inquirers do indeed aim at truth. Inquirers aim at getting things right or at something that goes beyond the best that they can do here and now. Peirce and Rorty certainly agree about the correspondence theory of truth. Peirce takes one of the most pressing problems for the correspondence theorist to be that he fails to make the aim of inquiry “readily comprehensible” (CP 1.578). How could anyone aim for a truth that goes beyond experience or beyond the best that inquiry could do? How could an inquirer adopt a method that might achieve that aim? The correspondence theory makes truth “a useless word” and “having no use for this meaning of the word ‘truth,’ we had better use the word in another sense” (CP 5.553). What distinguishes the Peirce from the Rorty is that the former thinks that there is another perfectly good sense of the word “truth.” Today we might put his thought like this. In all domains of inquiry and deliberation, we distinguish between thinking we are right and being right, we criticize the beliefs and actions of others, and we think that we can improve our judgments, learn from our mistakes, etc. These distinctions and practices are quite literally dependent on the notion of truth—we can understand them only by supposing that we aim at the truth. Peirce’s argument against Rorty would be that he has an impoverished view of practice. As Jeffrey Stout puts it, “getting something right . . . turns out to be among the human interests that need to be taken into account” (2007, 18).

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It may already be clear that pragmatism, as expressed by Peirce, and deflationism, as expressed by some of the purity theorists, have much in common. They share the naturalist thought that there is an unseverable connection between making an assertion and claiming that it is true. What we do when we offer a justification of “p is true” is to offer a justification for the claim that p. If we want to know whether it is true that Toronto is north of Buffalo, there is nothing additional to check on (“a fact,” “a state of affairs”)—nothing over and above our consulting maps, driving or walking north from Buffalo to see whether we get to Toronto, etc. Inquiring about the truth of the statement does not involve anything more than investigating the matter in our usual ways. Pragmatism and deflationism share, that is, an aversion to empty metaphysics. The difference between the two positions is that Peirce would think that the purist’s quest to keep truth away from the ideas of verification, success, and the like is bound to result in an empty and useless account. The way to deflate truth—the way to make it less metaphysical—it is link truth to these down-to-earth notions, not to claim independence from them. The difference between Peirce’s view and the purist’s view is precisely the difference between Crispin Wright’s view and the purist’s view. Both think that although the deflationist offers a fine nominal definition of truth, more needs to be said. And both think, in Wright’s words, that what needs to be said is that truth is a special kind of warranted assertion: A statement is superassertible . . . if and only if it is, or can be, warranted and some warrant for it would survive arbitrarily close scrutiny of its pedigree and arbitrarily extensive increments to or other forms of improvement of our information. (1992, 48) The pragmatist (at least the pragmatist of the Peircean variety) and the analytic truth theorist are not as far apart as they first seemed to be. 4. GENUINE BELIEF AND DEFORMED BELIEF There is a long-standing interest among truth theorists in some phenomena associated with the concept of truth. Much of that interest has been in the phenomenon of lying, mostly due to issues involving the liar paradox. But recently there has been some attention paid to a related kind of speech—bullshitting—thanks to the reissue of Harry Frankfurt’s On Bullshit (2005). The liar, Frankfurt thinks, is more closely involved in the truth business than is the bullshitter. Of course, the liar has an aim other than truth—he aims to mislead the hearer of his utterance so that he can satisfy some end. But in order to do this, the liar is “inescapably concerned with truth-values” (Frankfurt 2005, 51). He must respond to the truth or pay close attention to it, for he believes that what he is saying is not true and he intends to utter those untruths. The concept of lying is thus very much parasitic on the concept of truth. The bullshitter, Frankfurt argues, ought to be distinguished from the liar. The bullshitter does not know that he is uttering falsehoods, with the intention to mislead. For the bullshitter does not care whether what he is saying is true or

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false—he is indifferent to how things really are (Frankfurt 2005, 34). “He does not care whether the things he says describe reality correctly. He just picks them out, or makes them up, to suit his purpose” (2005, 56). Like the liar, the bullshitter has strategic ends and it is those other ends that matter. Perhaps he wants others to think that he is clever or interesting. Perhaps he wants to impress by speaking colorfully or vivaciously (Frankfurt 2005, 31). So bullshitters and liars, with a strategic end explicitly or implicitly in view, represent themselves falsely as endeavoring to communicate the truth (2005, 54). It is just that one of them has to pay attention to what is true, whereas the other does not. Frankfurt distinguishes another kind of speech act—that found in a “bull session” or in “shooting the bull.” Here “participants try out various thoughts and attitudes in order to see how it feels to hear themselves saying such things and in order to discover how others respond, without its being assumed that they are committed to what they say” (2005, 36). The purpose is not to communicate beliefs, but to take an experimental approach to a subject matter. Participating in these bull sessions is not so bad, by Frankfurt’s lights, for there is no pretense at trying to communicate the truth. That is what he is dismayed by: those who do not respect the truth or who hold the truth in contempt. And here the liar comes out looking better than the bullshitter.At least the liar “assumes that there are indeed facts that are in some way both determinate and knowable” (2005, 61). The liar knows that there is a difference between getting things wrong and getting things right. One reason there is so much bullshit around these days, Frankfurt suggests, is that there is a rampant skepticism about our ability to have any access to reality. No doubt Frankfurt would place pragmatism among these dangerous “anti-realist doctrines.” Let’s take it for granted that Frankfurt’s main concern is legitimate—that bullshitting is a common and unwelcome phenomenon and that bullshitters are encouraged by anti-realist views of truth. The more interesting question for the epistemologist, I think, is whether there are epistemological, as well as moral, grounds for criticizing someone who discards the aim of truth. Why should we value truth for its own sake, rather than value it for some strategic end? Here a sharp query is indeed raised for the Jamesian/Rortyian pragmatist, who seems to say that it does not make sense to talk about “truth for its own sake.” We value truths insofar as they contribute to the satisfaction of our aims. The question is how this kind of pragmatist can possibly distinguish between the strategic ends of the liar and bullshitter, on the one hand, and the presumably better ends of the scientist and honest deliberator on the other. How can the pragmatist maintain that the aims of understanding the world, predicting the future course of experience, and the like are better than the aims of getting agreement in the community, making me feel comfortable, or even making me look clever and interesting? James and Rorty seem determined to turn their backs on this question. James infamously argues in “The Will to Believe” (1897/1979) that if the belief in God makes a satisfactory impact on my life, then I can take it to be true. For James,

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non-epistemic criteria, such as making one more comfortable or making one’s life more harmonious, seem to be relevant to belief acceptance and to truth. The Jamesian pragmatist seems to be exactly the sort of person Frankfurt has in his sights on—someone who is not concerned about whether or not his belief is true in the sense of really getting things right. Indeed, as soon as James started publishing on the issues, this was the charge laid against him. Here is J. B. Pratt in 1909, taking on James view that religious hypotheses can be believed to be true if so believing would be good for one: Pragmatism . . . seeks to prove the truth of religion by its good and satisfactory consequences. Here, however, a distinction must be made; namely between the “good,” harmonious, and logically confirmatory consequences of religious concepts as such, and the good and pleasant consequences which come from believing these concepts. It is one thing to say a belief is true because the logical consequences that flow from it fit in harmoniously with our otherwise grounded knowledge; and quite another to call it true because it is pleasant to believe. (1909, 186–87) The difference between the views of Peirce and James can be nicely summarized by Pratt’s distinction. Peirce, with two important caveats, holds that “a belief is true because the logical consequences that flow from it fit in harmoniously with our otherwise grounded knowledge” and James seems to hold that a belief is true “because it is pleasant to believe” (1897/1979) One of the caveats with respect to Peirce’s view is that, as we have seen, he insisted that he was not giving a reductive definition of truth.The other is that he insisted on a subjunctive formulation:A true belief is such that the logical consequences would fit harmoniously with our otherwise grounded knowledge, were we to pursue our investigations as far as they could fruitfully go. Peirce did not shy away from the kind of question prompted by Frankfurt’s analysis of bullshit. He argued that the pragmatist can justify the aims of understanding the world, predicting the future course of experience, and the like over the aims of getting agreement in the community, making one feel comfortable, and making one look clever and interesting. He was one of those who reacted strenuously to James’ view: “I thought your Will to Believe was a very exaggerated utterance, such as injures a serious man very much.”10 The aims of science, Peirce thought, clearly trump the aims that James put forward. In a nutshell, his argument is that we have no choice but to pay attention to the course of experience, which gives us indexical connection to the real world. Experience impinges upon us, forcing us to take it seriously. And when we do take it seriously, we find that it tends not to lead us astray.11 Hence, the method of science, which has experience and observation at its core, is the method we ought to adopt. These are epistemic reasons for discriminating between the different aims 10. Quoted in Perry (1948, 291). 11. For the sustained argument, see Misak (1991/2004), chap. 2.

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we might have. These are epistemic reasons for preferring the aims of the scientist or the honest inquirer over those of the liar or bullshitter. The Peircean pragmatist, that is, is not the “anti-realist” Frankfurt is set against. The Peircean pragmatist thinks that in engaging in the practices of believing, asserting, and acting in the world, we presume that there is a way the world is and that we are trying to articulate how it is. We cannot hope to get this exactly right, as if we could have access to the way the world is independently of our ways of trying to find out about it. But that does not toss us into a sea of conflicting aims and values, with no way of adjudicating which are better than others. REFERENCES Carus, Paul. 1911. Truth on Trial: An Exposition of the Nature of Truth. Chicago: Open Court. Reprinted in Early Critics of Pragmatism, vol. 3, ed. John Shook, 1–143. Bristol, England: Thoemmes Press, 2001. Davidson, Donald. 1996. “The Folly of Trying to Define Truth.” Journal of Philosophy 87: 263–78. Fine, Arthur. 2007. “Relativism, Pragmatism, and the Practice of Science.” In New Pragmatists, ed. Cheryl Misak, 50–68. Oxford: Oxford University Press. Frankfurt, Harry. 2005. On Bullshit. Princeton, NJ: Princeton University Press. Horwich, Paul. 1990. Truth. Oxford: Basil Blackwell. James, William. 1897/1979. The Will to Believe and Other Essays in Popular Philosophy. In The Works of William James, vol. 6, ed. Frederick H. Burkhardt, Fredson Bowers, and Ignas K. Skrupskelis. Cambridge, MA: Harvard University Press. ———. 1907/1949. Pragmatism: A New Name for Some Old Ways of Thinking. New York: Longmans Green and Co. ———. 1909/1914. The Meaning of Truth: A Sequel to Pragmatism. New York: Longmans Green and Co. Misak, Cheryl. 1991/2004. Truth and the End of Inquiry: A Peircean Account of Truth, 2nd ed. Oxford: Oxford University Press, 2004. ———. In press. “The Reception of Early American Pragmatism.” In The Oxford Handbook of American Philosophy, ed. Cheryl Misak. Oxford: Oxford University Press. ———. Forthcoming. The American Pragmatists. Oxford: Oxford University Press. Moore, G. E. 1992. “Professor James’s Pragmatism.” In William James’s Pragmatism In Focus, ed. Doris Olin, 161–96. London: Routledge. Olin, Doris, ed. 1992. William James’ Pragmatism in Focus. London: Routledge. Peirce, Charles Sanders. 1931–35, 1958. Collected Papers of Charles Sanders Peirce, i–iv, ed. C. Hartshorne and P. Weiss, 1931–35; vii–viii, ed. A. Burks, 1958. Cambridge, MA: Belknap Press. ———. Unpublished. Charles S. Peirce Papers. Houghton Library, Harvard University. Perry, Ralph Barton. 1948. The Thought and Character of William James. Cambridge, MA: Harvard University Press. Pratt, James B. 1909. What is Pragmatism? Reprinted in Early Critics of Pragmatism, vol. 1, ed. John Shook, 1–269. Bristol, England: Thoemmes Press, 2001. Putnam, Hilary. 1981. Reason, Truth and History. Cambridge, England: Cambridge University Press. Russell, Bertrand. 1992. “William James’s Conception of Truth.” in William James’s Pragmatism In Focus, ed. Doris Olin, 196–212. London: Routledge. Rorty, Richard. 1979. Philosophy and the Mirror of Nature. Princeton, NJ: Princeton University Press. ———. 1982. Consequences of Pragmatism (Essays 1972–80). Minneapolis: University of Minnesota Press. ———. 1995. “Response to Richard Bernstein.” In Rorty and Pragmatism: The Philosopher Responds to his Critics, ed. H.J. Saakamp, 68–72. Nashville, TN: Vanderbilt University Press.

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———. 2000.“Universality and Truth.” In Rorty and his Critics, ed. Robert Brandom, 1–30. Oxford: Oxford University Press. Sellars, Wilfrid. 1962. “Truth and Correspondence.” Journal of Philosophy, 59: 29–56. Stout, Jeffrey. 2007. “On Our Interest in Getting Things Right: Pragmatism without Narcissism.” In New Pragmatists, ed. Cheryl Misak, 7–32. Oxford: Oxford University Press. Wiggins, David. 2002. “An Indefinibilist cum Normative View of Truth and the Marks of Truth.” In What Is Truth? ed. R. Shantz, 316–33. Berlin: DeGruyter. ———. 2004. “Reflections on Inquiry and Truth arising from Peirce’s Method for the Fixation of Belief.” In The Cambridge Companion to Peirce, ed. Cheryl Misak, 87–126. Cambridge, England: Cambridge University Press. Wright, Crispin. 1992. Truth and Objectivity. Cambridge, MA: Harvard University Press.

Midwest Studies in Philosophy, XXXII (2008)

Alethic Pluralism, Logical Consequence and the Universality of Reason MICHAEL P. LYNCH

INTRODUCTION Much of the work in philosophy of language and metaphysics over the last century has been directed at the following puzzle. We judge radically distinct kinds of propositions to be true—ranging from morality to mathematics to art—and yet, when we look around the world for the objects and properties that could make many such judgments true, we find ourselves at a loss. Put another way, for many of the judgments we make, there appears to be no facts in the natural world that could make them true. As a consequence, many a philosopher has concluded that the troublesome sorts of judgments—no matter how commonly made in daily life— simply are not true, either because they are all false, or because they were not really in the game of truth or falsity in the first place. A more recent, and increasingly popular, response to this puzzle rejects one of its principal assumptions; namely, that if a judgment or its propositional content is going to be true, it must be true because it has some robust property— such as corresponding to the facts—that makes it true. Rather than signaling a special property that all and only true propositions have in common, the deflationist takes it that the concept of truth is a mere expressive device, useful for purposes of generalization and semantic ascent. Truth, or rather “true,” is an honorific that all propositions therefore compete for equally. Since there is no special property in which being true consists, there is no special problem of trying to figure out whether all kinds of propositions can have it. The puzzle goes away. Midwest Studies in Philosophy: Truth and its Deformities Volume XXXII Editor by Peter A. French and Howard K. Wettstein © 2008 Wiley Periodicals, Inc. ISBN: 978-1-405-19145-6

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The deflationist picture is extremely attractive. But it comes at a price. That price is that it removes truth from our explanatory toolkit. If the deflationist is right, we are barred from appealing to truth and its nature to help explain other items of philosophical interest: meaning, content determination, knowledge, the norms of belief, and so on. And that may well give one pause. These latter items are difficult enough to understand without barring ourselves in advance from appealing to some of the more obvious tools at our disposal. Over the last few decades, a new response to our puzzle has begun to appear. It offers something of a middle road past deflationism and traditional theories of truth. It is the view, roughly, that propositions can be true in different ways. Ethical propositions might be true, for example, in a very different way than the propositions about the middle-sized dry goods of our daily life. The correspondence theory of truth, in other words, need not be the only true theory of truth. In some domains, truth may amount to something closer to coherence. Crispin Wright, its earliest advocate, initially put the suggestion this way: The proposal is simply that any predicate that exhibits certain very general features qualifies, just on that account, as a truth predicate. That is quite consistent with acknowledging that there may, perhaps must be more to say about the content of any predicate that does have these features. But it also consistent with acknowledging that there is a prospect of pluralism—that the more there is to say may well vary from discourse to discourse.1 Wright’s suggestion is now known as alethic pluralism. Like the deflationist, the pluralist takes it that the essential features of truth are given by certain platitudes. Moreover, both views reject the assumption that gets the above puzzle going, namely that if judgments are true, they must be true by corresponding to some mind-independent facts. As such, both views buy truth aptness for normative and mathematical judgments on the cheap. But unlike the deflationist, the pluralist thinks there are some nontrivial things to say about truth in different areas of inquiry (or discourses, as Wright puts it). By saying as much, the pluralist looks to preserve the idea that truth remains a substantive matter for philosophical research. The thought is that its plural nature can help us answer other important questions, such as, to cite one example, why the content of normative judgments differs in kind from the content of more descriptive judgments. I believe that this combination of virtues is good reason to take alethic pluralism seriously. But theories cannot live on promise alone. Since its inception, alethic pluralism has faced a family of apparently crippling problems. These problems all revolve around the fact that we reason across domains of inquiry. Reason, by its nature, is universal in its scope—it allows us to combine propositions from different domains into more complex propositions, and to make inferences across different subjects—as when we draw moral conclusions from partly nonmoral premises. But the very universality of reason raises an obvious question for the 1. Crispin Wright, Truth and Objectivity (Cambridge, MA: Harvard University Press, 1992), 38.

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pluralist. If what it is to be true varies across domains, how can reason universally apply in every domain? If alethic pluralism is correct, how are we to understand the scope of reason? I will argue that pluralists can answer this question. Or, at any rate, I think that a view which has all the advantages of pluralism can answer it. But I also think the problem is more difficult to solve than some—including my prior self—have believed. For the problem forces the pluralist to confront the possibility that their view may imply a type of logical pluralism as well. The paper is divided into three sections. In the first, I say something about the problems facing alethic pluralism which concern how we reason across domains. In the second, I sketch a pluralist-friendly position—which I have developed at greater length elsewhere—which seems to initially avoid these problems. In the third, I reveal how these problems return and implicate the truth pluralist as a pluralist twice over. MIXED INFERENCES AND MIXED COMPOUNDS Pluralism’s problem with the universality of reason has several faces. The two most striking concern so-called mixed inferences and mixed compounds.2 Since they pose the most obvious threat for what I will call simple alethic pluralism (SAP), it will be helpful to consider them in that context first. Simple alethic pluralism is the view that “true” is ambiguous in the way that “bank” is ambiguous. It has different meanings and therefore denotes distinct properties. In some domains of inquiry, it picks out one of the traditionally cited properties while in other domains it picks out a different property. Thus, when the subject matter is the middle-sized dry goods of everyday life, the SAP theorist might say the truth predicate ascribes the property of corresponding to the facts simply because on those domains “true” means “corresponding to fact.” In other domains, “truth” would denote, and “true” would ascribe a different property because the predicate would have, in those domains, a very different meaning. What other meaning? Let us pause briefly to consider an example of another property a pluralist might take as ascribed by “true”: what I will call superwarrant.3 The proposition that p is superwarranted just when it is warranted without defeat at some stage of inquiry and would remain so at every successive stage of inquiry. A stage of inquiry is a state of information; it is always open to extension, and potentially incomplete: At any particular stage of inquiry, we may have no warrant 2. See C. Tappolet, “Mixed Inferences: A Problem for Pluralism about Truth Predicates,” Analysis 57 (1997): 209–10; JC Beall, “On Mixed Inferences and Pluralism About Truth Predicates,” The Philosophical Quarterly 50 (2000): 380–82; M. Sainsbury “Crispin Wright: Truth and Objectivity,” Philosophy and Phenemological Research 56 (1996): 899–904; Lynch, Truth in Context (Cambridge, MA: MIT Press, 1998), chap. 5, and “A Functionalist Theory of Truth,” in The Nature of Truth, ed. M. Lynch (Cambridge, MA: MIT Press, 2001), 723–50; J. Dodd, “Recent Work on Truth,” Philosophical Books 43 (2002): 279–91; N. Pedersen, “What Can the Problem of Mixed Inferences Teach us About Alethic Pluralism?” The Monist 89, no. 1 (2006): 103–17; D. Edwards, “How to Solve the Problem of Mixed Conjunctions,” Analysis 68, no. 2 (2008): 143–49. 3. See Wright, Truth and Objectivity.

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for a proposition and no warrant for its negation. A belief is warranted without defeat at a stage of inquiry as long as any defeater for the belief at a given stage is itself undermined by evidence available at a later stage. In a sentence: To be superwarranted is to be continually warranted without defeat. So according to the SAP, “true” might just mean “corresponding to fact” in some domains of inquiry, and “superwarranted” in others. Many critics of pluralism have taken this to be what CrispinWright was advocating—and indeed, Wright’s early talk of different “truth predicates” suggested this.4 In any event, and whether or not Wright ever advocated the view, SAP is deeply implausible. According to a standard way of understanding validity, validity preserves truth. That is, a valid argument is one where if the premises are true, the conclusion must be true. Now consider the argument that If you hold a prisoner indefinitely and without charge, you violate his rights. This prisoner has been held indefinitely and without charge. Therefore, this prisoner’s rights have been violated. The second premise of this argument is a claim about the physical facts about a prisoner’s incarceration. The conclusion is a normative claim. Suppose “true” picks out different properties in these domains. If so, then it means something different to say that the second premise is true than to say that the conclusion is true. Consequently, there is no single property being preserved from premises to conclusion in this argument. As a result, the advocate of SAP must either explain validity in some less than standard way, or she must admit that there is a univocal concept of truth after all. A related problem concerns the truth of compound propositions. Consider the proposition that Murder is wrong and two and two make four. Intuitively, the conjuncts of this proposition are from very different domains. What explains, then, the truth of the conjunction itself? In response, the advocate of SAP may say: A conjunction is true just when its conjuncts are both true in some sense or other. Perhaps, but this reply begs the real question, which concerns not the conjuncts but rather the sense in which the conjunction itself is true. This is a problem not just for conjunctions but for the truth of disjunctions and conditionals as well.5 4. Sainsbury, “Crispin Wright,” 899–904; Pettit, “Realism and Truth: A Comment on Crispin Wright’s Truth and Objectivity,” Philosophy and Phenomenological Research 56 (1996): 883–90 originally interpreted Wright as embracing SAP; for recent allegations of the same kind, see W. Künne, Conceptions of Truth (Oxford: Oxford University Press, 2003). 5. Williamson first raised this problem against Wright, “A Critical Study of Truth and Objectivity,” International Journal of Philosophy 30 (1994): 130–44; see also C Tappolet, “Truth Pluralism and Many-valued Logic: A Reply to Beall,” Philosophical Quarterly 50 (2000): 382–85. Tappolet calls this the problem of mixed conjunctions; but it seems apparent that the problem extends farther than conjunctions. It might be thought that the truth of a mixed disjunction could be

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Together, these considerations suggest that a univocal concept and property of truth fulfills certain logical needs—needs emerging from the universality of reason. To my mind, this suggests in turn that if pluralism is going to be coherent, it is must find a way to pay some homage to the thought that Truth is One: There is a single property named by “truth” that all and only true propositions share. Yet clearly, if the pluralist is still going to be a pluralist in any sense worthy of the name, she must also maintain: Truth is Many: There is more than one way to be true. In short, if she is going to acknowledge the breadth of reason, the pluralist needs to meet both these demands. She must allow that truth is many and one. ALETHIC PLURALISM AS FUNCTIONALISM So if pluralism is to make sense at all, it must find some way to acknowledge both the unity and disunity of truth. In my view, the best way to accomplish this is to say that pluralism enters not into our account of the truth property per se, but into our account of the properties that, as I shall say, manifest truth. But which properties are these—and how are they related, exactly, to truth itself? As I have argued elsewhere, a helpful approach to these questions comes from the philosophy of mind.6 There, we are familiar with the idea that mental states like pain can be both one and many in form. States like pain can be understood as functional properties that are capable of being multiply realized by distinct lower-level neural properties each of which plays the pain role for a kind of organism. Similarly, why not understand the alethic pluralist’s suggestion as the view that: (F) ("x) x is true is true if, and only if, x has a property that plays the truth-role. Call this the functionalist theory of truth. It tells us the conditions under which propositions are true—they are true when they have a property that plays the truth-role. To play a functional role is to satisfy a job description of sorts, one which picks out features that anything that has that job must possess. And for a property to play the truth-role is for it possess what we might call the truish features. These handled by saying that such a disjunct is true just when at least one of its disjuncts is true in some sense or other. But again, we might ask: in what sense is the disjunction itself true? Similarly for conditionals. Negations, presumably, can be handled by saying that the negation of a proposition is true or false in the same sense that the original proposition is true or false. 6. See, for example, Lynch, “A Functionalist Theory,” 729–33; and “Truth and Multiple Realizability,” Australasian Journal of Philosophy 82 (2004): 384–408.

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are the features of the property implicitly given by the most central folk platitudes or conceptual truisms about truth. Such truisms will represent those core implicit beliefs about truth such that were one to deny them, one’s fellows would believe you had changed the subject. Collectively, they individuate truth by relating it to other, intimately related properties. Just which principles about truth we should count as these core truisms is a substantive question in its own right. But in all likelihood they will include some version of these three historically prominent and familiar principles: Objectivity: My belief that p is true if, and only if, things are as I believe them to be. Norm of belief: It is prima facie correct to believe the proposition that p if and only if the proposition that p is true. End of inquiry: Other things being equal, true beliefs are a worthy goal of inquiry.7 So according to the functionalist, a proposition is true when it has a property that plays the truth-role, and a property plays the truth-role just when it has (at least) the above truish features. Here is a simple way to unpack the metaphysical details of the account. Properties can have their features essentially or accidentally. Functional properties are defined by their functional role, that is, by the sum of their relational features. Those features can therefore be thought to be essential to it.Thus, the functionalist, like the monist, can claim that there is a single property of truth. The property of truth is the property that has the truish features essentially or which plays the truth-role as such. It is the property that is, necessarily, had by belief contents just when things are as they are believed to be; had by propositions believed at the end of inquiry and which makes propositions correct to believe. Yet the functionalist can also claim that truth is, as it were, immanent in other properties. Let us say that a property X is manifested by property Y just when it is a priori that X’s essential features are a subset of Y’s features. Since every property’s essential features are a subset of its own features, every property will manifest itself. So manifestation, like identity, is reflexive and transitive. But unlike identity, it is nonsymmetric. Where M and F are ontologically distinct properties— individuated by nonidentical sets of essential features and relations—and M manifests F, F does not thereby manifest M. Applied here, this framework allows us to say that a given property M, such as correspondence, plays the truth-role, or manifests truth if, and only if, it is a priori that the truish features are a subset of M’s features. This captures the thought, voiced by Wright above, that there may be more to say about how a proposition is true that goes beyond what is captured by the platitudes or truisms. 7. For a fuller list of truisms that can be used to pick out the truth-role, see Lynch (2001, 2004) and Truth as One and Many (Oxford: Oxford University Press, forthcoming). The strategy has obvious overlaps with that of Crispin Wright; see his Truth and Objectivity.

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Just as the psychological functionalist will claim that which physical property realizes pain in a given organism is determined facts about the organism, the alethic functionalist will claim that which property manifests truth for a particular proposition will depend on facts about that proposition.8 In particular, it will depend on (1) the proposition’s logical structure; and (2) the domain of inquiry the proposition belongs to. The first condition, as we will see in more detail in a moment, is familiar from traditional correspondence views, according to which the only sort of propositions which correspond to facts are atomic propositions. The second condition is what captures the pluralist intuition that there is more than one way for propositions to be true. In short, the functionalist can say that for atomic propositions, manifestations of truth are manifestations for a domain, where a domain is essentially composed of a kind of atomic content. That is, the functionalist will embrace: (M): Necessarily, where P is an atomic proposition of a domain D, P is true if, and only if, P has the property that manifests truth for propositions of D. And moreover, she will take it that: Necessarily, where P is an atomic proposition of D, P has the property M that manifests truth for propositions of D if, and only if, it is a priori that the truish features are a proper subset of M’s features. So an atomic proposition is true when it has the distinct further property that plays the truth-role—manifests truth—for the domain of inquiry to which it belongs. Not being true consists in lacking that property, either because there is no such property, in which case the content in question is neither true nor false, or because there is such a property, but the proposition in question fails to have it, in which case it is false. In sum, the general metaphysical picture the functionalist theory offers the pluralist is this: She should claim that where superwarrant or correspondence manifests truth, it is necessary that propositions that have that property are true, but it is not necessary that superwarrant, etc., manifest truth for every kind of proposition. Some properties play the truth-role accidentally. But only truth plays it as such, or essentially.9 8. Manifestation is distinct from realization insofar as the latter is typically understood as a relation that holds between properties a posteriori. For a parallel, immanence account of realization, see S. Shoemaker, “Realization and Mental Causation,” in Physicalism and its Discontents, ed. Gillett and Lower (Cambridge: Cambridge University Press, 2001), 174–98. See also S. Yablo, “Mental Causation,” Philosophical Review 101 (1992): 245–80, and D. Pereboom, “Robust Nonreductive Physicalism,” Journal of Philosophy 99 (2000): 499–531. 9. Our functionalist account takes truth to be a unique property with certain features. In other words, truth is that property that has certain properties, and only those properties, essentially. The fact that, like any other property, truth has properties does not make it a second order property. Something has a second order property just when it has a property of having some distinct property. This is distinct from saying that truth is a first order property that (again, like any other first order property) itself has certain other properties.

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This allows us to understand how truth can be both many and one. Truth is many because different properties may manifest truth in distinct domains of inquiry. Truth is one because there is a single property so manifested, and “truth” names that property. In all possible worlds and contexts where “truth” refers at all, it refers to the property that has the truish features essentially or has the features picked out by the core truisms in the actual world.10 Functionalism also gives us a head start in handling the twin problems of mixed inferences and mixed compounds. Take mixed inferences. Recall the problem they caused for SAP. If “true” denotes one property in the case of moral propositions and another property in the case of propositions about the causal bases of our mental states, then there is no single property preserved in such inferences. But if we now understand truth as an immanent functional property, then a single truth property is preserved in such inferences, and moreover, we are able to say why this is so by giving a general characterization of consequence. To wit: A valid inference is one where truth is preserved across its manifestations from the premises of the argument to its conclusion. The problem of mixed compounds is more difficult. We have said that an atomic proposition of some domain is true if, only if, it has the particular property that manifests true for propositions in that domain. Compound propositions might still seem to present a problem: What property manifests truth for the proposition that murder is wrong and electrons have negative charge? Surely not some mixed “moral/physical” property? It is worth emphasizing that even putting aside “mixed” examples, the truth of compound propositions is a general problem. Correspondence theories, for instance, have typically faced embarrassing questions about whether there are conjunctive or disjunctive facts to which conjunctive and disjunctive propositions correspond. Thus, the functionalist, like the correspondence theorist, must have something to say about compound propositions. An obvious tactic—and again one often adopted by correspondence accounts—is to appeal to a broadly recursive strategy. It is open to the functionalist, as it is to any theory of truth, to apply the theory in the first instance to atomic propositions, and then to understand the truth of a compound proposition in the standard recursive way, namely as a truth function of the atomic propositions of which it is composed. The truth of compound propositions is a logical consequence of the truth-values of their component parts, together with rules governing the use of the relevant connectives. Applied to our functionalist theory, we will say that the proposition that A & B is true because it is a truth-functional compound of conjuncts both of which do manifest truth; the proposition that A or B is true because it is a truth-functional compound of two disjuncts at least one of which manifests truth and so on. At this point a natural question arises: Do compound propositions have a property that manifests truth or not? If they do, what sort of property is it?

10. Likewise, “is true” will be a rigid predicator—a rigidified description ascribing a single property in all worlds.

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The functionalist has at least two general answers she might give to this question. The more traditional-sounding answer would be to claim that compound propositions are true without manifesting truth. The rationale behind this answer would be the same as what drove logical atomism or most truth-making theories. Thus, according to Russell there was no need to appeal to disjunctive or conjunctive facts; disjunctive or conjunctive propositions were true or false depending on the truth-value of their simple parts.11 Or as the early Wittgenstein remarked, My fundamental idea is that the “logical constants” do not represent; that the logic of facts does not allow of representation.12 One way of reading this is that the only goal of a truth theory is to tell us how the atomic propositions are true (or in Wittgenstein’s terms, represent). Recursion takes care of the rest. Applied to the present theory, this implies that compound propositions are true or false only in a derivative sense by being truth-functional compounds of propositions which can manifest truth. Thus we can say, for example, 〈A & B〉 is derivatively true just when 〈A〉 manifests truth and 〈B〉 manifests truth. This traditional sort of account, with its associated distinction between true and derivatively true propositions, has some merits. It accords with Wittgenstein’s intuition that nothing out in the world makes a compound proposition true save the truth of its component parts. Nor is it unexpected. Just as some truth maker theorists hold that, strictly speaking, there are no compound truth makers, so the functionalist on this approach holds that there are no properties which manifest truth for compound propositions. But the account also has some costs worth bearing in mind. One such cost, seldom noted in the parallel literature on correspondence, is that it makes our extensional definition of truth disjunctive. As such, it entails revising our original theory. Our original theory explained playing the truth-role in terms of manifestation. That, together with (F) above, implies that For all propositions P, P is true if and only if it has a property that manifests truth. Rather than accepting this, however, we now replace it with the following characterization: A proposition is true iff it has a property that manifests truth or is a derivatively true truth-functional compound proposition. 11. “The Philosophy of Logical Atomism”, in his Logic and Knowledge: Essays 1901–1950 (London: George Allen & Unwin, 1956). 12. L. Wittgenstein, Tractatus Logico-Philosophicus (London: Routledge & Kegan Paul, 1922), 4.0312.

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This is tantamount to saying that any proposition that is true is either atomic or logically derivable from atomics. This in turn suggests that the account is wedded to a fully satisfactory completion of recursive analyses for all compounds. Some compounds, such as counterfactuals and subjunctives, are notoriously difficult to understand in this way. So while the use of recursive analyses in truth theory is familiar, the nature and extent of such analyses is a vexed issue.13 Fortunately, there is a another way to answer the problem of compound propositions which, while building on the intuitions that drive the above analyses, is both simpler and follows more directly from our earlier account. It begins by granting what seems obvious: that whether or not a recursive account of all compound propositions can be given, there is something right about the insight that guides such analyses.What’s right about it could be captured by saying that all truth is grounded in a certain sense. There can be no change in the truth-value of a compound proposition without change in the truth-value of some atomic propositions. The truth-value of compounds supervenes on the truth-value of atomic propositions. Call this the weak grounding principle. According to the theory that truth is an immanent functional property, a property M manifests truth just when the truish features are a subset of the features and relations of M. Manifestation, as noted above, is a reflexive relation, since every set is a subset of itself. Thus all properties, including truth, selfmanifest. When a proposition is true only in virtue of having the property of truth as such, we can say that the relevant proposition is plainly true. What makes a proposition plainly true? Given our weak grounding principle, the natural thought is that propositions are plainly true, or self-manifest truth, if and only if their truth is grounded. That is, only if their truth-value supervenes on the truthvalue of propositions which have a property other than truth which manifests truth. So even if it turns out that a recursive analysis does not apply to every compound proposition (like subjunctive conditionals, for example), the functionalist can accept the weak grounding principle. Moreover, she will have independent motivation to do so. For she is already committed (1) to the thought that what’s true depends on what is true in a particular way; and (2) via her account of propositional domains, to the idea that true atomic propositions have further properties like superwarrant that manifest truth. Consequently, it seems reasonable for her to hold that a compound proposition’s truth is ultimately grounded on

13. The issue of their general applicability concerns, as noted, has to do with the question of how to handle expressions which are not straightforwardly truth-functional; while the nature of the analyses will depend on, among other things, the type of quantification involved and how “fullfledged” a recursive analyses is attempted—for example, whether it appeals to the structural components of the relevant truth bearers. As far as I can see, the alethic pluralist who uses such analyses is not committed to any particular answer to any of these questions, nor that these issues remain any thornier for her than for any of the other numerous theories that wish to appeal to some form of recursion. Nonetheless, it would be good to avoid them. For commentary on these issues see, M. David, Correspondence and Disquotation (Oxford: Oxford University Press, 1994), 117–23; S. Soames, Understanding Truth (Oxford: Oxford University Press 1999), 86–92; R. Kirkham, Theories of Truth (Cambridge, MA: MIT Press, 1992), 139ff.

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the truth-values of its atomic components. So compound propositions, but not atomic propositions, are true because they self-manifest truth. Assuming that the weak grounding principle is accepted, the second approach seems preferable; it is simpler and entails no revision to the functionalist theory. Every proposition, even a compound proposition, is true because it has a property that plays the truth-role—or manifests truth. MORE THAN ONE LOGIC? Functionalism about truth allows us to understand how truth can be both one and many. So on the face of it, the functionalist offers a way out to the alethic pluralist from the vexing problem of the universality of reason. But the solution, as so far developed, ignores an important—and pressing—possibility. That possibility is that even the sort of alethic pluralism allowed by functionalism may well bring logical pluralism in its wake. And as we shall see, this brings back the problem of the universality of reason with a vengeance. Logical pluralism is the thesis that there is more than one logic governing our reasoning. Since logics can be individuated by their account of consequence, one can say that logical pluralism is the view that there is more than one relation of logical consequence, or validity. Intuitively, an argument is valid when its premises necessitate (in some sense) its conclusion. And as we have already noted, validity is usually defined in terms of truth: an argument is valid just when if the premises are true the conclusion is (or must be) true. So, we might ask, if there is more than one property that manifests truth, could this entail that there is more than one way for an argument to be valid? Prior to grappling with this question, it will be helpful to say something about logical pluralism in its own right. JC Beall and Greg Restall have recently argued for just such a position. They do so by defining validity by reference to what they call “cases,” as so: VALID: An argument is valid if and only if, in every case where the premises are true, so is the conclusion.14 They argue that this minimal concept of validity, however, is permissibly enrichable in more than one way, so long as the enrichment satisfies three platitudes about consequence: that it is a necessary relation, that it is a normative relation, and that it is a formal relation in at least some of the relevant senses of that term.15 Thus, for example, one might endorse: CLASSICAL: An argument is valid if and only if in every possible world where the premises are true, so is the conclusion. 14. JC Beall and G. Restall, Logical Pluralism (Oxford: Oxford University Press, 2006), 27. 15. Ibid., 14–20.

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Here we take the “cases” referred to in VALID to be classically constrained possible worlds. An altogether different enrichment would take cases as stages of inquiry: CONSTRUCTIVIST: An argument is valid if and only if at every possible stage of inquiry where the premises are true, so is the conclusion. Here stages of inquiry are understood as they are in our definition of superwarrant above.They are both extensible (additional information might always come in) and inclusive (the additional information is just that—additional; all successive stages of inquiry include the information warranted at prior stages). Again, as with our definition of superwarrant above, stages are potentially incomplete—a given stage of inquiry may warrant neither a claim nor its negation. Consequently, we lack warrant for thinking that the law of excluded middle holds in all stages, and likewise for double-negation elimination. Roughly speaking, we can say that CONSTRUCTIVIST is an intuitionistic logic.16 One does not need to adopt Beall and Restall’s definition of validity in terms of cases, however, in order to understand logical pluralism. In particular, our definition of superwarrant allows us to state Beall and Restall’s CONSTRUCTIVIST definition of consequence in terms of possible worlds: CONSTRUCTIVIST*: An argument is valid if and only if at every possible world where the premises are superwarranted, so is the conclusion.17 Once again, the ensuing logic does not accept the law of excluded middle (LEM), since it is consistent with the notion of superwarrant that there is some proposition P such that we will have no reason to believe that either it or its negation are superwarranted, and therefore no reason to believe that LEM holds of all propositions. Likewise with the semantic principle of Bivalence. Now suppose that CONSTRUCTIVIST* were to govern our reasoning in some domains, but CLASSICAL governs our reasoning in the rest. If so, then we would presumably be committed to what we might call domain-specific logical pluralism (or DLP): Distinct domains of inquiry would be governed by different logics. In any event, two relevant questions arise about DLP and its relation to alethic pluralism. First, does any type of alethic pluralism entail this sort of logical pluralism, and in particular, does the functionalist version sketched above entail it? Second, whether or not the functionalist is committed to DLP, how would her view be affected should she, for whatever reason, think it is true? Let’s take these questions in order. Strictly speaking, there appears to be no direct argument from any alethic pluralism to DLP. This is because if consequence 16. Obviously CLASSICAL and CONSTRUCTIVIST are only stand-ins for full logics; moreover there are other logics one might want to consider (and Beall and Restall do consider). 17. Here, we are not, as will become clear below, assuming that possible worlds are complete sets of propositions.

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is, roughly, a matter of truth-preservation, then just because there is more than one way for a proposition to be true does not mean that there must be more than one way for truth to be preserved from one proposition to another. Truth is one thing; truth-preservation is another. So it might be that there is only one way for truth to be preserved from premises to a conclusion even if there is more than one kind of truth to be preserved. Suppose, for example, that truth is plural but no kind of truth requires a revision of the classical laws of logic. If so, then CLASSICAL would be the one and only consequence relation.18 The conclusion is the same when we restrict our attention to functionalism. Validity could be a functionally defined relation and still only be manifested in one way. So there is no direct route from functionalism about truth to DLP. Nonetheless there is, it seems, an indirect argument. It is indirect because it involves several additional, if plausible assumptions: Namely, first, that truth is variably manifested, and second, that one of the properties that can manifest truth is superwarrant. Wright has argued that superwarrant is a candidate for manifesting truth in any domain which meets (along with other constraints): EC: If P, then it is feasible to have warrant for believing P. Assume that there is some domain of which this principle is true. Grant that superwarrant or some similar property plays the truth-role for the propositions of that domain. If stages are defined as CONSTRUCTIVIST* defines them above, then, intuitively, the law of excluded middle cannot be known to hold for that domain. The intuitive case rests on—the admittedly plausible sounding assumption—that there is no guarantee that inquiry is complete at any stage. If so, then there may be propositions of the domain for which no warrant either for or against is ever available—even in principle. Consequently, there may be some proposition P in the relevant domain such that we are not warranted in holding: superwarrant P or superwarrant ~P. And if we are not warranted in accepting that, then neither, presumably, are we warranted in accepting that LEM holds for every proposition. Consequently, we are not warranted in including LEM into our logic for that domain.19 CONSTRUCTIVIST* is intended to allow for this. So if superwarrant manifests truth in a given evidentially constrained domain, then the consequence relation in that domain will be better construed as CONSTRUCTIVIST* and not CLASSICAL. Thus the indirect route from alethic functionalism to DLP: If there is more than one way to manifest truth, and some of the manifesting properties are epistemically defined properties like superwarrant, and some not, then different domains will admit of different manifestations of the consequence relation. And this means, among other things, that argument forms that are valid in some 18. The case is perhaps not as clear when the question is whether logical pluralism entails alethic pluralism. Beall and Restall deny it (see Logical Pluralism, 100); Stephen Read, “Plural Signification and the Liar Paradox,” Philosophical Studies (forthcoming), argues otherwise. I remain neutral on the issue as of this writing. 19. This is not to say that LEM is false; see Crispin Wright, “On Being in a Quandary: Relativism, Vagueness, Logical Revisionism,” Mind 110 (2001): 45–98.

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domains may not be so in others. All this of course, assumes that there is more than one way to play the truth-role. If there is not, then there may still be more than one consequence relation, but this will presumably be motivated by other things than a view about the nature of truth.20 The indirect argument for the conclusion that alethic functionalism involves a commitment to DLP can be resisted along a number of fronts. The two most obvious routes are first, to deny that truth is variably manifested; or second, to claim that our truisms about truth themselves constrain the logic that govern any domain. The former route is to deny pluralism. The latter is open to any one who wishes to claim, for example, that among the core truisms that demarcate the truth-role are foundational principles of classical logic, including paradigmatically, Bivalence. If this principle is a core truism, it picks out an essential feature of truth. It will therefore be a necessary truth that every proposition is either true or false.21 In any event, both of these routes are consistent with the functionalist theory of truth presented in this essay, and the latter is consistent with pluralism as well. Thus—to stress the point again—nothing forces the alethic pluralist to be a logical pluralist, domain-specific or otherwise. But if we assume for the moment that none of these routes for resisting the indirect argument is taken, the question remains as to how an admission of DLP will affect the alethic pluralist. The general upshot, again, is this. In domains where propositions are made true by an epistemically constrained property like superwarrant, and where it is plausible that not every proposition will be either true or false, then the logic in that domain will be best modeled by CONSTRUCTIVIST*. Two specific upshots are these. First, anyone who claims that distinct domains of discourse are governed by different logics must say something about mixed compounds, such as: (1) The cat is on the mat and torture is wrong. (2) Torture is wrong or grass is green. Second, the functionalist/logical pluralist must also say something about mixed inferences, for example MIX: Torture is wrong or grass is purple; grass is not purple, so torture is wrong. Earlier we noted that for functionalists about truth, there is only one property of truth, even if that property can be variably manifested. Thus it is that single property that is preserved in a valid inference like MIX. Likewise, compounds like (1) or (2) are not true in some special “mixed” sense of “true,” nor are they true in

20. Compare Beall and Restall, Logical Pluralism, 100–101. 21. A third route to resisting the indirect argument would be to hold alethic pluralism to insist that CONSTRUCTIVIST* (or something like it) is the universal logic. We will return to this more complicated option below.

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virtue of some special mixed property of truth. They are true in the same sense any other proposition is true: Such propositions self-manifest truth. So the functionalist qua functionalist, has no particular problem with either mixed inferences or mixed compounds. These issues arise again only when logical pluralism is on the table. Propositions like (1) and (2) above are both plainly true, like any true compound, mixed or not. But as our reasoning above indicates, the fact that all compounds are true in the same sense does not solve the problems generated by DLP. And if, as we are assuming for the moment, the functionalist is likely to be a logical pluralist, then the problems of DLP are problems for the functionalist. Let’s look at these problems in a bit more detail. Consider any conjunction or disjunction where one component is a proposition from a domain where truth is manifested by superwarrant, and the other component is from a domain where truth is manifested by some form of correspondence. Suppose, for sake of argument, that the moral domain admits of a nonclassical (CONSTRUCTIVIST*) consequence relation as defined above. The question will then be what to say about mixed compounds like the following: (3) Grass is green and, Sophie’s choice is morally right. (4) Grass is green or, Sophie’s choice is morally right. Sophie, as in the book by William Styron, is forced by the Nazis to choose which of her two young children will live and which will die. Suppose that our moral theory tells us that it is simply not decidable whether her resulting decision is the right one in the sense that we will never have warrant for or against it. If so, then we have no warrant for thinking either that it is superwarranted that her decision is right or superwarranted that her decision is not right. Thus we will not accept that Sophie’s choice is morally right or it is not; nor, if truth is superwarrant, will we accept as true or false that (S) Sophie’s choice is morally right. What then do we say about the value of (3) and (4) (assuming that “grass is green” expresses a true proposition)? Linked to this problem is the question of what to do about mixed inferences, such as MIX or NIX: If it is not the case that Sophie’s choice is morally right, then grass is not green. But grass is green; so Sophie’s choice is morally right. The example is a toy one. But the possibility it raises is real. We often do infer across domains, and we often wish to infer moral conclusions from premises that include some nonmoral considerations. Yet which logic should we use for the evaluating such inferences? One which, like CLASSICAL, counts NIX as valid? If so, then we are in the unfortunate situation of countenancing as valid an argument

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that fails to preserve truth—since the conclusion (S), is (let us continue to imagine) counted as neither true nor false in the moral domain.22 It should be stressed that the above problem does not arise solely for those who have come to DLP via truth pluralism. The issue of how to deal with mixed inference and compounds is an issue for any logical pluralist who takes it that distinct logics operate in different domains of discourse. Fortunately for both sorts of pluralists, there appears to be a single solution available to logical pluralists for the problem of mixed inferences and the problem of mixed compounds.23 The solution has two parts. First, the advocate of DLP, being a pluralist after all, will take it that within a domain, what qualifies as the governing logic will be determined by what manifests truth in that domain. Thus, where the propositions that compose a compound are all from a single domain, and the premises and conclusion of a given inference are all from a single domain, the appropriate logic will be that which governs the simple propositions from that domain. So if the domain of propositions about physical objects is governed by CLASSICAL, then all inferences and compounds within that domain will be governed by CLASSICAL as well. This is all just a natural consequence of being a logical pluralist, as we have understood the position. The second, and central, aspect of the solution is to endorse a principle of logical modesty. Two such principles recommend themselves. The first can be summarized as follows. Let’s say that a compound’s weakest member is the atomic proposition whose domain has the weakest logic relative to the logics in play so to speak (i.e., relative to the other logics governing the domains of the other atomic propositions composing the compound in question). Likewise, an argument’s weakest member is that premise whose logic is the weakest in play. The weakest logic in play is that which has the fewest logical truths or which sanctions the fewest valid inferences. MODEST: Where a compound proposition or inference contains propositions from distinct domains, the default governing logic is that of the compound or inference’s weakest member. Thus in the case of NIX above, the first premise is the weakest member because it is a compound whose weakest member is a moral claim. And (we have been imagining) the moral domain is best modeled by a logic that is weaker than CLASSICAL, that is, CONSTRUCTIVIST*. Hence, according to MODEST, the inference itself is governed by CONSTRUCTIVIST*, and is therefore not valid. Likewise in the case of (3) and (4). Here again (S) is the weakest member in the defined sense, and thus in each case the governing logic will be the logic of (S). How this pans out for the truth-value of either (3) or (4) depends, of course, on how one understands that logic. But for sake of illustration, suppose that we take the 22. Moreover, the argument will count as invalid by the lights of CONSTRUCTIVIST*, since it implicitly employs DNE twice, the final use of which would be traditionally disallowed by such logics. So we might as well ask: Is the argument valid or invalid? 23. Examples of this sort were originally urged on me by Aaron Cotnoir and Nikolaj Pedersen.

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logic governing (S) to be a CONSTRUCTIVIST* logic according to which LEM and Bivalence are not guaranteed to hold of every proposition. If so, then (3) will not be true and (4) will be true. (3) will not be true because its second conjunct, (S) will not be true (or false); (4) will be true because its first disjunct is true. The MODEST principle implies that, under this assumption, CONSTRUCTIVIST* is the default logic for mixed compounds and mixed inferences. In saying this, we imply that the logic appropriate for plain truth is CONSTRUCTIVIST* unless (a) The propositions that compose the compound or inference are all from a single domain. And (b) The property that manifests truth in that domain is epistemically unconstrained. This gives us a rule, in effect, for deciding which logic is appropriate for any given kind of proposition. Of course the solution just offered depends on whether a motivation can be supplied by the advocate of DLP for MODEST. Interestingly, one drops right out of a previous commitment to pluralism about truth. The truth pluralist will take it that some kinds of propositions will have their truth manifested by correspondence, while others will have their truth manifested by superwarrant.Likewise,the domainspecific logical pluralist will take it that CLASSICAL may well govern our inferences in our thought about certain domains, perhaps those of the natural sciences and mathematics. But in other domains, such as the moral or aesthetic domains, it will not. In the latter sort of domains, we might well take it that claims like (S) are indeterminate in truth-value.Why? Our pluralist twice over has an obvious answer: because such indeterminancy is enforced by the property that manifests truth in the relevant domain.And this is what we should expect, if as is natural, we take it that the underlying nature of truth for a domain dictates what logic holds for that domain. Consequently, given this direction of explanation, we will not want to endorse as valid any inference that would violate our truth pluralism.That is, we do not want to count as valid any inference that would require that propositions like (S) be either true or false. To put it still another way, when reasoning across domains, logical caution is in order:We want to limit the number of logical truths that we endorse, so as to respect those domains which, by virtue of the property that plays the truth-role within them, enforce less logical laws than others. So alethic pluralism supplies a motivation for MODEST. And that is an implication worth flagging all by itself. For it is only by adopting MODEST, I have argued, that the domain-specific logical pluralist can deal with the problems for her position that arise from the universality of reason. And that means that, anyone attracted to DLP—anyone, for example, who thinks that different logics might govern our reasoning about morality and physics—would do well to take alethic pluralism very seriously as well.

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One reason why some may be uncomfortable with MODEST is that it depends on the assumption that the logics in question can be ordered, in the sense that the stronger logics are extensions of the weaker logics, or that all the models of the former are models of the latter. And of course not all logics are so strictly ordered. But one who embraces DLP need not accept that they are—just as doing so does not mean that one must embrace any old logic. Rather, what the domainspecific logical pluralist must accept is that the domain-specific logics are ordered. She need not accept that all logics are domain-specific. And it does not seem an unreasonable constraint on those logics that apply only to specific domains of inquiry that—in virtue of the content that composes that domain—they be capable of being ordered along a continuum of weaker to stronger. A more concessive response to this worry is available however. This brings us to our second way of approaching the modesty condition. This second approach might be summarized as: MODEST*: Where a compound proposition or inference contains propositions from distinct domains, the default governing logic is that comprised by the intersection of the domain-specific logics in play. The thought here might be put by saying that any domain-specific logics in play are partially ordered in the sense that there will always be a further logic that is comprised of their intersection. Like its cousin principle, MODEST* cautions a type of logical conservatism. Thus, it will supply the same results for (3) and (4) as MODEST. This is because CLASSICAL contains CONSTRUCTIVIST* as a part. Thus, the intersection of the weaker CONSTRUCTIVIST* and CLASSICAL is itself CONSTRUCTIVST*. Moreover, MODEST* does not require that all domain-specific logics be ordered along a continuum of weaker to stronger. It is consistent, for example, with the thought that some domain-specific logics are of equal strength.24 Consequently, MODEST* seems an attractive option.25 Finally, some might wonder whether there is a significant difference between adopting the modesty approach—in either of its guises—and claiming that while truth is plural, there is a single, weak logic, along the lines of CONSTRUCTIVIST*. For again, traditional intuitionist logics like CONSTRUCTIVST* contain classical logic as a proper part. Therefore, why not say that CONSTRUCTIVIST* is not only the default logic, it is the only logic, and that domains whose logic appears classical only do so because we are employing only the classical portion of the one true logic? Alethic pluralism, at least in the functionalist guise I have presented here, is certainly consistent with this suggestion. But the suggestion comes at a price. According to the suggestion, CONSTRUCTIVIST* holds in all domains. 24. As one might think would be the case if the two logics were duals of each other, as in the case of supervaluationism and subvaluationism. See D. Hyde, “Pleading Classicism,” Mind 108 (1999): 733–35, for discussion of this possibility. 25. Of course, it requires the assumption that all domain-specific logics (although not all logics) be commensurable. But that seems reasonable in any event, given the fact that we do in fact reason across domains—that is, given the universality of reason.

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Bivalence is not recognized as a logical principle by CONSTRUCTIVIST*. Therefore in every domain, bivalence is not recognized as a logical principle. Therefore in domains which, according to this suggestion, nonetheless appear classical—and therefore abide by bivalence—bivalence must be true for some non-logical reason. And one might wonder what that reason might be. A full assessment of this suggestion, therefore, requires drawing the boundaries of logic, an issue well beyond the scope of the current essay. But one small point is worth making: It seems natural that if one domain allows some inferences as valid and another does not, they have different logics. And domains where bivalence holds will allow some inferences as valid that other domains (which do not sanction bivalence) will not. So the natural thought is that they have different logics. Now according to the present suggestion, it might be that some inferences are counted as valid in a given domain not because the logic counts them as so, but because there is an additional metaphysical assumption that, together with the logic, allows them to count as so. But that just seems to mean that principles which function like logical principles are not logical principles, and again, one might wonder why that would be. CONCLUSION Adopting a functionalist theory of truth allows us to make sense of the basic idea behind alethic pluralism while retaining the common-sense thought that there is a single property of truth preserved across logical consequence. Moreover, the alethic functionalist, even the functionalist who believes that truth is variably manifested, is not required to endorse DLP. But it is likely that she will. And if she does, she is wise to be modest, for that provides at least a start on the thorny question of how to understand the issues raised by the universality of reason.26

26. Thanks to Stewart Shapiro, Stephen Read, Crispin Wright, Douglas Edwards, Colin Caret, and JC Beall for useful comments and discussion, and especially to Patrick Greenough, Marcus Rossberg, Nikolaj Pedersen, and Aaron Cotnoir for extensive comments on earlier drafts of this paper.

Midwest Studies in Philosophy, XXXII (2008)

Grading, Sorting, and the Sorites TIM MAUDLIN

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ague predicates admit of borderline cases. One is commonly inclined to regard certain claims about the borderline cases as violating bivalence: If John has a borderline case of baldness, then it is neither correct nor incorrect to call him bald, and so the claim that he is bald is neither true nor false. Vague predicates are also commonly supposed to lack sharp boundaries.There is no precise point in time when a balding man becomes bald, or when a tall person becomes tall. There was no exact nanosecond when Muhammad Ali became famous, even though at some time he was not famous and at some later time he was. These notions are evidently linked: In the process which took Ali from not being famous to being famous, he spent some (vaguely defined) time as a borderline case of being famous. The usual approach to vagueness treats these features of vague predicates as semantic, rather than epistemic, matters. In a borderline case of baldness, there may nothing relevant that is unknown, either about the state of the head in question or about the meaning of the term “bald.” Rather, that meaning simply fails to determine a classical truth value in the case at hand. The epistemic view of vagueness, in contrast, maintains that even in borderline cases, a claim like “John is bald” is either true or false, and that if John becomes bald, there is a perfectly exact moment in the course of his hair loss at which he became bald. According to the epistemic view, John is a borderline case of baldness only because it is in principle unknowable whether or not he is bald, but every borderline bald person is either a person who is, in fact, bald or a person who is not. There are three main lines of defense of the epistemic view. One is a purely logical argument contending that the denial of bivalence entails a contradiction,

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and so cannot be consistently maintained. The second adverts to the Sorites argument, which is taken to show that, contrary to the naive view, there must be an absolutely exact boundary that separates the bald from the not-bald, the famous from the not-famous. The third argument is by elimination: Various alternatives to epistemicism are examined and found to be untenable. At the end of the investigation, only epistemicism is remains as a viable alternative. The logical argument attempts to show that the denial of bivalence leads to contradiction:The claim that some meaningful utterance or sentence is neither true nor false is supposed to imply a straightforward contradiction, in the form of the conjunction of a sentence with its negation. I have dealt with this argument elsewhere (Maudlin 2004, 196–199), and will not repeat the details here. Suffice it to say that the argument begs the question at hand. Anyone who denies bivalence will automatically be committed to the existence of several distinct extensions of classical negation, which differ with respect to the truth value of the negation of sentences that are neither true nor false. The more distinct semantic values one recognizes (e.g., if one recognizes not only borderline cases, but borderline borderline cases, and so on), the more forms of truth-functional negation one will be committed to. The “logical” argument, as constructed by, for example, Timothy Williamson (1992, 145–147; 1994, 187–89) and Paul Horwich (1990, 90), presumes that there is only one form of negation.1 Once the natural multiple forms are allowed, the denial of bivalence can be framed so that no contradiction validly follows from it. But this observation does nothing to defuse the Sorites, nor does it provide any positive account of semantics from which the failure of bivalence follows. What is wanted is a theory of the meaning of vague terms from which the possibility of borderline cases can be derived. Such a theory ought also to explain both the manifest appeal and the ultimate resolution of the Sorites argument. “Meaning” is a notoriously obscure notion, so asking after the meaning of a term like “heap” or “bald” is not yet to set an entirely clear problem. Slogans such as “meaning is use” or “meanings determine truth conditions” are of little help in this regard. So what I propose to do is simply ignore the question of meaning at the outset of this paper. Instead, I would like to examine in some detail a particular practice, whose workings are sufficiently well-known and transparent to be uncontroversial. Then I will suggest that the use of terms like “bald” and “heap” are sufficiently similar to this practice to be illuminated by it. I will not be arguing that this is a useful way to regard meaning in general, but that the structure of this practice does help us understand “heap” and “bald” and kindred terms. The practice I have in mind is the practice of grading. At the end of a semester, the instructor of a class is obliged to assign the students in the class grades. There is typically a relatively small set of grades available: A, B, C, D, and F, supplemented, perhaps, by pluses and minuses. It is also 1. While some approaches to vagueness, such as that of Williamson, simply overlook the possibility of distinct extensions of classical negation to cover a multivalent semantics, others, such as that of Kit Fine, rule it out by means of a formal principle. In Fine’s (1975), the condition called Stability rules out the form of negation which maps borderline sentences to true sentences. Fine’s defense of the Stability principle (p. 275), however, is rather poorly motivated.

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not unusual to have, as the basis of assigning the grade, an aggregate numerical score ranging from 0 to 100, a weighted sum of numerical scores achieved on various exams and quizzes. The task of the instructor is then to assign grades on the basis of that aggregate numerical score. For the purposes of this paper, I will idealize somewhat and assume that the aggregate score is the only piece of information used to assign the grade. In practice, of course, one often takes into account other factors: class participation, attendance, and so on, but that would needlessly complicate the account, so I will omit them. We can therefore call the aggregate numerical score the objective basis for the assignment of the final grade. That is not to say that the numerical score was itself arrived at objectively (in some sense) but that the score is the only input from the side of the student into the final decision process. Assignment of final grades given the objective basis is a procedure that has normative rules associated with it. Our first task is to try to be very precise about what those rules are. I will be describing the rules I myself use in this sort of situation. To begin with, the rules have some Absolute Paradigms. To take an obvious case, anyone whose aggregate score is 95 or above must get an A (we do not have the grade A+ available) and anyone whose aggregate score is 50 or below must get an F. Anyone who matches an Absolute Paradigm can be assigned a grade immediately, without regard to the rest of the class. We could obviously set the first paradigm higher and the second lower, but they are more informative this way. There is another absolute rule: any student who gets a better grade than another must have a higher aggregate score than the other. There follows a sort of “supervenience” principle for grades: students who get the same aggregate score must get the same grade. The grades “supervene” on the objective basis. I have put scare quotes around “supervenience” as an alert that the exact content of this principle will be further articulated. Let us call this principle Dominance, since it says that if one student dominates another in final grade, she must dominate the other in the objective basis. Dominance and Absolute Paradigms are the only unbendable rules governing the assignment of final grades. Were either of these to be violated, a student would have, ipso facto, legitimate grounds to appeal the final grade. What follow them are softer rules that can be violated, and whose violation can be defended in particular instances, but which one would prefer to respect. With the highest and lowest grades, one can have absolute conditions for their application, but with the intermediate grades one has instead a Soft Target. For example, I think of an 85 as a sort of paradigm B: Absent some other mitigating factor, a student who gets an aggregate of 85 will get a B. An example of a possible mitigating factor is when 85 is the highest aggregate score in the class, so one “grades on a curve.” One can deviate from a soft target, but only when there is some particular circumstance that can be used to justify the deviation. Another soft constraint, one which will much concern us, we may call the Epsilon Principle. The Epsilon Principle states that students whose aggregate scores are very close to each other (within some vaguely indicated small amount epsilon) ought to get the same final grade. In a typical course, epsilon is often

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around a point in the aggregate score. One dislikes, and tries to avoid, giving a certain grade to one student and a worse grade to a student whose aggregate is within a point of the first. The justification of the Epsilon Principle is straightforward. The purpose of giving final grades is to convey information about the students’ performance in the class. That performance, we may suppose, is quantified by the value each student has in the objective basis. The final grades constitute a sort of coarse-graining of the objective basis, and in the process of coarse-graining, information is lost: Students who performed differently in the class are nonetheless assigned the same final grade. The loss of information seems particularly unjust when the performance of two students is nearly the same, but they nonetheless they are given different final grades. The small difference is magnified by the coarse-graining. There is the appearance of a kind of injustice here, although not the form that would automatically invalidate the grades, as a violation of the absolute principles would. So one tries, insofar as is possible and consistent with the other soft and absolute constraints, so satisfy the Epsilon Principle in assigning final grades. Let us call the four principles listed above, Absolute Paradigms, Dominance, Soft Targets and the Epsilon Principle, the Ideal for Grading. The most satisfactory outcome, when assigning grades, is when all of the principles in the Ideal can be satisfied. There is no logical guarantee that the Ideal can be satisfied in any given class: That depends on the actual distribution of aggregate scores. It may happen that no way of assigning grades will meet the Ideal. It may also happen that several ways of assigning grades can meet all of the principles in the Ideal. That too is somewhat problematic, since the Ideal gives no further guidance about which of those assignations to make.We could, of course, expand the Ideal to include further principles, in hopes of reducing these sorts of ties, but we won’t. We therefore have a ranking of possible situations, depending on the distribution of aggregate scores. In the best of all possible worlds, the Ideal can be satisfied, and only in one way. In the next best case, the Ideal can be satisfied in multiple ways. One will have to choose among these different solutions, and the choice will be somewhat arbitrary, leading to a certain sense of injustice with respect to students whose grades depend on that arbitrary choice. Below these are the situations in which the Ideal cannot be satisfied: At least one principle must be violated. In my own case, there is a clear order ranking here: I will more easily give up the Soft Targets than the Epsilon Principle. Of course, the choice between giving up Soft Targets or the Epsilon Principle is itself a matter of degree: I will allow the grades to shift from the ideal Soft Targets to some degree in order to satisfy the Epsilon Principle, but there is a (vague) limit to how far I would allow them to shift just to save that principle. In practice, then, here is how I assign grades at the end of term. I calculate an aggregate score for each student. I then write on a piece of paper, in descending order, the numbers from 100 to 50 (less than 50 is always F), and make a tally mark for each student next to their aggregate score. This gives me a distribution of tally marks ranged down the paper. I then look for clumps of marks with gaps between the clumps. If, for example, there is a clump of marks centered near 85, I look for a gap above it so that I can have the Bs go up to the gap, with the B+s starting above it, and a gap below so the Bs go down to the gap. with the C+s starting below it

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(we don’t have the minus grades). In a class of 40 or so students, there are usually such gaps in the distribution of aggregate scores. There is evidently no guarantee of this—each score from 60 to 100 could be represented by exactly one student—but as a matter of fact the scores tend to cluster and the clusters leave gaps. By separating the grades by the gaps, I can satisfy the Epsilon Principle (for the value epsilon equals one point), and I let the placement of the separations be influenced by the score distribution in this way. I imagine that the way I assign grades is fairly typical. If the distribution of aggregate scores is full, with every possible score occupied, then there is no way to satisfy the Epsilon principle, and students with almost identical scores will end up with different grades. One might have Very Soft Target Boundaries for this case: precisely defined division lines to use for separating the grades. And if there are hundreds of students, rather than just 40, the chances of gaps is almost nil. But even when there are hundreds of students, appeal to target boundaries is a last resort. If the distribution of grades is not flat, there will be hills and valleys in the distribution of aggregates scores, and running the grade boundaries through the valleys will minimize the violation of the Epsilon Principle, and maximize the amount of information about the objective basis conveyed by the grades. So the only case where target boundaries would need to be invoked is when the distribution is both full and flat—no gaps, no hills, no valleys- and that practically never occurs. The procedure I have just described is pedestrian. But there are aspects of it which on reflection are rather surprising. The first point has to do with the scope of situations to which the principles apply. The Ideal for Grading is used in a particular grading situation—when assigning grades at the end of one semester to the students in that class. The principles apply to that class only. So, for example, giving one grade to a score of 90 and another to a score of 89 in the same class violates the Epsilon Principle, but giving one grade for 90 in one semester and another for 89 for the same course taught in another semester violates no principle at all. Even more striking, Dominance only applies to students in the same class. A student who gets an 89 in a course one semester can get an A, while a student who took the same course a year earlier and got 90 could get a B+. There is no doubt a certain uneasiness about this, but in practice the second student would have no grounds for complaint. If the students had been in the same class, the grading policy could not be defended. Doubtless, one reason for this is that there is no guarantee that the classes were taught exactly the same way, or the exams equally difficult. But on the other hand, the courses might have been identical, and the first student could benefit simply from having duller classmates. In any case, the principles apply only intraclass, not interclass.That is why we had to put scare quotes around “supervenience” above: Dominance guarantees only that students in the same class with the same objective basis get the same grades, not students in different classes. It is essential that the scope of the principles be confined to a single class: If one had to aggregate all the students one ever taught (even in the same course), the chance of gaps in the objective basis would disappear, and the distribution would be more likely to lack the sorts of hills and valleys the Epsilon Principle needs. And

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if one were to consider merely possible students, then the practice would collapse entirely. In the first place, there would be no distribution in the objective basis at all, and in the second, pesky students would constantly try to slip their way up the slope to a better grade by filling in gaps between their score and the lowest score that got a higher grade with merely possible students. The gaps and distributions that make the Epsilon Principle useful are contingent matters, and contemplation of counterfactual grades given to non-actual students will tend to obscure the practical utility of the Principle. In the worst case, contemplation of merely possible students will deflect one’s attention from the actual task at hand to the worst case scenario: flat distributions with no gaps on which one needs to draw boundaries. At this point, connections to the Sorites arguments are manifest, so it is worthwhile to get a bit more exact.What is the logical form of the Epsilon Principle as an ideal that we would like to come out true? The Principle states that any pair of students whose aggregate scores are within epsilon of each other should get the same grade. If we represent the relation of having scores within epsilon of each other as E(x,y), and the relation of having the same grade as S(x,y), the Principle becomes

∀x∀y ( E ( x, y ) ⊃ S ( x, y )) . In cases where the Ideal can be satisfied, the sentence above will be true. The quantifier in the sentence ranges only over members of the class at issue. If we introduce predicates that correspond to the possible scores in the objective basis, for example, 100(x), 99(x), 98(x), etc., then the Epsilon Principle can be written in a logically equivalent way as the conjunction of a series of conditionals: ( ∃x100 ( x ) ⊃ ∀y ( 99 ( y ) ⊃ S ( x, y ))) & ( ∃x99 ( x ) ⊃ ∀y ( 98 ( y ) ⊃ S ( x, y ))) & . . .

The conditionals appear similar to those commonly used in constructing a Sorites, but the quantificational structure renders them harmless if there happen to be the right sorts of gaps in the distribution.A student with a 95 can get an A and a student with a 50 an F, as the Absolute Paradigms require, without rendering any of the conditionals false. If there happens to be at least one student with each possible aggregate score, then at least one conditional must be false, but that is a contingent matter. Let’s now consider some examples from the taxonomy of cases given above. The best case is when there is a unique assignment of grades that satisfies the Ideal. If, for example, the grade distribution has clusters of aggregate scores that are confined to intervals 94–96, 84–86, 74–76 and 35–50, then the only way to satisfy the Ideal is to assign all of the first group As, the second Bs, the third Cs and the last Fs. Anyone trying to satisfy the Ideal would come up with the same final assignment. The next best case is when the Ideal can be completely satisfied, but in several different ways. If one only has the straight letter grades to assign (without pluses or minuses), then adding a single student with an aggregate score of 90 to the

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distribution above produces such a case. The student could be given either an A or a B without violating the Ideal, so something beyond the Ideal must be employed to decide the case. Such a student is a benign borderline case: borderline because equally acceptable grade assignments assign him different grades, and benign because no deviation from the Ideal is required. It is important to note that the task at hand is simply to assign grades to all the students. The Ideal concerns evaluation of such assignments. The task is not to “draw boundaries” for each grade. In the first example discussed above, one simply has to decide what grade each actual student gets, not which aggregate score will separate the As from the Bs. If one had to draw boundaries, then even in the first case many distinct ways of drawing the boundaries would be equally acceptable. But since we are engaged simply in sorting the actual cases, not in drawing exact boundaries, the solution that satisfies the Ideal is unique. In the first case described above, there is a clear sense in which the grades assigned to the students are objectively determined. The objective basis together with the Ideal determines a unique grade for each student, so the role of the teacher evaporates into an entirely mechanical task. Similarly, in the second case, the grades of the non-borderline students are objectively determined, since they are required to get the grades they do if the Ideal is to be satisfied. We can even say that in the second case the student with 90 is objectively borderline, since there are alternative ways to satisfy the Ideal that assign him different grades. The instructor will play an ineliminable role in assigning the borderline case a particular grade, but plays no role in making the borderline case a borderline case. So if the Ideal can be met at all, every student in the class will either have an objectively determined grade or will be objectively borderline. And anyone who engages in the practice or grading in accordance with such an Ideal can employ the notion of a “borderline case” unproblematically in these circumstances. Clearly, being an objective borderline case in the sense defined above has nothing to do with ignorance of anything. One may be ignorant of something, for example, ignorant of which grade will ultimately be assigned to a borderline case, but the definition of a borderline case does not advert to any ignorance. In real life, the existence of objective borderline cases presents a natural temptation to expand the relevant taxonomy. Since an objective borderline case is separated by at least epsilon from the clear cases both above it and below it, if one invents a new taxonomic category, one can then satisfy the Ideal uniquely. If one were grading papers, rather than assigning from a fixed set of final grades, the borderline case above would get an A/B or an A- or a B+. Taxonomic innovation of this sort often wears its origin on its sleeve.There is a utensil that has both a bowl and several prongs called a spork; my daughter sometime wears apparel with legs like shorts but a front like a skirt called a skort, and everyone is familiar with the oddly place meal called brunch. Of course, any new taxonomic structure will itself be liable to objective borderline cases: one of Homer Simpson’s claims to fame is that he “discovered a meal between breakfast and brunch.” Expansion of a taxonomy would likely be accompanied by a reduction in the size of epsilon: the more pigeonholes there are to sort things into, the less of a gap one needs between the objects sorted. Epsilon as a precise magnitude is in any case

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an evidently false idealization: rather than have a fixed value for epsilon, one looks for both a taxonomy and a value of epsilon that renders the sorting objectively determined. This puts pressures on epsilon in both directions: set epsilon too large and no sorting will satisfy the principle, set epsilon too small and many will. So far, we have normative standards than can govern a method of sorting individuals into a taxonomy. We have seen that in a particular judgment situation, if the distribution of the individuals in the objective basis has the best form, the sorting can be objectively determined. In the second best case, the sorting for some individuals will be objectively determined and the rest will be objectively borderline. There is no guarantee that either the best or second best case will obtain: there are distributions such that the epsilon principle will be violated for any reasonable setting of epsilon. But let’s leave these worst-case scenarios aside for a moment and make contact with semantics. Suppose a student is objectively determined to get an A in a class. Then it is tempting to say, even before the final grades have been officially assigned, that the student was an A student: the instructor, upon examining the distribution of aggregate scores discovers rather than decides what the grade is. Since any other assignment of a grade would violate the Ideal, the instructor has no choice in the matter. Of course, all of this talk about the discovery of a “pre-existent fact” carries no ontological weight. The only objective contribution on the side of the student is the aggregate score: there is no property that any student has that corresponds to “being an A student.” There is a sense in which the grades given a class reflect nothing over and above their aggregate scores, since the scores are the only contribution from the side of the students into the process and since (in the favorable case) those scores, together with the Ideal, determine a unique sorting. But one must be careful about exactly how this ontological point is made. When a student’s grade is objectively determined it is tempting to say that a student’s grade supervenes on her aggregate score, but for most of the technical senses of supervenience this is false. For students in the same class, there is a supervenience thesis: difference in grade implies difference in aggregate score. If this were to fail, then there would be a violation of Dominance. But for students in different classes, no such guarantee holds. An 89 in one class could be a B, and in another an A. In this obvious sense, the assignment of grades can be contextual, but may still be perfectly objective in a given context. We can make the relevant metaphysical point without recourse to the notion of supervenience: it is not that the grade supervenes on the aggregate score, but that from the point of view of ontology all that exists is a distribution of aggregate scores and a sorting procedure. The input to the sorting procedure is a judgment situation: a specification of a collection of students and a value for each student in the objective basis. In the most favorable cases, there is only one sorting of the students that completely satisfies the Ideal, so every student gets a grade. In the next most favorable situation, there are several sortings that satisfy the Ideal, so some get grades and some are objectively borderline. But the result of this sorting procedure, even in these favorable cases, does not imply the existence of anything at all in the world beside the students and their aggregate scores.

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In favorable cases, not only does the distribution of aggregate grades and the “meaning” of the grading system determine which students get particular grades and which are borderline, it also determines truth values for some counterfactuals. Suppose, in the favorable case described above, Sue’s grade falls in the cluster around 85, and she gets a B. Had she gotten ten points more, she would have gotten an A. If Sue lost 10 points on one question, she can rightly say: those 10 points made the difference between an A and a B. In such a case, for the counterfactual to be clearly true, the point difference being considered must be greater than epsilon; otherwise the counterfactual distribution of aggregate scores will not objectively determine that Sue would have gotten a different grade. So a sufficiently large jump in a score can objectively determine a change in grade, while a sufficiently small one cannot. If one happens to be thinking of changes in grades that are objectively determined, then it is correct, given the Ideal, that a difference in aggregate score less than epsilon cannot “make the difference” between grades. This is surely the sort of thing one has in mind in typical Sorites cases when one affirms that loss of one hair cannot make one bald, or gain of a penny make one rich. The locution “the loss of one hair makes the difference” directs one’s attention to cases where the objective basis (in this case, hair distribution) objectively determines the sorting. Indeed, one can even say that it is analytic, that is, follows from the meaning, that is, a consequence of the Ideal, that a difference in grade less than epsilon cannot make an objectively determined difference in a grade, while a difference greater than epsilon can.2 So far, the only place we have mentioned truth values is with regard to certain counterfactuals about grades, but we are evidently very close to making direct contact with semantics. Before we take that last step, though, let’s quickly review what has and what has not been done. We have seen so far that, given a certain grading procedure, in some favorable judgment situations it is objectively determined what grades some students get or whether they are objectively borderline. We have not, as yet, had any discussion at all of the unfavorable situations: situations where, for example, the Epsilon Principle cannot be satisfied. The usual Sorites problem presents us with exactly such a situation, so we have not yet begun to address those problematic cases. But the strategy at this point is just to convince ourselves that there are unproblematic cases for sorting in accord with the Ideal: this explains why the Ideal is useful, and why the procedure need not be abandoned even if there are some problematic cases for it. We should also note that although some account has been given of sorting in favorable situations, we have not delineated the favorable situations in completely precise language. If one were given the task of sorting judgment situations into the

2. In very special circumstances, when Sue is the outlier in a distribution that employs gaps just above epsilon, one can construct a case where changing her grade by less than epsilon would shift the sorting and therefore change her grade. But such cases rely on the fiction that epsilon is a precisely defined magnitude and the rules are applied in some ironclad fashion. In practice, all of these things are themselves vague.

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categories favorable and unfavorable, no doubt one would confront borderline cases or other problematic cases. So if we follow usual usage, and call any taxonomy cum sorting procedure vague if the sorting procedure sometimes recognizes borderline cases, then not only is the grading system vague, but the distinction of judgment situations into favorable and unfavorable and the distinction between the most favorable and next most favorable cases are also vague. There is, in this sense, second-order (and higher order) vagueness. It is almost an autonomic reaction among philosophers to point out this sort of second-order vagueness. At the moment, we merely need to note it, and also to note that there is nothing particularly threatening or worrying about it. Since our overall strategy is to emphasize the utility, coherence, and objectivity of the procedure in the favorable cases, it does not matter that the favorable cases be precisely defined, just that there be favorable cases in which it is unproblematic that we have a favorable case. Anyone who thinks that we are likely to come to grips with vagueness by analyzing vague language in completely precise terms is advised to consult the founding documents of the Neurath Ship Refurbishing Corporation. Bearing all this in mind, let’s make the connection to semantics proper. The suggestion is obvious. Suppose one is given a particular judgment situation, including the student Sue. If it is objectively determined that Sue should get a B in the situation, let us say that “Sue is a B student” is true. If it is objectively determined that Sue should get a grade other than a B, or is objectively a borderline case between two grades neither of which is a B, then let us say that “Sue is a B student” is false. And if it objectively determined that Sue is a borderline case between A and B or B and C, let us say that “Sue is a B student” is borderline. So in either of the favorable judgment situations, “Sue is a B student” is assigned one of three possible semantic values. If we accept this suggestion, then we have already established that it is sometimes true, sometimes false, and sometimes neither true nor false to assert that Sue is a B student, so bivalence fails. We have also established that “is a B student” is a vague predicate since it admits of borderline cases. We have also established that the vagueness is not epistemic. The Ideal for Grading has been made explicit, and even if there are vague elements in it, the vagueness of those elements plays no role in establishing the existence of benign borderline cases. We get the benign cases not because we are unsure of how to understand the Ideal, but because we see that, in some circumstances, the Ideal can be equally satisfied in more than one way.The existence of such cases may prompt the recommendation that the Ideal be amended by adding procedures for breaking ties in this sort of case, but we are not concerned here about criticizing the Ideal. The Ideal as it stands does a job: It guides the assignment of grades in a judgment situation. As a practical matter, it may do its job well enough for our purposes in most cases. An epistemicist about vagueness, or any defender of bivalence, must reject the suggestion made above for assigning semantic values in the favorable cases. I do not see how it can be disputed that, in the favorable cases discussed above, the assignment of a grade or the recognition of borderline status is determined by the Ideal. So any objection must be made at the point where these facts are used as a

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basis for assigning semantic values to sentences such as “Sue is a B student.” What sorts of objections are likely to arise there? Here is one possible objection. In order to have a semantic value at all, a sentence must express a proposition. But a proposition is a set of possible worlds, or a total function from possible worlds to semantic values, or a total set of truth conditions, framed to cover every possible situation. The account of the “semantic value” of “Sue is a B student,” though, is not complete in the way it would have to be to specify which proposition that sentence expresses. For although some account is given of what semantic value a sentence gets in a favorable judgment situation, not every possible judgment situation is favorable. In particular, there are Sorites sorts of situations, such as a completely flat and gapless distribution of aggregate grades. No assignment of grades in such a situation can satisfy the Ideal. Since no account has yet been given of how to deal with those cases, no proposition has been associated with the sentence, so it can’t be true. (This sort of argument has been defended by Ted Sider and David Braun [2007].) In its own terms, this objection is perfectly clear.The only question is why one should accept the animating proposal that a sentence must express a proposition (in the sense explicated) in order to be true in any circumstances. Indeed, the proposal is in serious tension with the idea that vague language is vague exactly because the applicability of terms has not been determined for all circumstances, but that nonetheless vague language can be used to express truths. That is, the proposal seems to rather seriously beg all of the foundational questions about vagueness. Why should the truth conditions of a sentence be determined in all possible circumstances in order for it to be determined in some possible circumstances? We admit that the Ideal for Grading does not display perfect universal decisiveness: in some cases it underdetermines the sorting into grades because its conditions can be met in several different ways, while in other circumstances (which we have yet to discuss) its conditions cannot be met at all. But just because a normative standard has some problematic cases, it does not follow that every case is problematic. So again, what can be said against the proposal that the sentence “Sue is a B student” is true when Sue is objectively determined to get a B? A rather convoluted sort of objection takes a long detour through metaphysics. It contends that “Sue is a B student” predicates the property of being a B student of Sue. And the truth conditions of such a sentence are just that Sue have the property so predicated. But as a matter of metaphysics, any object either has or fails to have a given property. So it is incoherent to suppose that a sentence like “Sue is a B student” could be other than true or false: it is true if she has the property and false if she does not. The answer to this metaphysical gambit has already been given. We explicitly reject the idea that as a matter of ontology there is any property of being a B student that Sue could even possibly have. On Sue’s side of the metaphysical equation, all she has is an aggregate score. Her score together with the scores of the other students in the judgment situation form the complete ontological input into the grading process. Whether that process manages to determine a specific grade for her or not makes no metaphysical difference at all to her or her classmates.

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Lying behind this sort of an objection is a rather seductive picture of the relation between semantics and metaphysics that deserves some attention. When we do semantics for a formal language, as in first-order logic, we explicate how an atomic sentence in subject/predicate form gets a truth value as follows. First, one has to supply the language with an interpretation. This means specifying a domain, which is just a set of elements. One then associates with each individual constant an element in the domain, and with each predicate a subset of the domain. An atomic sentence of subject/predicate form is true if the object associated with the individual constant is an element of the set associated with the predicate, and false otherwise. This picture of semantics encourages a method by which we try to discover the correct ontological account of the world by first collecting together sentences we take (for one reason or another) to be true and then considering what objects must be in the world and what subsets must be associated with predicates in order for the sentences to come out true. And if one adds that the most obvious way to associate a subset with a predicate is to associate a property to it, then we are well on our way to trying to discern both what objects and what properties the world contains by reflection on sentences we accept as true together with the semantics of the predicate calculus. No doubt, if an individual term somehow denotes an object in the world, and if a predicate somehow denotes a property, then the truth conditions for a sentence which predicates the predicate of the term should be that the corresponding object have the corresponding property. But there is no reason to suppose that every true sentence of subject/predicate form has truth conditions of this kind. What is on the table now is a different proposal for understanding how sentences like “Sue is a B student” can be assigned a truth value in a particular judgment situation, even though the predicate does not denote any property. Some such proposal must be on offer if, on the one hand, we want to maintain that sentences involving vague predicates can sometimes be true, and on the other, we don’t want to cram our ontology with properties that correspond to each vague predicate. The method for assigning truth values offered above secures a connection between the truth value assigned to “Sue is a B student” and the truth value of the subjunctive conditional “If someone following the Ideal were to assign grades to this class, he would assign Sue a B.” If Sue is objectively determined to get a B, then the subjunctive conditional is true; if she is objectively determined not to get a B, then it is false. If Sue is objectively borderline, then the truth value of the subjunctive conditional depends on how the semantics for modal discourse is constructed. If we treat all assignments of grades that satisfy the Ideal as possible worlds, all equally accessible and equally distant from the actual world, then there are some such worlds in which Sue is assigned a B and some in which she isn’t. We might argue that in such a situation the subjunctive conditional is neither true nor false, in which case the conditional fails to have a classical truth value whenever Sue is objectively borderline. But it is exactly because the semantics of the subjunctive conditional is controversial that I do not want to analyze the truth value of “Sue is a B student” in terms of the associated subjunctive conditional. We have already given semantic conditions for “Sue is a B student” that do not advert to what

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anyone would do. In the favorable cases, the role of the person assigning the grades disappears from view, and there is no reason to gratuitously let it back in via the subjunctive conditional. If the world were guaranteed only to contain favorable judgment situations, our work would be done. The Sorites argument, however, is the starkest possible reminder that the world need not be so accommodating. So it is time to turn to the unfavorable situations. SORTING WITHOUT GAPS Unfortunately, we sometimes have to assign grades even when the distribution in the objective basis presents no epsilon-sized gaps. If the distribution is both gapless and flat, the objective side of the sorting process provides no useful input about how to sort, so the decision about where to stop giving one grade and start giving another must be motivated by something other than the Ideal, just as the final decision in the case of objective borderline cases is not dictated by the Ideal. What sort of semantics is appropriate to this situation? As a warm-up to this question, let’s first engage in a bit of fiction. We have said that the four conditions listed in the Ideal are ranked: Most important to satisfy are Absolute Paradigms and Dominance, less important are the Soft Targets and the Epsilon Principle. Suppose the ranking were otherwise, and the Epsilon Principle were more important to maintain than Absolute Paradigms. Then when faced with a flat, gapless aggregate score distribution, one would be required to give all the students in the class the same grade. Since the Ideal does not put requirements on what that grade should be, every member of the class would be objectively borderline. Knowledge of the Ideal and the distribution in the objective basis would not allow one to predict what any grade given to any student will be. If the Ideal were arranged in this way, then the Epsilon Principle would always be satisfied in any judgment situation, but the “Absolute” Paradigms would no longer be Absolute: They would be defeasible. In some classes, either students with an aggregate score of 95 would not be assigned an A, or students with a 50 would not be assigned an F, or both. And the answer to the Sorites paradox would be straightforward. The paradox arises from the desire to satisfy the Absolute Paradigms and also to satisfy the Epsilon Principle in a flat gapless judgment situation. That, of course, is impossible: One or the other must be violated. If the Absolute Paradigms were violated, then there would be no problem about “hidden lines” or “unknowable boundaries,” since no such boundary (between different assigned grades) would exist in the problematic situation. One would have to concede that in some situations, Sue’s getting an aggregate score of 95 does not make “Sue is an A student” true, and does not constitute a guarantee that she will be assigned an A. But that does not mean that “Sue is an A student” is never true in any judgment situation. Nor would it render the whole practice of assigning grades in accordance with the Ideal empty or pointless, since many judgment situations are not problematic. Where the Ideal can be fully satisfied, it does not matter how the different principles mentioned in the Ideal are ranked, so having an Absolute Epsilon

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Principle and Defeasible Paradigms would make no material difference in favorable situations. The Sorites situation, no matter how it is dealt with, cannot be parlayed into a threat against the use of the Ideal in all situations. The reason that the Sorites situation might appear to be a general threat to the practice of assigning grades is because one can easily lose sight of the important role that the judgment situation plays. Presented with Sue, who has an aggregate grade of 95, one is inclined to say: if this isn’t an A student then no one is. More formally, one might mistakenly believe that the truth value of “Sue is an A student” must strongly supervene on her aggregate score, so whatever goes for her goes for all students with that score. If so, then the problems that arise in the Sorites situation will export to all situations: If all the students in that situation are borderline, then every student in every situation is borderline. But as we have seen, the truth value of “Sue is an A student” need not supervene on Sue’s aggregate score. The only relevant supervenience thesis governs complete judgment situations, not individuals: If two judgment situations are identical with respect to the objective basis, then a student in one class will be objectively determined to have a grade, or to be borderline, if and only if the corresponding student in the other class is. Two students with identical aggregate grades can be objectively determined to have different grades if they happen to inhabit different classes. So the Sorites would not present much of an analytical problem under the revised Ideal: one would simply point out that in certain situations, the Defeasible Paradigms are, in fact, defeated. How exactly they are defeated will depend on the arbitrary decision of the grader. No more can be said. But although the revised Ideal would make life easy for philosophical analysis, actual grading adheres to the original Ideal, and we must deal with it. The problem with the revised Ideal is that it defeats the very purpose of grading in the problematic situation. Grades are supposed to provide coarse-grained information about the distribution of aggregate scores in the judgment situation. If every student in a class with a flat, gapless distribution gets the same grade, then the grades convey no information at all about the objective basis.The Epsilon Principle is defended, but only by undermining the whole point of the exercise. So in practice, it is the Epsilon Principle that is defeasible and the Paradigms that are absolute. Even in a flat, gapless distribution, anyone who has a 95 aggregate score will get an A and anyone with a 50 will get an F. And therefore, somewhere or other, students with scores that differ by less than Epsilon will nonetheless get different grades.And the Ideal does not specify where those breaks will come: they are not determined by the “meaning.” What about semantics in unfavorable situations? Suppose we have 201 students in the class, each conveniently with a different integer or half-integer aggregate score. As usual, we use the score as a name of the student. What then should be the semantic value of “100 is an A student” or “92 is an A student” or “3 is an A student”? So far we have only provided semantic conditions for sentences of this form for favorable judgment situations: “92 is an A student” is to be true if 92 is objectively determined to get an A, that is, if the Ideal can be satisfied and if every

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way it can be satisfied assigns 92 an A. In a Sorites situation, though, no one is objectively determined to be anything, since the Ideal cannot be satisfied. Still, we would like it to come out, even in this situation, that “100 is an A student” is true and “3 is an A student” is false. This can be done in several ways. The simplest way is this. Even where the Ideal cannot be fully satisfied, it does not become irrelevant to the assignment of grades. We have specified that when not all of the conditions in the Ideal can be met, Dominance and Absolute Paradigms take precedence over the Epsilon Principle. So even in the Sorites situation, everyone at 95 and above must get and A, and everyone at 50 and below must get an F. The first suggestion, then is this: let “n is an A student” be true in this situation iff n’s aggregate score is 95 or above. And let “n is an A student” be false in this situation if it is true that n is a student with some other grade, for example, if “n is an F student” is true. And similarly, let “n is an F student” be true if n’s aggregate score is 50 or lower. Then it will be true that 100 is an A student and false that 3 is, as we wished. Here’s a second suggestion. Since 95 is a paradigm A, and since the Epsilon Principle reflects our desire to treat differences less than epsilon as insignificant for grading purposes, let’s let “n is an A student” be true if n’s score is within epsilon of a paradigm A score, and similarly for F. Then “n is an A student” will be true for all students with scores 94 and above, and “n is an F student” true for all scores 51 and below. This “stretching” of the truth range must not, of course, be iterated. That is, one must not argue that since it is true that 94 is an A student, it follows that 94 is a paradigm A student, so it must be true that 93 is an A student. The method does not condone such iteration, which only results from confusing the truth value of “n is an A student” with the status of n as a paradigm. It would be natural, in a Sorites situation, to apply the same technique to the intermediate grades, using the Soft Targets rather than the Absolute Paradigms. Since the distribution is both gapless and flat, the Epsilon Principle will be equally violated no matter where the boundary between different grades is put, so there is no pressure to shift the Soft Targets. (If the distribution were gapless but not flat, with scores piled up more in some regions than others, then there would be pressure to run the boundaries through the valleys in the distribution, as we have seen.) So presumably any student who exactly hits the Soft Target for a B will be assigned a B, and anyone who is within epsilon of that soft target will also get a B. With epsilon set at 1 and the soft target for a B at 85, then, “n is a B student” will be true for any student with a score between 84 and 86. “n is an A student” will therefore be false for students in the region, and also for any students with lower scores, since by Dominance they can’t get A’s if the students above them get B’s. If we only have the grades A, B, C, D, and F available, and we set the Absolute Paradigms for A and F at 95 and 50 respectively, and the Soft Targets for B, C, and D at 85, 75 and 65 respectively, it is easy to calculate the results. “n is an A student” is true for student 94 but neither true nor false for student 93.5. The borderline A/B cases run from 93.5 to 86.5, while it is true to say that 86 is a B student and false to say that he is an A student. And so on. Once again, a sentence of the form “n is an A student” can have either of three truth values: true, false, and borderline. And once again, the truth values of

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the sentence will presumably have predictive power when it comes to guessing how the final distribution of grades will go. When the instructor finally settles on grade, all of the students for which “n is an A student” is true will get A’s, and the borderline between the A’s and the B’s will run somewhere in the region where both “n is an A student” and “n is an B student” are borderline. There is an obvious sense in which this semantics has sharp cutoffs: the semantic value of “94 is an A student” differs from that of “93.5 is an A student,” and if there had been even more students, whose scores were separated by even smaller gaps, there would be students whose aggregate scores are as close together as one likes, but still for whom the corresponding sentences get different truth values. Such sharp cutoffs in the semantics are generally thought to be objectionable in an account of vagueness, and we will turn to those objections presently. But for the moment, let’s just leave the semantics as specified and analyze the Sorites Paradox. We can think of the Sorites Paradox as having a certain canonical form.There is some predicate P, there is some conditional connective fi, and there is some (usually finite) series of individuals 1, 2, . . . N who differ from each other in only very small amounts in the objective basis. For heaps, the objective basis is usually numbers of grains, for baldness, number of hairs, for richness net worth. (These are obvious simplifications: It is both number and distribution and length of hair that determines baldness, both number and distribution of grains heapishness, and so on.) One then considers the set of sentence: {P(1), P(1) fi P(2), P(2) fi P(3), . . . P(N - 1) fi P(N), P(N)}. It is impossible for these four conditions to jointly hold: P(1) is true, P(N) is not true, all the conditionals are true, and the conditional supports modus ponens as a valid (i.e. truth-preserving) rule of inference. For any such Sorites series, then, at least one of the conditions must be rejected. We get a particular Sorites argument by specifying both the relevant predicate P and by specifying the relevant conditional fi. In our case, there is a substantial risk of confusion since there are various predicates and various conditionals from which a Sorites argument can be constructed. In particular, there are three different sorts predicate that we have made use of: “x is an A student,” “x is objectively determined to get an A,” and “x is assigned an A.” The truth conditions for these predicates are obviously different: a student can be assigned an A in a class even though she was not objectively determined to get an A (maybe she was objectively borderline), and it can be true that a student is an A student even though she is not objectively determined to get an A (e.g., in a Sorites situation). And as a matter of logic, a student can be assigned any grade no matter what grade she is objectively determined to get, since the instructor can refuse to abide by the Ideal. If we restrict our attention to instructors who do not needlessly violate the Ideal, then the truth of “n is objectively determined to get an A” guarantees the truth of “n is assigned an A” as well as “n is an A student.” On the side of the connective, there are two obvious candidates. We can use a material conditional of some sort, or a subjunctive conditional. So all told, there are six different possible Sorites arguments we can construct, depending on choice of predicate and conditional. We need to consider all six, because the resolution of different arguments is different.

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Let’s begin with the arguments using the material conditional. The first predicate to consider is “x is an A student.” This gives us a Sorites series that starts with “100 is an A student,” end with “0 is an A student,” and has conditionals of the form “If 95 is an A student, then 94.5 is an A student.” The first sentence is true, the last sentence is false, and modus ponens for the material conditional is valid. So at least one of the conditionals must not be true. And, indeed, several are not true. In particular, “If 94 is an A student, then 93.5 is an A student” is not true, so the argument becomes unsound when it employs that conditional. Of course, “If 94 is an A student, then 93.5 is an A student” is not false either: its semantic value is borderline. So there is no problem resolving this Sorites argument. One might, of course, have been misled if one thought that every untrue sentence is false, for then there would have to be a sharp cutoff between students of whom it is true to say they are A students and students of whom it is false to say that. There is no such sharp boundary, exactly because the true sentences are separated from the false ones by a buffer of borderline sentences. We were only able to identify the first premise that fails to be true because the semantics provides a sharp cutoff.And, as noted above, this sharp cutoff may be objectionable. But we are holding off that objection for the moment, so let’s go on. The second Sorites argument uses the predicate “x is objectively determined to get an A.” In a Sorites situation, “x is objectively determined to get an A” is always false: since no sorting can fully satisfy the Ideal, no student is objectively determined to get any grade. So the resolution of the Sorites is easy: All the conditionals are true, and two unconditional sentences are false. The argument is again valid but unsound. The third argument uses the predicate “x is assigned an A.” Now we have to assume that the unlucky instructor, faced with this difficult situation, has in fact given out the grades. The grades will presumably satisfy Absolute Paradigms and Dominance, but violate the Epsilon Principle: Some students will get different grades even though their aggregate scores differ by less than a single point. The resolution of this Sorites is also trivial: “100 is assigned an A” is true, “0 is assigned an A” is false, and exactly one of the conditional premises is false. The false premise will fall wherever the instructor decided to put the boundary between grades, and we are not in a position to identify that location. Different instructors, faced with the same grading situation, will put the boundaries in different locations, and all equally legitimately. The instructor could even flip a coin to decide where in the borderline region the boundary should run, and no one would have a complaint against the method. Unlike the first case, there is not merely an untrue conditional sentence, but a false one. But also unlike the first case, the location of the false premise is determined by extra-semantic facts. Nothing in the meaning (i.e. in the rules governing the grading procedure) determines where the boundary runs. So if one understands the claim that the grading system is vague as the claim that the rules of the system do not determine, in every instance, exactly who gets what grade, then the system is still vague. If the system directed the instructor in a case like this exactly where to draw the line, the system would not be vague.

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The resolutions to these paradoxes are perhaps a bit too straightforward to be entirely satisfying. After all, a paradox is only a paradox if one feels a strong inclination to accept all the premises, but an equally strong inclination to reject the conclusion. In the first and last cases, the resolution comes by rejecting one of the conditional premises. In the second case, all of the conditional premises are true, but only trivially so: they are true just because their antecedents are uniformly false. So the question is: Why would anyone have been strongly attracted to the collection of conditional premises in the first place? Surely not because, on one reading of the predicate, they are all trivially true. There is already some explanation for our attraction to the conditionals, even in the first and third forms of the paradox. As we have noted, in the first form, none of the conditionals is false, so we might feel inclined to regard them all as true. And in the third, exactly one conditional will be false, but we have no means to tell a priori which it is. So in either case, rejecting a particular conditional might be uneasy. But I don’t think these explanations go to the heart of the matter. Our attachment to the conditionals is more robust, and has a deeper source, than these explanations indicate. In order to understand that source, we need to look at the forms of the arguments that employ the subjunctive conditional rather than the material conditional. In particular, we need to consider the form that uses the predicate “x is objectively determined to get an A” together with the subjunctive conditional. The unconditional premises remain the same, but the conditionals have forms like: “If 94 were objectively determined to get an A, then 93.5 would be objectively determined to get an A,” and so on. Once again, in the Sorites situation the unconditional premises are false, since no one in this situation is objectively determined to get any grade. But the subjunctive conditionals in this case are all true, and not for trivial reasons. The subjunctive conditionals are all true exactly because the Ideal contains the Epsilon Principle. If 94 had been objectively determined to get an A, then there would have been some way to completely satisfy the Ideal, and every such way would assign 94 an A. And since 93.5 is within epsilon of 94, every such way of satisfying the Ideal would also have assigned 93.5 an A. So 93.5 would also have been objectively determined to get an A. In this sense, the truth of these subjunctive conditionals is “analytic”: it follows from the very content of the Ideal. Our insistence on (ambiguous) conditionals like “If 94 is an A then surely 93.5 is,” or “if this guy is bald, then surely the next guy, with only one more hair is,” arises from the role that the Epsilon Principle plays in the Ideal.And properly understood, they are all true.As we survey the long Sorites series, we recognize not only that we do not know where to put a line between, for example, those who are bald and those who are not, but also that the very practice that governs the use of “bald” (defeasibly) enjoins us not to make a distinction between men who differ in only one hair. Furthermore, if most judgments situations are favorable, we are typically able to obey the injunction. In most cases, we do not make a distinction in final

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grade between two students whose aggregate grades differ only by half a point. When we can, we take positive measures to avoid such a result, by letting the boundaries between grades vary from class to class. We also become acutely aware, when such a distinction must be made, that it is we ourselves, without any direction from the Ideal, who must decide where the ax is to fall. We give the grades with an uneasy conscience, since students who performed so similarly are being treated so differently. The arbitrariness of the distinction is manifest. On the other hand, as we have seen, in favorable judgment situations, the Ideal does all the work: The students “sort themselves” into their grades. And because of the Epsilon Principle, in these situations, students with nearly identical aggregate scores never sort themselves into different grades. So as we survey the long Sorites series, with no noticeable gaps, we feel at each location that we would not make a distinction here if we could avoid it. Of course, if forced to sort into the bald and the non-bald, or the heaps and the non-heaps, then we cannot avoid making a cut somewhere, and we do. The other two Sorites arguments, using the subjunctive conditional and the other predicates, do not yield much new. For in those cases, the first unconditional premise, “100 is an A student” or “100 is assigned an A,” is true, and a subjunctive conditional with a true antecedent is usually considered to have the same truth conditions as the material conditional. So the series of subjective conditionals will depart from being true at exactly the same point that the series of material conditionals did. Even so, the subjunctive conditional allows us to use conditionals to get at elements in the Ideal. Consider, for example, the subjunctive conditionals “If 34 were an A student, then 35 would be an A student,” “If 34 were assigned an A, then 35 would be assigned an A” and “If 34 were objectively determined to be an A, then 35 would be objectively determined to be an A.” All of these subjunctive conditionals have impossible antecedents: in no circumstance could the antecedent be true. Nonetheless, all three subjunctive conditionals are unproblematically true, and not because the antecedents are impossible. They are all unproblematically true because the Ideal contains Dominance as an absolute principle. Similarly for a case of two borderline A/B students with scores of 89 and 90: if the 89 were an A (in any sense), so too would the 90 be. These sorts of subjunctive conditionals are what Kit Fine calls “penumbral truths” (Fine 1975, 270). Fine has noted that there are “penumbral connections” among vague terms, and has tried to express the content of those connections in some penumbral truths. He then complains that approaches to vagueness that use multiple truth values and truth-functional connectives cannot get the penumbral truths right. And that is right: the material conditional “If 90 is an A student then 89 is” is borderline, since the antecedent and consequent each are. The right conclusion to draw is that penumbral connections are reflected in (non-truthfunctional) subjunctive conditionals, not material conditionals. The deeper conclusion is that the right way to get at penumbral connections is not through penumbral truths in the first place. What backs the penumbral truths is the structure of the Ideal. It is the Ideal that specifies how different vague terms, and judgments employing them, are to be related to one another. The truths are

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signs of the structure of the Ideal, but the direct route to the connections is through the Ideal itself. The advantage to this way of understanding things is that there can be penumbral connections, elements of the Ideal, that do not always give rise to truths. Such is the Epsilon Principle: It does constitute a penumbral connection, since it specifies a constraint on how nearby borderline cases are to be resolved. But it is a defeasible condition, and so it does not always guarantee the truth of the claim that nearby borderline cases are resolved the same way. By focusing on the Ideal rather than the semantic status of sentences governed by the Ideal (such as the penumbral truths), finer distinctions can be drawn. We might finally note that the existence of the various predicates comports well with some terminology that almost spontaneously appears when discussing vagueness. Attempts to construct a formal language suitable for vague predicates often introduce an operator read “determinately,” or make a distinction between sentences that are true and those that are determinately true. The function of the operator, and the distinction between the two kinds of truth, however, can be obscure. A different understanding of the intuitive meaning of “determinately,” though, is available to us. The adverb is used not as a sentence operator, but as an indication that the predicate under consideration concerns what is objectively determined. Thus “Determinately, Sue is either an A or a B, but she is neither determinately A nor determinately B” can be reexpressed as “Sue is objectively determined to get either an A or a B, but not objectively determined to get an A nor objectively determined to get a B.” This sentence can be true if Sue is objectively borderline between A and B. Similarly, “John is bald but not determinately bald” could be rendered “John is bald, but not objectively determined to be bald.” If John is, for example, only slightly more hairy than a paradigm bald man in a Sorites series, this could be true. The supposed distinction between truth and determinate truth would be an illusion: to say that a sentence is determinately true is just to say that the sentence prefixed by “Determinately” is true, which is to say that the sentence is true when the predicates are understood to refer to what is objectively determined.

SHARP SEMANTIC CUTOFFS AND HIGHER-ORDER VAGUENESS Our account so far has provided conditions under which a sentence can fail to have a classical truth value. In the Sorites situation, the account has even specified a place in the Sorites sequence where the classical truth values stop and the truth value borderline begins. This is almost universally regarded as an objectionable feature of any account of vagueness. Let’s begin by clearly separating three sorts of objections. The first objection is the most radical. It contends that the existence of sharp cutoffs indicates that what is been proposed is not an account of vagueness at all. The language described has no vague terms: It has perfectly precise terms, albeit with nonclassical truth values. A vague language simply contains no sharp

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boundaries anywhere, so the very existence of such sharp semantic boundaries shows the language isn’t vague. This objection is just a non sequitur. The account above describes a language with something vague in it: The method for assigning final grades on the basis of aggregate scores is vague. That method does not determine, in all cases, exactly what grade a student with a perfectly determinate aggregate score, in a class of students with perfectly determinate aggregate scores, should get. That method admits of borderline cases, in which different final grades can be assigned with equal (and maximal) legitimacy. It is the existence of such borderline cases that signals vagueness: Whether there is a sharp boundary between the borderline cases and non-borderline cases is neither here nor there. That rather concerns the question of whether the predicate “borderline” is itself vague. Furthermore, the semantics does not require that there by any “sharp boundaries” between the borderline and non-borderline cases. In a favorable situation of the second sort, there are objectively borderline cases, but no such exact boundary. The sorting of students into the categories “borderline” and “non-borderline” is objective, but that sorting nowhere draws a line in the continuum of possible aggregate scores. It is only when dealing with non-favorable cases, like the Sorites situation, that we have introduced machinery that allows such a line to be drawn. The second sort of objection to sharp cutoffs is not really an argument against them: It is a tu quoque argument meant to support the epistemicist. The epistemicist seizes upon the existence of sharp semantic cutoffs between, say, true sentences and borderline sentences to argue by analogy for the acceptability of a sharp cutoff between true sentences and false sentences. After all, the epistemicist complains, if you are allowed your sharp semantic divisions why aren’t I allowed such sharp cutoffs? The main objection to epistemicism is the postulation of a line that separates the bald from the non-bald: What advantage is there in rejecting this in favor of a sharp line that separates the bald from the borderline bald? Timothy Williamson uses this sort of tu quoque repeatedly. He even imagines a very fanciful scenario, with several omniscient agents who are instructed to resolve all possible vagueness in a certain way, simply to argue that any account of vagueness must be committed to some sort of sharp cutoff between something and something else. As Williamson states it: “Thus, if all are instructed to be conservative, all will stop at the same point [i.e. all will stop answering ‘yes’ to ‘Is this a heap’ when asked sequentially about a Sorites series].You do not know in advance where it will come. It marks some previously hidden boundary, although it may be a delicate matter to say just what it is a boundary between” (Williamson 1994, 200). And then, in conclusion, “Once hidden lines are admitted, why should a line between truth and falsity not be one of them?” (Williamson 1994, 201). Well, the account above does postulate a line between true sentences and borderline sentences, but the reason that gives us no reason to accept a line between true sentences and false sentences is that, in that account, it is not a line between true sentences and false sentences. And in the account above, there is no such line between true sentences and false sentences, between the students of which it is true to say they are A students and the students of which it is false to say

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they are A students. And furthermore, the account given above, which rejects bivalence and epistemicism, is actually an account of how the language works. Williamson offers no such account, but only the bare assertions that maybe, somehow or other, our usage determines a meaning that draws a sharp line between true and false. And he certainly can’t help himself to our account in defense of his supposed sharp boundaries. The third objection against sharp cutoffs is of an entirely different tenor. It objects not that the sharp cutoffs render the language precise, rather than vague, or that they render the account no more plausible than epistemicism, but that the sharp cutoffs are simply implausible. In the case, we have discussed, the objection is perfectly valid. It turns out, however, not to be particularly significant. Why did we get, in the Sorites series, a perfectly sharp cutoff between students of whom “is an A student” is true and those of whom it is borderline? Because the terms in which the relevant part of Ideal was formulated were supposed to be perfectly precise. We have been imagining that the Ideal supplies an exact number, in the objective basis, for the Absolute Paradigms, and also that the value of epsilon is perfectly precise. Since we used these values to determine where the true sentences end and the borderline sentences begin, we could draw a precise boundary. We got precision out in the semantics because we put precision in in the Ideal. And this is clearly inaccurate, even in the very artificial case of assigning grades. When I assign grades, I use the system outlined here, but I do not have any precise values in the objective basis for the Absolute Paradigms, nor any precise value for epsilon. Both of these are themselves vague. And since these are vague, to try to draw a boundary between the true sentences and the borderline sentences by subtracting the value of epsilon from the value assigned to the paradigm is not to succeed in drawing a sharp boundary. The vagueness in the language used to frame the Ideal leads to second order vagueness in the system governed by that Ideal. Not only may there be (first-order) borderline cases, where the Ideal does not determine a grade, there can be (second-order) borderline cases where the system does determine whether or not a case is a (first-order) borderline case. All of this is perfectly correct. But the overriding question that arises is: So what? What difference does it make if there is second-order, or third-order, or higher-order vagueness? The existence of higher order vagueness certainly does not undercut the account we have given of vagueness. There is vagueness because there are borderline cases. We have seen how borderline cases can arise even if the language used to “give the meaning” (state the Ideal) is perfectly precise. Making that language itself vague rather than precise will not make the first-order vagueness go away. There are cases where is it objectively determined that a student gets an A. The actuality, or mere possibility, of borderline A’s does not threaten this. Similarly, there are cases where a value for epsilon is appropriate. In the case of grading, if we can satisfy the Epsilon Principle with epsilon equal to two, that epsilon is clearly appropriate. No one could complain that epsilon was set too low. And similarly, there are values of epsilon that are clearly inappropriate. If epsilon is set at 0.01, and the grading boundaries are shifted to run them through gaps of only just that

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size, that is clearly inappropriate. But in some situations, there will be a wide range of settings for epsilon all of which are appropriate, and all of which would give the same objective sorting. In those cases, the vagueness in setting epsilon makes no difference. The machinery works perfectly well even though no exact value for epsilon has been set. The point of the account so far is to show how there can be unproblematic situations where grades are assigned even though the grading system is vague, and can run into cases where arbitrary decisions must be made. If that account is correct, then there can be situations where the application of the Ideal is unproblematic even though, being vague, the Ideal may have its own problematic situations. As a matter of empirical fact, my own grading often confronts first-order vagueness and almost never second-order. I often have to decide borderline grades, but almost never find myself wondering whether a gap in the grading distribution is large enough to be used as a break between grades. How many orders of vagueness are there? We have seen that a perfectly precise Ideal would give rise to first order but not second order vagueness. In the grading situation, there is certainly second-order vagueness because the terms of Ideal are themselves vague. What if we try to formulate an Ideal for, say, setting the value of Epsilon? Will it also be vague, leading to third-order vagueness, or not? It all depends on the language used to specify that Ideal. If it is perfectly precise, then there will be second-order vagueness in the grading system but not third-order. If it is vague, there will be more orders. At this point, we have two choices. Either we think that some perfectly precise fragment of language is possible, or we do not. If we do think it possible, then how many orders of vagueness there are in any given case is contingent. We start explicating the vague terms by means of Ideals. If those have vague terms, we do the same. If we eventually manage to reach a point where an Ideal can be specified in the precise fragment of the language, then the iteration stops. It stops where it does, at the fourth or eighteenth level, because that’s where the precise fragment suffices. Alternatively, the iterations may never end, either because there is no precise fragment of the language at all, or because it never provides the resources to specify the relevant Ideal. If one is inclined to think that a precise language is in principle impossible, that all language is vague, then one will obviously conclude that there are unending orders of vagueness. This would be an interesting result, but not an especially important one. Or at least, the account of vagueness we have offered is not hostage to this question. However, it turns out, the basic account of vagueness on offer will be unchanged. JUDGMENT SITUATIONS We have used the practical problem of assigning grades on the basis of aggregate scores as an instructive example of how vagueness may arise in a system. In outlining the normative rules governing the assignment of grades, we initially also made an unrealistic idealization: We imagined that various elements of the Ideal were themselves precisely defined when in reality they are vague. But the

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institution of grading involves yet another peculiarity that we have made use of, and which has no exact analog when it comes to sorting collections of grains into heaps and non-heaps, or sorting men into the bald and the non-bald. For in grading, there is always a precisely defined judgment situation, a specific set of students with specific aggregate scores who must be sorted into the different final grades. The judgment situation has played an important role in our account: The very same student, with the very same aggregate score, can be objectively determined to get an A in one class and objectively determined to get a B in another. By analogy, we would have that a particular man could be objectively determined to be bald in one judgment situation (where the only salient break between the bald and the nonbald occurs above him in hair-distribution space) and objectively determined to be not bald in another (where the only salient break is below him).3 So whether it is true or false to say he is bald would depend on the judgment situation in which he is considered. There is a bad reason to be worried about this that we have already noted. It is a consequence of this account that “Sam is bald” can change from true to false (or borderline to true or to false) simply by relocating Sam from one judgment situation to another. But, the worry goes, how can “Sam is bald” change its truth value without the hair on Sam’s head changing? The truth value of “Sam is bald” must supervene on the state of his head, and so cannot change just because he is being considered in different contexts. If baldness were any sort of property at all, this would be a real problem. For if baldness was any sort of property at all, then it would presumably be an intrinsic property of Sam’s head, and hence Sam could not lose the property without his head changing its physical state. And if baldness were any sort of property at all then “Sam is bald” would be true just in case Sam had the property and false just in case he didn’t. So the sentence could not change truth value without an intrinsic change to Sam. We have already rejected the claim that baldness is a property of any sort, and a fortiori that it is an intrinsic property. We therefore have no commitment to the supervenience of the truth value of “Sam is bald” on the state of Sam’s head. But one still may worry that in real life (unlike in grading) we are not confronted with clear-cut judgment situations, so the whole machinery we have advocated can get no purchase. The only completely objective judgment situation relevant to the baldness of men, for example, is the situation that includes all actual men from all times. But that distribution is clearly a Sorites distribution: It will contain no salient gaps that could be used to separate the bald from the non-bald. The problem of the judgment situation is a problem, but it ought not to be overstated. In many real-life situations, the relevant class to be sorted is uncontroversial. If I have to sort my silverware into the little bins in the drawer, the existence of sporks somewhere in the universe need not detain me. If the shoe store manager tells an employee to put the shoes on one side and the boots on the other,

3. The man in question would have to be hairier than an Absolute Paradigm bald man, and balder than an Absolute Paradigm non-bald man.

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the existence elsewhere of borderline cases between the two, or even worse, the merely possible existence of borderline cases, will not keep “This is a shoe” from being objectively determined to be true. Sorites situations occur when the judgment situation contains too many items that are too closely spaced in the objective basis. One might worry about the opposite problem: Isn’t a shoe sitting alone in the desert, with nothing else to compare it with, still truly a shoe? This is less of a problem: Absolute Paradigm shoes, we think, mark out a region in “shoe space” which, by Dominance, guarantees that many things are truly shoes. It is important to note in this regard that the greatest utility comes from Absolute Paradigms that are not at extremes in the objective basis. The student who gets a 100 is not a useful Absolute Paradigm A, since few grades will be settled by comparison to her. What one wants is the lowest grade that can count as a paradigm A, and the highest that can count as an F. These, plus Dominance, will settle the most cases and leave the smallest range of borderline cases. (There is, however, some counter-pressure here: the smaller the gap between a Paradigm bald and Paradigm non-bald person, the less likely it is that an epsilon-sized gap in the distribution will run through the region between them that can serve to objectively determine the sorting.) So it is not clear after all that vagueness about the judgment situation will be of much material consequence in usual situations. There is, however, one circumstance where the option of changing the judgment situation seems quite important. Suppose one is confronted with a Sorites series. Suppose, to vary the example, one is confronted with a very long line of color tiles which change, by insensible gradations, from fire-engine red to a pastel pink. Starting at the red end of the series, one is to walk along and call out the color of the tiles.The only colors one can call are “red” and “pink.” The situation has been described so that the judgment situation includes all of the color tiles. But still, as one stands at one end of the series there is a strong inclination to include only the first part of the series, the part in view, in the judgment situation. Relative to that judgment situation, all of the tiles are objectively determined to be red: the Epsilon Principle can be satisfied by counting all the tiles as the same color, and the only color consistent with the Absolute Paradigms in that situation is red. Once the judgment situation expands to include paradigm pink tiles, there will be no way to satisfy the Ideal, but at one end of the series there is little pressure to include the distant pink tiles in the consideration. As we walk down the series of tiles, there will be a strong inclination to treat the series as a sequence of small judgment situations rather than as a single large judgment situation. Suppose we include in the situation only the next ten or twenty tiles, along with the last twenty that we have already passed. At the beginning, all the tiles are objectively red. Once the lightest paradigm red tile is far enough behind us not to be included in the situation, all the tiles will be objectively borderline, so we could properly either judge them all to be red or all pink. There is probably some mental inertia that will induce us to continue calling the tiles red, but that is a matter of contingent psychology. As we pass through the border region, well beyond the last paradigm red and well before the first paradigm pink, there will be increasing pressure to call all of the tiles in the present judgment

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situation pink, and when the first paradigm pink tile comes into consideration, all the tiles in the restricted judgment situation will be objectively determined to be pink. So at some time we will stop calling the tiles red and start classing them pink. But if this is how we treat the situation, the switch from “red” to “pink” will not be occasioned by ever making the judgment of two adjacent tiles that one is red and the next is pink. Rather, the shift will be associated with a change in psychological “set”: the tile before us will appear to be pink, but so will many of the tiles behind us, which we had already denominated red. If we were allowed to, we would change our earlier denominations given our present judgment situation. So given the constraints of the task, there will be a particular point at which we switch from saying “red” to “pink,” but that change will not come because we ever have the impression that the Epsilon Principle is being violated. It never seems to us that a tile is a different color from an adjacent tile, it rather seems, all of a sudden, that a whole set of tiles (the present small judgment situation) are a different shade from an immediately previous set even though the two sets have most of their tiles in common. Indeed, it is perfectly possible that we will suddenly feel as though the color of a set of tiles has changed even though it is the very same set:The change in appearance is a subjective change of the set as a whole, much like the subjective change of appearance in a Necker cube. And just as we know, when we study the Necker cube, that the change in its appearance to us does not reflect any change in the drawing, so too we know that a change in psychological set is a change in us, not a change in the objects being observed. This is another reason why we are so loath to reject any of the conditionals used in the Sorites argument. For not only is it never the case that one tile is objectively determined to be red and the adjacent tile objectively determined to be pink, and never the case that it is true that one tile is red and true that the adjacent tile is pink, it is also never the case that one tile will appear to us to be red and simultaneously the adjacent tile appear to us to be pink. It seems to follow that if the first tile appears to us to be red, then they will all appear to be red. Like the frog in the slowly heated pot who boils to death rather than jumping out because the temperature rises so slowly, it seems as though we will be induced to call even the pale pink tile “red” since we could never distinguish between two adjacent tiles. But the conclusion does not follow: It only follows that when we finally change our mind about the color, we will at the same time change our mind about some tiles we had already called “red.” So yet another diagnoses of the appeal of the conditionals used in the Sorites is this: The conditionals are each individually appealing because for each conditional of the form “If n is red, then n + 1 is red” there is a judgment situation in which it is, unproblematically, true. Furthermore, these judgments situations are all proper subsets of the complete Sorites situation:They can be constructed by simply deleting some of the cases to be judged. But although there is, for each conditional, a situation in which it is true, there is no situation in which they are all simultaneously true. We balk at rejecting any particular conditional because we can easily find a judgment situation in which that conditional ought not to be rejected. According to this analysis, what fails in the Sorites argument is its validity. Since the truth value of some claims may depend on the particular judgment

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situation, the claims themselves have to be indexed to the situation. The validity of modus ponens should be expressed: If in some judgment situation A is true, and in the same judgment situation A ⊃ B is true, then in that judgment situation B is true. To argue that the truth of A in one judgment situation and the truth of A ⊃ B in another judgment situation entails the truth of B in any judgment situation is to commit something like a fallacy of ambiguity. In the Sorites argument, the first unconditional premise, “Tile 1 is red,” may be objectively determined to be true (in some judgment situation), and every one of the conditionals “If tile n is red then tile n + 1 is red” objectively determined to be true (in some other judgment situations)4, and the final unconditional premise “Tile N is red” objectively determined to be false (in yet another judgment situation). It is not quite accurate to say that this is because “red” is ambiguous: “red” may be governed by a single Ideal, just as the grading system is. Nor is it right to say that “red” is indexical:The truth value is not determined by the particular tokening. But the dependence of the semantic value on a judgment situation can give rise to invalid arguments that look, on the surface, to be valid. The usual Sorites paradox, then, arises because we are asked to confront a sort of judgment situation that we are commonly able to avoid. Since we are usually somewhat free to delimit a judgment situation, we can restrict our attention to a subset of cases that admit of a sorting that satisfies the Ideal. Although the Ideal cannot be satisfied in every judgment situation, latitude in determining the relevant judgment situation at a given time can often allow us to avoid violating the Ideal. And since we are not often required to make judgments that violate the Ideal, we can easily come to feel that all of the principles mentioned in the Ideal are equally essential to it: We can easily overlook the fact that the Epsilon Principle is a defeasible constraint on sorting while Dominance and Absolute Paradigms are not. In being asked to sort all the members in a Sorites series at once, we are being asked to apply the norms governing the sorting system to the least favorable judgment situation.This is an obvious source of distress, and we are likely to remain somewhat dissatisfied no matter how we sort the case, since the arbitrary nature of the boundaries used in the sorting will be manifest. But it is not warranted to conclude from this circumstance that the sorting system, or the Ideal governing it, 4. There is a small technical detail about how to understand the semantic value of, say, “If tile M is red then tile M + 1 is red” in a judgment situation where both tile M and tile M + 1 are objectively borderline. Suppose, for example, the judgment situation contains only those two tiles, and they fall between the lightest paradigm red and the darkest paradigm pink (not within epsilon of either). And suppose the shades of the two tiles are within epsilon of each other. Then they are both objectively borderline: denominating them both “red” or both “pink” would satisfy the Ideal. If the connective in “If tile M is red then tile M + 1 is red” is treated truth-functionally, then the conditional may be borderline: at least some truth-functional extensions of the classical connective will give this result. But on the other hand, one could treat the molecular sentence supervaluationally. Since in every sorting into red and pink that satisfies the Ideal, “If tile M is red then tile M + 1 is red” comes out true, we can say that the conditional is objectively true, and similarly for “Tile M is red if and only if tile M + 1 is red”. I see no reason to choose between these ways of ascribing a semantic value to the conditional. As an abstract matter, both the truth-functional connectives and the method of supervaluation exist. In a particular instance, it may be clear that one or the other is meant.

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is somehow incoherent or fatally flawed. In most judgment situations, the sorting procedure works fine, and renders objectively determined results. To conclude from a Sorites situation that there is something fatally defective in the predicate “heap” or “bald” would be as much of an overreaction as concluding that there is never any coherent way to assign grades just because sometimes arbitrary decisions must be made in assigning them. In favorable judgment situations our methods for sorting students into final grades, or collections of grain into heaps and non-heaps, or silverware into forks and spoons, works flawlessly. The sorting, given the Ideal, is objectively determined by the distribution in the objective basis. And even in unfavorable situations, some collections of grain are unproblematically heaps and some men are unproblematically bald. I see no reason, in such favorable circumstances, to withhold the semantic status of truth from the corresponding sentences: If someone is objectively determined to be bald, then it is true to say he is bald.And if someone is objectively determined not to be bald, then it is false to say he is bald. The price of assigning classical truth values in these favorable cases, though, is that it leaves us with the unfavorable cases: The objectively borderline cases and the situations where the Ideal cannot be met. I see no reason not to introduce a third semantic value for these cases, and even more semantic values if there is higher-order vagueness. This reflects our preanalytic intuition that in some cases it is neither true nor false to say of someone that he is bald. Nothing in the Sorites situations forces us to abandon this commonsense view.

REFERENCES Braun, David, and Theodore Sider. 2007. “Vague, so Untrue.” Nous 41: 133–56. Fine, Kit. 1975. “ Vagueness, Truth and Logic.” Synthese 30: 265–300. Horwich, Paul. 1990. Truth. Oxford: Basil Blackwell. Maudlin, Tim. 2004. Truth and Paradox. Oxford: Oxford University Press. Williamson, Timothy. 1992. “Vagueness and Ignorance.” Proceedings of the Aristotelian Society Supp. 66: 145–62. ———. 1994. Vagueness. London: Routledge.

Midwest Studies in Philosophy, XXXII (2008)

Where the Paths Meet: Remarks on Truth and Paradox* JC BEALL AND MICHAEL GLANZBERG

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he study of truth is often seen as running on two separate paths: the nature path and the logic path.The former concerns metaphysical questions about the “nature,” if any, of truth. The latter concerns itself largely with logic, particularly logical issues arising from the truth-theoretic paradoxes. Where, if at all, do these two paths meet? It may seem, and it is all too often assumed, that they do not meet, or at best touch in only incidental ways. It is often assumed that work on the metaphysics of truth need not pay much attention to issues of paradox and logic; and it is likewise assumed that work on paradox is independent of the larger issues of metaphysics. Philosophical work on truth often includes a footnote anticipating some resolution of the paradox, but otherwise tends to take no note of it. Likewise, logical work on truth tends to have little to say about metaphysical presuppositions, and simply articulates formal theories, whose strength may be measured, and whose properties may be discussed. In practice, the paths go their own ways. Our aim in this paper is somewhat modest. We seek to illustrate one point of intersection between the paths. Even so, our aim is not completely modest, as the point of intersection is a notable one that often goes unnoticed. We argue that the “nature” path impacts the logic path in a fairly direct way. What one can and must * Portions of this material were presented at the Workshop on Mathematical Methods in Philosophy, Banff International Research Station, February 2007. Thanks to all the participants there for valuable comments and discussion, but especially Solomon Feferman, Volker Halbach, Hannes Leitgeb, and Agustín Rayo. Special thanks to Aldo Antonelli, Alasdair Urquhart, and Richard Zach for organizing such a productive event. Midwest Studies in Philosophy: Truth and its Deformities Volume XXXII Editor by Peter A. French and Howard K. Wettstein © 2008 Wiley Periodicals, Inc. ISBN: 978-1-405-19145-6

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say about the logic of truth is influenced, or even in some cases determined, by what one says about the metaphysical nature of truth. In particular, when it comes to saying what the well-known Liar paradox teaches us about truth, background conceptions—views on “nature”—play a significant role in constraining what can be said. This paper, in rough outline, first sets out some representative “nature” views, followed by the “logic” issues (viz., paradox), and turns to responses to the Liar paradox. What we hope to illustrate is the fairly direct way in which the background “nature” views constrain—if not dictate—responses to the main problem on the “logic” path. (We also think that the point goes further, particularly concerning the relevance and appropriate responses to “Liar’s revenge.” We will return to this briefly in the concluding Section 4.) In Section 1, we discuss two conceptions of truth; one in the spirit of contemporary deflationism, and the other in the spirit of the correspondence theory of truth. The given conceptions (or “views”) serve as our representatives of the nature path. In Section 2, we briefly present issues relevant to the “logic” path, and particularly the Liar paradox. In Section 3, we show that our two views of the nature of truth lead to strikingly different options for how the paradox—how questions of logic—may be addressed. We show this by taking each view of the nature of truth in turn, and examining the range of options for resolving the Liar they allow. We close in Section 4 by considering one further point where the two paths meet, related to how to understand “revenge paradoxes.” 1 NATURE: TWO CONCEPTIONS OF TRUTH We distinguish two paths in the study of truth: the nature path and the logic path. The nature path is traditionally one of the mainstays of metaphysics (and perhaps epistemology as well). It was walked, for instance, by the great theories of truth of the early twentieth century: the correspondence theory of truth, the coherence theory of truth, and the pragmatist theories of truth. The same may be said of more recent philosophical views of truth, including, on a more skeptical note, deflationist theories of truth. The logic path is usually thought of as studying the formal properties of truth, and in particular, studying them with the goal of resolving the well-known truth-theoretic paradoxes such as the Liar paradox. In this section, we articulate two ways of approaching the metaphysics of truth—two ways of following the nature path. One is a “deflationary” conception of truth, and the other “correspondence-like.” Many approaches to the metaphysics of truth have been developed over time, and we do not attempt to survey them all. Instead, we briefly discuss these two accounts, which we think are fairly representative of the main trends in the metaphysics of truth, and also, fairly familiar.1 Once we have presented these two ways down the nature path, we turn to the logic path, and then to how the two meet. Before launching into our two representative views,

1. We also confess to having strong bias towards the given accounts, with each author favoring a different one.

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however, we pause to explore a little further what the nature path in the study of truth seeks to accomplish. The touchstones for current philosophical thinking about truth are the theories developed in the early twentieth century, such as the classic coherence and correspondence theories of truth. It is not easy to give a historically accurate representation of either of these ideas. But for our purposes, it will suffice to make use of the crude slogans that go with such theories.The correspondence theory may be crystallized in the view that truth is a correspondence relation between a truth bearer (e.g., a proposition) and a truth maker (e.g., a fact). The correspondence relation is typically some sort of mirroring or representing relation between the two. In contrast, a coherence theory holds that a truth bearer is true if it is part of an appropriate coherent set of such truth bearers.2 Caricatures though these slogans may be, they are enough to see what the main goal of theories of this sort is. They seek to answer the nature question: what sort of property is truth, and what is it that makes something true? As such, they have no particular interest in the extent question: What is the range of truths?3 We take philosophical theories of truth to be theories that answer the nature question. Hence, we call the path that pursues traditional philosophical questions about truth the nature path. Contemporary discussion of the nature question has focused on whether there is really any such thing as a philosophically substantial nature to truth at all. Deflationists of many different stripes argue there is not. Descendants of the traditional views, especially the correspondence theory, hold that there is, and seek to elucidate it. The “semantic” view we discuss below seeks to do so in a way that is less encumbered by the metaphysics of the early twentieth century—especially, the metaphysics of facts—but still captures the core of the correspondence idea. We shall thus present two representative views, which we believe give a good sample of the options for the nature path. The first, which we call the semantic view of truth, is a representative of a substantial and correspondence-inspired answer to the nature question. The second, which we call the transparent view of truth, is a form of deflationism, taking a skeptical stance towards the nature question. Obviously, these by no means exhaust the options, or even the options that have received strong defenses in recent years, but they give us typical examples of the main options, and so allow us to compare how philosophical accounts of the nature of truth relate to the formal or logical properties of truth.

2. For a survey of these ideas, and pointers to the literature, see Glanzberg (2006b). The correspondence theory is associated with work of Moore (e.g., 1953) and Russell (e.g., 1910, 1912, 1956), though their actual views vary over time and are not faithfully captured by the correspondence slogan. (Indeed, both started off rejecting the correspondence theory in their earliest work.) Notable more recent defenses include Austin (1950). The coherence theory is associated with the British idealist tradition that was attacked by the early Russell and Moore, notably Joachim (1906), and later Blanshard (1939). (Whether Bradley should be read as holding a coherence theory of truth has become a point of scholarly debate, as in Baldwin 1991.) For a discussion of the coherence theory, see Walker (1989). 3. Some philosophers, notably Dummett (e.g. 1959, 1976) approach both nature and extent questions together.

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Parenthetical remark. One issue that was often hotly debated in the classical nature literature was that of what the primary bearers of truth are.4 For purposes of this essay, we take a rather casual view towards this question. We will talk of sentences as the bearers of truth; particularly, sentences of an interpreted language. At some points, it will be crucial that our sentences be interpreted, and have rich semantic properties. When we make reference to formal theories, sentences are the convenient elements with which to work. But it would not matter in any philosophically important way if we were to replace talk of interpreted sentences with talk of utterances which deploy them, or propositions whose contents they express, or any other favored bearers of truth. End parenthetical. 1.1 Semantic Truth The first view of the nature of truth we sketch is what we call the semantic view of truth. We see it as a descendant of the classical correspondence theory, and a representative of that idea in the current debate. The view we sketch takes truth to be a key semantic property. This is a familiar idea. It is the starting point to many projects in formal semantics, which seek to describe the semantic properties of sentences in terms of assignments of truth values (or more generally, truth conditions). It is also the starting point of any model-theory-based approach to logic. Just what sorts of semantic values may be assigned, and what is done with them, differ from project to project, but that there are theoretically significant semantic values to be assigned to sentences, and that one of them (at least) counts as a truth value, is a common idea in logic and semantics.5 This idea is familiar, but it is also familiar to see it contested.As our goal is to present a representative approach to truth, we will not pause to defend it, so much as see how the familiar idea leads to a view of the nature of truth. Theories of semantics or model theory of this sort use a “truth value,” but it is typically a rather abstract matter just what a “truth value” in such a theory is. It is, for most purposes, an arbitrarily chosen object, often the number one. What is important is the role that assigning that object to sentences plays in a semantic or logical theory. The semantic view of truth takes the next step, and holds that for the right theory, a theory of this semantic value is indeed a theory of the nature of truth. Truth is this fundamental semantic property, and the nature of truth is revealed by the nature of the underlying semantics. The truth predicate, which expresses truth, has as its main job to report this status. The “nature” of the concept expressed by a truth predicate Tr is the nature of the underlying semantic property that the truth predicate reports. We have suggested that the semantic view of truth (as we use the term) is the heir to the classical correspondence view of truth. Put in such abstract terms, it may 4. For instance, the question of whether there are propositions, and whether they can serve as truth bearers, was crucial to Russell and Moore’s turn from the identity theory of truth to the correspondence theory. 5. In semantics, one can see any work in the truth-theoretic tradition, for example, Heim and Kratzer (1998) or Larson and Segal (1995). In logic, any book on model theory will suffice. To see such ideas at work in a range of logics, see Beall and van Fraassen (2003).

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not be obvious why, but it becomes more clear if we think of how the truth values of sentences are determined, and how this is reflected in semantic theories. Let us assume, as is fairly widely done, a broadly referential picture. Terms in our sentences denote individuals. Predicates one way or another pick out properties (or otherwise acquire satisfaction conditions). A simple atomic sentence gets the value 1 (t or whatever the theory posits) just in case the individual bears the property. A semantic theory in the truth-conditional vein tells us how a sentence gets is semantic value in virtue of the referents of its parts. Our semantic view of truth holds that this is in fact telling us what it is for the sentence to be true. But here, we see the correspondence idea at work. What determines whether a sentence is true is what in the world its parts pick out, and whether they combine as the sentence says. The semantic view of the nature of truth does not rest on a metaphysics of facts, as many forms of the classical correspondence theory did.6 Rather, determinate truth values are built up from the referents of the right parts of a sentence. Whereas a classical correspondence theory would look for some sort of mirroring between a truth bearer and a truth maker, like a structural correspondence between a fact and a proposition, the semantic theory rather looks to the semantic properties of the right parts of a sentence, and builds up a truth value based on them for the sentence as a whole, according to principles of semantic composition. Reference for parts of sentences, plus semantic composition, replaces correspondence. Though the metaphysics of facts is not required, this is an account of truth in terms of relations between sentences and the world. Especially, if we take the route envisaged by Field (1972), which seeks to spell out the basic notions like reference on which the semantic view is built, this view shows truth to be a metaphysically nontrivial relation between truth bearers and the world. The relation is no longer one of a truth bearer to single truth maker, but it remains a substantial wordto-world relation, which we may think of as correspondence, or rather, all the correspondence we need.7 The semantic view is thus, we say, a just heir to the correspondence theory. It can likewise support the questions of realism and idealism that were the focus of the correspondence theory. It seeks an answer to the nature question for truth which follows the lead the correspondence theory set down.8 As we use the term “semantic truth,” its key idea is that the predicate Tr reports a semantic property of sentences. Notoriously, Tarski (1944) talked about a “semantic conception of truth.” We are not at all sure if our semantic truth is what 6. This is not to say that the “semantic view,” as we use the term, cannot rest on a metaphysics of facts. See Taylor (1976) for one example, as well as Barwise and Perry (1986), and Armstrong (1997). 7. There are contemporary views that put much more weight on the existence of the right object to make a sentence true, such as the “truth maker” theories discussed by Armstrong (1997), Fox (1987), Mulligan, Simons, and Smith (1984), and Parsons (1999). 8. There are classical roots for this sort of theory. It echoes some ideas tried out by Russell in the so-called “multiple relation theory” (e.g., Russell 1921). Perhaps more tendentiously, we believe that it is close to what Ramsey had in mind (1927) (in spite of Ramsey usually being classified as a deflationist). (An ongoing project by Nate Smith is developing the point about Ramsey in great detail.)

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Tarski had in mind, and his own claims about the semantic conception are not clear on the issue. Regardless, we have clearly borrowed heavily from Tarski (especially Tarski (1935)) in formulating the semantic view.9 We shall use our notion of semantic truth as a representative of a substantial correspondence-inspired view of truth. 1.2 Transparent Truth So far, we have briefly described one approach to the nature question: our correspondence-inspired semantic view of truth. In the current debate, perhaps the main opposition to views like this one is deflationist positions that hold that there is not really any substantial answer to the nature question at all. Our next view of the nature of truth, which we call the transparent view of truth, is a representative of this sort of approach. There are many forms of deflationism about truth to be found. Transparent truth takes its inspiration from disquotationalist theories. According to these theories, there is no substantial answer to the nature question, as the nature question, though grammatical, asks after something that does not exist. Truth, according to these views, is not a property with a fundamental nature; it is simply an expressive device that allows us to express certain things that would be difficult or in-practice impossible without it. As is commonly noted, for instance, truth allows the expression of generalizations along the lines of “Everything Max says is true,” and allows for affirmation of claims we cannot repeat, along the lines of “The next thing Agnes says will be true.” Truth is a device for making claims like this, and nothing more; it is thus not in any interesting way a property whose “nature” needs to be elucidated. Notionally, we may think of such an expressive device as added to a language. Adding the device increases its expressive power, but not by adding to its “ideology” (as Quine (1951) would put it). The crucial property that allows truth to play this role is what we call transparency. A predicate Tr(x) is transparent if it is see-through over the whole language: Tr(⎡f⎤) and f are intersubstitutable in all (non-opaque) contexts, for all f in the language.10 Transparency is the key property that allows truth to affect expressive power. It does so by supporting inferences from claims of truth to other claims. For instance, we can extract the content of “everything Max says is true” by first identifying what Max says, and next applying the transparency property. A transparent predicate is a useful way to allow generalization over sentences, and to extract content from those generalizations.11 9. That Tarski’s work might be pressed into the service of a correspondence-like view was also noted by Davidson (1969). 10. At the very least, such intersubstitutability amounts to bi-implication. So, the transparency of Tr(x) amounts to the following. Where b is any sentence in which a occurs, the result of substituting Tr(⎡a⎤) for any occurrence of a in b implies b and vice versa. 11. The disquotationalist variety of deflationism stems from Leeds (1978) and Quine (1970); the particular case of the transparent view is discussed by Beall (2005, 2008d) and Field (1986, 1994). Other varieties of deflationism include the minimalism of Horwich (1990), and various forms of the redundancy theory, such as that of Strawson (1950) and the view often attributed (we think mistakenly) to Ramsey (1927). The latter is developed by Grover, Camp, and Belnap (1975). For discussion of deflationary truth in general, see the chapters in Armour-Garb and Beall (2005).

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The transparent view of truth has it that truth is simply a transparent predicate, and so can perform these expressive functions. There is nothing more to it. As we mentioned, it is useful to think of a transparent truth predicate as having been added to a language, to add to its expressive power. But importantly, a transparent truth predicate is defined to be fully transparent; it allows intersubstitutability for all sentences of the language, including those in which the truth predicate figures. This is the defining feature that allows the truth predicate to play its expressive role, and so, to the transparent view, it is the defining feature of truth. The transparent view of truth will be our representative deflationist approach, and our second representative philosophical approach to truth. Each of our representative views takes a stand on the nature question. We thus have one substantial correspondence-like view of truth, and one deflationary view, to represent the nature path to truth.12 2 BACKGROUND ON LOGIC AND PARADOX In order to discuss the “logic” path, and where our two paths meet, we need to set up a bit of background. This section provides the needed background on logic, formal theories of truth, and the Liar paradox. Where the two paths come together is discussed in the following Section 3. 2.1 Background on Logic In discussing logics, our main tool will be that of interpreted formal languages. For our purposes, an interpreted formal language (or just a “language”) L is a triple 〈L, M, s〉, where L is the syntax, M a “model” or “interpretation,” and s a “valuation scheme” (or “semantic value scheme”). We do not worry much about syntax here, though from time to time we are careful to note whether a given language contains a truth predicate Tr in its syntax. Unless otherwise noted, we assume the familiar syntax of first order languages. Elements of interpreted, formal languages to which we do pay attention are models and valuation schemes. A model M provides interpretations of the nonlogical symbols (names, predicates, and if need be, function symbols). A model has a domain of objects, and names are assigned these as values. To allow for a suitable range of options for dealing with paradox, we are more generous with the interpretations of predicates (and sentences) than might be standard. A predicate P will be assigned a pair of sets of (n-tuples of) elements of the domain, written 〈P+, P-〉. P+ is the extension of P in M, and P- is the anti-extension. Importantly, P can be given a partial interpretation, or an overlapping or “glutty” interpretation. If D is the domain of M, we do not generally require either of the following. • Exclusion constraint: P + 傽 P − = ∅ • Exhaustion constraint: P+ 艛 P- = Dn. 12. For more comparisons between correspondence and deflationary views, see David (1994).

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Classical models satisfy both the Exhaustion and Exclusion constraints, but we consider logics where they do not hold.13 With neither Exhaustion nor Exclusion guaranteed, we have to be more careful about how we work with values of sentences. This is where a valuation scheme comes into the picture. The job of a valuation scheme s, relative to a set V of so-called “semantic values,” is to give a definition of semantic value for sentences of L, from the interpretations of nonlogical expressions in a model M. Furthermore, having a valuation scheme allows us to describe notions of validity and consequence, as we allow models to vary. We will illustrate with three important examples: a Classical language, a Strong Kleene language, and a Logic of Paradox language. First, a Classical language. Fix a model M obeying the Exhaustion and Exclusion constraints. The Classical valuation scheme t is defined on a set of semantic values V = {1, 0}. We use |f|M for the semantic value of f relative to M. The main clause of the Classical valuation scheme t is the following.

P ( t1, . . . , t n ) M =

{

1 if t1 M , . . . , t n M ∈ P + 0 if t1 M , . . . , t n M ∈ P −

Clauses for Boolean connectives and quantifiers are defined in the usual way. Interpreted languages give us logical notions in the following way. For a fixed syntax and valuation scheme, we can vary the model, and in doing so, ask about logical truth and consequence. In the Classical case, we have the following. We say that a set G of sentences classically implies a sentence f if there is no classical model in which t assigns every member of G the value 1, and f the value 0. The apparatus of interpreted languages allows us to explore many nonclassical options as well. We mention two examples, beginning with an example of a “paracomplete logic” based on the familiar Strong Kleene language. (For more on the “paracomplete” and “paraconsistent” terminology, see Section 3.) Strong Kleene models are just like classical models except that they drop the Exhaustion constraint on predicates (but keep the Exclusion constraint). The Strong Kleene valuation scheme k expands the set V of “semantic values” to { 1, 12 , 0 }. The clause for atomic sentences is modified as follows.14 + − ⎧1 if t1 M , . . . , t n M ∈ P \P ⎪ P ( t1, . . . , t n ) M = ⎨0 if t1 M , . . . , t n M ∈ P − \P + ⎪ 1 oth herwise. ⎩2

Three-valued logical connectives may be defined by the following rules. For negation: |¬f|M = 1 - |f|M. For disjunction: |f ⁄ y|M = max{|f|M, |y|M}. (These rules work 13. Hence, for classical languages, it is common to dispense with P-, as P- = Dn\P+, where X\Y is the complement of Y in X (i.e., everything in X that is not in Y ). 14. NB: The set complementation is unnecessary in Strong Kleene, since K3 embraces the Exclusion constraint; however, it is necessary in the dual paraconsistent case, which we briefly sketch below.

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equally well for the Classical t or the Strong Kleene k, but the range of values involved is different for each.) We define Strong Kleene consequence—or K3 consequence—much as before: f is K3 implied by G if there is no Strong Kleene model in which k assigns every element of G the value 1 and fails to assign f the value 1. Finally, we look at a so-called paraconsistent option, the Logic of Paradox or LP. One way of presenting an LP language is in terms of a K3 language. LP models differ from K3 models in that they drop the Exclusion constraint, but keep the Exhaustion constraint. The LP valuation scheme r is based on the three values { 1, 12 , 0 }, and we may leave the clauses for atomic sentences, negation, and disjunction as they were for k. The difference appears when we come to consider logical consequence. K3 was explained in terms of preservation of the value 1 across chains of inference. This is usually put by saying that 1 is the only designated value for K3. For LP, the value 12 , in addition to value 1, is designated in the LP scheme r. So, G implies f iff whenever every element of G is designated in a model, so is f. Thus, for r, true in a model is defined as having either value 1 or 12 . An interpreted formal language is a tool with which issues of truth and issues of logic can be explored, as we have seen with each of our Classical, Strong Kleene, LP examples. We can think of each of these sorts of languages as representing different sorts of logical properties. LP languages, for instance, bring with them a paraconsistent logic, K3 languages a paracomplete logic, and of course, Classical languages a classical logic. (Again, see Section 3 for terminology.) There are many other options we could consider, notably relevance logics.15 2.2 Background on Truth: Capture and Release So far, we have explored the idea of an interpreted language, which brings with it a logic. We have looked at options for logic, both classical and nonclassical. We now turn our attention to the “logic” of truth itself. The term “logic” here is fraught with difficulty. We are highly ecumenical about logic, and have already surveyed a number of options for what we might think of as logic proper. What we now consider is the basic behavior of the truth predicate Tr, described formally, in ways we can incorporate into formal interpreted languages. In some cases, this may require specific features of logic proper, but in many, it is independent of choices of logic. We continue to talk generally about the logic path as encompassing both the formal behavior of the truth predicate, and logic proper, as the two are not always easy to separate. But it should be stressed that there are often different issues at stake for the two. 15. It is not easy to document the sources of the ideas we have presented in this section. For the machinery of interpreted languages, an extended discussion is found in Cresswell (1973), and more recently in Beall and van Fraassen (2003). The Classical language, of course, follows the path set down by Tarski (e.g., 1935). The Strong Kleene language is named after Kleene (1952). The Logic of Paradox was developed by Priest (1979), and explored at length in his recent work (2006a, 2006b).

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The behavior of the truth predicate—the “logic” of Tr, if you will—centers around two principles, which have been the focus of attention since the seminal work of Tarski (1935). We label these Capture and Release, which may be represented schematically as follows. Capture: f fi Tr(⎡f⎤). Release: Tr(⎡f⎤) fi f. We understand “fi” to be a place-holder for a number of different devices, yielding a number of different principles. (If it is a classical conditional, then these are just the two directions of Tarski’s T-schema.) Many approaches to truth, and especially to the Liar paradox, turn on which such principles are adopted or rejected. Intuitively, all the principles that fall under the schema seek to capture the same idea, that the transitions from Tr(⎡f⎤) to f and from f to Tr(⎡f⎤) are basic to truth. They embody something important about what truth is, and flow from our understanding of this predicate. If someone tells you that it is true that kangaroos hop, for instance, you may conclude that according to them, kangaroos hop, without further ado. The leading idea in the study of the formal properties of the truth predicate is that if you understand the right forms of Capture and Release, you understand how the truth predicate works. We will mention a few important examples of how Capture and Release may be filled in, which will be important in the discussion to come. 2.2.1 Classical conditional (cCC & cCR) This treats “fi” as the classical material conditional, making Capture and Release two sides of the Tarski biconditionals or T-schema in (classical) materialconditional form:

Tr ( ⎡φ ⎤ ) ↔ φ. Other classical options are available, but we will use this as our main example.16 2.2.2 Nonclassical conditional (CC & CR) There are various options for nonclassical treatments of the conditional. One might stick with the material approach to a conditional, defining it as ¬a ⁄ b, but use a nonclassical treatment of negation or disjunction to cash out the given “conditional.” One might, instead, go to a nonclassical treatment of a conditional that’s not definable in terms of the basic connectives. Prominent options include conditionals of relevance logic and paraconsistent logic, and the more recent work of Field (2008a).17

16. For other classical options, see Friedman and Sheard (1987). In their terminology, Classical conditional Capture (cCC) is called Tr-In, and Classical conditional Release (cCR) is called Tr-Out. 17. On relevance (or relevant) and paraconsistent logics see Dunn and Restall (2002), Restall (2000), and Priest (2002).

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2.2.3 Rule form We can replace “fi” with a rule-based notion. One option is to include a rule of proof, which allows inferences between Tr(⎡f⎤) and f. We thus have rules: Rule Capture (RC) f ⵫ Tr(⎡f⎤). Rule Release (RR) Tr(⎡f⎤) ⵫ f. Alternatively, we could think of these as sequents in a sequent calculus. Regardless, we will have to work with logics which allow these rules to come out valid.18 Fixing on the right form of Capture and Release is one of the important tasks in describing the formal behavior of the truth predicate. Indeed, it is generally taken to be the main task. The reason why is at least clear in the classical setting. cCC and cCR together with facts not having anything to do with truth suffice to fix the extension of the truth predicate. They thus seem to tell us what we want a formal theory of truth to tell us about how truth behaves. The same holds, with some more complications as the logics get more complicated, for nonclassical logics. 2.3 Background on the Liar We have, in passing, mentioned the truth-theoretic paradoxes. We will restrict our attention to a simple form of the Liar paradox. The basic idea of the Liar is well known: Take a sentence that says of itself that it is not true. Then that sentence is true just in case it is not true. Contradiction! We will fill in, slightly, some of the formal details behind this paradox. To generate the Liar, we assume our language has a truth predicate Tr, and that it has some way of naming sentences and expressing some basic syntax.We will help ourselves to a stock of sentence names of the form ⎡S⎤. (Corner quotes might be understood as Gödel numbers, but for the most part, they may be taken as any appropriate terms naming sentences.) The Liar, in its simple form, is the result of self-reference (we will not worry if this is essential to the paradox or not). So long as our language is expressive enough, this can be achieved in the usual (Tarskian-Gödelian) ways. With these tools, we can build a canonical Liar sentence: A sentence L which says of itself only that it is not true. In symbols:

L := ¬Tr ( ⎡L⎤ ) L will be our example of a Liar sentence. 18. In settings where the deduction theorem holds, the differences between the Rule and Classical conditional forms of Capture and Release tend to be minimal, but in other settings they can be quite important. We also stress that there are other rule forms which are substantially different from RC and RR. Prominent options typically provide closure conditions for theories, telling us if a theory G proves f, then G proves Tr(⎡f⎤) as well, and likewise for the Release direction. Rules like these can be very weak. One of the results of Friedman and Sheard (1987) shows that the collection of all four rules governing Tr and negation is conservative over a weak base theory.

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Parenthetical remark. If instead of Gödel coding we have names of each sentence, readers can think of our target L as a sentence arising from a name l that denotes the sentence ¬Tr(l). If we use angle brackets for “structural–descriptive terms,” our Liar L arises from a true identity l = 〈¬Tr(l)〉. Applying standard identity rules, plus enough classical reasoning (see below), gives the result. End parenthetical. The Liar sentence L leads to a contradiction when combined with Capture and Release in some forms. For instance, the classical paradox:

Classical logic + L + cCC + cCR = Contradiction. The same holds for classical logic and the rule forms of Capture and Release.19 Of course, once we depart from classical logic, whether or not we have a contradiction, and what the significance of it is, will depend on what conditional or rule is employed, and what the background logic is. The Liar paradox is thus easy to generate, but does rely on some assumptions, both about the formal behavior of truth, and about logic proper.

3 NATURE AND LOGIC In preceding sections we’ve discussed the “nature” and “logic” paths. We now turn to the crossing. The salient point of crossing, at least for our purposes, comes at the question of the Liar’s lesson: What does the Liar teach us about truth? The nature path constrains the logic path by constraining the answers available to the Liar question. We maintain that the nature path does not merely motivate views on the logic path; rather, in some respects, it dictates the available answers to the paradox, and the available views of the logic of truth. We will show this by asking what the available responses to the Liar are, in light of each of our two representative views of the nature of truth. We will see that they result in very different logical options. Assuming a semantic view of truth, we find that a different account of the formal behavior of the truth predicate is required than we might have expected; but otherwise, the logic may be whatever you will. If classical logic was your starting point, truth according to this view offers no reason to depart from it. In sharp contrast, the transparent view of truth requires the overall logic to be nonclassical. We will show this by discussing each view of the nature of truth in turn. We first discuss transparent truth, and then semantic truth. 3.1 Transparent Truth What does the Liar teach us about truth? In particular, if we embrace the transparent view of truth, what is the lesson of the Liar?

19. Some more subtlety about just which classical principles lead to inconsistency can be found, again, in Friedman and Sheard (1987).

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Unlike the case with semantic truth (on which see Section 3.2 below), the notable lesson is plain: The logic of our language is nonclassical if, as per the transparent view, our language enjoys a transparent truth predicate. To see this, consider the following features of classical logic. ID j ⵫ j. LEM ⵫ j ⁄ ¬j. EFQ j, ¬j ⵫ ⬜. RBC If j ⵫ g and y ⵫ g then j ⁄ y ⵫ g.20 Assume, now, that our language has a transparent truth predicate Tr(x), so that Tr(⎡a⎤) and a are intersubstitutable in all (non-opaque) contexts, for all sentences of the language. ID, in turn, gives us RC and RR. Assume, as we have throughout this essay, that our given language is sufficiently rich to generate Liars. Let L be such a Liar, equivalent to ¬Tr(⎡L⎤). By RC, we have it that ¬Tr(⎡L⎤) implies Tr(⎡L⎤). ID gives us that Tr(⎡L⎤) implies itself. But, then, Tr(⎡L⎤) ⁄ ¬Tr(⎡L⎤), which we have via LEM, implies Tr(⎡L⎤), which, via RR implies ¬Tr(⎡L⎤). Given EFQ, ⬜ follows. The upshot is that no classical transparent truth theory is nontrivial. If our language is classical, then we do not have a nontrivial see-through predicate. On the transparent view, then, the lesson of the Liar is that we do not have classical language. There’s no way of getting around this result. Of course, one might suggest that the transparent truth theorist restrict the principles governing “true” or the like. If one restricts either RR or RC, then the above result is avoided. What we want to emphasize is that, on the transparent conception, restriction of the principles governing “true” is simply not an option. After all, at least on the transparent view, truth—or “true”—is a see-through device over the entire language. As such, if the logic enjoys ID, then there’s no avoiding RC and RR; the latter follow from ID and intersubstitutability of Tr(⎡f⎤) and f. If one suggests that “true” ought not be transparent over the whole language, one needs an argument. Presumably, the argument comes either from the “nature” of truth or something else. Since the nature route, at least on the transparent conception, is blocked, the argument must be from something else. But what? One could point to the issue at hand: viz., Liar-engendered inconsistency. But this is not a reason to restrict RR or RC, at least given a transparent view. What motivates the addition of a transparent device is (practical) expressive difficulty: Given our finitude, we want a see-through device over the whole language in order to express generalizations that we could not (in practice) otherwise express. (This is the familiar “deflationary” story, which we discussed in Section 1.2.) What the Liar indicates is that our resulting language—the result of adding our see-through predicate—is nonclassical, on pain of being otherwise trivial. If one restricts RR or RC, one loses the see-through—fully intersubstitutable—feature of transparent truth. In turn, one winds up confronting the same kind of expressive limitations

20. This is sometimes known as ⁄ Elim or, as “RBC” abbreviates, reasoning by cases.

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(limitations on generalizations) that one previously had. The natural route, in the end, is not to get rid of transparency in the face of Liars; it is to accept that the given language is nonclassical. So, the lesson of the Liar, given the transparent conception, is that our underlying logic is nonclassical. The question is: What nonclassical logic is to underwrite our truth theory? Though rejecting any of LEM, EFQ, RBC (or any of the steps— even background structural steps) are “logical options,” two basic approaches have emerged as the main contenders: paracomplete approaches and paraconsistent approaches. Here, we briefly—briefly—sketch a few of the basic ideas in these different approaches. 3.1.1 Paracomplete Paracomplete theorists reject that negation is exhaustive; they reject some instances of LEM. The term “paracomplete” means beyond completeness—where the relevant “complete” concerns so-called negation-completeness (usually applied to theories). A paracomplete response to the Liar is one that rejects Liar-instances of LEM. Without the given Liar-instance of LEM, the result in Section 3.1 is blocked. A familiar paracomplete theory of transparent truth is Kripke’s (1975) Strong Kleene theory (with empty ground model). If you look back at Section 2.1, wherein we briefly sketch the Strong Kleene scheme, one can see that classical logic is a proper extension of the K3 logic: anything valid in K3 is classically valid, but some things are classically valid that are not K3 valid.The important upshot, at least for philosophical purposes, is that a Strong Kleene language, while clearly nonclassical, may enjoy a perfectly classical proper part. And this is what comes out in the relevant Kripke picture. Suppose that our “base language”—the “semantic-free” language to which we add our transparent device—is classical. What Kripke proves is that one may nonetheless enjoy a transparent truth predicate over a language that extends the base language: the base language may be perfectly classical even though, owing to Liars in the broader language, our overall—“true”-ful—language is nonclassical (in fact, paracomplete). We leave details for other sources, but it is important to note that the relevant Kripke theory is a good example of a (limited) paracomplete theory of transparent truth, one in which much of our language is otherwise entirely classical. Parenthetical remark. The reason we call Kripke’s theory “limited” is that it fails to have a “suitable conditional,” a conditional such that both of the following hold. cID ⵫ j → j. MPP j, j → y ⵫ y While the “hook,” namely ¬j ⁄ y, satisfies MPP in K3, it fails to satisfy cID. After all, we do not have LEM in K3, and so do not have ¬j ⁄ j, which is the hook version of cID. The task of extending a K3 transparent truth theory with a suitable conditional is not easy, owing to Curry’s paradox (Beall 2008a); however, Field’s

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recent work (2008a) is a major advance. (For related issues and discussion of Field’s paracomplete theory, see Beall (2008c).) End parenthetical. 3.1.2 Paraconsistent Another—in fact, dual—approach is paraconsistent, where the logic is Priest’s LP.21 As in Section 2.1, LP is achieved by keeping all of the Strong Kleene clauses for connectives but designating the “middle value.” With respect to truth, one can dualize the Kripke K3 “empty-ground” construction: Simply stuff all sentences into the intersection of Tr(x)+ and Tr(x)-, and (in effect) run the Kripke march upwards following the LP scheme (which is monotonic in the required way).22 Unlike the paracomplete transparent truth theorist, who rejects both the Liar and its negation, the paraconsistent one accepts that the Liar is both true and false—accepting both the Liar and its negation.At least one of us has defended this sort of approach (Beall 2008d), but we point to it only as one of the two main options for transparent truth. Parenthetical remark. The noted “limitation” of the Kripke paracomplete theory similarly plagues the LP theory. In particular, the LP-based transparent truth theory does not have a suitable conditional (in the sense just discussed in Section 3.1.1). Unlike the K3 case, we get cID in LP, but we do not get MPP. (A counterexample arises from a sentence a that takes value 12 and a sentence b that takes value 0.) The task of extending an LP transparent truth theory with a suitable conditional is not easy, due (again) to Curry’s paradox; however, work by Brady (1989), Priest (2006b), and Routley and Meyer (1973) have given some promising options, one of which is advanced and defended in Beall (2008d). End parenthetical. 3.2 Semantic Truth and Logic We have now seen something about how the transparent view of the nature of truth constrains the logic path. In this section, we turn to the semantic view. For this section, we thus adopt the semantic view of the nature of truth. The result is a more fluid situation than we saw in the case of transparent truth. The transparent view, as we have seen in Section 3.1, takes the lesson of the Liar to be a nonclassical logic for the overall Tr-ful language. In contrast, the semantic view of truth does not start with logical or inferential properties of truth, but rather with the underlying nature of the property of truth. This will allow us to consider what formal principles govern the truth predicate, and how they may function in a paradox-free way. We will find that this may be done without paying much attention to logic proper. 21. We should note that Priest’s own truth theory is not a transparent truth theory. Indeed, the main point of disagreement between Priest (2006b) and Beall (2008d) is the relevant truth theory. Both theorists endorse a paraconsistent theory; they differ, in effect, over the behavior of “true” and the extent of “true contradictions”—with Beall being much more conservative than Priest. 22. For constructions along these paraconsistent lines, see Dowden (1984), Visser (1984), and Woodruff (1984), but of particular relevance Brady (1989) and Priest (2002).

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Let us start with a Classical interpreted language as discussed in Section 2.1, with classical model M and classical valuation scheme t. We have already seen in Section 2.3 that if our language L contains a truth predicate Tr, and Classical Capture (cCC) and Classical Release (cCR) hold, we have inconsistency. What are we to make of this situation? The first thing we should note is that the semantic view of truth takes the basic semantic properties of the interpreted languages with which we begin seriously. As we sketched the idea behind the semantic view of truth, it starts with the semantic properties of a language, particularly, those which lead us to assign semantic values to sentences of the language. This is just what our interpreted languages do. Our models show how the values are assigned to the terms and predicates of a language, and the valuation scheme shows how values of sentences are computed from them. Now, the semantic view of truth takes this apparatus to reveal something metaphysically fundamental about how languages work, and typically, also seeks to explain the metaphysical underpinnings of the formal apparatus of interpreted languages. Our Classical interpreted languages fit very nicely with the rough sketch of the semantic view of truth we offered in Section 1.1. But regardless of which logic we think is right, it is a metaphysically substantial claim. Most importantly, it is not one that is up for grabs when we come to the Liar and the behavior of the predicate “true.” Whatever the right semantic properties of a language are, and whatever logic goes with them, is already taken as fixed by the semantic view. For exposition purposes, we will take that logic to be classical logic. If there are reasons to depart from classical logic on the semantic view, they are to be found in the metaphysics of languages, not the formal properties of truth, so this assumption is innocuous for current purposes.23 Assuming we were right to opt for classical logic to begin with, the semantic view of truth will not allow us to change it in light of the Liar. This implies that if we are to avoid inconsistency, we must find some way to restrict Capture and Release. This is a hard fact, proved by our classical Liar paradox of Section 2.3. Fortunately, in the setting of the semantic view, restricting Capture and Release is a coherent possibility, and indeed, the semantic view provides us with some guidance on how to do so. The semantic view will not completely settle how we may respond to the Liar, and what the formal properties of truth are, but it tells us what determines those properties. This follows, as the semantic view tells us that the function of the truth predicate is to report the semantic values of sentences (in a classical language, those with value 1). This gives us much, but not quite all, of what we need to know about the formal behavior of the predicate Tr(x).The semantic view indicates we should have Tr(⎡f⎤) if and only if |f|M = 1. As we are assuming that our interpreted language L already contains Tr, this corresponds to the formal constraint that |Tr(⎡f⎤)|M = 1 iff |f|M = 1. Assuming that the semantics of the language is the fundamental issue, and

23. The idea that foundational semantic considerations might lead to nonclassical logic has been explored by Dummett (1959, 1976, 1991) and Wright (1976, 1982).

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the truth predicate should accurately report it, this is just what we should want.This is what is often called a fixed point property for truth.24 The fixed point property, together with classical logic, gives us the force of cCC and cCR. It tells us that |f → Tr(⎡f⎤)|M = 1 and |Tr(⎡f⎤) → f|M = 1. This makes the Liar a very significant issue for the semantic view of truth, and indeed, more significant than the view often assumes. For, it appears that our philosophical view of truth has already dictated the components of the Liar paradox, including classical logic and Classical Capture and Release (cCC and cCR). Does this show the semantic view to be incoherent? We believe it does not (at least, one of the authors does). It does not, we will argue, because the semantic view also gives us the resources for a much more nuanced look at the nature of Liar sentences, and what their semantic properties are. In effect, the response to the Liar on the semantic view is a closer examination of L and its semantic properties. However, we will see that along the way, this will show us ways that we can keep to the fixed point property, and still restrict Capture and Release. Thus, we will both reconsider the semantic properties of L, and the underlying behavior of Capture and Release. We describe three ways to go about this. The first and most familiar, Tarski’s hierarchy of languages, will be presented in a way that illustrates the reconsideration of L in the setting of semantic truth. Tarski’s hierarchy has been subject to extensive criticism since its inception. Bearing this in mind, we present two further options. The second, the classical restriction strategy, will show how we can reconsider Capture and Release in a semantic setting. Finally, the third, contextualist strategy, shows how both Tarskian and classical restriction ideas can be combined. (One of the authors believes the contextualist strategy is the most promising line of response to the Liar.) 3.2.1 Tarski’s Hierarchy Our first example of a response to the paradox consistent with the semantic view of truth is Tarski’s hierarchy of languages and metalanguages. This will illustrate the response of reexamining the Liar sentence L. As is well known, Tarski (1935) proposes that there is not one truth predicate, but an infinite indexed family of predicates Tri.25 In our framework, Tarski is proposing an infinite hierarchy of interpreted languages. We begin with a language L0 which does not contain a truth predicate. We then move to a new language L1 with a truth predicate Tr1. Tr1 only applies to sentences with no truth predicate, that is, sentences of L0. We extend this to a whole family of languages Li+1, where each Li+1 contains a truth predicate Tri+1 applying only to sentences of Li. Tri+1 thus applies only to sentences which contain truth predicates among Tro, . . . , Tri. It does not apply to sentences containing it itself. Each language Li+1 thus functions as a metalanguage for Li, in which the semantic properties of Li can be expressed. 24. This fixed point property becomes extremely important in the Kripke construction we alluded to in Section 3.1.1. 25. Tarski did not then really consider how large this family is. For some more recent work on this issue, see Halbach (1997).

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Each truth predicate Tri+1 does for the language Li exactly what the semantic view of truth asks.We can make sure that Tri+1 is interpreted so as to apply to all and only the true sentences of Li, that is, all the sentences of Li that are assigned value 1 by M and the classical valuation scheme t. (We will skip the details, which are familiar from any exposition of Tarski’s work. A nice presentation may be found in McGee (1991).) Along the way, we make true all the instances of Classical Capture and Release. A Tarskian truth predicate does formally just what the semantic view of truth describes philosophically. What of the Liar? Within the hierarchy of languages, there can be no sentence of any language Li which predicates truth of itself. The Liar sentence L of Section 2.3 simply ceases to exist. It can easily be proved that each language Li consistently assigns values to sentences, and so there is no problem of the Liar for languages of the Tarskian hierarchy. Under the Tarskian approach, the Liar genuinely goes away. As we see it, Tarski’s point is a syntactic one. He raises the question of just what sort of restrictions may apply to the distribution of truth predicates, and comes to the conclusion that there are strong syntactic restriction. In effect, any well-formed sentence of the Tarskian hierarchy must meet the syntactic restriction of having its truth predicates properly indexed, so as to ensure each truth predicate in it applies only to sentences of appropriately lower-level language. Sentences of the Tarskian hierarchy of languages must meet a syntactic requirement of being well-indexed. Thought of this way, Tarski’s proposal can be seen as one in the long tradition of care about the nature of truth bearers. Though he does not worry about questions of the nature of propositions, Tarski does direct our attention to what sorts of sentences, of what sorts of languages, truth may be appropriately applied. Tarski thus shows us that we can respond to the Liar while keeping the semantic view of truth, along with classical logic, and the basic forms of Capture and Release that go with them. We do so by paying more attention to what sorts of languages enter into the semantic view, and what truth bearers they really provide. 3.2.2 The Classical Restriction Strategy Tarski’s solution to the Liar follows the lead of the semantic view of truth, and does so without finding any reason to depart from classical logic. But it has some well-known costs. Many sentences which seem to us to be intuitively reasonable turn out not even to be well formed syntactically on Tarski’s approach. And, as Kripke (1975) famously showed, even when we do not face brute syntactic illformedness, the syntactic demand to assign fixed levels to sentences seems to misdescribe the ways we use truth predicates in discourse. Tarski’s proposal comes at significant cost in restricting what we can do with truth predicates. It buys a full implementation of a semantic view of truth in a way that avoids paradox, but the cost is very high. Many, if not most, researchers have found this cost too high to pay. However, we can think of Tarski’s theory as an early instance of a more general strategy for resolving the paradox within the semantic view of truth, which

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we call the classical restriction strategy. Tarski’s proposal does not restrict Classical Capture and Release within any given language Li of the Tarskian hierarchy. But looked at another way, it does restrict their application. If we widen our view to include sentences outside of the Tarski hierarchy of languages—sentences which contain truth predicates without Tarski’s syntactic restrictions—then we can see Tarski’s proposal as one to restrict Classical Capture and Release to sentences which meet the syntactic restrictions. As we put it a moment ago in Section 3.2.1, Tarski can be seen as restricting Capture and Release to sentences which are well-indexed, and so can be placed in the Tarskian hierarchy of languages. Restricting Capture and Release this way does nothing to weaken classical logic. Tarski’s theory can thus be thought of as restricting the domain of application of Classical Capture and Release by syntactic means, to retain consistency and keep our model theory classical, and keep the semantic view of truth. Behind this idea, we can see a more general theme: We can achieve these goals if we can find principled reasons to restrict Classical Capture and Release. We can find such reasons, the idea goes, by examining the nature of truth bearers. Not every seemingly good sentence really provides us a truth bearer, while Capture and Release need only apply to genuine truth bearers. Tarski does this in rather stringent syntactic terms. The classical restriction strategy pursues this idea more generally, by looking for more plausible, and more flexible, restrictions on genuine truth bearers than Tarski’s. Typically, the classical restriction strategy seeks to reevaluate truth bearers in semantic, rather than syntactic, terms. For instance, it may invoke the idea that there is more to being a truth bearer than simply being a well-formed sentence. Intuitively, we might think about which sentences really express propositions, or otherwise have the right semantic properties. Liar sentences, according to this strategy, are well formed sentences, but are not semantically in order. Of course, Capture and Release are only to apply to sentences which do have the right semantic properties, and so, will be restricted to avoid the Liar. A strategy like this needs to be implemented with care. Especially, if we are to keep the underlying classical semantics, then we cannot simply deny Liar sentences values in a model. Every sentence in a classical model gets either the value 0 (false) or 1 (true). Every sentence in a classical interpreted language thereby seems to count as semantically “good.” At this point, the classical restriction strategy is well advised to steal a play out of the transparent truth playbook, and in effect, borrow a Kripke fixed point construction from the K3 paracomplete approach. This gives us a partial predicate, which for now, to highlight its intermediate status, we might call Kr. As a fixed ˆ 3 = |Kr(⎡f⎤)|K ˆ 3. The Liar sentence L falls in the point, we have for a K3 language |f|K + “gap” for Kr: L ∉ Kr and L ∉ Kr . Kr is a fairly good self-applicative truth predicate, and in being a fixed point, it does a fairly good job of reporting the semantic properties of a K3 language. We can convert Kr into a classical predicate by the “closing-off” trick.Assuming Kr is the only nonclassical expression of our language, we turn our K3 model into a classical model by closing off the gap in Kr. We let the extension of Tr be exactly the extension Kr+, and make the model classical by dropping the

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anti-extension (equivalently, by putting everything in the gap in the antiextension). This is what is often known as the closed-off Kripke construction.26 Now, with our closed-off Kripke interpretation of Tr, we need to be careful about Capture and Release. The Liar sentence L was in the gap for the original Kripke construction, and so was its negation. Thus, both fall out of the extension of Tr on this interpretation. This will lead to contradiction if Capture and Release apply to them. But, this tells us what the mark of pathological sentences is. Pathological sentences are those which were counted as gappy in the Kripke construction. The negations of these sentences are also pathological. Hence, our pathological sentences and their negations will both fall out of the extension of our interpretation of Tr. We then want Capture and Release to apply only to nonpathological sentences, that is, those for which we have Tr(⎡f⎤) or Tr(⎡¬f⎤). What we thus need is a restricted combination of Capture and Release, along the lines of a T-schema with an antecedent: [Tr ( ⎡φ ⎤ ) ∨ Tr ( ⎡ ¬φ ⎤ )] → [Tr ( ⎡φ ⎤ ) ↔ φ ].

This restricts Capture and Release to sentences which are well behaved on Tr. In fact, if we use the closed-off Kripke construction, we validate this scheme in our Classical interpreted language. Technically, the closed-off Kripke construction provides us a way to get restricted forms of Classical Capture and Release to come out true in a classical model. It also gives us some idea how to make sense of what “genuine truth bearers” might be for the classical restriction strategy. Genuine truth bearers are those sentences which are semantically well behaved; that can be described as those for which we have either Tr(⎡f⎤) or Tr(⎡¬f⎤) come out true in our model. These are sentences whose truth values can be determined in the orderly inductive process by which the Kripke fixed point was built, that is, those whose semantic value depends on the way the world (or the model) is without too much pathology intervening. It is open to the classical restriction strategy to say that this is a good account of—or at least a good first pass at—what it is to really be a truth bearer. If so, then the restricted forms of Capture and Release do just what they should, as they restrict Capture and Release to genuine truth bearers. How does this square with the semantic view of truth? The semantic view helps itself to Classical interpreted languages, and sees the job of the truth predicate as simply to report having the semantic value 1 in such a language. In face of the Liar, the classical restriction strategy cannot do this fully. On the closed-off Kripke interpretation, the Liar sentence L falls outside of the extension of Tr, so ¬Tr(⎡L⎤) is classically true. Our truth predicate does not reflect this, as it classifies both the Liar and its negation as pathological. Tr does not completely accurately report the classical semantics of our interpreted language. How much of a problem this is may be debated. Those who defend the classical restriction strategy will argue that what we have to do in the face of the 26. This was suggested by Kripke (1975) himself, and was anticipated by an idea of Parsons (1974). The use of Kripke constructions in a classical setting was explored in depth by Feferman (1984).

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Liar is refine the semantic view of truth. The idea of the semantic view is that the truth predicate reports the key semantic property of sentences. With the Liar and classical logic and Capture and Release, that property cannot simply be classical semantic value. But, according to the classical restriction strategy, it is a more nuanced property of having a semantic value determined in the right way, as the Kripke construction shows us. The truth predicate on the closed-off Kripke construction does accurately report the semantic values of those sentences. Hence, we might argue, once we refine our notion of what a semantically well-behaved sentence is, that is, what a genuine truth bearer is, we find that our truth predicate does accurately report the semantic status of genuine truth bearers. Correspondingly, we have Capture and Release for those sentences. Thus, it might be argued, we have done what the semantic view of truth really required. 3.2.3 The Contextualist Strategy It is not clear whether this defense of the classical restriction strategy really succeeds. The problem with it can be made vivid by the following observation: according to the classical restriction approach, the Liar sentence is not true. It is not assigned the semantic value 1. Furthermore, it is a semantically pathological sentence, that is, not a genuine truth bearer. For this reason, both it and its negation fall out of the extension of the predicate Tr. But this is just to say that it is not true. It is not true by lights of the classical semantics, and it is also not true by lights of the more nuanced approach to truth bearers the classical restriction strategy proposes. This fact cannot be reported by the classical restriction strategy. It cannot say that the Liar sentence is not true, using the truth predicate Tr. Any attempt to do so winds up with a semantically pathological sentence, rather than a correct report of the semantic status of the Liar. This is the only result possible as any other would drive us back into paradox. This is what is often called the Strengthened Liar paradox, and it is a form of what has come to be called a revenge paradox. We will have more to say about revenge paradoxes in Section 4. For the moment, we may simply note that it raises two problems. First, it suggests we have not really gotten a satisfactory resolution of the Liar, as we still have not accurately explained the Liar’s semantic status in a stable way. Perhaps more importantly, it makes clear why one might find the classical restriction strategy unsuccessful as a way of understanding the semantic view of truth. It makes vivid that we have not accurately reported the fundamental semantic status of the Liar, either on a nuanced view, or a crude one. Thus, our truth predicate has yet to live up to the demands of the semantic view. We (one of us, anyway) think the right way out of this problem is to pursue a contextualist strategy. Our goal in this paper is not really to advocate for any one approach to the Liar, so we do not argue directly for contextualism, nor do we go into the contextualist strategy in as much depth as such an argument would require. Rather, we present this strategy as a further development of the classical restriction idea. It will thus provide a further, and we think more comprehensive, example of how the Liar may be addressed within the semantic view of truth.

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The contextualist strategy, as we understand it, combines features of the classical restriction strategy and the Tarskian one. From the classical restriction strategy, it takes the idea of paying more attention to the semantic properties that make sentences genuine truth bearers. From the Tarskian strategy, it takes the idea of an open-ended hierarchy. Unlike a Tarskian hierarchy, however, it is not strictly a hierarchy of languages syntactically defined. The contextualist strategy begins with the notion of a truth bearer. It notes that in general, sentences with context-dependent elements cannot be said to be true or false simpliciter, and their behavior is not accurately reflected by the formal apparatus of interpreted languages. What is left out is the role of context, which helps determine what such sentences say, and thus what their truth values are. Relative to a given context, we can think of an interpreted language as representing what speakers can say using their ordinary language in that context. We can thus think of interpreted languages as indexed by contexts. The difference between such languages is not in their syntax, but rather in how their sentences are interpreted. We thus can think of a hierarchy of “languages” indexed by contexts, though it might be better described as a hierarchy of what can be expressed by a language within contexts. Relative to a fixed context, we can pursue the classical restriction strategy.This will give us an account of a self-applicative (non-Tarskian) truth predicate as used in a language relative to a given context.As we have seen, such a truth predicate might not fully capture the semantic status of every sentence, especially the Liar sentence. It thus may not fully implement the semantic view of truth. But the presence of multiple contexts allows us to work with this fact. Once we have a language with a truth predicate relative to a given context, we can indeed step back and observe that according to it, the Liar sentence is not a proper truth bearer.27 We can then conclude that the Liar sentence is not true. But now, we have at our disposal the resources to see this claim as being made from a distinct context.The contextualist proposes that within this sort of reasoning about the semantic status of the Liar sentence is a context shift. The conclusion that the Liar sentence is not true is correct, but made from a new “reflective” context. This can be done without any threat of paradox, as from that new context we can say, with expanded expressive resources, that the Liar sentence as it appeared in the prior context fails to be a proper truth bearer, and so fails to be true. This is a basically Tarskian conclusion. We invoke not a syntactically distinct truth predicate, but rather new expressive resources in a new context, which allow us to draw wider conclusions about truth than we could in the original context. Many questions may be raised about this sort of proposal: Why is there any such context dependence with Liar sentences, why is there a context shift in Liar reasoning, and what is the status of Liar sentences relative to a given context? We will not pursue these here.28 Rather, we merely comment on how this strategy, 27. The term “stepping back is borrowed from Gauker (2006), though Gauker is critical of contextualist proposals of the sort we sketch here. 28. They have been pursued at length. The original idea stems from work of Parsons (1974) and then Burge (1979), and has been developed, in very different ways by Barwise and Etchemendy (1987), Gaifman (1992), Glanzberg (2001, 2004a, 2004b), and Simmons (1993). The term “reffective context” is from Glanzberg (2006a).

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however it may be developed, combines Tarskian and classical restriction features. Its Tarskian nature is clear. There is a hierarchy. It is a hierarchy of contexts, and of what can be expressed in those contexts, rather than a hierarchy of languages syntactically individuated. But it is a hierarchy nonetheless. To avoid the Liar, it must have the same open-ended feature as Tarski’s own hierarchy. The contextualist strategy also takes up the classical restriction idea that we can explain the formal behavior of truth by paying attention to what really makes a sentence a well-behaved truth bearer. It does this by paying attention not to static semantic status, as our original classical restriction strategy did, but to how that status may change as context changes. It thus will invoke restricted forms of Capture and Release, along the lines we sketched in Section 3.2.2, but it will see these restrictions as showing what it takes for a sentence to be a truth bearer in a given context. Strengthened Liar reasoning shows us that this status is apt to change. Like the Tarskian theory, we believe the contextualist strategy is more faithful to the semantic view of truth. Both views offer truth predicates which correctly report the semantic status of sentences, and both may happily do so using classical logic and semantics. Both do so by placing some limits on what we can say, in some form. The Tarskian view does so rather drastically, ruling much that seemed to be perfectly plausible semantic talk to be syntactic gibberish. The contextualist view, we think, does so rather more gently. It merely says that certain claims can only be made from certain contexts, and you might not be able to say as much as you thought you could without moving to a new context. Because there are such expressive limits, each individual context shows some properties of classical restriction, and we cannot get a truth predicate to behave exactly right on every sentence in any one context. But so long as we allow ourselves to move through contexts judiciously, we can deploy our truth predicate exactly as it was supposed to be deployed to report the semantic status of sentences. It is now the semantic status of sentences in contexts that we report, and that is a more delicate matter than our original statement of the semantic view might have envisaged. But it is still the job of truth to report basic semantic status, and the restrictions imposed by the contextualist view, we think, do not undermine this. 3.2.4 The Liar and Semantic Truth We have now seen three examples of how one might go about addressing the Liar if one starts with a semantic view of the nature truth. This will be enough to draw some conclusions about how the logic and nature paths intersect in this case. Generally, the semantic view tells us something specific about what the task of resolving the Liar is. If we take the basic standpoint of the semantic view, then our task in the face of paradox is to try to understand better what semantic notions like semantic value are, and how they behave. If we follow the Tarskian line, we do so by paying attention to what sentences are really like. If we follow the contextualist strategy, we do so by paying more attention to what is involved in assigning semantic values in contexts. If we follow the classical restriction strategy, we do so by reconsidering what the basic semantic status to be reported by the truth

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predicate is. Regardless, each strategy pays attention to the fundamental building blocks of semantics, and each find as a result some way to restrict Capture and Release.29 The result for each strategy is a more refined picture of the formal properties of Tr—more refined versions of Capture and Release—which allow the truth predicate to function as the semantic view requires and retain consistency. Though at some points, we looked to techniques from nonclassical logic, we have seen no independent motivation to make any genuine departures from classical logic. The semantic view of truth tells us nothing directly about logic.30 Rather, the semantic view constrains us to resolve the paradox by a more careful examination of the behavior of Tr (and related notions) directly, and it provides the means to do so. 4 AND NOW REVENGE We have now illustrated some ways in which the nature path impacts the logic path. In one case—the transparent view of the nature of truth—the nature path dictates logic proper; particularly, logical options for resolving the Liar paradox. In the other—the semantic view—the nature path requires us to resolve the paradox by restricting the formal principles governing truth (Capture and Release), and it also provides us with resources for doing so. In both cases, we get significant constraints on how we may understand the logic of truth from how we understand the nature of truth, and indeed, we get significantly different constraints depending on the case. The nature path and the logic path thus do indeed meet. We have thus reached the main goal of this paper. As a further application of the point we have made here, we conclude by considering an issue that has proven difficult for the logic path: the problem of so-called “revenge” paradoxes. The significance of these revenge paradoxes has been a significant question in the literature on the logic of truth. We suggest here that what that significance is, and how revenge paradoxes must be treated, depends on views of the nature of truth. Again, we see the nature path constraining the logic path. In this case, we suggest, seeing how it does helps to answer a question that has preoccupied the logic path itself. We have already seen something of a “revenge paradox” in Section 3.2.3, where we observed that according to the classical restriction account, the Liar sentence is not true. This was presented as a reason to reject the classical restriction strategy. But the style of reasoning it represents applies much more widely, and just what it shows is often hard to assess.

29. The semantic view also helps, we think, to explain the goal of the Revision Theory of Truth of Gupta and Belnap (1993). Though, for reasons of space, we will not pursue it in any depth, we can think of this theory as making an even more far-reaching proposal for how to properly understand the fundamental building blocks of semantics. It in effect suggests that we should not think of the basic semantic property as a semantic value at all, but rather as a sequence of such values, under rules of revision. 30. Or at least, not much. It might tell us that logic must be based on a semantics according to which we can make sense of the semantic view of truth.

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The typical pattern of a revenge objection is as follows.We start with a formal theory, like a theory of truth. We then show that there is some notion X used in the formal construction of the theory which is not expressible in the theory, on pain of Liar-like paradox. Typically, X is on the surface closely related to the notion our theory was developed to explain, and is expressible in the target language our theory is supposed to illuminate. Hence, the revenge objection concludes that in not being able to express X, our theory fails to be adequate. Here is another example. Take as our theory the standard Kripke K3 construction (empty ground model, least fixed point). The formal object language L+ of this theory may be the language of arithmetic L supplemented with Tr. We have seen that Tr serves as a transparent truth predicate for L+ (though as we observed in Section 3.1.1, in a limited theory). L+ is an interpreted language. Its model M is produced by the Kripkean fixed point technique.As it is a K3 language, its valuation scheme is the Strong Kleene k (as we discussed in Section 2.1). We construct M in a classical metalanguage suitable for doing some set theory, which we may call M(L). Our metatheory is classical, so we may conclude in it that every sentence of L+ is true in M or not, in that either |f|M = 1 or it does not. (We may appeal to LEM in our classical metatheory.) Indeed, this notion is used in the construction of M. We now have the setup for revenge. We have our theory—the interpreted language of the Kripke construction. We also have the metatheoretic notion of being true (having value 1) in M. This is our notion X from above, which, at least on the surface, seems to be related to truth itself. The revenge recipe tells us to consider what would happen if this notion were expressible in our theory. Thus, towards revenge, suppose that there is a predicate TM(x) in L+ that expresses what we, in M(L), express using “true in M” (i.e. having value 1). Consider the resulting Liar-like sentence l equivalent to ¬TM(⎡l⎤). A few classical steps, all of which hold in M(L), lead to contradiction. In turn, one concludes that L+ (interpreted via M) enjoys consistency—more generally, nontriviality—only in virtue of lacking the expressive resources to express TM. Our broader language enjoys this power; indeed, the metalanguage M(L) does. Moreover, TM appears to be a notion of truth—indeed, a notion of truth for L+, and L+ cannot express it. In turn, revenge concludes that L+ is inadequate as a theory of truth: It fails to capture truth for L+, and so it fails to illuminate how our language, with its expressive resources, can enjoy a consistent (or at least nontrivial) truth predicate.31 This is clearly related to the objection raised in Section 3.2.3, which also argued for the inadequacy of a theory based on its failure to capture a modeltheoretic notion used in the construction of the theory. There are a great many related forms of revenge paradox, and it is not our aim to explain their structure in detail. Rather, we wish to consider the question of how effective such revenge paradoxes are as objections to a theory, and note that the answer depends on what view of the nature of truth is assumed.32 31. For a more leisurely and more detailed discussion of revenge, see the papers in Beall (2008c). 32. Our discussion is brief here. For more details, see Beall (2008b), Field (2008b), and Shapiro (2008).

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As we did in Section 3, we will show this by considering how the question should be answered under the transparent and semantic views of the nature of truth, in turn. We begin with the transparent view. As we have said, this view holds that “true” is only a logical, express device; it is brought in for practical reasons, to overcome practical limitations of finite time and space. As the transparent view is a species of deflationism, it importantly does not see “true” as naming any important property—a fortiori, not some property essentially tied to semantics or meaning. On “deflationist” views in general, fundamental semantic properties— including anything that determines linguistic meaning—are not to be understood along truth-conditional lines at all.33 (Using a transparent truth predicate, we may state truth conditions, but this can play no explanatory role in semantics.) Something similar holds for the notion of truth in a model. This cannot be seen by deflationist views as a formal representation of a fundamental semantic property, not even an idealized one. The transparent view of truth does not—cannot—hold that truth in a model is a property of fundamental importance to understanding the nature of languages. But, then, the models involved in giving a model theory for a formal theory of truth are at best convenient tools, which do not themselves amount to anything of theoretical importance. They are basically heuristic guides to logic.34 With this in mind, we can see that the transparent view of truth allows revenge paradoxes to be dismissed in many cases. It is crucial to the revenge problem that failing to express the revenge notion X amounts to a failure of adequacy. In our example cases, it is argued by the revenge objection that failure to express a model-theoretic notion used in constructing a theory amounts to a failure of adequacy. But given the transparent view of truth, even if such an inexpressibility result holds, it is not obviously a defect. If a model-theoretic notion, like truth in a model, is merely a heuristic device for specifying logic, we cannot conclude that failure to express it is any kind of failure of adequacy for a theory meant to capture the notion of truth. The most we can conclude is that there is some classical model-theoretic notion (e.g. truth in a model) that is used in the metalanguage of the construction but that our formal theory cannot nontrivially express.35 Though this could turn out to be a problem for the theory, and show it to be inadequate, we have yet to see any reason why. More importantly, simply displaying the “revenge” form of the paradox does not demonstrate that it is. If we hold a transparent view of the nature of truth, the model-theoretic revenge paradoxes in logic fail to show the inadequacy of a theory of truth. To the transparent view, revenge—at least of the “model-theoretic” sort we have discussed—is not serious.

33. Frequently deflationists opt for something like conceptual role semantics. See Field (1986, 1994) for discussion. Strictly speaking, the transparent view does not need to take a stand on semantics, as it is a view about the nature of the truth predicate. 34. Model theory can also be an important technical device, which provides a host of techniques of interest to logicians. See Dummett (1978, 1991) and Field (2008a) for discussion of these issues. 35. Whether this is the case really does depend on the details. For useful discussion, see Field (2008b) and Shapiro (2008).

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What of the semantic view? We have already seen that the semantic view leads to very different conclusions about revenge, such as the one we drew in Section 3.2.3.We have also seen that the semantic view takes a very different stance towards issues of semantics and model theory. The version of the semantic view we sketched in Section 1.1 starts with the idea that there is a fundamental semantic property described by assigning (the right sort of) semantic values to sentences. It also holds, as we discussed in Section 3.2, that the notion of truth in a model provides a theoretically useful way of representing this notion formally. According to the semantic view of the nature of truth, the model-theoretic notion of truth in a model reveals an important property, of explanatory significance. The job of the term “true” is to report that property. Thus, where the transparent view sees truth and truth conditions as merely heuristic notions, the semantic view sees them as fundamental explanatory notions for semantic theory and for meaning in general. Indeed, the core of the theory, on this view, is the theory of truth conditions, semantic values, and related notions.36 If we think of truth this way, then the revenge charge of inadequacy is very plausible, and we believe, in some cases, devastating.37 In particular, the modeltheoretic revenge problem, of the sort we just reviewed, is serious for the semantic view of truth, as it was in Section 3.2.3. If the notion of truth in a model provides a fundamental semantic concept, and indeed, the very one that our target notion of truth is supposed to capture, then failing to express it is just the failure of our theory to do its intended job. If we take the semantic view of truth, then typical revenge paradoxes, including the two we have seen here, are just ways to observe that a theory fails to live up to its own goals. That—in purest form—is inadequacy. Thus, what the significance of revenge paradoxes is turns out to be strongly influenced by views of the nature of truth. This reinforces our main conclusion, that the two paths—nature and logic—do meet, and do so in interesting ways. On the surface and in practice, the two have seemed not to intersect. We hope to have illustrated that this is not so. We have shown that responses to the Liar are strongly influenced by the nature path. Whether such a response results in a nonclassical logic, or restrictions on the principles governing truth, depends on views of the nature of truth. Whether or not revenge paradoxes are significant does as well. Not only do the two paths meet, but the logic path can learn something from following the nature path.

36. We have taken a model-theoretic stance towards theories of truth conditions, but that is but one tool that might be invoked here. So long as there is a substantial semantic theory, which yields truth conditions in some form, one can hold the semantic view of truth. Hence, as we mentioned in Section 1.1, taking a more Davidsonian view of semantics is no impediment to the semantic view. The idea that natural languages may be modeled with the tools of formal logic, in either model-theoretic or proof-theoretic terms, is basic to much of contemporary semantic theory. It is common today to grant that these tools apply differently in the semantics of natural language than they do in logic proper, though from time to time, the stronger view has been advocated (cf. Montague 1970). 37. One of us (viz., Glanzberg), who prefers the contextualist approach to the Liar, sees the right form of “revenge” as simply the issue of the Liar.

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Armour-Garb, B., and Beall, JC, eds. 2005. Deflationary Truth. Chicago: Open Court Press. Armstrong, David M. 1997. A World of States of Affairs. Cambridge: Cambridge University Press. Austin, J. L. 1950. “Truth.” Aristotelian Society Supp. Vol. 24: 111–29. Reprinted in Austin, J. L. Philosophical Papers, ed. J. O. Urmson and G. J. Warnock. Oxford: Clarendon Press, 1961. Baldwin, Thomas. 1991. “The Identity Theory of Truth.” Mind 100: 35–52. Barwise, Jon, and Etchemendy, John. 1987. The Liar. Oxford: Oxford University Press. Barwise, Jon, and Perry, John. 1986. Situations and Attitudes. Cambridge, MA: MIT Press. Beall, JC. 2005. “Transparent Disquotationalism.” In Deflationism and Paradox, ed. JC Beall and B. Armour-Garb, 7–22. Oxford: Oxford University Press. ———. 2008a. “Curry’s Paradox.” In Stanford Encyclopedia of Philosophy, ed. E. N. Zalta, http:// plato.stanford.edu/entries/truth/. ———. 2008b. “Prolegomenon to Future Revenge.” In Revenge of the Liar, ed. JC Beall, 1–30. Oxford: Oxford University Press. ———. ed. 2008c. Revenge of the Liar. Oxford: Oxford University Press. ———. 2008d. Spandrels of Truth. Oxford: Oxford University Press. Beall, JC, and van Fraassen, Bas C. 2003. Possibilities and Paradox. Oxford: Oxford University Press. Blanshard, Brand. 1939. The Nature of Thought. London: George Allen and Unwin. Brady, Ross T. 1989. “The Non-Triviality of Dialectical Set Theory.” In Paraconsistent Logic: Essays on the Inconsistent, ed. G. Priest, R. Routley, and J. Norman, 437–70. Munich: Philosophia Verlag. Burge, Tyler. 1979. “Semantical Paradox.” Journal of Philosophy 76: 169–98. Reprinted in Martin, Robert L. ed., Recent Essays on Truth and the Liar Paradox. Oxford: Oxford University Press, 1984. Cresswell, M. J. 1973. Logics and Languages. London: Methuen. David, Marian. 1994. Correspondence and Disquotation. Oxford: Oxford University Press. Davidson, Donald. 1969. “True to the Facts.” Journal of Philosophy 66: 748–64. Reprinted in Davidson, Donald, Inquiries into Truth and Interpretation. Oxford: Oxford University Press, 1984. Dowden, Bradley H. 1984.“Accepting Inconsistencies from the Paradoxes.” Journal of Philosophical Logic 13: 125–30. Dummett, Michael. 1959. “Truth.” Proceedings of the Aristotelian Society 59: 141–62. Reprinted in Dummett, Michael, Truth and Other Enigmas. Cambridge: Harvard University Press, 1978. ———. 1976. “What is a Theory of Meaning? (II).” In Truth and Meaning, ed. G. Evans and J. McDowell, 67–137. Oxford: Oxford University Press. Reprinted in Dummett, Michael, The Seas of Language. Oxford: Oxford University Press, 1993. ———. 1978. Truth and Other Enigmas. Cambridge, MA: Harvard University Press. ———. 1991. The Logical Basis of Metaphysics. Cambridge, MA: Harvard University Press. Dunn, J. Michael, and Restall, Greg. 2002. “Relevance Logic.” In Handbook of Philosophical Logic, 2nd ed., ed. D. Gabbay and F. Guenthner, 1–136. Dordrecht, The Netherlands: Kluwer. Feferman, Solomon. 1984. “Toward Useful Type-Free Theories, I.” Journal of Symbolic Logic 49: 75–111. Reprinted in Martin, Robert L., ed., Recent Essays on Truth and the Liar Paradox. Oxford: Oxford University Press, 1984. Field, Hartry. 1972. “Tarski’s Theory of Truth.” Journal of Philosophy 69: 347–75. ———. 1986.“The Deflationary Conception of Truth.” In Fact, Science and Value, ed. C. Wright and G. MacDonald, 55–117. Oxford: Basil Blackwell. ———. 1994. “Deflationist Views of Meaning and Content.” Mind 103: 249–85. ———. 2008a. Saving Truth from Paradox. Oxford: Oxford University Press. ———. 2008b. “Solving the Paradoxes, Escaping Revenge.” In Revenge of the Liar, ed. JC Beall, 78–144. Oxford: Oxford University Press. Fox, John. 1987. “Truthmaker.” Australasian Journal of Philosophy 65: 188–207.

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Friedman, Harvey, and Sheard, Michael. 1987. “An Axiomatic Approach to Self-Referential Truth.” Annals of Pure and Applied Logic 33: 1–21. Gaifman, Haim. 1992. “Pointers to Truth.” Journal of Philosophy 89: 223–61. Gauker, Christopher. 2006. “Against Stepping Back: A Critique of Contextualist Approaches to the Semantic Paradoxes.” Journal of Philosophical Logic 35: 393–422. Glanzberg, Michael. 2001. “The Liar in Context.” Philosophical Studies 103: 217–51. ———. 2004a. “A Contextual-Hierarchical Approach to Truth and the Liar Paradox.” Journal of Philosophical Logic 33: 27–88. ———. 2004b. “Truth, Reflection, and Hierarchies.” Synthese 142: 289–315. ———. 2006a.“Context and Unrestricted Quantification.” In Absolute Generality, ed. A. Rayo and G. Uzquiano, 45–74. Oxford: Oxford University Press. ———. 2006b. “Truth.” In Stanford Encyclopedia of Philosophy, ed. E. N. Zalta, http:// plato.stanford.edu/entries/truth/. Grover, Dorothy L., Camp, Joseph L., and Belnap, Nuel D. 1975. “A Prosentential Theory of Truth.” Philosophical Studies 27: 73–125. Gupta, Anil, and Belnap, Nuel. 1993. The Revision Theory of Truth. Cambridge, MA: MIT Press. Halbach, Volker. 1997. “Tarskian and Kripean Truth.” Journal of Philosophical Logic 26: 69–80. Heim, Irene, and Kratzer, Angelika. 1998. Semantics in Generative Grammar. Oxford: Blackwell. Horwich, Paul. 1990. Truth. Oxford: Basil Blackwell. Joachim, H. H. 1906. The Nature of Truth. Oxford: Clarendon Press. Kleene, Stephen Cole. 1952. Introduction to Metamathematics. Princeton, NJ: Van Nostrand. Kripke, Saul. 1975. “Outline of a Theory of Truth.” Journal of Philosophy 72: 690–716. Reprinted in Martin, Robert L., ed., Recent Essays on Truth and the Liar Paradox. Oxford: Oxford University Press, 1984. Larson, Richard, and Segal, Gabriel. 1995. Knowledge of Meaning. Cambridge, MA: MIT Press. Leeds, Stephen. 1978. “Theories of Reference and Truth.” Erkenntnis 13: 111–29. McGee, Vann. 1991. Truth, Vagueness, and Paradox. Indianapolis: Hackett. Montague, Richard. 1970. “English as a Formal Language.” In Linguaggi nella Società e nella Tecnica, ed. B. Visentini, 189–224. Milan: Edizioni di Comunità. Reprinted in Montague, Richard, Formal Philosophy, ed. R. Thomason. New Haven, CT: Yale University Press, 1974. Moore, George Edward. 1953. Some Main Problems of Philosophy. London: George Allen and Unwin. Mulligan, Kevin, Simons, Peter, and Smith, Barry. 1984. “Truth-Makers.” Philosophy and Phenomenological Research 44: 287–321. Parsons, Charles. 1974. “The Liar Paradox.” Journal of Philosophical Logic 3: 381–412. Reprinted in Martin, Robert L., ed., Recent Essays on Truth and the Liar Paradox. Oxford: Oxford University Press, 1984. Parsons, Josh. 1999. “There is No ‘Truthmaker’ Argument against Nominalism.” Australasian Journal of Philosophy 77: 325–34. Priest, Graham. 1979. “The Logic of Paradox.” Journal of Philosophical Logic 8: 219–41. ———. 2002. “Paraconsistent Logic.” In Handbook of Philosophical Logic, 2nd ed., ed. D. Gabbay and F. Guenthner, 287–393. Dordrecht, The Netherlands: Kluwer. ———. 2006a. Doubt Truth to Be a Liar. Oxford: Oxford University Press. ———. 2006b. In Contradiction. 2nd ed. Oxford: Oxford University Press. Quine, W. V. O. 1951. “Ontology and Ideology.” Philosophical Studies 2: 11–15. ———. 1970. Philosophy of Logic. Cambridge, MA: Harvard University Press. Ramsey, Frank P. 1927. “Facts and Propositions.” Aristotelian Society Supp. Vol. 7: 153–70. Reprinted in Ramsey, Frank P., The Foundations of Mathematics and Other Logical Essays. London: Routledge and Kegan Paul, 1931. Restall, Greg. 2000. An Introduction to Substructural Logics. Oxford: Routledge. Routley, Richard, and Meyer, Robert K. 1973. “Semantics of Entailment.” In Truth, Syntax, and Modality, 194–243. Amsterdam: North Holland. Russell, Bertrand. 1910. “On the Nature of Truth and Falsehood.” In Philosophical Essays, 147–59. London: George Allen and Unwin. ———. 1912. The Problems of Philosophy. London: Oxford University Press.

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———. 1921. The Analysis of Mind. London: George Allen and Unwin. ———. 1956. “The Philosophy of Logical Atomism.” In R. C. Marsh, ed., Logic and Knowledge, 177–281. London: George Allen and Unwin. Originally published in The Monist in 1918. Shapiro, Lionel. 2008. To appear. “Revenge and Expressibility.” Simmons, Keith. 1993. Universality and the Liar. Cambridge: Cambridge University Press. Strawson, Peter F. 1950. “Truth.” Aristotelian Society Supp. Vol. 24: 129–56. Reprinted in Strawson, Peter F., Logico-Linguistic Papers. London: Methuen, 1971. Tarski, Alfred. 1935. “Der Wahrheitsbegriff in den Formalizierten Sprachen.” Studia Philosophica 1: 261–405. References are to the translation by J. H. Woodger as “The Concept of Truth in Formalized Languages” in Tarski, Alfred, Logic, Semantics, Metamathematics, 2nd ed., ed. J. Corcoran, trans. J. H. Woodger. Indianapolis: Hackett, 1983. ———. 1944. “The Semantic Conception of Truth.” Philosophy and Phenomenological Research 4: 341–75. Taylor, Barry. 1976. “States of Affairs.” In Truth and Meaning, ed. G. Evans and J. McDowell, 263–84. Oxford: Clarendon Press. Visser, Albert. 1984. “Four Valued Semantics and the Liar.” Journal of Philosophical Logic 13: 181–212. Walker, Ralph C. S. 1989. The Coherence Theory of Truth. London: Routledge. Woodruff, Peter W. 1984. “Paradox, Truth, and Logic Part 1: Paradox and Truth.” Journal of Philosophical Logic 13: 213–32. Wright, Crispin. 1976. “Truth-Conditions and Criteria.” Aristotelian Society Supp. Vol. 50: 217–45. Reprinted in Wright, Crispin, Realism, Meaning and Truth, 2nd ed. Oxford: Blackwell, 1993. ———. 1982. “Anti-Realist Semantics: The Role of Criteria.” In Idealism: Past and Present, 225–48. Cambridge: Cambridge University Press. Reprinted in Wright, Crispin, Realism, Meaning and Truth, 2nd ed. Oxford: Blackwell, 1993.

Midwest Studies in Philosophy, XXXII (2008)

Pointless Truth JONATHAN KVANVIG

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y primary interest is in the value of knowledge and understanding, and the view I wish to defend is that these values are unrestricted. I believe there is a difference between the values in question, but will not pursue that issue here, since I have pursued it elsewhere.1 Instead, I’ll pursue a strong objection to the unrestricted value that I claim knowledge and understanding have in common. The objection arises because of the factive nature of knowledge and understanding, which leads to a dependence of the value in question on the value of truth itself. If truth does not have unrestricted value, then knowledge and understanding do not either, and the objection claims that truth does not have such value. I will begin by describing the kind of value I take knowledge and understanding to share in order to unearth the difficulty for this position, a difficulty arising from the problem of pointless truth. I will then argue that the problem does not undermine the fully general and unrestricted value of knowledge and understanding.

1. In The Value of Knowledge and the Pursuit of Understanding (Cambridge: Cambridge University Press, 2003), though my earliest thinking about the matter traces to “Why Should Inquiring Minds Want to Know?” The Monist 81.3 (1998): 426–51 (reprinted in Sosa, Kim, Fantl, and McGrath, ed., Epistemology: An Anthology, 2nd ed. (Oxford: Blackwell, 2008). And even earlier to Jonathan Kvanvig and Christopher Menzel, “The Basic Notion of Justification,” Philosophical Studies 59 (1990): 235–61. Midwest Studies in Philosophy: Truth and its Deformities Volume XXXII Editor by Peter A. French and Howard K. Wettstein © 2008 Wiley Periodicals, Inc. ISBN: 978-1-405-19145-6

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Jonathan Kvanvig I. THE UNQUALIFIED VALUE OF KNOWLEDGE AND UNDERSTANDING

A beginning point in thinking about the value of knowledge and understanding is that such value is universal and unqualified, but counterexamples abound. We are told that a little knowledge is a dangerous thing, we know that there are things we are better off not knowing, and we realize that Socrates was right in pointing out to Meno that a guide who knows the way to Larissa is no better, as a guide, than one who merely has a true opinion about it. In these ways, and many others, the view that these values are universal and unqualified is threatened. These facts have led a number of philosophers to give qualified endorsement only to the value of knowledge. Williamson says that knowledge is valuable when the cognitive faculties are in good order,2 Swinburne qualifies the value as obtaining “almost always,”3 and Percival in a similar vein says “by and large.”4 Ward Jones expresses a similar idea when he writes, I value going to fairs because I have fun when I go to them, even though I can distinctly remember occasions when I got sick on the rides and did not have any fun at all. The fact of my having fun at fairs is responsible for the value I place on fairs, but my having fun is only a contingent property of my attending them. Knowledge is like fairs. We value them both even though we do not always get what we want from them.5 Each in their own way qualify the claim that knowledge is always and everywhere and of necessity valuable, and though they do not address the question of the value of understanding, there is no reason to suppose their appraisal would change if they were remarking about it instead. Moreover, what they say clearly has a ring of truth to it, given even a cursory acquaintance with the initial points made above. A little knowledge can be a bad thing; there are some things we are better off not knowing; and knowledge is typically no better than true opinion in satisfying our practical interests. Even so, nothing in the above undermines the claim that knowledge and understanding have universal and unqualified value. When it is pointed out that true opinion gets us all the practical benefits that knowledge does, a quite natural response is to insist that practical value is not the kind of value one has in mind when one claims that knowledge is more valuable than true belief. Upon being shown the disastrous consequences of learning what it takes to construct nuclear weapons, a defender of the value of knowledge will want to distinguish the initial value of knowledge from the overall value that results when knowledge is put to use. 2. Timothy Williamson, Knowledge and Its Limits (Oxford: Oxford University Press, 2000), 79. 3. Richard Swinburne, Providence and the Problem of Evil (Oxford: Oxford University Press, 1999), 64. 4. Philip Percival, “The Pursuit of Epistemic Good,” Metaphilosophy 34 (2003): 38. 5. Ward E. Jones, “Why do we Value Knowledge?” American Philosophical Quarterly 34.4 (October 1997): 434.

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We thus notice that two distinctions are needed to understand and appreciate the plausibility of the claim that knowledge and understanding have universal and unqualified value. The first distinction is between all-things-considered value and prima facie value. Suppose an epistemic terrorist, opposed to the proliferation of knowledge, threatens to kill you if you happen to know a specific claim. Such knowledge would be immensely disvaluable for you, but one ought not confuse this all-things-considered disvalue with the limited and positive prima facie value that knowledge possesses in itself, apart from such farfetched consequences. This prima facie value does not disappear in the presence of untoward consequences, but rather is defeated by these other factors.When the story is told about the all-thingsconsidered disvalue of knowing that specific claim, the story includes the prima facie value of knowledge and the fact that it is overridden by the negative practical consequences engendered by such knowledge. This distinction helps us to understand the quote above from Jones comparing knowledge and fairs. At the level of all-things-considered value, there is an analogy: fairs are sometimes not fun, and knowledge sometimes causes harm. But fairs have nothing intrinsic going for them. There is no special kind of value that resides in fairs, considered in themselves. They have no prima facie value in themselves that must be overridden or defeated for the experience of going to fairs to have neutral or negative value. The value of fairs is nothing over and above the question of whether fairs are typically associated with having fun. But the value of knowledge is not like this, at least not when the associated value is all-thingsconsidered value. Pieces of knowledge can be all-things-considered disvaluable, just as fairs could typically be no fun at all, but the former possibility can only arise by having the intrinsic value of knowledge and understanding overridden or defeated by competing values. No such remarks about the value of fairs would be correct. This point leads to a second distinction, one aimed at clarifying the nature of the value in question that knowledge and understanding possess. We first distinguish among different types of value: practical, social, moral, political, religious, and aesthetic. We can then use such a list to clarify the notion of all-things-considered value (it is some sort of function on all the kinds of value in question), and point out the need for an additional kind of value as well. In addition to practical concerns, there are purely theoretical ones displayed in the ubiquitous phenomenon of curiosity. Such a purely theoretical value is different from any of the values listed to this point, and it is this kind of value involved in the claim that knowledge and understanding have universal and unqualified value. Given these distinctions, the value claim in question is very much akin to the claim that causes raise the likelihood of their effects. This latter claim about causes is subject to counterexample. Taking birth control pills causes thrombosis, but the statistical probability of getting thrombosis is lower for those who take the pill than for those who do not. The crucial factor at work here is interaction of causal factors: pregnancy also causes thrombosis, and taking the pill reduces the probability of pregnancy. The lesson here is not that it is a mistake to think of causes as probability enhancers, but that the truth of the claim that causes are probability enhancers can only be seen by controlling for other causal factors. Just so with the

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value of knowledge and understanding: to find this value, we have to control for the presence of competing values that may generate an overall disvalue for any given state of knowledge or understanding. Just as we do not want a theory of causality that rests content with the claim that causes sometimes raise the probability of their effects and sometimes do not, we should not be satisfied with a theory of knowledge or understanding that addresses the value question only by a similar “sometimes yes, sometimes no” approach. Once we move beyond such remarks by putting the right controls in place, we can see both how causation is related to probability and the universal and unqualified value of knowledge and understanding. We can put the view in question in terms of the language of defeasible reasoning. Finding out that a given cognitive state is a state of knowledge or understanding is a defeasible reason for thinking that the state is all-thingsconsidered valuable. Finding out that a given cognitive state is a state that came into existence on a Tuesday in the middle of July is not such a reason. In both cases, the overall value of the state can vary from quite valuable to quite disvaluable, but we miss the central axiological feature when we attend only to the overall results in question. By distinguishing purely theoretical value from other kinds of value, and by distinguishing prima facie from ultima facie value, we have a pleasing account of the idea that knowledge and understanding are always and everywhere and of necessity valuable. There remains a problem for this view, however. The value of knowledge and understanding presupposes the value of truth itself, for these cognitive states are factive states, in the sense that one cannot know or understand that p without it being true that p.6 Moreover, when we move beyond the propositional level to the objectual level, something similar is true. One can understand the rise and fall of the Third Reich without having every feature exactly right, but at least for the central features of the correct account of this rise and fall, error is not compatible with understanding. In this way, objectual knowledge and understanding are at least quasi-factive. Clarifying this notion of quasi-factivity would take us too far afield, so I will not address this point further, for the point of significance for our context is the way in which the importance of truth underlies the value of knowledge and understanding, given this factivity. If truth does not matter, the value of knowledge and understanding is threatened; and if some truths are significant and others not, the universal and unqualified value is threatened as well. Here I will not address points of view that claim that truth has no significance whatsoever. There is a growing body of literature addressing this strange doctrine, and I will not add to it here.7 I will assume that truth matters, but even given this

6. This point should not be confused with the claim that there are no uses of the terms “know” and “understand” that are not factive uses. If knowledge and understanding are not factive states, it may in fact be easier to sustain their universal, unqualified, and necessary value. So one may take the factivity claim in the text in terms of granting an assumption to make the defense harder, if one thinks these states are not factive. 7. See Michael Lynch, True to Life: Why Truth Matters (Cambridge, MA: MIT Press, 2004); Bernard Williams, Truth and Truthfulness: An Essay in Genealogy (Princeton, NJ: Princeton

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assumption a problem remains. It is the problem of axiologically negative truths, to which I now turn.

II. BAD TRUTH AND POINTLESS TRUTH As with knowledge itself, the value of truth clearly varies. Sometimes, the truth will set you free, and sometimes, the truth hurts. Other times, the truth is pointless, or uninteresting, or trivial. At the same time, knowledge matters, and understanding is to be prized, and at first pass, at any rate, the verbs “know” and “understand” are factive in central epistemic uses.8 These cognitive achievements are important and valuable in part because of this factive character, and thus the value of knowledge and understanding depends on the value of truth. So if truth has negative or neutral value, it becomes difficult to endorse the view that knowledge and understanding have unrestricted value. I will argue, however, that these difficulties can be overcome. I will argue that the problems created by bad truth and pointless truth do not undermine the universal and unqualified value of knowledge and understanding. Consider first the examples of bad truth. We can take the same approach to the problem of bad truth that we took to the possibility of knowledge that is bad for us. First, we should remind ourselves that the value involved in claims about the significance or importance of knowledge and understanding is a purely theoretical or cognitive value, and thus that if such value depends on the value of truth, the relevant kind of value must be purely theoretical as well. As is often the case in philosophy, the purchase power of a characterization depends on its contrasts. Here, the notion of a purely cognitive value derives its purchase power from a contrast between the cognitive and the affective aspects of human beings. Beliefs and knowledge are cognitive states; desires, hopes, wishes, and wants are affective states. We might then put the point about purely cognitive value in terms of something that would matter to an individual when we ignore anything that matters to that individual in virtue of some relationship to affective states. In short, something has purely cognitive value when it has value to individuals who care about nothing, though of course such a characterization is not quite accurate: we do not really know whether it is even possible to care about nothing at all. But hyperbole can be instructive nonetheless, to point us to the idea of purely

University Press, 2002); Paul Boghossian, Fear of Knowledge: Against Relativism and Constructivism (Oxford: Oxford University Press, 2006); and Simon Blackburn, Truth: A Guide (New York: Oxford University Press, 2005). 8. Catherine Elgin argues that understanding is not factive, and Allan Hazlett questions the same claim about knowledge. See Elgin, Considered Judgment (Princeton, NJ: Princeton University Press, 1996); and Hazlett, “The Myth of Factive Verbs,” Philosophy and Phenomenological Research (forthcoming). I believe that distinguishing between understanding a theory and understanding the reality the theory attempts to characterize is the key to avoiding Elgin’s arguments (for the development of this claim, see Jonathan L. Kvanvig, “Responses to Critics,” in Epistemic Value Essays, ed. Duncan Pritchard (Oxford: Oxford University Press, forthcoming 2008)), and even if Hazlett is correct, there are still central and important uses of “knows” that are factive, and it is legitimate for the epistemologist to focus on one of these, as I am doing here.

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theoretical value in contrast with other values including practical value. To have purely theoretical value is thus a value that remains even when these other values are controlled for. We can think of the way out of the problem of bad truth in the following way (a way that is doubly useful because it not only addresses the problem of bad truth but also will help us see why the same kind of reply cannot be given to the problem of pointless truth). The space of value can be modeled in terms of a twodimensional vector space. Values of every kind are represented in this space as vectors, vectors for moral value, aesthetic value, epistemic value, practical value, etc. Such vectors, to simplify, obey the standard operations of addition, multiplication, and negation, thereby generating overall results for combination of vectors, allowing the space in question to represent the all-things-considered value of any given item in addition to representing all the subspecies of overall value as well. In light of such a model, we can explain away the negative remarks about truth that constitute the problem of bad truth. In this category are truths which generate negative moral and practical value through our awareness of them. They also generate positive value of the sort related to epistemology in virtue of their purely cognitive and theoretical value, but there is no guarantee that such value trumps the negative moral and practical value of the truth in question. It thus may be that we are better off remaining clueless concerning such truths. The problem of bad truth is thus no different in kind from the issue raised by the idea that a little knowledge is a dangerous thing and that true opinion works just as well as knowledge for securing practical benefits. All that is needed is a distinction between prima facie value of a purely cognitive or theoretical sort and ultima facie value, and the problem is solved. Pointless truths (such as the truth about the precise number of grains of sand in a given container), however, raise a different issue. If we suppose that calling a truth pointless is to make a remark about the all-things-considered value of a given truth, then we should be able to explain how the mathematical operations on the various vectors of the space in question generate the zero vector as the result for such a truth. For we are assuming that every truth has epistemic value, and thus if a given truth ends up being all-things-considered pointless, we need an explanation if such a neutral value is compatible with positive epistemic value. To reach this conclusion, we have to identify some negative vector or vectors to offset the positive value the truth has in virtue of its purely cognitive or theoretical value. But when dealing with typical examples of pointless truths, there are no such negative values (e.g., counting the grains of sand may be tiring, but then again, it may invigorate; it may waste time, but one may have time to waste, etc.). So the existence of all-things-considered pointless truths raises a problem for the understanding of the value of truth just presented. What is needed to retain the unqualified value of truth and the related factive cognitive states is the possibility of undercutting values or the absence of such, so that the complete absence of any value beyond epistemic value may in some cases undercut the cognitive value in question. For such undercutting values, modeling by a two-dimensional vector space is not possible, since the interaction in question is not an instance of the addition or multiplication of two vectors. In some cases,

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a neutral value for practical and other non-epistemic concerns leaves overall value intact (perhaps the deep truths about distant regions of our universe are like that) and in other cases a neutral value for practical and other non-epistemic concerns undercuts epistemic value, leaving the truth in question a pointless one. It is this difference between two types of pointless truths, both of which have no nontheoretical value but only one of which seems to have theoretical value that underlies, I believe, Ernest Sosa’s remark that the view that truth always and everywhere has positive value is one that he “hardly understands.”9 If we classify one kind of pointless truth in terms of the concept of basic research of the sort we engage in for its own sake, such as investigating far reaches of the universe solely for the purpose of understanding what the universe is like, there remains the other class of pointless truths, of which a good example might be the precise number of blades of grass in my yard. There is, of course, no perplexity involved in the idea that a thing having a certain kind of value can fail to be all-things-considered valuable. No one should be perplexed anymore by the interaction of different types of value. But the problem of pointless truths cannot be explained away in terms of the interaction of values. Instead, the problem of pointless truths is that the absence of other values sometimes resembles the situation of basic research that we do not judge to be worthless, and sometimes resembles the situation of counting blades of grass in my yard, which we do judge to be worthless. One can say that what is happening in the latter case (but not in the former) is an undercutting of the value of truth by the absence of other values, but why should we? Why not just grant the point that there are some truths that have nothing going for them from an axiological point of view? I think there is a good answer to this question, and thus a good defense of the undercutter model of the ubiquitous and unrestricted value of truth, but it is worth approaching this issue a bit more indirectly. The indirect approach begins with a position hardly any philosopher will accept, but which has fairly wide currency in our culture. Once we see why we should not accept this unrefined and boorish approach, we will be in a position to see why the undercutter model is the right way to understand the value of pointless truths. I begin, then, with the ham-fisted and indelicate view that when all noncognitive values go to zero, so does overall value; every pointless truth is in the same category, not deserving of any of our time or attention. Call this position “crass pragmatism.” According to the crass pragmatist, there is no such thing as purely cognitive value, at least when no other values are present, so there is no more reason to engage in basic research whose sole purpose is to further our understanding than there is to count blades of grass in my yard. Any given person might have idiosyncrasies that lead to an interest in such things, but being valued by a person or even by a large group of people should not be confused with such a thing being valuable. The crass pragmatist exploits this truism to infer that any truth lacking other than purely theoretical value is an indefeasibly pointless truth. Such 9. Ernest Sosa, “For the Love of Truth?” in Virtue Epistemology: Essays on Epistemic Virtue and Responsibility, ed. Abrol Fairweather and Linda Zagzebski (Oxford: Oxford University Press, 2001), 49–62.

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a position may maintain that cognitive value is one kind of value, but not that important a value, since it cannot exist on its own apart from other values. Armed with such a view, it is easy to argue that basic research should not be pursued and that public policy should never favor funding basic research. By “basic research,” I mean research that has no practical benefit and aims at no success other than that of knowing more and understanding better. Noting this implication of the view should give us pause, since, to resort to a bit of hyperbole, nobody in their right mind thinks that only applied research is worth doing. Not only does basic research sometimes yield unexpected practical benefits, but investigation aimed solely at understanding a given phenomenon often involves such pure joy and satisfaction that one wonders what is wrong with those who want it excluded from an account of what makes life good. So, if the undercutter model is going to be avoided, it will not be on the basis of crass pragmatism. Instead, some more sophisticated view will be needed that recognizes that not all pointless truths are in the same category. If we grant the point that some basic research is worth doing in spite of the fact that it aims at truths that are, theoretical understanding aside, pointless truths, appealing to pointless truths to undermine the claims I have made about the value of understanding and knowledge requires an explanation of why basic research truths are valuable in spite of being pointless. If the best explanation of the value of basic research can be extended easily to any truth whatsoever that lacks nontheoretical value, then we are well on our way to defending the undercutter model of pointless truth and thus the unrestricted value of truth. The question we should ask, then, is what sort of explanation can be given for the value of basic research? III. BASIC RESEARCH AND POINTLESS TRUTH The crass pragmatist insists that basic research is not worth doing because it is aimed at pointless truths, but there is a more enlightened pragmatism that finds room for such research. The enlightened pragmatist still opposes the intellectualist view that even what I’m calling pointless truths have purely intellectual value and are thus worth knowing. The enlightened pragmatist takes comfort in a point highlighted by the paradox of hedonism. Even if aiming at pleasure or happiness is not the best way to achieve it, it does not follow that goodness and rightness are not best understood in such terms. Just so, even if basic research involves inquiry for its own sake, it does not follow that its value is not best understood in terms of some connection to nonintellectual concerns. We have already noted that basic research is not aimed at solving practical problems and difficulties, and there is no obvious way to show that solutions to problems of practice are best found by doing basic research. The refuge taken by the enlightened pragmatist is in the idea that basic research is worth doing, not because of its practical benefits, but because of the possibility or chance of such. The intellectualist doubts that the enlightened pragmatist can give a suitable clarification of that view that will yield the conclusion that there are some truly pointless truths, ones for which there is no need to cite any factor of any sort to undercut or undermine some supposed value they have, and in the present context,

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such a result is needed in order for the appeal to enlightened pragmatism to have the consequences sought of it. Since the difference between these two kinds of point truths lies in the possibility or chance or potential for practical significance, the enlightened pragmatist needs to give us an account of the key notion of the possibility or potential for practical benefit so as to distinguish between the pointless truths that are suitable objects of basic research and the remainder of pointless truths. Here the pure intellectualist, aiming to defend the undercutter model of the unrestricted value of truth, will claim that there is no explanation available to do the job. If the possibility in question is logical or metaphysical possibility, the pure intellectualist wins, since it is hard to find any truth not significant in this sense. Any truth can be important in this sense, if only because there could be an unusual and powerful ruler who made it worthwhile to believe. The appeal to logical or metaphysical necessity lacks the power to sort pointless truths into those that are worth investigating and those that are not. The issue is similar when the appeal is to chance rather than mere possibility. Which truths have no chance of being significant to our practical or nonintellectual interests? To hold that there are such truths, we’d need a notion of chance that tells us that even though it is possible that there is an unusual ruler of the sort imagined above, there is no chance of there being such a ruler. We might wonder how to tell the difference between possibilities that have no chance of obtaining and those that have some chance of obtaining, but the enlightened pragmatist can insist that we not confuse the metaphysical point about which truths are worth knowing with the epistemological point about how we’d be in a position to know which truths have that feature. Even if we would find it difficult or impossible to know which truths have no chance of being practically significant, the enlightened pragmatist can still maintain that this is just another regrettable feature of the human condition. We muddle through here as best we can, such a pragmatist may note, but what counts is the existence of a chance of practical significance for any truth worth knowing, not whether we can know which truths fall into this category. There is a more basic problem with the proposal, though. At this point, all the enlightened pragmatist can legitimately claim is the following possibility: some truths might have no chance of practical significance even if it is possible for them to have such significance. But sheer speculation can replace needed argument in defense of enlightened pragmatism. The claim that needs defense is that there is a difference between pointless truths worth investigating and those not worth investigating. The proposal is that the difference depends on the chance of something significant coming out of the investigation. To defend the proposal, the enlightened pragmatist must argue that some pointless truths have no chance of significance; merely to point out that some truths might have no chance of significance is not on point. Such mere speculation gives us only the weakest epistemic possibility of such, on par with the claim that, given the nature of our experience, we might be brains in a vat. Arguing that the central theses of a view are merely epistemically possible in this sense does not count as a defense of the view. It does not even count as a defense of the logical or metaphysical possibility of the view, as is shown by the fact that, until seeing the point of Russell’s paradox, the comprehension axiom was epistemically possible for Frege.

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Moreover, if the standard is raised so that the enlightened pragmatist has to find examples regarding which we know or rationally believe them to have no potential or possibility for a connection to practical interests, the enlightened pragmatist’s position will not withstand scrutiny. It must be admitted that any truth can come to be practically significant—that is the lesson of the example of the unusual ruler above. Moreover, it is easy to imagine such a ruler only counting prior knowledge of the truth in question: once he or she comes to power, only those who’ve already investigated the question get the reward. The enlightened pragmatist can point out that this possibility should have little or no effect on our practical decisions about what kind of research to fund and what questions to investigate, and that point is surely correct. But the point is irrelevant. The enlightened pragmatist, in the present context, needs an account on which some truths are truly pointless in the sense that no potential or possibility of a connection to practical interests can explain any interest in such truths in order to provide an account on which truth lacks the ubiquitous and unrestricted value the intellectualist claims. These difficulties with enlightened pragmatism will not be decisive unless the alternative, intellectualist position can explain the role that practical concerns legitimately play in curtailing and encouraging intellectual discovery. We thus turn to the intellectualist model to see its resources on this issue, and the implications of this position for the idea that there are some truly pointless truths. IV. INTELLECTUALIST POSITIONS As with the pragmatic view, the intellectualist view comes in two varieties. The simple version of the view is the bullet-biting version. When faced with apparent counterexamples to the ubiquitous value of truth, such as the example concerning the number of blades of grass in my yard, the bullet-biters simply shake their head in disagreement. All truth is valuable, they insist, and there is nothing more that needs to be said. One could wish for a more sophisticated response, especially since the bulletbiting version of the view has no resources to explain the obvious point that some investigations really are not worth undertaking. The more sophisticated intellectualist view grants that there are examples such as the blades of grass example that need to be explained away, and the sophisticated view claims to provide such an explanation. The sophisticated intellectualist has two resources for handling them, one on the practical side and one on the theoretical side. On the practical side, the sophisticated intellectualist does not deny or ignore the pressing practical context in which all of life finds itself, and may readily grant that failure of practical import may often trump intellectual value alone (though, as I will suggest below, some cultures, such as our own, find it too easy to resort to this idea, and to their detriment). In some cases of failure of practical import, the intellectualist may agree with the enlightened pragmatist that the potential or possibility of practical benefits can all-things-considered justify inquiry. But even when such potential or possibility does not justify inquiry, the intellectualist notes that it does not follow that the truths are pointless. Instead, the source of our lack of concern for such truths is the pressing practical issues we face that require, all

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things considered, to favor inquiry at least indirectly justified in terms of practical issues over those known or justifiedly believed to have no such potential. If our pressing practical concerns were absent, both individually and corporately, the worry about pointless truths arising from practical concerns would not arise, and the value of such truths would not be threatened by the overriding concerns of practical life. There is a similar point to be noted on the theoretical side. In purely theoretical inquiry, there is a trade-off between truth and informational content. Adding one to every known sum will generate additional truths, and endless applications of disjunctive syllogism will do the same, but will do little to enhance informational content. The significance of informational content, however, does not undermine the value of truths that are useless from the point of view of the systematization involved in theories, where the basic features of the theory rate high in terms of informational content. The importance of such systematization has two sources, one in the value of truth itself (since there are truths about how best to systematize the truths about a given subject matter) but also from our cognitive limitations. We have only a 3-pound brain, and its capacities are limited by basic biology. With these limitations, efficiency in cognition is a high priority, and systematization of information contributes importantly to efficiency in thought and action. As with the practical insignificance of some truths, the intellectualist here can explain away the source of the pointlessness idea through appeal to contrasting tasks and comparative judgments: the importance of informational content derives from limitations on our cognitive abilities, showing that the need for informational content may often trumps the value of inquiry revealing truths with little or no informational content or potential for usefulness in systematizing a body of information into a simple and wieldy theory. But such a contrast is no different from the contrast between truth and potential for practical significance used to explain why basic research is often worth doing. In each case, the fact that there is something else more worthy of pursuit does not show that the less worthy is of no worth at all. The intuition of no worth at all is seated in recognition of the importance of practical matters and the need for information content, but the no-worth conclusion does not follow, says the sophisticated intellectualist. All that follows is that the value in question cannot be revealed except when we imaginatively control for these trumping factors. To imagine such a situation is to imagine a world where no practical needs are left unmet and where no limitation of cognitive power creates any need for informational content to trump any value for truths with little or no content. For such beings, there is no need to favor organized theories or elegant axiomatizations based on any practical or nonepistemic interests such as efficiency for prediction and control or even the beauty of such a system. There is also, of course, no reason to castigate such systematizations. They have the same value that any truth has, says the intellectualist. Moreover, there is a fairly decisive way to appreciate why the intellectualist is right about such an imaginative situation. We should ask ourselves, regarding possible individuals in such a cost-free environment, what the cognitive ideal would involve. Here the intellectualists have millennia of theological reflection on their side. Part of the cognitive ideal, whatever else it may involve, is knowledge of all truths;

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omniscience, for short. But for omniscience to be part of the ideal, no truth can be pointless enough to play no role at all in the story of what it takes to be cognitively ideal. Moreover, any weaker account of the cognitive ideal quickly collapses into the traditional account. Suppose we say that the cognitive ideal only requires knowing important truths and does not require knowing (all) trivial and pointless truths. Even so, it will be important to know what the difference is between the two classes of truths, and what features make a given truth belong in one class rather than in another. Given this fact, the inference from the restricted account to the traditional account is fairly obvious: to know these things requires knowing which truths are in fact pointless, and thus knowing all the pointless truths. So whatever account one gives of pointless truths, they cannot have a nature which is such that it is not part of the cognitive ideal to know that they are true. One might try to avoid this implication by claiming that one can classify certain issues or problems as trite, trivial, or pointless, and do so without knowing on which side the truth falls. Thus, one might know that, regardless of the exact number of blades of grass in my yard, the exact number is a pointless truth. There is a simple thought experiment to show why this idea will not work. Imagine a world with two beings, each claiming to be cognitively ideal. One is omniscient and the other is not. The less-than-omniscient being claims to be cognitively ideal in virtue of knowing all the important truths, but the omniscient being demurs. For among the important truths are the claims about what the omniscient being knows that the less-than-omniscient being does not know. Even if the issue concerning a given proposition is assumed to be pointless and not worthy of being known, the fact that the omniscient being knows the truth value in question and the less-than-omniscient being does not is itself a distinctive difference between the two beings. Moreover, the specific knowledge in question is also an important difference: that the omniscient being knows that the claim is true, for example, and that the less-than-omniscient being does not, establishes a significant different in terms of their grasp of the precise nature of the world in which they find themselves. Once one appreciates this result of the thought experiment, one can see why lesser accounts of the cognitive ideal collapse into the stronger account.10 So the point remains that the cognitive ideal in terms of omniscience, or something as close as possible to omniscience, still provides an argument for the intellectualist’s undercutting model of the unrestricted and ubiquitous value of truth. The existence of pointless truths is compatible with the undercutting model and the facts about cognitive ideality show that this model is the best explanation of such truths. This result shows that pointless truths are not pointless in any way that undermines the universal and unqualified value of truth and the related values of knowledge and understanding. 10. The issues in the text should not be confused with orthogonal issues about the paradoxes of completeness discussed in, for example, Patrick Grim’s The Incomplete Universe (Cambridge, MA: MIT Press, 1991). The pointless truths in focus in the text are not the sort of things that create such paradoxes, and if incompleteness of the sort Grim argues for is unavoidable, the distinction between two beings, one that approaches omniscience but never reaches it and one that doesn’t approach it because of never attending to pointless truths, remains.

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CONCLUSION So the way in which omniscience provides a clear picture of the cognitive ideal presents a strong argument on behalf of intellectualism. The most plausible version of intellectualism also recognizes the way in which practical concerns are typically so pressing that the value of truth can disappear from view because of the overriding importance of these concerns. But an overridden value is a value nonetheless, and the presence of such a value allows the account of the universal and unqualified value of knowledge and understanding to withstand the challenge of pointless truths. There are truths that are not worth knowing and which do not deserve our attention, but these points are best interpreted in terms of overall value in which the value of truth is undercut by other factors and issues. Such truths thus do not threaten the more fundamental and ubiquitous values from which overall value are generated. Every truth has such fundamental value, and the best account of the value of knowledge and understanding is in terms of the same type of fundamental value, one that is defeasible but ever present nonetheless. The most general way to put this point is as follows. There are two kinds of pointless truths. One kind is explained by the vector space model, in which the defeasible value of truth of rebutted by other values in that vector space. The other kind is not explained by the vector space model. This kind of pointless truth is pointless because the intrinsic value of truth is undercut, but not rebutted, by the lack of other positive values. And the argument that this latter category is a case of undercutting, rather than a case of no intrinsic value for such truths, is the argument from the cognitive ideal, which cannot be satisfied without knowing all truths. So the proper conclusion to draw is that there are pointless truths, but their existence does not undermine the unrestricted value of truth, and hence that nothing about the value of truth undermines the idea that the knowledge and understanding possess their cognitive value in a fully unrestricted way, both in terms of space and time and in terms of modality. It is important to note that nothing about this account presupposes any particular answer to the hard questions about how the value vectors interact or under what conditions undercutting occurs. The defeat of the intrinsic value of truth might occur quite regularly and across a broad range of topics and issues, so that the crassest of restrictions on basic research is justified; or such defeat might be so rare that nearly every restriction on basic research is unwarranted. Nothing I have written implies anything one way or another on these questions. But since much of what I have written adopts a perspective for the sake of argument that takes a rather restrictive tone on this question, I would be remiss not to point out the dangers of such a perspective. Unreflective perspectives on this issue are typically crassly pragmatic, but even cursory reflection on the human condition reveals that first-glance perspectives on anything so complicated are suspect in the extreme. Furthermore, when we contrast this unreflective perspective with a more reflective contrast between the cultural experience of American consumer culture and what J.S. Mill would call higher quality pleasures, it is very difficult to come to any conclusion other than that our own culture is vastly mistaken about the conditions under which intellectual value is defeated by practical concerns of this

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sort (to say nothing of the horrendous distortion of what our practical concerns really are). Such issues are ones for another time and place, but since I have been willing to grant something like this perspective for the sake of argument above, it would be misleading here to close without distancing myself from such a perspective. One can adopt this perspective and still retain the intellectualist model. But the beautiful pictures of the good life contrast with this quotidian picture of the good life in the way that, say, Monet’s paintings contrast with velvet Elvises.

Midwest Studies in Philosophy, XXXII (2008)

Indeterminate Truth PATRICK GREENOUGH

1. PREAMBLE Can a truth-bearer be true but not determinately so?1 On the enduringly popular standard supervaluational conception of indeterminacy, under which the principle of bivalence is invalid, the answer is a straightforward No. On such a conception, truth just is determinate truth—truth in all admissible interpretations.2 For that reason, a more interesting question is: can a truth-bearer be true but not determinately so on a conception of indeterminacy under which both classical semantics and classical logic remain valid?3 Under such a conception, very roughly, a truthbearer is indeterminate in truth-value just in case it is either true or false but it is not determinate that this truth-bearer is true and not determinate that it is false. Within such a classical framework, the possibility of indeterminate truth has proved to be at best elusive, at worst incoherent. On this score, Crispin Wright alleges that it 1. Following Williamson (1996, 44), I take “definitely” and “determinately” to be interchangeable, though I will use the latter term throughout. 2. See van Fraassen (1966, 1968), Thomason (1970), Dummett (1975), Fine (1975), Keefe (2000). Given supervaluational semantics, a truth-bearer can be true on one but not all admissible interpretations (and so not determinately true). However, this does not entail that the truth-bearer is true simpliciter (but not determinately so). 3. Classical semantics is taken to include bivalence, “bi-exclusion” (the thesis that no truthbearer is both true and false), the appropriate disquotational schemas for truth and denotation, plus the claim that validity is necessary preservation of truth. Midwest Studies in Philosophy: Truth and its Deformities Volume XXXII Editor by Peter A. French and Howard K. Wettstein © 2008 Wiley Periodicals, Inc. ISBN: 978-1-405-19145-6

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does not seem intelligible that there should be any way for an utterance to be true save by being definitely true—at any rate, there is no species of indefinite truth (Wright 1995, 143; see also Dummett 1975; Wright 1987). And in a similar vein, Tim Williamson puts the challenge this way: Definite truth is supposed to be more than mere truth, and definite falsity more than mere falsity. But what more could it take for an utterance to be definitely true than just for it to be true? [ . . . ] Such questions are equally pressing with “false” in place of “true.” Again, “TW is thin” is no doubt definitely true if and only if TW is definitely thin, but what is the difference between being thin and being definitely thin? Is it like the difference between being thin and being very thin? Can “definitely” be explained in other terms, or are we supposed to grasp it as primitive? (Williamson 1994, 194–95; see also his 1995). Williamson suggests that the only way to make sense of the “determinately” operator is to treat it as equivalent to “knowably” (Williamson 1994, 195; 1995). Hence, to say that a truth-bearer is indeterminate in truth-value is just to say that it has an unknowable truth-value: indeterminate truth is just unknowable truth. The trouble with this suggestion is that any model of indeterminacy that validates classical logic and classical semantics must then represent indeterminacy to be an exclusively epistemic phenomenon. But even if we are happy to grant the validity of classical logic and classical semantics across the board, it is questionable to assume from the outset that all genuine forms of indeterminacy are epistemic. For example, certain sorts of quantum phenomena exhibit what is best seen as nonepistemic indeterminacy.4 Somewhat more controversially, the future may be objectively open whereby actuality is composed of a tree of branching histories such that future contingent sentences have indeterminate truth-values.5 Whether there are any further species of non-epistemic indeterminacy is a controversial matter (see below). However, it ought to be clear that it is far too hasty to assume that the validity of classical logic and classical semantics rules out the possibility of any non-epistemic species of indeterminacy.6 With these observations in hand, our question now becomes: can a truthbearer be true but not determinately so on a non-epistemic conception of indeterminacy under which both classical semantics and classical logic remain valid? In other words: is it intelligible to speak of non-epistemic indeterminate truth? 4. I take the two-slit experiment to be a paradigm case of quantum indeterminacy (see Maudlin 2005 for relevant discussion). 5. See McCall (1994), Belnap et al. (2001), MacFarlane (2003), and Greenough, “The Open Future” (unpublished ms.). 6. Williamson (1994, passim) also (implicitly) assumes that the validity of classical logic and classical semantics is a necessary condition for a conception of vagueness to be epistemicist. From a terminological point of view, this is unhelpful since there are extant hybrid conceptions of vagueness under which first-order vagueness is taken to be semantic and second-order vagueness is taken to be epistemic (see, e.g., Koons 1994; Heck 2003).

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(Hereafter, I will drop the qualification “non-epistemic.”) To vindicate the intelligibility of indeterminate truth, it is necessary to do at least two things. First, one must find some framework within which the notion can be coherently expressed and elucidated. Second, one must show how positing indeterminate truth can do substantial theoretical work—in particular, one must show that indeterminate truth can help us resolve, or at least illuminate, a range of puzzles concerning indeterminacy, such as the sorites paradox, the problem of the many, the open future, the liar paradox, and so on. The focus of this paper is mainly on the first of these tasks, though we shall encounter various applications as we proceed. The structure of the paper is as follows: in sections 2–4, I survey three extant ways of making sense of indeterminate truth and find each of them wanting.7 All the later sections of the paper are concerned with showing that the most promising way of making sense of indeterminate truth is via either a theory of truthmaker gaps or via a theory of truthmaking gaps. The first intimations of a truthmaker– truthmaking gap theory of indeterminacy are to be found in Quine (1981). In section 5, we see how Quine proposes to solve Unger’s problem of the many via positing the possibility of groundless truth. In section 6, I elaborate and extend the truthmaker gap model of indeterminacy first sketched by Sorensen (2001, chap. 11) and use it to give a reductive analysis of indeterminate truth. In section 7, I briefly assess what kind of formal framework can best express the possibility of truthmaker gaps. In section 8, I contrast what I dub “the ordinary conception of worldly indeterminacy” with Williamson’s conception of worldly indeterminacy. In section 9, I show how one can distinguish linguistic from worldly indeterminacy on a truthmaker gap conception. In section 10, I briefly sketch the relationship between truthmaker gaps and ignorance. In section 11, I assess whether a truthmaker gap conception of vagueness is really just a form of epistemicism. In section 12, I propose that truthmaker gaps can yield a plausible model of (semantic) presupposition failure. In section 13, in response to the worry that a truthmaker gap conception of indeterminacy is both parochial and controversial—since it commits us to an implausibly strong theory of truthmaking—I set forth a truthmaking gap conception of indeterminacy. In section 14, I answer the worry that groundless truths, of whatever species, are just unacceptably queer. A key part of this answer is that a truthmaker–truthmaking gap model of indeterminacy turns out to be considerably less queer than any model of indeterminacy which gives up on Tarski’s T-schema for truth (and cognate schemas). 2. CONCEPTUAL PRIMITIVISM CONCERNING “DETERMINATELY” Perhaps “determinately” is a conceptually primitive notion, one that cannot be analyzed in more fundamental terms. There are at least two forms such conceptual primitivism might take. On the first form, one grasps the meaning of “determi7. This survey is incomplete. In Åkerman and Greenough, “Vagueness and Non-Indexical Contextualism” (unpublished ms.), it is argued that one can also make sense of indeterminate truth given either MacFarlane–Richard style relativism concerning truth or given what MacFarlane calls “Nonindexical Contextualism” (see Richard 2004; MacFarlane 2005, 2008).

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nately” by repeated exposure to exemplars of truth-bearers which are determinately true/false and exemplars of truth-bearers which are not determinately true/ false (or by exposure to exemplars of determinate cases of F/not-F and exposure to cases which are neither determinately F nor determinately not-F). If bivalence is taken to be valid, then exposure to truth-bearers which are not determinately true/false provides one with a grasp of how a truth-bearer can be true/false but not determinately so. Call that the exemplar model.8 The second form of conceptual primitivism has been defended by Field (1994, 2001, 226–34) who alleges that the sentence functor “It is definitely/ determinately the case that” is a primitive functor “that we come to understand in the same way we come to understand such operators as negation and disjunction and universal quantification: by learning how to use it in accordance with certain rules” (2001, 227). In other words, Field proposes that we learn how to use “determinately” by coming to grasp the introduction and elimination rules for the operator. Call that inferential primitivism.9 With respect to exemplar primitivism, Williamson has argued that, in exhibiting exemplars of determinacy and indeterminacy, [n]othing has been said to rule out the possibility that “definitely” has acquired an epistemic sense, something like “knowably.” If further stipulations are made in an attempt to rule out that possibility, it is not obvious that “definitely” retains any coherent sense (Williamson 1994, 195).10 The point being made here is that we can all agree that indeterminacy either gives rise to or consists in a particular kind of ignorance. Given this, if I point to a future contingent sentence, for example, with the aim of communicating a non-epistemic understanding of “determinately,” and say “That sentence is neither determinately true nor determinately false” then my declaration is arguably true but, for all I have said, it could be true merely in virtue of the epistemic properties of the sentence. Moreover, it does not help to add “and what makes this sentence lack a determinate truth-value is that the future is objectively open,” for that is compatible with an epistemic reading of “determinately.” Williamson’s point carries over to inferential primitivism. For all that Field has said, the rules governing “It is determinately the case that” may, as it turns out, confer an epistemic reading onto this operator. In order to ensure that “It is determinately the case that” does not have the same meaning as an operator such as “It is knowable that” (or “It is known that”) then something must be added to the simple inferentialist model proposed by Field.11 But what could be added to 8. Parsons (2000, 109) also commits himself to primitivism concerning determinacy but from within a non-bivalent framework. See also Hyde (1994, 40). 9. The two sorts of conceptual primitivism are presumably not exclusive. 10. Williamson does not disagree with conceptual primitivism per se since he defends such primitivism for “knows” (Williamson 2000). 11. Indeed, the weak modal logic Field seems to have in mind for the determinacy operator (i.e., KTB) is also plausibly the same logic we need for knowledge. Field (2001, 233, final paragraph) is aware of this problem but offers no clue as to how his proposal could be better motivated.

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secure a non-epistemic reading short of offering a non-primitive analysis? Moreover, Field is far too hasty in assuming that an explicit analysis of determinacy is not in prospect—conceptual primitivism concerning determinacy is a counsel of despair. So how might we give such an analysis? 3. INCOHERENTISM AND INDETERMINATE TRUTH McGee and McLaughlin (1995, 208–19) propose to offer a reductive analysis of indeterminate truth by alleging that there are two distinct and competing notions of truth present in natural language: a disquotational notion of truth (truth simpliciter) and a correspondence notion of truth (determinate truth). The disquotational notion (for sentence truth) is given to us by all instances of the following version of Tarski’s T-schema for truth: If a sentence S expresses the proposition that p then S is true if and only if p.Very roughly, the correspondence notion, on the other hand, tells us that (1) the truth-conditions for S are established by the thoughts and practices of speakers of the language;and (2) S is true just in case the world determines that these conditions obtain. Furthermore, on the view in hand, these two notions of truth “come into conflict” when dealing with sentences which exhibit indeterminacy. That’s because the disquotational notion of truth entails that all sentences which say that something is the case have truth-values, while the correspondence notion of truth pushes us to say that some such sentences do not have truth-values. In other words, the rules governing the use of “is true” in natural language are incoherent: we are given conflicting instructions as to how to deploy the truth predicate.12 Hence, if we want to coherently characterize indeterminacy using the notion of “truth” then either the disquotational or the correspondence notion must be abandoned. As it turns out, McGee and McLaughlin (p. 217) propose that we abandon the correspondence notion in favor of the disquotational—at least when it comes to specifying the truth-conditions of sentences which admit of indeterminacy. On the face of it, McGee and McLaughlin’s proposal meets the Wright– Williamson challenge: it is intelligible to speak of indeterminate truth since a sentence can be true in the disquotational sense, but not in the correspondence sense; that is, a sentence can be true but not determinately so. The trouble with this proposal is that a sentence can only be true but not determinately so within a language which is governed by incoherent rules for the use of the truth predicate. But then we have hardly found a coherent way of expressing the possibility of indeterminate truth. A far more plausible view is that there is but one notion of truth, but different ways in which a sentence can be true. In other words, determinate truth is not a different species of truth, but rather a different mode of truth: being determinately true is a way of being true.13 I suspect that the real reason why Field (in his 2001 book at least) is driven to conceptual primitivism for determinacy is his commitment to deflationism concerning truth for he seems to think that a substantial analysis of the notion of determinate truth is bound to draw on inflationary resources. In Field (2003), he is more sanguine about the prospects for analyzing “determinately,” but this is because Field now gives up on classical logic. 12. Cf. Tarski (1944). 13. Cf. Necessary truth as a mode of being true.

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Slater (1989) offers a conception of vagueness under which there is a non-epistemic distinction between indeterminate truth and determinate truth and moreover he also speaks of determinate truth as a mode of being true. Indeed, Slater anticipates the non-standard bivalent form of supervaluation given in McGee and McLaughlin (1995), whereby determinate truth is truth in all admissible interpretations but truth is not determinate truth. With respect to indeterminate truth, Slater says: what must be expressly allowed for is a situation where a “truth value” is not given. [ . . . ] That does not mean we cannot say the proposition is true or false, for we can always make a decision whether someone is, say, bald or not, in any borderline cases—one just decrees or legislates to that effect. [ . . . ] But introducing this way of settling whether a proposition is true means we have a new decision to cater for [ . . . ] namely the distinction between central and borderline cases in the application of a concept. This is not now a distinction between cases where “he is bald” has and hasn’t a value but a distinction between the different backings there may be for any truth claim in the two cases. In central cases, the criteria for baldness are appealed to and settle the matter; but in borderline cases the criteria for baldness do not settle the matter, and any judgment is conceived as a matter of choice (1989, 241–42). So, a sentence “John is bald” can be true but not determinately so in cases where the criteria for the application of “bald,” together with the facts about the number and distribution of hairs on John’s head, do not settle whether the sentence is true, but nonetheless the truth-bearer can be true in virtue of the fact that someone chooses to evaluate the sentence as true. In many respects, this proposal can be read as a precursor of the kind of response-dependent models of vagueness given by Raffman (1994) and Shapiro (2003, 2006) whereby in the borderline area vague sentences are true in virtue of being judged to be true by competent speakers (under normal conditions of judgment). The worry with any such proposal concerns the truth-values of meaningful but vague sentences which have not, and indeed could not, be (competently) judged to be true, because their meaning is far too complex to be contemplated by any speaker of English. It looks like Slater (and Shapiro and Raffman) must take these sentences to lack truth-values despite the fact that these sentences succeed in expressing a proposition. But then classical semantics is no longer valid for all meaningful sentences in the language. Upshot: Slater’s theory of vagueness is not an answer to our question since we wanted to know how indeterminate truth is possible within a (coherent) classical framework. 5. QUINE, INDETERMINATE TRUTH, AND THE PROBLEM OF THE MANY A more promising way to make sense of indeterminate truth is to posit that a truth-bearer can possess a truth-value groundlessly. Roughly, truth-bearers which

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are indeterminate in truth-value are such that they are either true (simpliciter) or false (simpliciter); it’s just that nothing (in either the world or in thought or in language) grounds the truth-value that they have. The first intimations of such a view (in the modern indeterminacy debate at least) appear in a rather overlooked paper by Quine (1981). In this paper, Quine proposes that Unger’s problem of the many (but not all cases of vagueness itself) effectively requires us to recognize the possibility of groundless truth.14 Take the case of the table before me. Common sense tells us that there is one and only one table present. Nonetheless, the surface of the table is indeterminately demarcated such that it is unclear, and indeed indeterminate, whether or not a particular molecule belongs to the table. However, it now seems we have many different sets of molecules, M1, M2, M3, . . . which are all equally good candidates to compose the table. But if that is so then what grounds the fact that a particular set of molecules, say M2, composes the table rather than any of the others. Indeed, symmetry considerations dictate that if one of the sets of molecules counts as being a table then they all do. Upshot: if one of the sets of molecules composes a table then we have many tables rather than one or if we don’t have many tables present then we don’t have any tables present. Either way, our common-sense intuition must be given up. Quine’s response is as follows: Where to draw the line between heaps and non-heaps [ . . . ] or between the bald and the thatched, is not determined by the distribution of microphysical states, known or unknown; it remains an open option [ . . . ] On this score the demarcation of the table surface is on a par with the cases of heaps and baldness. But it differs in those cases in not lending itself to any stipulation, however arbitrary, that we can formulate; so it can scarcely be called conventional. It is neither a matter of convention nor a matter of inscrutable but objective fact. Yet we are committed nevertheless, to treating the table as one and not another of this multitude of imperceptibly divergent physical objects. Such is bivalence [ . . . ] What we now observe is that bivalence requires us [ . . . ] to view each general term, e.g. “table,” as true or false of objects even in the absence of what we in our bivalent way are prepared to recognise as objective fact. (p. 94) What this passage intimates is that out of the multitude of overlapping (or nested) table-candidates M1, M2, M3 . . . , there is indeed but one table. Moreover, that the table-candidate M2, say, rather than the table-candidate M1 or M3 . . . , composes the table is something that is not determined by what facts obtain. That is, there is no linguistic fact (such as a linguistic convention) nor any nonlinguistic fact, which determines that M2, rather than M1 or M3 . . . composes a table. So, the sentence “The table is composed of M2” is a groundless truth, a truth which is not grounded in the facts. One obvious advantage of such a response is that it preserves not only 14. See Unger (1980). Quine seems to have been the first to respond to the problem.

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classical logic and classical semantics but common sense. One disadvantage is that it involves denying the following schema: (FACT) If S expresses the proposition that p then if S is true then it is a fact that p. Whether it is at all plausible to deny FACT (and cognate schemas) is an issue to be addressed in the penultimate section. 6. TRUTHMAKER GAPS AND INDETERMINATE TRUTH Sorensen (2001, 2005a, 2005b), independently of Quine, has outlined a very similar model of groundlessness but instead of talking about an absence of fact, Sorensen speaks of a truthmaker gap.15 In effect, Sorensen embeds his theory of indeterminacy within the framework of truthmaker theory. In this section, I elaborate and extend Sorensen’s model and use it to make sense of indeterminate truth. Consider then the following generic truthmaker principle: (TM) If a truth-bearer is true then something makes that truth-bearer true.16 A strong truthmaker theory enjoins Truthmaker Maximalism—the thesis that the schema TM ranges over all truth-bearers. Thus, logical truths, mathematical truths, modal truths, general truths, and negative truths, are all made true by something in the world. Given Truthmaker Maximalism, TM is interderivable, given certain background assumptions, with the following generic falsemaker principle: (FM) If a truth-bearer is false then something makes that truth-bearer false. What about the nature of the truthmaking relation expressed in TM/FM? Do truthmakers necessitate, in some sense, that a truth-bearer is true? That is, is Truthmaker Necessitarianism called for? A common view is that if a truth-bearer is made true by a truthmaker T then the existence of T entails that this truth-bearer is true.17 For the purposes of floating a truthmaker gap theory of indeterminacy, we can remain neutral on this issue—a theory of truthmaker gaps should be 15. Throughout by “truthmaker gap theory of indeterminacy” I mean a bivalent truthmaker gap theory (as opposed to a non-bivalent theory which recognizes truthmaker gaps). 16. A closely related principle is: if a truth-bearer is true then there is something in virtue of which it is true. See Rodriguez-Pereyra (2005, 18) who takes the relation “in virtue of” to be primitive. 17. Armstrong accepts that truthmakers necessitate the truth of a truth-bearer. This follows from his view that the truth-making relation is an internal one in the sense that if the relata of the relation exist then the relation necessarily holds of the relata (see Armstrong 2004, 9, 50–51). Armstrong (2004, 10–12) also alleges that the notion of entailment must be suitably non-classical if we are to avoid the problem whereby every truthmaker is a truthmaker for not only every necessary truth but every truth whatsoever. For relevant discussion of this issue, see Restall (1996), Read (2000), Rodriguez-Pereyra (2006).

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compatible with either view.18 With respect to the primary truthmakers, are they facts, states of affairs, events, tropes, bundles of properties, or some other kind of truthmaker? Again, we can remain largely neutral as to the nature of the basic truthmakers. Indeed, it is a key virtue of the truthmaker gap theory of indeterminacy developed here that it is compatible with a wide range of candidate truthmakers and ontological theories. We do, however, need to demand that the primary truthmakers are sufficiently fine-grained.A coarse-grained conception of the truthmakers, whereby, for example, the truthmakers are simply taken to be truth-values will not do for otherwise a theory of truthmaker gaps collapses into a theory of truth-value gaps.19 What of the primary truth-bearers? Standard theories of truthmaking typically take the primary truth-bearers to be propositions. In order to give a complete theory of indeterminacy, one which accommodates the possibility of both linguistic and worldly indeterminacy, let the primary truth-bearers be sentences (relativized to contexts), that is sentence-context pairs (hereafter, just “sentences”). TM and FM should be rewritten as: (TM1) If S expresses 〈p〉 then if S is true then something makes 〈p〉 true. (FM1) If S expresses 〈p〉 then if S is false then something makes 〈p〉 false. Here, “S” is a quotation name for a declarative sentence relativized to a context, and “〈p〉” abbreviates “the proposition that p.” So, while sentences are the primary truth-bearers, the truthmaking relation itself holds between the primary truthmakers and propositions. A final feature of this strong truthmaker theory is that the following converse conditionals are valid: (TM2) If S expresses 〈p〉 then if something makes 〈p〉 true then S is true. (FM2) If S expresses 〈p〉 then if something makes 〈p〉 false then S is false.20 Given the strong truthmaker theory just sketched, we are in a position to analyze a notion of determinacy, call this determinacy1, as follows: (D1) If S expresses 〈p〉 then S is determinately1 true if and only if something makes 〈p〉 true. (D2) If S expresses 〈p〉 then S is determinately1 false if and only if something makes 〈p〉 false. 18. See Parsons (1999) for some relevant discussion. 19. Cf. the two notions of fact set forth in Fine (1982).There are good heuristic reasons to take facts to be the primary truthmakers because we want a theory of indeterminacy to make sense of the everyday locution “there is no fact of the matter” (see section 8). The notion of fact defended by Armstrong (1997, 113–18; 2004, 48–49) is suitably fine-grained. 20. Cf. the cognate principles given in Restall (1996, 333), Read (2000, 68).

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Given D1/D2, we can now make proper room for a cognate notion of indeterminacy—indeterminacy1. (Occasionally, I shall omit the subscript when speaking of indeterminacy/determinacy in some undifferentiated sense or where the context makes clear what species of indeterminacy/determinacy is in play.) To say that a sentence S is true/false but not determinately1 so is just to say that this sentence is true/false but lacks a truthmaker/falsemaker. In other words, there are indeterminate1 truths/falsities just in case TM1/FM1 failed to be valid. Thus the following principles are central to a truthmaker gap theory of indeterminacy: (I1) If S expresses 〈p〉 then S is true but not determinately1 so if and only if S is true but there is nothing which makes 〈p〉 true. (I2) If S expresses 〈p〉 then S is false but not determinately1 so if and only if S is false but there is nothing which makes 〈p〉 false. Here the rough idea is that some sentences of the language are meaningful (in that they succeed in expressing propositions and so succeed in being bivalent) and yet the world is somehow factually defective. If the primary truthmakers are facts— then this means that there is no fact of the matter. Hence, there is a failure of correspondence between sentences and the world: when there is a truthmaker gap then there is nothing on the right-hand-side of the correspondence relation. But rather than think this gives rise to a truth-value gap, we should simply see this as a truthmaker gap for a bivalent truth-bearer. As we proceed, I shall try to flesh out just what this involves. First, we need to know just what formal framework is required to model truthmaker gaps. 7. THE LOGIC OF DETERMINACY Suppose that all logical truths have truthmakers.21 So, for example, the law of excluded middle has a truthmaker. Thus, to borrow the example from above, the following instance of the law of excluded middle has a truthmaker: either the table is composed of the set of molecules M2 or the table is not composed of the set of molecules M2. However, both disjuncts have indeterminate1 truth-values (despite being bivalent). Given principle I1/I2, both disjuncts are neither made true by something nor made false by something. Thus, we have a disjunction which is made true despite the fact that neither disjunct is made true. In other words, the predicate “is made true by something,” and the sentence functor “Something makes it true that,” are not truth-functional. Nonetheless, “Something makes it true that” is factive. Moreover, this functor also seems to be closed across entailments which are themselves made true. Finally, being neither made true nor made false is formally 21. Indeed, we can allow that Truthmaker Maximalism is valid when TM1 is restricted to those truths which do not admit of indeterminacy1. For the purposes of this paper, I remain neutral on whether Truthmaker Maximalism is valid in this way. In Greenough “The Open Future” (unpublished ms.), I employ a supervaluational semantics (for determinate truth, where truth is not determinate truth) under which all logical truths are determinately true and so have truthmakers.

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analogous to the property of contingency—being neither necessarily true nor necessarily false. Given these observations, the resultant logic for a truthmaker gap model of indeterminacy1 ought to be a normal modal logic, whereby the main modal operator is “It is determinately1 true that” (“Something makes it true that”), and where classical logic remains valid. If higher-order indeterminacy1 is not possible, then the logic of determinacy1 should be KT4 or KT5. If higher-order indeterminacy1 is possible then the logic should be KT or KTB. Perhaps vagueness calls for the possibility of higher-order indeterminacy1.22 Plausibly, future contingents have indeterminate1 truth-values; however, there does not seem to be any higher-order indeterminacy1 attaching to future contingents and so KT4 or KT5 is called for. In part at least, the Wright–Williamson challenge has been met: it is possible to give a reductive analysis of the distinction between determinate and indeterminate truth, and moreover, we can formally express these notions in a very familiar logical framework. However, in order to get a better grip on the type of indeterminacy under consideration, we also need to know what it is for reality to be indeterminate and what it is for indeterminacy to be “worldly” rather than linguistic. 8. WORLDLY INDETERMINACY: WILLIAMSON’S CONCEPTION AND THE ORDINARY CONCEPTION What is it for reality to be indeterminate? With respect to vagueness in the world, Williamson (2005, 701) says that reality is vague just in case there is “some state of affairs that neither definitely obtains nor definitely fails to obtain.”23 Extending this to indeterminacy in general, we thus have: there is indeterminacy in reality just in case there is some state of affairs that neither determinately obtains nor determinately fails to obtain.24 In more generic truthmaker terms, there is indeterminacy in reality just in case there is some truthmaker T such that T neither determinately obtains nor determinately fails to obtain. Call this conception, “Williamson’s conception of worldly indeterminacy.” On a truthmaker gap conception of indeterminacy,Williamson’s conception is simply incoherent as an account of (first-order) indeterminacy since states of affairs either obtain simpliciter or do not obtain simpliciter—there is no such thing as an indeterminately obtaining state of affairs (at least if we are solely concerned with first-order indeterminacy). Moreover, Williamson’s account fails to capture the ordinary thought that there is indeterminacy in reality (with respect to the state of 22. See Williamson (1999) for much of the formal details. 23. With respect to states of affairs, he says: “For any object o and property P, there is a state of affairs that o has P. For any objects o1 and o2 and any binary relation R, there is a state of affairs that o1 has R to o2; it obtains if and only if o1 has R to o2.” Williamson is also assuming that there is a coherent non-epistemic notion of “definitely” for the purposes of uncovering the commitments of non-epistemic theories of vagueness with respect to metaphysical vagueness. He doesn’t really believe that there is such a notion. However, as is argued in section 1, even Williamson must recognize certain kinds of non-epistemic indeterminacy and so there must be such a notion to be elucidated. 24. Parsons (2000, 13) advocates a similar view.

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affairs that p) just in case there is no fact of the matter as to whether p. If states of affairs are taken to be the primary truthmakers, what may be termed “the ordinary conception of worldly indeterminacy” then runs as follows: reality is indeterminate just in case there is some state of affairs such that it and its complementary state of affairs both fail to obtain (in the monadic case, the complement of the state of affairs that o has the property P is the state of affairs that o lacks the property P). As it is stated, the ordinary conception is silent as to whether bivalence is valid.25 The problem with the ordinary conception is that it looks like all indeterminacy in truth-value turns out to be worldly indeterminacy. This worry applies to both a truth-value gap version of the ordinary conception and a bivalent version of the ordinary conception. To simplify, I will focus on the bivalent case. 9. MINIMAL VERSUS ROBUST FORMS OF WORLDLY AND LINGUISTIC INDETERMINACY Say that reality is indeterminate1 with respect to the state of affairs that p just in case the state of affairs that p, and the complementary state of affairs that not-p, both fail to obtain. Suppose the sentence S expresses 〈p〉. From I1/I2 we can infer: if the sentence S is true/false but not determinately1 so then S is true/false but there is nothing which makes 〈p〉 true/false. Plausibly, there is nothing which makes 〈p〉 true/false if and only if the state of affairs that p, and the complementary state of affairs that not-p, both fail to obtain. We can then derive: if S is true/false but not determinately1 so then the state of affairs that p, and the complementary state of affairs that not-p, both fail to obtain. And so, given that S expresses 〈p〉, if S is true/false but not determinately1 so then reality is indeterminate1 in respect of the state of affairs that p. But now any indeterminacy1 in truth-value exhibited by a sentence entails indeterminacy1 in reality. This certainly doesn’t seem right for all possible applications of a truthmaker gap conception of indeterminacy1. Consider the case of incomplete stipulations: let a sufficient condition for x to be a dommal be that x is a dog; let a necessary condition for x to be a dommal be that x is a mammal.This stipulation is incomplete for we have no clear answer to the question: is a cat a dommal?26 Sorensen (2001, chap. 11) has proposed that the sentence “All cats are dommals” is either true or false but there is nothing which makes it true and nothing which makes it false. If that is so, the indeterminacy exhibited by this sentence seems clearly to be linguistic indeterminacy1 which arises from features of language and not from any facts concerning the nonlinguistic portion of reality. To resolve this worry, we need to allow that the indeterminacy1 of truth-value exhibited by some sentence S (which expresses 〈p〉) has two potential sources: either this indeterminacy1 issues from there being no fact of the matter as to whether p (in 25. The ordinary conception is a gappy version of worldly indeterminacy. A glutty version runs: reality is indeterminate just in case there is some state of affairs such that it and its complementary state of affairs both obtain. A unified theory, which recognizes the possibility of both gaps and gluts in the world, runs: reality is indeterminate just in case there is some state of affairs such that it and its complementary state of affairs either both obtain or both fail to obtain. 26. The example is due to Williamson (1990, 107).

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which case it is worldly indeterminacy1), or this indeterminacy1 issues from there being no fact of the matter as to whether S expresses 〈p〉 (in which case it is linguistic indeterminacy1). In other words, we need to recognize that such claims as “S expresses 〈p〉” can themselves have groundless truth-values. The trouble is, the presentation so far has not allowed for this.To illustrate: suppose there is a fact of the matter as to whether p.That is, either the state of affairs that p obtains or the state of affairs that not-p obtains. That is, something makes 〈p〉 true/false. Thus, reality is determinate1 (in respect of the state of affairs that p). Suppose also that a sentence S, which expresses 〈p〉, has a groundless truth-value in virtue of the fact that it is indeterminate1 whether S expresses 〈p〉 (and so it is not determinate1 that S expresses 〈p〉). Suppose further that S is true. Recall that D1 tells us that: if S expresses 〈p〉 then S is determinately1 true if and only if something makes 〈p〉 true. Given what has been said, the right-hand side of the biconditional in the consequent of D1 is true, while the left-hand side of the biconditional is false. It follows that S does not expresses 〈p〉. But that contradicts our supposition that S does express 〈p〉. This reveals that the notion of indeterminacy1 analyzed in D1/D2, and I1/I2 is really just worldly indeterminacy—hence no surprise that all indeterminacy1 in sentential truth-value entails worldly indeterminacy. This notion of indeterminacy1 is primary in the explanatory order because facts about language (e.g., about what proposition is expressed by a particular sentence) are themselves, of course, just part of the world. What we need, then, is a notion of generic determinacy/ indeterminacy of truth-value, which attaches only to linguistic items. Call this determinacyG /indeterminacyG. First, we can adjust D1 and D2 as follows: (D1)G If it is determinate1 that S expresses 〈p〉 then S is determinatelyG true if and only if something makes 〈p〉 true. (D2)G If it is determinate1 that S expresses 〈p〉 then S is determinatelyG false if and only if something makes 〈p〉 false. So, when S expresses 〈p〉, and S is indeterminateG in truth-value, but something makes 〈p〉 true or something makes 〈p〉 false, then it is not determinate1 that S expresses 〈p〉. In such a case, S exhibits linguistic indeterminacy. Call that indeterminacyL. Equally, suppose S has an indeterminateG truth-value but that it is determinate1 that S expresses 〈p〉, then S exhibits worldly indeterminacy. Call that indeterminacyW. More generally, we have: (IW) A sentence S (which expresses 〈p〉) exhibits indeterminacyW if and only if S is bivalent but there is nothing which makes 〈p〉 true/false (that is, if and only if S is bivalent but it is indeterminate1 whether 〈p〉 is true/false). (IL) A sentence S (which expresses 〈p〉) exhibits indeterminacyL if and only if S is bivalent but there is nothing which makes 〈S expresses 〈p〉〉 true/false (that is, if and only if S is bivalent but it is indeterminate1 whether S expresses 〈p〉). (IG) A sentence S (which expresses 〈p〉) exhibits indeterminacyG if and only if it exhibits either indeterminacyW or indeterminacyL or both.

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Take the case of incomplete stipulations. Suppose I introduce the term “bigster” via the following (incomplete) definition: for all natural numbers n, if n ⱖ 64 then n is a bigster and if n ⱕ 62 then n is not a bigster. Thus, “bigster” is undefined for 63. Suppose the sentence “63 is a bigster” expresses 〈63 ⱖ 64〉. Then this sentence is false. However, it is fully determinate1 whether or not 63 ⱖ 64 since there is something which makes 〈63 ⱖ 64〉 false. (Truthmaker Maximalism is in play here with respect to those truths which do not admit of indeterminacy.) Suppose the sentence expresses 〈63ⱖ63〉. Then this sentence is true. However, it is fully determinate1 whether or not 〈63ⱖ63〉 since there is something which makes 〈63ⱖ63〉 true. Either way, given IW, the sentence does not exhibit indeterminacyW. Given that “63 is a bigster” is nonetheless indeterminate in truth-value then, given IG, it exhibits indeterminacyL. This is just as we should expect. Note that if one thinks that the only type of proposition that gets expressed by the sentence “63 is a bigster” is just the disquoted proposition 〈63 is a bigster〉 then the analysis yields the wrong results. In particular, we will have the result that there is nothing which makes 〈63 is a bigster〉 true/false and so, via IW, “63 is a bigster” will exhibit indeterminacyW. Moreover, since it is presumably determinate1 that “63 is a bigster” expresses 〈63 is a bigster〉 then, via IL,“63 is a bigster” does not exhibit indeterminacyL. Does this suggest that in applying the analysis across all cases one must never invoke the disquoted proposition on the right-hand side of the expressing relation? Take the problem of future contingents. Take the sentence “There will be a sea-battle at 12 pm on 31st March 2008.” Suppose there are just two future histories h1 and h2 such that it is open which of these histories will come to obtain at the moment of utterance of the sentence. Thus the sentence exhibits indeterminacyG. Suppose that the proposition expressed by this sentence is 〈A sea-battle takes place at 12 pm on 31st March 2008 on h1〉. Given the two-branch tree structure of actuality, it is determinate1 whether a sea-battle takes place on 12 pm on 31st March 2008 on h1. (That’s because what happens on a future branch is fully determinate since branches are just linear pathways through the tree.) It follows, given IL, that the sentence “There will be a sea-battle at 12 pm on 31st March 2008” does not exhibit indeterminacyW. Indeed, since the sentence exhibits indeterminacyG, then, via IG, it exhibits indeterminacyL. But this gets things the wrong way round. Yet to get things the right way round we have to say that the proposition expressed by our sentence is the disquoted proposition 〈A sea-battle takes place at 12 pm on 31st March 2008〉. At the time of utterance there is nothing which makes this proposition true/false and so, given IW, the (bivalent) sentence exhibits indeterminacyW. Moreover, if it does indeed express the disquoted proposition then is it determinate that it does so. Hence, given IL, the sentence does not exhibit indeterminacyL. So, using the disquoted proposition gets matters the right way round in the case of future contingents but the wrong way round in the case of incomplete stipulations. Does this show that the analysis is ad hoc? No. What this shows is that we can and should use intuitions as to what are clear cases of linguistic indeterminacy and what are clear cases of worldly indeterminacy to guide us as to the kind of proposition that may be expressed by some class of sentences. In the case of incomplete stipulations, we have clear intuitions that this is a case of linguistic

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indeterminacy, and so the proposition expressed cannot be a disquoted proposition. In the case of future contingents, we have clear intuitions that this is a case of worldly indeterminacy, and so the proposition expressed needs to be the disquoted proposition.27 Moreover, there are no independent reasons to doubt that the sentence “the table contains molecule m1 as part” and the sentence “63 is a bigster” express propositions of the same general type. In the absence of such independent reasons, then we have grounds to say that if the former sentence is indeterminateG then it exhibits just the same kind of indeterminacy, namely indeterminacyL, as is exhibited by the latter sentence.28 That will be an unwelcome result for some. However, the burden of proof is then on those who deny that such sentences as “the table contains m1 as part” exhibit robust linguistic indeterminacy (namely, the kind of indeterminacy whose source is in language and not the nonlinguistic part of the world) to offer an alternative framework within which to express the distinction in hand. Moreover, they must do so without appealing to an unanalyzed notion of “determinately.” How then do truthmaker gaps impact upon knowledge? 10. TRUTHMAKER GAPS AND KNOWLEDGE Suppose we allow that some meaningful sentences express propositions that are neither true nor false. If the truth-value of a sentence, which expresses 〈p〉, is knowable then either 〈p〉 is true or 〈p〉 is false. So, if 〈p〉 is neither true nor false then the truth-value of S is unknowable (given that S expresses 〈p〉). That’s hardly surprising—where there is no truth-value, there can be no knowledge of truthvalue. Likewise, where there is no fact of the matter, there can be no knowledge. On a truthmaker gap conception, the following principle is valid: (K) If S expresses 〈p〉, then if it is metaphysically possible to know whether or not S is true then either something exists which makes 〈p〉 true or something exists which makes 〈p〉 false. From K, plus TM2, it follows that: if S expresses 〈p〉, then if it is known that S is true/false then something makes the proposition that p true/false.29 27. In this latter case, we have independent grounds not to build an argument place for a history into the structure of the proposition expressed since histories are world-like and we don’t build in an argument place for a world (if we did all propositions would be necessarily true). 28. An alternative suggestion to the strategy in hand is to allow that the proposition stated by disquoting “63 is a bigster” is indeterminate in the sense that, whichever proposition this sentence expresses that can be stated that way, it is indeterminate that the sentence expresses that very proposition. So, it is not determinate that “63 is a bigster” expresses that 63 is a bigster. What is determinate is that, whichever proposition “63 is a bigster” expresses, that proposition can be stated by means of disquoting “63 is a bigster”—however, this does not entail that it is determinate that “63 is a bigster” expresses that proposition. (Thanks to Sven Rosenkranz here.) 29. Sorensen (2001, chap.11) holds that truths without truthmakers are “epistemic islands.” By this he means there is no epistemic route (“no trail of truthmakers”) via which we can come to know that they are true. Hence K.

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There are three points of note. First, given principle K, God cannot know all truths, just those truths which it is metaphysically possible to know—hence God is not omniscient in the standard sense. For example, if we accept the Quinean solution to the problem of the many, God cannot know the truth-value of the sentence “The table is composed of the set of molecules M2.” Equally, if we accept Sorensen’s account of incomplete stipulations, then God cannot know the truthvalue of “All cats are dommals.” If future contingents have indeterminate1 truthvalues then God cannot know whether or not a future contingent is true (though he can know whether or not a future contingent is determinately true since determinate truth is just truth in all future histories).30 Second, it is common to think that, in some sense, the truths of logic and mathematics are brutely true. Does this mean that such truths lack truthmakers in just the same way in which I am assuming that indeterminate truths lack truthmakers? No. Given principle K, all the truths of logic and mathematics would then be unknowable. Hence, if such truths are “brutal,” their brutality is of a different order from that posited by a truthmaker gap theory of indeterminacy. Perhaps such truths have primitive truthmakers as follows: “If p & q then p” is true in virtue of the fact that: if p & q then p (or true in virtue of the fact that “If p & q then p” is true). However, indeterminate truths are not even true in virtue of such primitive facts—they lack any kind of truthmaker, primitive or otherwise. Third, what has just been said reveals important limits to the scope of a truthmaker gap theory of indeterminacy. For example, it looks like such a theory cannot resolve the indeterminacy exhibited in the Kripke–Wittgenstein rulefollowing paradox.31 One possible response to the rule-following problem is to hold that the semantic truth “ ‘+’ means addition and not quaddition” is a brute truth, a truth whose truth-value does not supervene upon the whole pattern of usage of “+.” But if this just means that this semantic truth is a truth without a truthmaker then, given K, skepticism about meaning is still with us. So, either K must go (and a truthmaker gap solution to the problem is in prospect), or such brutality is compatible with there being a brute truthmaker for the semantic truth in question (perhaps this truth simply supervenes upon the fact that “+” means addition and not quaddition or simply supervenes upon itself). But K seems prima facie plausible and so a truthmaker gap model of indeterminacy cannot resolve the Kripke– Wittgenstein rule-following paradox.32

30. Wright (2001, 2003) has argued that, in the case of vagueness at least, the status of being borderline does not rule out the possibility of knowledge. For a criticism of this element of his view, see Greenough (2008). 31. See Kripke (1982). 32. Similar remarks apply to Quine’s problem of the indeterminacy of translation (since Quine seems to be right to take his problem to be a special case of the rule-following problem). As it turns out, there may be some scope to deny K in certain cases of indeterminacy, though this is not an issue I can pursue here.

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11. EPISTEMICISM, THIRD POSSIBILITY VIEWS, AND INDETERMINATE TRUTH Sorensen (2001) alleges that the truthmaker gap theory of vagueness he puts forward is a form of epistemicism since on this theory vague terms draw sharp but unknowable boundaries across their associated dimension of comparison. Despite the fact that Sorensen coined the term “epistemicism,” his theory is not a form of epistemicism at all. Whether or not a theory of vagueness or indeterminacy counts as an epistemic theory is something which depends on the source of the indeterminacy. All theorists can agree that vagueness gives rise to ignorance; what they disagree about is the source of this ignorance. As mentioned in section 1, the validity of classical logic and classical semantics (and so the resultant commitment to sharp boundaries for vague terms) is not sufficient for a theory of vagueness/ indeterminacy to count as epistemic. A theory of vagueness is epistemic if the ignorance exhibited by the relevant truth-bearers is due entirely to our limited powers of discrimination and/or our fallibility as knowers. If some special semantic or metaphysical feature of vague sentences is posited in order to (help) explain the ignorance which is symptomatic of the presence of vagueness then the theory is not an epistemic theory.33 With respect to Sorensen’s truthmaker gap conception, the boundary drawn by a vague predicate is a groundless boundary—there is no fact in either language or the nonlinguistic portion of reality which determines that it falls in one place rather than another. But this feature of vague predicates, together with principle K, explains why such a boundary is unknowable. Hence, Sorensen’s theory is not a form of epistemicism despite the fact that vague terms draw sharp and unknowable boundaries. Wright (1995, 2001, 2003) has complained that most extant non-epistemic theories of vagueness are entirely misguided because they assume that being indeterminate in truth-value is a status incompatible with the poles of truth and falsity. Such “third possibility” views (such as a standard three-valued model of indeterminacy or a standard supervaluational model) are misconceived according to Wright since being borderline is a status such that matters have been left open, a status compatible with the poles of truth and falsity.34 It ought to be clear that a truthmaker gap theory of indeterminacy is not a third possibility view as Wright conceives of such views. However, a truthmaker gap conception is a third possibility view in the sense that indeterminacy is a third status incompatible with the poles of there being a truthmaker for p and there being a falsemaker for p. That much follows from a commitment to the ordinary conception of worldly indeterminacy.35 Arguably, however, all that is required for genuine openness is that being 33. On this score, it is notable that Williamson’s own form of epistemicism is an impure form of epistemicism since Williamson posits a special semantic feature of vague predicates (in addition to our limited powers of discrimination) in order to account for our ignorance in borderline cases, namely that vague predicates have sharp but unstable boundaries (see Williamson 1994, 230–37). 34. It’s hard to square this claim with Wright’s other claim, quoted in section 1, that there is no species of indeterminate truth. I put this matter aside. 35. On this score, a bivalent version of the conception of worldly indeterminacy offered by Williamson is not a third possibility view in either sense.

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indeterminate is compatible with the poles of truth and falsity and so this particular feature of the view is not problematic. 12. SEMANTIC PRESUPPOSITION FAILURE AND INDETERMINATE TRUTH In addition to incomplete stipulations and vagueness, Sorensen (2001) applies a truthmaker gap model of indeterminacy to the case of the truth-teller paradox (and certain—allegedly—kindred paradoxes). I do not propose to assess the merits of these various applications in this paper.36 Various other applications suggest themselves. Here I consider just one: (semantic) presupposition failure.37 On the standard semantic account of presupposition, for all sentences S and R, which say that something is the case, S (semantically) presupposes R just in case, necessarily, if S is true/false then R is true. So, if the presupposition R is false then S is neither true nor false (despite still expressing a proposition).38 While the semantic account is certainly problematic in that it cannot account for all the data, one of its biggest drawbacks is that classical semantics and classical logic are invalidated.39 Can we do better? If S does lack a truth-value, then via TM2/FM2, the proposition expressed by S lacks a truthmaker and a falsemaker. In other words, on the standard truth-value gap account, S is “factually defective” if R is false. (Here the standard account entails the ordinary conception of worldly indeterminacy.) But a truthmaker gap conception of indeterminacy allows us to respect the intuition that S is factually defective, if R is false, without giving up on bivalence. A proto truthmaker gap account (which is as yet neutral as to whether classical semantics is valid) runs as follows: for all sentences S and R, which say that something is the case, S (semantically) presupposes R just in case, necessarily, if there is something which makes the proposition expressed by S true/false then R is true. This proto truthmaker gap theory of semantic presupposition is equivalent to the truth-value gap theory given the validity of TM1/FM1 and TM2/FM2. If TM1/FM1 is given up because of the observation that sentences with false presuppositions are factually defective but nonetheless bivalent, then the proto theory becomes a proper (classical) truthmaker gap theory of semantic presupposition. And so we have: for all sentences S and R, which say that something is the case, if S (semantically) presupposes R and R is false then S remains bivalent but there is nothing which makes the proposition expressed by S true/false. As we shall see in the penultimate section, positing truth-value gaps is more queer than positing truthmaker gaps. For that reason, if one is tempted to think that a semantic account of presupposition still has legs 36. See Greenough (forthcoming), for reasons to think that truthmaker gaps/truthmaking gaps cannot illuminate the nature of the truth-teller (and the nature of the so-called “no-no paradox”). 37. See Greenough, “The Open Future” (unpublished ms.) for an application of truthmaker (and truthmaking) gaps to the case of future contingents. 38. See Strawson (1952, 175ff), van Fraassen (1966, 1968). 39. See Karttunen (1973), Schwarz (1977) on the so-called “projection problem” for compound sentences.

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(in the face of various competing pragmatic accounts) then one should plump for the (bivalent) truthmaker gap version. 13. TRUTHMAKING GAPS AND INDETERMINATE TRUTH A truthmaker gap conception of indeterminacy may be felt to be both controversial and parochial owing to the fact that Truthmaker Maximalism is nonetheless taken to hold for all truths which do not admit of indeterminacy. In this section, we will gradually retreat from Truthmaker Maximalism in order to find a theory of indeterminacy which is compatible with certain (allegedly) less controversial conceptions of truthmaking. The first point of retreat is to the following claim: where S expresses a contingent truth, the absence of a truthmaker for S is both necessary and sufficient for S to be true but not determinately so. (And so, principles D1/D2 remain valid for contingent truths and so TM1/FM1 are thereby valid when restricted to contingent truths which do not admit of indeterminacy.) Even though that makes the theory of indeterminacy on offer somewhat less parochial, it is still incompatible with all conceptions of truthmaking whereby so-called “negative truths” are truths without truthmakers. Take an utterance of the negative existential “There are no dodos.” Suppose that this utterance is determinately true. Given D1, this truth has a truthmaker. But what sort of thing could make this negative claim true? Equally, what sort of entity could make an utterance of the positive existential “There are dodos” false? If facts are taken to be the primary truthmakers, then the quick answer is: negative facts. Many have baulked at positing such facts.40 An alternative response is to restrict the scope of the principles TM1, D1, and I1 to so-called “positive truth-bearers” with the upshot that FM1, D2, and I1 are no longer derivable from the newly restricted versions of TM1, D1, and I1, respectively.41 Thus, the proposition expressed by the sentence “There are no dodos” is a truth without a truthmaker and the proposition expressed by the sentence “There are dodos” is a falsity without a falsemaker. With respect to giving a truthmaker gap theory of indeterminacy, the result is that being true but lacking a truthmaker is a necessary but not a sufficient condition for being true but not determinately so. Nonetheless, we can still have the following three clauses: (1) a positive truthbearer is a truth without a truthmaker if and only if this positive truth-bearer is true but not determinately so; (2) a positive truth-bearer is true but not determinately so if and only if the corresponding negative truth-bearer is false but not determinately so; and (3) a negative truth-bearer is true but not determinately so if and 40. Russell famously thought it necessary to posit such negative facts. Armstrong (2004, chap. 5) argues that we can get by with so-called “totality facts.” Equally, one might seek to defend what Armstrong calls “the incompatibility solution” whereby, assuming propositions to be the truth-bearers, for every negative truth not-p, there is a positive truth q which is incompatible with p such that the truthmaker for this positive truth is thereby a truthmaker for the negative truth not-p (see Armstrong 2004, 60–63 for a critical discussion of the incompatibility solution). 41. The character “Mid” in Simons (2000) suggests that TM1 should be restricted to atomic, and so to positive, truths.

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only if the corresponding positive truth-bearer is false but not determinately so. The trouble with this proposal is that there are no clear criteria to distinguish positive from negative truth-bearers—either when utterances of sentences or propositions are taken to be the primary truth-bearers.42 A further solution to the problem of negative truthmakers is to adopt the following disjunctive version of the truthmaker principle: (TM-v) If S expresses the contingent proposition that p then either (necessarily) if S is true then something makes 〈p〉 true or (necessarily) if S is false then something makes 〈p〉 false.43 This principle can be taken to range over both positive and negative truthmakers and so there is no call for a principled distinction between these species of truthbearer. Suppose that S is the negative existential “There are no dodos.” Let’s concede that the proposition expressed by this sentence is a truth without a truthmaker. It follows that the left disjunct of TM-v fails. Nonetheless, the right disjunct holds because in all worlds where the sentence is false there will be a falsemaker for the proposition expressed by this sentence, namely the existence of at least one dodo. The key thesis of a truthmaker gap theory of indeterminacy thus becomes: a sentence (which expresses a contingent proposition) is indeterminate in truth-value just in case this sentence is a counterexample to TM-v. That is: (I3) If S expresses the contingent proposition that p then S is indeterminate in truth-value if and only if S is true but 〈p〉 lacks a truthmaker or S is false but 〈p〉 lacks a falsemaker. The trouble with TM-v is that there are disjunctive claims that are counterexamples to TM-v and yet these claims are perfectly determinate in truth-value. Take the disjunctive proposition 〈there is a dodo or there are no artic penguins〉. Since there are no dodos then the left disjunct is false and so not made true. Nonetheless, the right disjunct is true. But, given that negative truthmakers are not admissible, the right disjunct is a truth without a truthmaker. Either way, both disjuncts are not made true and so the disjunction is a truth without a truthmaker. Suppose that the disjunction is false—hence both disjuncts are false. The left disjunct is not made false because there is no negative fact to make the disjunct false. But a disjunction is made false only if both disjuncts are made false and so the disjunction is thus false but lacks a falsemaker. Thus, the disjunction in hand is a counterexample to TM-v despite being determinate in truth-value.44 (More complex counterexamples can be found whereby the main connective of the sentence is a conjunction or a conditional.) One way of addressing that problem is to restrict the scope of TM-v to sentences whose logical form is not expressed using & or V or → (or any other 42. See Dummett (2006, 7–8). 43. Parsons (2005, 168) offers a distinct but related disjunctive formulation of the truthmaker principle: “for all truths p, either p has a truthmaker, or p’s negation would have a truthmaker, were it true.” 44. Here I improve upon a counterexample of Parsons (2005, 168).

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binary connectives such as the Scheffer stroke). Thus, S is indeterminate in truthvalue just in case S expresses a contingent and non-binary bivalent proposition which whenever it is true it lacks a truthmaker and whenever it is false it lacks a falsemaker. The trouble with this suggestion is that just as we lack clear criteria for distinguishing positive from negative truth-bearers, we lack clear criteria for distinguishing sentences whose logical form is canonically expressed using a binary logical connective and sentences whose logical form is canonically expressed using a unary connective. So, it’s hard to see how TM-v could be appropriately restricted. One popular response to these (and related) worries is to retreat to some version of Bigelow’s slogan: truth supervenes upon being, where this slogan applies to contingent truth only. Suppose that being is constituted by what things there are then this slogan articulates the following claim: “If something is true, then it would not be possible for it to be false unless either certain things were to exist which don’t, or else certain things had not existed which do” (Bigelow 1988, 133). When sentences, rather than propositions, are taken to be the primary truth-bearers then this principle becomes: (SUP1) If a sentence S expresses a contingent proposition then the truthvalue of S supervenes upon what things there are. We have been assuming all along that “S” denotes a sentence-context pair, where a context determines a world. For this reason, SUP is best expressed as follows: if a sentence type s is true (relative to a use in a world W) but false (relative to a use in a world V) then there is a difference in population between these worlds: either something exists in W but not V or something exists in V but not W. The truth-value of s may differ relative to the two uses for three reasons: either the use of s expresses a different proposition across the two uses, or the subject matter of the proposition expressed by the use of s differs across the two uses, or both these scenarios obtain. Roughly, a difference in truth-value entails a difference in meaning or a difference in fact (or both). Suppose instead that being is taken to be constituted by what things there are and how those things are, then the Bigelow slogan articulates the following claim: if a truth-bearer differs in truth-value across worlds then either a particular or a universal exists in one but not the other of these worlds or there is a difference in the pattern of instantiation of particulars and universals (see Bigelow 1988, 38; Dodd 2002, 73–81; Lewis 1999, 206; 2001, 613). So, we have: (SUP2) If S expresses a contingent proposition then the truth-value of S supervenes upon what things there are and how those things are. So, if a sentence type s is true (relative to a use in a world W) but false (relative to a use in a world V) then that need not entail a difference in population between W and V, but simply a difference in the pattern of instantiation of the fundamental properties and relations shared between the two worlds. Like TM-v, both SUP1 and SUP2 do not require us to posit negative truthmakers thus allowing that some contingent truths do not have truthmakers. If

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“There are dodos” is true (as used in W) but not true (as used in V), and this sentence expresses the same proposition in both worlds, this merely entails that something—the sum of all dodos—exists in W but not V. It does not entail that something else—the absence of dodos—exists in V but not W. Better still, unlike TM-v, both SUP1 and SUP2 do not need to be restricted to atomic truth-bearers. It’s a further question as to whether SUP2 is preferable to SUP1. One reason to prefer SUP2 over SUP1 is because SUP1 depends on the somewhat contentious idea that reality is simply a collection of objects such that to furnish an inventory of these objects is to give an exhaustive characterization of reality.45 Another, and stronger, reason to prefer SUP2 over SUP1 is that SUP2 permits a more parsimonious ontology since, given SUP2, every difference in being need not be a difference in population. Even though for the purposes of giving a theory of indeterminacy we can remain neutral on this vexed issue, I propose that SUP2 is taken to be the canonical truthmaking principle on the grounds that it is neutral between a wide range of ontological theories. The result is that we can make room for truthmaking without truthmakers.46 A difference in truth-value need not entail a difference in what things there are but simply a difference in the pattern of instantiation of what particulars and universals that there are. We are now in a position to articulate a far less parochial model of determinacy—call this determinacy2—and indeterminacy—call this indeterminacy2. First, we have the following (equivalent) principles: (D3) If S expresses a contingent proposition then S is determinately2 true if and only if S is true and the truth-value of S supervenes upon what things there are and how those things are. (D4) If S expresses a contingent proposition then S is determinately2 false if and only if S is false and the truth-value of S supervenes upon what things there are and how those things are.47 Given D3 and D4, to say that a sentence is true/false but not determinately2 so is to say this it is true/false but its truth-value does not supervene upon what things there are and how those things are. And so we have: (I4): If S expresses a contingent proposition then S is indeterminate2 in truth-value if and only if S is either true or false but S’s truth-value does not supervene upon what things there are and how those things are.48 45. Williamson (2005, 705–6) makes just this complaint. 46. See Melia (2005, 78–84) for a rather intriguing nominalistic truthmaking theory which allows there to be truthmaking without truthmakers without any commitment to a modal principle like SUP2. 47. These principles are equivalent given that they range over both atomic and non-atomic truth-bearers. They also permit logical truths/falsities to be determinately2 true/false (which allows, but does not require, the logic of determinacy2 to be a normal modal logic). 48. While there are strong hints of a truthmaker–truthmaking gap theory of indeterminacy in McGee and McLaughlin (1995), McLaughlin (1997), and McGee and McLaughlin (2004), it is clear that these authors (see esp. their 2004, 126–27) accept that whether or not a truth-bearer is true

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So, on this conception, sentences which are indeterminate2 in truth-value are counterexamples to SUP2.49 So, there is a world W and a world V such that the sentence type s is true (relative to a use in W) yet false (relative to a use in V) and yet W and V are indiscernible. On this interpretation, a sentence is indeterminate in truth-value just in case it gives rise to truthmaking, rather than truthmaker, gaps. There are thus three classes of (contingent) sentences: those whose truth-values are supervenient and true, those whose truth-values are supervenient and false, and those that fall in the truthmaking gap, as it were, such that their truth-value does not supervene upon what things there are and how those things are. Ungrounded truth (indeterminate2 truth) is not a distinct species of truth, it is simply a mode of truth—a way of being true. Likewise for grounded truth. We have now made room for a species of indeterminate truth, namely indeterminate2 truth, within a far less parochial framework of truthmaking, a framework which is arguably available to most partisans as to the nature of being. Again, the Wright–Williamson challenge has at least been partly met: indeterminate truth is a (prima facie) intelligible notion.50 To make the notion somewhat more intelligible it is necessary to answer what I term the queerness objection. 14. THE QUEERNESS OBJECTION The two models of indeterminacy on offer are hostage to what may be termed the queerness objection. This objection runs: to reject (or restrict) the thesis that the truth of a sentence supervenes upon what things there are and how those things are is to give up on a platitude concerning the most minimal relationship between language and the world. To do so is to posit a class of sentences whose truth-values float free in a void. That’s just unacceptably queer.51 Equally, to allow that a sentence, which expresses 〈p〉, is true but that there is no fact of the matter as to whether p is, again, just unacceptably queer. Though this objection is well taken, there is a package of responses that can be marshalled in response. Response One: In the first place, queerness is to be expected—the truth about indeterminacy must be strange. All theories of indeterminacy—however, prepossessing—have a bump in the carpet.52 Whether such queerness is unacceptable depends, in part, on the corresponding virtues exhibited by the theory in depends only on what the world is like such that the truth-value of this truth-bearer supervenes upon what things there are and how those things are. Hence, these authors explicitly do not offer a truthmaking–truthmaker gap theory of indeterminacy despite wishing to draw a distinction between indeterminate truth and determinate truth. 49. Cf. Sorensen (2001, 173–74). 50. Just as with a truthmaker gap model of indeterminacy, a truthmaking gap model opposes an analogue of Williamson’s conception of worldly indeterminacy discussed in section 8.A classical version of this analogue is that reality is indeterminate just in case there is a world W and a world V such that a use of the sentence type s is true in W but a use of s in V is not true and yet it is indeterminate whether W and V are indiscernible. 51. McBride (2005, 122), for one, alleges that it is a “near truism” that “there cannot be a difference in the truth-value of a proposition without a difference in its subject matter.” 52. Cf. Williamson’s remark “the truth about vagueness must be strange” (Williamson 1994, 166).

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question. The key virtues of a truthmaker–truthmaking gap conception are manifold. In summary, they are: (1) Classical semantics is preserved, most notably bivalence, Tarski’s T-schema, and the disquotational schema for predicate denotation (and cognate schemas). (2) Classical logic is preserved in its entirety.The result is a theory which has the methodological virtues of simplicity, explanatory power, past success, and a high degree of integration with theories from other domains.53 Furthermore, since one cannot always read off from the syntax or logical form or meaning of a sentence whether or not it is (extensionally) indeterminate in truthvalue, those theories of indeterminacy which recommend restricting classical logic face the following dilemma: should one proceed cautiously and reason in the restricted logic or should one take a risk and reason in classical logic?54 A truthmaker–truthmaking gap theory of indeterminacy faces no such dilemma since it is always safe to reason classically in the face of potential indeterminacy. Response Two: Suppose the canonical truthmaker principle is read as follows: for any worlds W and V, if some proposition p is true in W but not in V then something exists in W but not in V (and so the principle is a “two-way” differencemaking principle). To allow for the possibility of indiscernible worlds, Lewis (2001) proposes what he takes to be an “easy and harmless” amendment to the truthmaker principle so read: Let a discerning proposition be one that never has different truth-values in two indiscernible worlds; understand [the truthmaker principle] to be restricted to discerning propositions. (Lewis 2001, 606) But now note that Lewis’s notion of a discerning proposition is effectively one way of expressing the notion of a determinate proposition. An indeterminate (or indiscerning) proposition, accordingly, can take different truth-values in two indiscernible worlds. Lewis’s “easy and harmless” restriction of (a propositional version of) the truthmaker principle is thus entirely analogous to a truthmaker-truthmaking gap strategy of allowing for indeterminacy. (This helps us locate a potential source of the anxiety over the queerness of truthmaker-truthmaking gap, namely the possibility of indiscernible worlds.) Response Three: As we saw in sections 2–4 above, a truthmaker–truthmaking gap theory is the only theory of indeterminacy which goes any way to making sense of the distinction between determinate truth and indeterminate truth in a classical framework.All other classical theories of indeterminacy considered are, it has to be said, conspicuous failures in this respect. Response Four: A truthmaker–truthmaking gap theory is methodologically principled. Given a philosophical conundrum, one should revise one’s philosophy before one revises one’s logic. In general, one should be bold and adopt classical

53. The methodological virtues of classical logic/semantics are endorsed by Quine (1981), Sorensen (1988, 2001, 8–20), and Williamson (1994, 186). 54. The scenario of risk here is, of course, taken from Kripke (1975), though Kripke doesn’t go on to motivate the dilemma just given.

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logic from the outset in one’s philosophical investigations—otherwise one is destined to fail to properly investigate and develop all the theories of indeterminacy under which classical logic is preserved.55 A truthmaker–truthmaking gap theory respects such a bold methodology since it merely restricts a piece of metaphysics, namely, either the thesis TM1 or the thesis SUP2 (or both).56 Response Five: In fact a much stronger methodological argument in favour of a truthmaker gap theory of indeterminacy is in the offing. To illustrate the point let me tell a story about how things might have turned out. Return to the beginnings of the modern indeterminacy debate sometime around 1918.57 Picture Łukasiewicz deciding how to respond to the indeterminacy exhibited by future contingent sentences. Assume that he is right to think that this indeterminacy is non-epistemic. But imagine, contrary to fact, that he was able to consider the following two options: Option One: Give up on classical logic and allow for truth-value gaps. Furthermore these gaps are to be modelled in the now very familiar threevalued truth-functional (Łukasiewicz) matrices (the intermediate status being “neither true nor false”). Option Two: Retain classical logic and allow for truthmaker gaps. Furthermore, these gaps are to be modelled in the now very familiar three-valued truth-functional (Łukasiewicz) matrices (the intermediate status being “no fact of the matter”). Łukasiewicz first supposes that Option One is correct. He supposes further that truth is the “strong” notion of truth whereby if a proposition is neither true nor false then the claim that this proposition is true is itself false. It follows that the following version of (one half of) the Tarski’s T-schema (with respect to propositional truth) is invalid since there is a “drop” in truth-value from antecedent to consequent:58 (TRUTH) If p then it is true that p. Now he supposes instead that Option Two is correct and notes that the following schema will be invalid. (FACT) If p then it is a fact that p. Łukasiewicz remains unsure which option to choose. Does he deny the (semantic) principle TRUTH or the (metaphysical) principle FACT? Either option seems to 55. These methodological strictures are due to Williamson (1997). See also Sorensen (2001, 8–20). 56. So, even though Williamson intended these methodological strictures to push us towards embracing epistemicism in the vagueness debate, they do no such thing in the indeterminacy debate at large given the possibility of non-epistemic bivalent models of indeterminacy. 57. See McCall (1967). 58. See Dummett (1978, 233).

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him a queer way to go. Nonetheless, if future contingents really are nonepistemically indeterminate in truth-value then choose he must. He runs through all the reasons mooted above in favour of Option Two but finds them insufficient to persuade him. Lurking in his mind here is the feeling that it is a lot more queer to deny FACT than it is to deny TRUTH such that these reasons cannot offset the oddity of denying FACT. He begins to veer towards choosing Option One but before he does so he reflects upon whether the following schema is valid: (LINK) If it is a fact that p then it is true that p, and concludes that LINK is indeed valid. LINK strikes Łukasiewicz as valid because: (1) given Option Two, LINK is not in any case under any threat; and (2) given Option One, although it might be thought that LINK should be given up along with TRUTH, this is not so. His reason for thinking this is that a truth-value gap conception needs LINK to explain why there is no fact of the matter as to whether p when neither p nor not-p is true. (Here Łukasiewicz finds no plausibility in Williamson’s conception of worldly indeterminacy but takes the ordinary conception of worldly indeterminacy to be the default view.) Łukasiewicz now notices that FACT plus LINK entail TRUTH. And so he realizes that if he takes Option One he will be not only committed to denying a prima facie plausible principle governing truth (namely TRUTH) but he will also be committed to denying a prima facie plausible principle concerning the relationship between propositions and the world (namely FACT). So, Option One strikes him as doubly queer. Indeed, he realizes that any logical theory in the future which abandons TRUTH will be in exactly the same predicament. He then notes that while a denial of FACT is indeed considerably queer, it is still much less queer to choose Option Two rather than Option One (at least if the ordinary conception of worldly indeterminacy is correct whereby indeterminacy consists in there being no fact of the matter). So, he proceeds to model future contingents using truthmaker gaps and uses his three-valued matrices to demonstrate, for example, that the claim that “Either it will rain tomorrow or it will not” is true but nothing makes it true since nothing makes either disjunct true.59 Looking back after many years he feels relieved not to have led the Academy astray by positing such doubly queer things as truth-value gaps. Of course things did not turn out this way. Since the 1920s, three-valued logics, many-valued logics, and their cousins (such as standard supervaluational logic) have proliferated and flourished. As we have just seen, under certain assumptions, a large class of such logics are doubly queer. For this reason, the modern indeterminacy debate got off on the wrong foot by being committed to far 59. The three-valued tables commit Łukasiewicz to a compositional model of indeterminacy whereby if both disjuncts of a disjunction are indeterminate then the disjunction is indeterminate. Thus, on such a view Truthmaker Maximalism is ruled out since the law of excluded middle lacks a truthmaker when both disjuncts do. In section 7, in contrast, a compositional model of indeterminacy was ruled out because Truthmaker Maximalism was taken to be valid for all sentences which do not admit of indeterminacy and hence the route to a normal modal logic of determinacy.

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more deviancy and queerness than is required to make sense of indeterminacy.60 Once this is realized, the queerness objection against truthmaker gaps (and truthmaking gaps) loses much if not most of its force. 15. CONCLUSION To vindicate the intelligibility of indeterminate truth one must find a coherent framework within which this notion can be expressed and elucidated. One must also show how the notion can help resolve, or illuminate, a range of puzzles and paradoxes concerning indeterminacy. I hope to have gone some way to meeting the first of these demands via the idea that a truth-bearer can have a groundless truth-value, where such groundlessness is explained via a theory of truthmaker gaps or via a theory of truthmaking gaps. In so doing, I hope to have made some sense of the distinction between linguistic indeterminacy and worldly indeterminacy. The second challenge is taken up elsewhere.61,62 REFERENCES Åkerman, J., and Greenough, P. Unpublished. “Vagueness and Non-Indexical Contextualism.” ms. Armstrong, D. 1997. A World of States of Affairs. Cambridge: Cambridge University Press. ———. 2004. Truth and Truthmaking. Cambridge: Cambridge University Press. Belnap, N. 2001. Facing the Future: Agents and Choices in Our Indeterminist World (with Michael Perloff and Ming Xu). Oxford: Oxford University Press. Bigelow, J. 1988. The Reality of the Numbers: A Physicalist’s Philosophy of Mathematics. Oxford: Clarendon Press. Dodd, J. 2002.“Is Truth Supervenient on Being?” Proceedings of the Aristotelian Society 102: 69–86. Dummett, M. A. E. 1975. “Wang’s Paradox.” Synthese 30: 301–24. ———. 1978. Truth and Other Enigmas. London: Duckworth. ———. 2006. Thought and Reality. Oxford: Oxford University Press. Field, H. 1994. “Disquotational Truth and Factually Defective Discourse.” Philosophical Review 103: 405–52. ———. 2001. Truth and the Absence of Fact. Oxford: Oxford University Press. ———. 2003. “A Revenge-Immune Solution to the Semantic Paradoxes.” Journal of Philosophical Logic 32: 39–77. Fine, K. 1975. “Vagueness, Truth, and Logic.” Synthese 30: 265–300. ———. 1982. “First-order Modal Theories III—Facts.” Synthese 53: 43–122. 60. Certain “gappy” theories allow Tarski’s T-schema to be valid by introducing a new conditional into the language (see, e.g., Field 2003) and so are not subject to the argument in the text. Even so, the law of excluded middle is given up. In the case of future contingents at least, this has no plausibility whatsoever, since “either a sea-battle will happen or not: a sea-battle will happen” ought to be valid on any promising conception of future contingents. Likewise, for the quasi-tautology “Either it will happen or it won’t.” 61. See Greenough (forthcoming), Greenough “The Open Future” (unpublished ms.). 62. Thanks to Sven Rosenkranz and Roy Sorensen for helpful feedback on an earlier version. Significant parts of this paper have been presented at: ANU, Auckland (AAP-NZ), Barcelona, Budapest, Joint Session of the Mind and Aristotelian Society at Bristol, Prague, The Scots Philosophical Club, Sheffield, St. Andrews, and Stockholm. Thanks to the audiences on those occasions for very valuable feedback. This paper was completed while I was a postdoctoral fellow in the Epistemic Warrant Project at ANU 2007–2008. I am greatly indebted to the philosophical community at ANU for their immense (philosophical) hospitality during my stay.

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Greenough, P. 2008. “On what it Is to Be in a Quandary.” Synthese DOI 10.1007/s11229-0089317-7. ———. Forthcoming. “Truthmaker Gaps and the No-No Paradox.” Philosophy and Phenomenological Research. ———. Unpublished. “The Open Future.” ms. Heck, R. 2003. “Semantic Accounts of Vagueness.” In Liars and Heaps, ed. J. C. Beall, 106–27. New York: Oxford University Press. Hyde, D. 1994. “Why Higher-order Vagueness is a Pseudo-problem.” Mind 103: 35–41. Karttunen, L. 1973. “Presuppositions of Compound Sentences.” Linguistic Inquiry IV, 169–93. Keefe, R. 2000. Theories of Vagueness. Cambridge: Cambridge University Press. Koons, R. 1994. “A New Solution to the Sorites Problem.” Mind 103: 439–49. Kripke, S. 1975. “Outline of a Theory of Truth.” Journal of Philosophy 72: 690–716. ———. 1982. Wittgenstein on Rules and Private Language. Cambridge, MA: Harvard University Press. Lewis, D. 1999. “A World of Truthmakers?” In Papers in Metaphysics and Epistemology, 215–20. Cambridge: Cambridge University Press. ———. 2001. “Truthmaking and Difference-making.” Noûs 35: 602–15. MacFarlane, J. 2003. “Future Contingents and Relative Truth.” The Philosophical Quarterly 53: 321–36. ———. 2005. “Making Sense of Relative Truth.” Proceedings of the Aristotelian Society 105: 321–39. ———. 2008. “Nonindexical Contextualism.” Synthese DOI 10.1007/s11229-007-9286-2. McBride, F. 2005. “Lewis’s Animadversions on the Truthmaker Principle.” In Truthmakers: The Contemporary Debate, ed. H. Beebee and J. Dodd, 117–40. Oxford: Oxford University Press. McCall, S., ed. 1967. Polish Logic 1920–1939. Oxford: Oxford University Press. ——— 1994. A Model of the Universe. Oxford: Oxford University Press. McGee, V., and McLaughlin, B. 1995. “Distinctions without a Difference.” Southern Journal of Philosophy 33 (Supplement): 204–51. ———. 2004. “Logical Commitment and Semantic Indeterminacy: A Reply to Williamson.” Linguistics and Philosophy 27: 221–35. McLaughlin, B. 1997. “Supervenience, Vagueness, and Determination.” Philosophical Perspectives 11: 209–39. Maudlin, T. 2005. “Metaphysics and Quantum Physics.” In The Oxford Handbook of Metaphysics, ed. M. Loux and D. Zimmerman, 461–87. Oxford: Oxford University Press. Melia, J. 2005. “Truthmaking without Truthmakers.” In Truthmakers: The Contemporary Debate, ed. H. Beebee and J. Dodd, 67–84. Oxford: Oxford University Press. Parsons, J. 1999. “There is no ‘Truthmaker’ Argument against Nominalism.” Australasian Journal of Philosophy 77: 325–34. Parsons, J. 2005. “Truthmakers, the Past, and the Future.” In Truthmakers: The Contemporary Debate, ed. H. Beebee and J. Dodd, 161–74. Oxford: Oxford University Press. Parsons, T. 2000. Indeterminate Identity. Oxford: Oxford University Press. Quine, W. V. O. 1981. “What Price Bivalence?” In Theories and Things, 31–37. Cambridge, MA: Harvard University Press. Raffman, D. 1994. “Vagueness without Paradox.” Philosophical Review 103: 41–74. Read, S. 2000. “Truthmakers and the Disjunction Thesis.” Mind 109: 67–99. Restall, G. 1996. “Truthmakers, Entailment, and Necessity.” Australasian Journal of Philosophy 74: 331–40. Richard, M. 2004. “Contextualism and Relativism.” Philosophical Studies 119: 215–42. Rodriguez-Pereyra, G. 2005. “Why Truthmakers?” In Truthmakers: The Contemporary Debate, ed. H. Beebee and J. Dodd, 17–31. Oxford: Oxford University Press. ———. 2006. “Truthmaking, Entailment, and the Conjunction Thesis.” Mind 115: 957–82. Schwarz, D. S. 1977. “On Pragmatic Presupposition.” Linguistics and Philosophy 1: 247–57. Simons, P. 2000. “Truthmaker Optimalism.” Logique et Analyse 43 (169–70): 17–41. Shapiro, S. 2003. “Vagueness and Conversation.” In Liars and Heaps, ed. J. C. Beall, 39–72. Oxford/New York: Oxford University Press.

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———. 2006. Vagueness in Context. Oxford: Oxford University Press. Slater, H. 1989. “Consistent Vagueness.” Noûs 23: 241–52. Sorensen, R. 1988. Blindspots. Oxford: Oxford University Press. ———. 2001. Vagueness and Contradiction. Oxford: Oxford University Press. ———. 2005a. “Précis of Vagueness and Contradiction.” Philosophy and Phenomenological Research 71: 678–85. ———. 2005b. “A Reply to Critics.” Philosophy and Phenomenological Research 71: 712–28. Strawson, P. F. 1952. Introduction to Logical Theory. London: Methuen. Tarski, A. 1944. “The Semantic Conception of Truth and the Foundations of Semantics.” Philosophy and Phenomenological Research, 4: 341–76. Thomason, R. 1970. “Indeterminist Time and Truth-value Gaps.” Theoria 3: 264–81. Unger, P. 1980. “The Problem of the Many.” Midwest Studies in Philosophy 5: 411-67. van Fraassen, B. C. 1966. “Singular terms, Truth-value gaps, and Free Logic.” Journal of Philosophy 63: 481–95. ———. 1968. “Presupposition, Implication, and Self-Reference.” Journal of Philosophy 64: 136–52. Williamson, T. 1990. Identity and Discrimination. Oxford: Blackwell. ———. 1994. Vagueness. London: Routledge. ———. 1995. “Definiteness and Knowability.” Southern Journal of Philosophy 33 (Supplement): 171–91. ———. 1996. “Wright on the Epistemic Conception of Vagueness.” Analysis 56: 39–45. ———. 1997. “Imagination, Stipulation, and Vagueness.” Philosophical Issues 8: 215–28. ———. 1999. “On the Structure of Higher-Order Vagueness.” Mind 108: 127–43. ———. 2000. Knowledge and its Limits. Oxford/New York: Oxford University Press. ———. 2005. “Vagueness in Reality.” In The Oxford Handbook of Metaphysics, ed. M. Loux and D. Zimmerman, 690–715. Oxford: Oxford University Press. Wright, C. 1987. “Further Reflections on the Sorites Paradox.” Philosophical Topics 15: 227–90. ———. 1995. “The Epistemic Conception of Vagueness.” Southern Journal of Philosophy 33 (Suppl.): 133–59. ———. 2001. “On Being in a Quandary.” Mind 110: 45–98. ———. 2003. “Vagueness; A Fifth Column Approach.” In Liars and Heaps, ed. J. C. Beall, 84–105. Oxford/New York: Oxford University Press.

Midwest Studies in Philosophy, XXXII (2008)

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emantic theories for natural languages purport to describe a central aspect of the meaning of natural language sentences. In doing so, they usually employ some notion of truth. Most semanticists, even those who have no objections to invoking propositions, will define a truth-predicate that applies to sentences. Some will also employ a notion of propositional truth. Both types of semanticist face the question whether and how the semantic notion(s) of truth they are employing is (are) related to the ordinary, pre-theoretic notion(s) of truth. It seems immediately problematic to say that the semantic truth notion is a pre-theoretic notion. For pretheoretically, we do not seem to apply “true” to sentences. So, if the semantic truth notion is in any interesting way related to a pre-theoretic notion of truth, then the relationship is more complex. As I shall explain in Section 2, however, there are some straightforward ways of postulating an analytic link between semantic truth notions and ordinary truth. Now, recently there have been a host of proposals to adopt a “relativistic” semantics of certain expressions, such as predicates of personal taste, epistemic modals, sentences about the contingent future, evaluative sentences generally, sentences attributing knowledge etc.1 All these proposals involve the claim that the truth of utterances or propositions depends on an extra factor. As we shall see, the answers standard semanticists can provide to the question of the status of their semantic truth-predicate do not transfer easily to these new, relativistic theories. In Section 3, I shall make some proposals as to how relativists can deal with these 1. For a fairly comprehensive survey see Kölbel (2008c). Midwest Studies in Philosophy: Truth and its Deformities Volume XXXII Editor by Peter A. French and Howard K. Wettstein © 2008 Wiley Periodicals, Inc. ISBN: 978-1-405-19145-6

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challenges. There is also a separate question for relativists about the relationship between their semantic theories and standard semantics: are relativists dismissing standard semantics as radically misguided, are they promoting an incommensurable new theory? In the final section, I shall argue that this is not the case: relativists can view their proposals as simply adding to the good work standard semanticists have been doing. I shall start out in Section 1 with a brief sketch of recent relativistic semantics, explaining the ways in which it differs from standard semantics. 1. RECENT RELATIVISM Contemporary relativists claim that the truth of some propositions varies with a novel parameter, for example, with a standard of taste, with a state of information, with interests or with a moral code. Non-relativists, by contrast, insist that the truth of a proposition at most varies with a possible world. But since there is one privileged world, the actual world, there is a good sense in which the non-relativist can say that propositional truth is absolute. Relativists are motivated in their claim by a perceived lack of objectivity of some propositions. For example, it seems that when I say “That coffee is tasty,” demonstrating a particular quantity of coffee, the content of my remark, and the content of the belief I thereby express, is not something that is absolutely true or false. For if it were, we would have to say that when someone else believes and says of the same quantity of coffee that it is not tasty, then one of us must have made a mistake. But it seems wrong to say this. It might be that the beliefs of each of us are unimprovable.2 On the other hand, there clearly seems to be some standard of correctness for beliefs and sayings as to the tastiness of things—we can be right or wrong about whether the coffee is tasty: I may order a coffee because I believe it will be tasty, yet be disappointed when I try it and realize my mistake. One minimal modification that preserves all these presumed data is to say that the contents of such beliefs (but not all contents) vary in truth-value not just with a possible world, but also with a standard of taste, and that the standard of taste relevant for the assessment of any belief or saying may vary depending on the believer or speaker involved. Thus my belief that that coffee is tasty may be true with respect to the standard of taste relevant for assessing my beliefs, while your belief that the same coffee is not tasty may at the same time be true with respect to the standard relevant for assessing your beliefs. Now, those who want to avoid absolutism about matters of taste are not condemned to accept the relativist’s solution. An alternative solution— contextualism—builds reference to a standard of taste into the content of the remark (of the belief). The contextualist might say, for example, that fully specified, what I say (and believe) when I sincerely utter “that coffee is tasty.” is that that coffee is tasty according to my own standard. This means that when you utter the words “that coffee is not tasty.” you express the content that that coffee is not tasty 2. See for example Kölbel (2002, 2003, 2008b, 2008c), MacFarlane (2005b, forthcoming), Egan et al. (2005) for more detailed expositions of this type of argument. See also Lasersohn (2005).

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according to your standard, thus you are not contradicting me. So there is no problem about each of the beliefs being unimprovable. There is a debate to be had, whether the relativist’s or the contextualist’s solution is the better one. The contextualist is able to maintain that all contents of speech and belief—propositions—have absolute truth-values, and therefore they are in the business of representing objective reality. But this comes at the cost of having to postulate implicit aspects of contents of utterances and beliefs, which requires her to explain away a number of appearances. For example, she needs to explain away the impression we have that what I say when I utter “that coffee is tasty.” is incompatible with what you say when you reply “that coffee is not tasty.”—incompatible in the sense that no one person could accept both.3 But the difficulties of contextualists are not the focus of the current essay but rather the relativist’s. The relativist has the advantage of being able to say that the way sentences express propositions is uniform across objective and nonobjective areas. Thus “That coffee is tasty.” and “That coffee is filtered.” are on a par in terms of the way in which the words used determine the proposition expressed. Each time the property expressed by the predicate is ascribed to the quantity of coffee in question. There is a difference between the properties expressed: being filtered is an objective property, while being tasty is not. However, this is not a linguistic difference. The relativist pays for this uniformity and convenience with the hostility of those who insist, as Frege did, that propositions, the contents of thought and speech, cannot but be the sort of entity that has its truth-value absolutely. But it is not only others’ dogmatic insistence on the absoluteness of propositional truth that creates problems for a relativist. There are also some tricky questions about the nature of the truth-predicate the relativist is using when she says that it is not an absolute matter whether a proposition is true. In order to be able to see what these questions are, I will first need to provide a sketch of the relativist’s semantic theory. Let us start with semantics as it is standardly pursued. In a standard semantics for a context-sensitive language (such as Kaplan 1977), each sentence of the language is assigned a character, which is a function from possible contexts of utterance to contents. Contents in turn are also functions: they are functions from circumstances of evaluation to truth-values. Standardly, the circumstances of evaluation are now thought of merely as possible worlds, though Kaplan himself thought of circumstances as involving several parameters including a world and a time. Formally, these assignments can be expressed by a definition of a notion of sentential truth (“TruthS”) relating sentences to contexts of utterance and circumstances of evaluation. Thus the semantics will entail for each sentence s a theorem of the form “For all contexts of utterance c, and all worlds w: TrueS(s, c, w) iff p.” To give a concrete example, the theorem for “I am hungry”. might read: “For all contexts c and worlds w: TrueS(“I am hungry”, c, w) iff the speaker of c is in the extension of “hungry” with respect to the time of c and the world of c.” The relativist basically thinks that in addition to a possible world, the truth of a sentence in context (or of a content) depends on a further factor. Let’s stick to 3. See Kölbel (2007) for some suggestions as to how the contextualist might do this.

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our example of a relativist about taste, who thinks that some propositions vary in their truth-value with a standard of taste. This relativist’s semantics will therefore involve a slightly different notion of a circumstance of evaluation according to which a circumstance of evaluation is an ordered pair consisting of a possible world and a standard of taste. Thus theorems would have the form: “For all contexts c, worlds w and standards of taste t:TrueS(s, c, 〈w, t〉) iff p.”A particular theorem might look like this: “For all contexts c, worlds w, and standards of taste t: TrueS(“that coffee is tasty.”, c, 〈w, t〉) iff the coffee demonstrated in c is in the extension of “tasty” at w and with respect to t.” Superficially, the adicity of the relativist’s sentential truth-predicate “TrueS” has not changed, because it still relates a sentence with a context and a circumstance. However, this is merely superficial. For one of the relata is now an ordered pair with two independently varying elements, one of which has been newly introduced, the other being one of the standard relata. We could—equivalently—have introduced the standard of taste parameter as an extra argument place of the sentential truth-predicate, so that formally the predicate becomes four-place.4 Whatever the formal articulation of the relativizing move (whether or not the adicity of the sentential truth-predicate is formally increased) we end up with a substantially different notion. For the relativist’s new notion allows a form of variation that the old one does not allow, namely variation in truth-value with a standard of taste. This variation is independent of the other factors on which sentential truth depends in standard semantics.Thus, the relativist’s truth-predicate in effect expresses a relation that has greater adicity than the relation expressed by the standard semanticist’s truth-predicate. 2. STANDARD SEMANTICS AND ORDINARY TRUTH Before we worry about the relation expressed by the relativist’s sentential truthpredicate, let us first consider the relation expressed by the sentential truthpredicate in standard semantics. What should a semanticist generally say about the status of the notion of sentential truth she is employing in her semantic theories, and about the relationship between this notion and any pre-theoretic notions of truth? A direct identification of the semanticist’s sentential truth with pre-theoretic truth is clearly not available. The semantic notion differs from any pre-theoretic notion in several fundamental respects: first, it concerns sentences, while ordinarily truth seems to be attributed to what people say or believe, that is, to contents or propositions. Secondly, the semantic notion is at least two-place (or if we count the world-parameter as increasing the adicity: three-place) and relates a sentence with a context (and a world). No ordinary notion seems to have this form: we seem to be attributing truth directly to what people say or believe. Sentential truth is a theoretical concept which, even though it is not identical to any pre-theoretic concept, nevertheless is meant to have clear analytic links to 4. John MacFarlane (e.g., 2003, 2005a, 2005b, 2008b), for example, treats the semantic truthpredicate as having argument places for a sentence, a context of use, a circumstance of evaluation and a context of assessment.

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pre-theoretical concepts. It is these links that underpin the impression that it is not a coincidence that the semanticist’s notion should be expressed by the word “truth,” and that in some sense the semanticist is indeed talking about truth as we know it pre-theoretically. There are a number of ways in which such links can be construed. Let me outline three fairly obvious ones. First, those semanticists who are comfortable with propositions can use the sentential truth-predicate to define the content or proposition expressed by a sentence in a context. If we think of propositions as sets of possible worlds, this is simple: (1) The proposition expressed by a sentence s in a context c = the set of possible worlds w such that TrueS(s, c, w). If our pre-theoretical concept of truth applies to the contents of belief and speech in an intuitive sense, then all we need to do is to claim that the contents of belief and speech are propositions in the sense of sets of possible worlds. A proposition is TrueP at a world just if that world is a member of it. So we have an obvious reductive principle that links “TrueS” with pre-theoretic truth: (P) What would be said by a sentence s, were it to be uttered in a context c, is true just if TrueS(s, c, @).5 Secondly, the same reduction is available to those who do not wish to identify propositions with sets of possible worlds, such as those who think of propositions as structured entities. In this case, propositions are too finely individuated to comply with (1). Nevertheless, champions of structured propositions can accept something weaker as a constraint on the proposition expressed by a sentence in a context: (2) The proposition expressed by a sentence s in a context c is TrueP at a world w just if TrueS(s, c, w). Again, if the proponent of structured propositions identifies the intuitive contents of speech with propositions as constrained in (2), then the same reductive principle (P) is available to her. Thirdly, those who are not comfortable with propositions (or with their role in semantics) will have to pursue a slightly different strategy. These theorists will presumably deny that the ordinary truth notion is applicable to contents of speech or propositions (unless they want to push an error theory about ordinary truth). When it seems like someone is applying truth to a content (as in “What he said is true.”) the truth-bearer is in fact an utterance event. On this view, there is a 5. I am writing “true” in lower case without superscript in order to indicate that this is meant to be the ordinary truth-predicate. It is worth mentioning that I am simplifying somewhat by just assuming that contexts, as they are employed in a semantic theory, are the sort of thing “in” which a sentence can be uttered.

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pre-theoretic notion of utterance truth which is linked to TruthS. An utterance of a sentence is true just if the sentence is TrueS at the actual world at the context of the utterance: (P*) An utterance of a sentence s in a context c is true just if TrueS(s, c, @). Principles like (P) and (P*), often implicitly, give content to natural language semanticists’ sentential truth-predicate and thereby give content to semantic theories that model natural languages.6 Both principles are meant to apply to declarative sentences only. However, they could be extended to the semantics of languages that contain non-declaratives—these can, for example, be treated as transformations from declaratives. Still, (P) and (P*) are at best extreme idealizations. In the case of (P), the most problematic aspect of this idealization is that it is assumed that there is a clear pre-theoretic sense in which utterances have unique contents, contents we pre-theoretically assess for truth, and contents that can be identified with propositions.7 This is problematic because natural language utterances often have multiple and diverse contents that all play a communicative role and can be assessed for truth. There is no clear pre-theoretic system for privileging a unique, literal content as the primary bearer of pre-theoretic truth. To give just one example, when Clinton famously uttered “I did not have sexual relations with that woman.”, was he speaking the truth? If we assume the Webster’s definition of “sexual relations” (as Clinton may well have done), thus ignoring the possibility of ambiguity, then there are at least two candidate contents to this utterance, namely that Clinton did not perform coitus with Lewinsky and that he did not engage in any sexual activities with her. The latter is false, the former true. Or consider an ironical utterance “Clinton did not have sexual relations with that woman.” Again, what is the content here? It is hard to see how a decision as to the content of such utterances can be made that is not motivated by theoretical considerations. This is in effect Grice’s strategy (1975). Grice makes no bones about the theoretical nature of his distinction between what is said and what is implicated (1975, 24–26). The way he draws the distinction is clearly guided by theoretical considerations. This is clear from the principle that what is said is close to the conventional meaning of the words used. It is even more clear from the way Grice draws a line between what is said and conventional implicatures, for here it can only be theoretical elegance or convenience that motivates the particular dividing line he draws. There are, of course, alternatives to Grice’s way of distinguishing the semantic content from other pre-theoretically accessible contents. Recent debates

6. For example, Kaplan (1977), Lewis (1975, 1980). 7. Cappelen and Lepore (1997, 2005) have done much to expose this simplification, and to show that natural language semantics cannot be founded on an intuitive notion of what is said in an utterance. However, their own solution (introduction of minimal contents) seems to throw the baby out with the bathwater, for there does not seem to be any pre-theoretic grounding for the minimal contents of utterances, let alone pre-theoretic judgments about their truth.

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on the notion of “what is said” (see, e.g., Carston 2002, Saul 2002, Bach 2001, Recanati 2004, Wilson and Sperber 2001) concern this very issue. Thus, sentential truth, as it is employed in semantic theories, can be viewed, with some good will, as a theoretical concept that is used to explicate a refined version of pre-theoretic propositional truth. Proponents of (P*) will have to refine any pre-theoretic notion of utterance truth in a similar fashion. 3. RELATIVIST SEMANTICS AND ORDINARY TRUTH The situation is more complex for the relativist. At first sight, the problem seems to have the same shape: sentential TruthS seems to be a four-place relation relating a sentence with a context, a world and a standard of taste, while ordinary truth is a one-place property of speech (and belief) contents. However, a reduction of ordinary truth via a principle in the style of (P) to TruthS is not available to the relativist. Let me explain why. As we saw, the strategy of the standard semanticist (proposition-friendly version) is to say that an utterance of a sentence in a context expresses a proposition, namely a proposition that is TrueP at exactly those possible worlds for which the sentence at the context and the actual world receives the value TrueS. Ordinary truth could then in turn be seen as TruthP at the actual world. Thus, the one-place property of ordinary truth is analyzed as the one-place complex property resulting from saturating the world-variable of TruthP with the actual world. The relativist can follow the standard semanticist in saying that sentences express propositions at contexts. However, according to the relativist, TruthP is not a two-place relation but a three-place one, for according to the relativist, a proposition can vary in truth-value not only from possible world to possible world but also from one standard of taste to another. The corresponding move for the relativist would therefore be to saturate both the world variable and the standard of taste variable in the three-place relation of TruthP, thus obtaining a relational one-place property with which ordinary propositional truth can be identified. This, however, does not seem to be possible. Suppose first, that the relativist identifies ordinary propositional truth with TruthP at the actual world and at a particular standard of taste, which we may call “the privileged standard”: (R1) What is said by an utterance of a sentence s in a context c is true iff TrueS(s, c, 〈@, the privileged standard〉). This is clearly not acceptable to the relativist. For if ordinary truth follows some privileged standard then the relativization to standards does nothing to help with the perceived lack of objectivity of matters of taste, and specifically with alleged cases of faultless disagreement (see Section 1 above). There are other ways to define an n-place relation in terms of an n + 1-place relation. Let us compare an example.We could use the two-place predicate “x loves y” to define at least the following one-place predicates: “the King of Spain loves y,” “x loves the king of Spain,” “There is an x such that x loves y,” “There is a y such

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that x loves y,” “x loves x’s mother.” (Thus defining respectively the properties of being loved by the King of Spain, loving the King of Spain, being loved by someone, loving someone and finally the property of loving one’s mother.) The relativist has similar options in trying to reduce ordinary truth to TruthP (or TruthS). However, none of them is viable. For example, if the relativist were to quantify over the standard of taste variable—truthP with respect to some/all standards and the actual world—the problem would again be that our apparent cases of faultless disagreement will never be faultless. It may appear more promising to say that each utterance context determines a unique standard of taste (say, the standard of taste of the speaker of the context), and to identify ordinary truth of what is said by an utterance of s in c with the TruthS of s at c, at @ and with respect to the standard of taste determined by c (thus mimicking the property of loving one’s mother): (R2) What is said by an utterance of a sentence s in a context c is true iff TrueS(s, c, 〈@, the standard determined by c〉). This would allow the relativist semanticist to maintain that sometimes an utterance of “That coffee is tasty.” and a reply “That coffee is not tasty.” are both without fault in the sense that both may be TrueS with respect to the standards respectively determined by the contexts in question. However, the semanticist would now be forced to say that both what was said by the first utterance is true, namely that that coffee is tasty, and that what was said by the reply is also true, namely that that coffee is not tasty. But how can it be true both that the coffee is tasty and that it is not? Assuming merely disquotational properties of ordinary truth, this would commit the relativist semanticist to an outright contradiction. If the ordinary truth-predicate could be treated as implicitly two-place, that is, as implicitly expressing a relation between speech contents and standards of taste, this might present a chance to identify the relation of TruthP at the actual world with it. However, this would seem to go against the spirit of relativism: one of the perceived advantages of relativism over contextualist rivals is that the relativist does not need to postulate hidden argument places in predicates of personal taste and other candidates for relativist treatment. So making this sort of maneuver in the metalanguage would be unattractive. In the absence of any further reductive proposals (and I personally cannot see any more promising options) we have to conclude that the relativist semanticist cannot offer an analogous reduction of ordinary truth to TruthS. How bad is this? Does it mean that the semantic TruthS-predicate remains somehow ungrounded? My answer will be that there is no problem, because (a) the semantic TruthS-predicate can be otherwise grounded; and (b) because some noncoincidental links with ordinary truth remain in place. In the remainder of this section, I shall explain both points. Let us return to principle (R2). (R2) suggests that an utterance says something true just if the proposition expressed is true with respect to the standard of taste determined by the context of utterance. To fix ideas, let us imagine that the standard of taste “determined” by a context is the utterer’s standard of taste. I

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showed that if truth is disquotational, this must be false. However, we can assess, and we do seem to assess, utterances or what they say in the way suggested by the right hand side of (R2). In other words, we can and do assess people’s assertions and beliefs with respect to their own standards. By this criterion of assessment, if I say that the coffee is tasty, and it is tasty by my own standard (i.e., I would respond in a certain favorable way to tasting it), then I achieve success, while if you say that the coffee is tasty, and it is not tasty by your different standards, then you fail to achieve this type of success. This form of assessing what people say (and believe) is natural and important. However, as I have shown, “truth” is not (or should not be) the term we use to describe success of this sort. For “true” in the ordinary sense supports the principle that every instance of the schema “it is true that p only if p” is acceptable. However, there is no bar to recognizing this form of assessment under a different name and to link it to our theoretical notions of TruthS and TruthP. The form of assessment in question is linked to competence in belief acquisition, that is, the correct application of concepts. Competence with a concept involves applying the concept only under certain conditions. In the case of some concepts, such as that of tastiness, these conditions will be sensitive to individual features of the believer, such as preferences, standards, gustatory responses. Thus, whether it is correct for some believer to judge a thing to be tasty will depend on certain individual properties of that believer, so that one and the same object may correctly be judged to be tasty by one believer while it is correctly judged not to be tasty by another, even where both have access to the same evidence. Objective concepts, such as being filtered, will not be like this: here it is an a priori matter that if one thinker believes the coffee to be filtered, and the other believes it not to be, then one of the two beliefs is incorrect. Correctness in this sense of beliefs can be extended to assertions, or to utterances of assertoric sentences: an assertion (or utterance of an assertoric sentence) is correct to the extent to which it is (or would be) correct for the utterer to believe the proposition asserted. What I would like to suggest is that TruthS can be grounded by linking it precisely to correctness in the sense discussed. The resulting explicative principle might look like this:

(R3) An utterance of a sentence s in a context c is correct iff TrueS(s, c, 〈@, the standard determined by c〉).

This means TruthS (and TruthP) are not involved in any direct reduction of ordinary truth. Thus, according to the relativist, the theoretical notion of TruthS employed in semantic theories is not grounded in our pre-theoretic notion of truth, as the standard semanticist maintains, but rather it is grounded in a different pretheoretical notion of correctness. Is the word “TrueS” a misnomer then, in that it suggests a connection with truth that does not exist? Not quite. For on most accounts of ordinary truth, correctness (the norm linked via (R3) to TruthS) coincides largely with truth. Let me briefly show this for two types of accounts of truth, deflationary and objective accounts.

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Let us first consider deflationary accounts of the ordinary concept of truth.8 According to such accounts, it is the point of the concept of truth to yield, when applied to any proposition, another proposition that is necessarily equivalent to the original one. Similarly, the point of the ordinary truth-predicate is to provide a means for expressing such a concept, so that the truth-predicate applied to any that-clause yields a sentence that expresses a proposition equivalent to the one referred to by the that-clause.9 If our relativist is a deflationist about truth then she will deny that the correctness of an utterance amounts to the truth of what is said by it. To see this consider nonobjective propositions, that is, propositions whose truth-value varies with an extra parameter, such as a standard of taste. Take, for example, the proposition I express when I utter the sentence “That coffee is tasty.” on some occasion. In such a case, the semanticist’s assessment as to truth of what I said and her assessment as to the correctness of my utterance can come apart. It may be that she agrees with what I said (that that coffee is tasty) but believes that it is not the view I should have given my standards and preferences. Conversely, it could be that she disagrees with what I said but believes that I expressed the view that it is right for me to have given my standard of taste. In either of these cases, her judgment that what I said is true, and her judgment that what I said is correct will come apart. However, this will only be the case with nonobjective propositions, that is, propositions whose TruthP-value varies with the extra parameter. For if a proposition is invariant in TruthP-value across all standards of taste (e.g. the proposition I might express on the same occasion by “That coffee is filtered.”), then judging what someone said to be true is tantamount to judging their utterance to be correct. For it will not make a difference which standard of taste we consider relevant. So it is not, according to the deflationist relativist, a complete coincidence that formal semantics should employ the word “true.” For if we were working out a semantics for an objective fragment of a language, nothing would stop us from identifying the truth of what someone says in an utterance with the TruthS of the sentence used in the context at @ and with respect to the relevant standard of taste. In other words, in the objective range, the correctness of an utterance, the notion linked reductively to TruthS, coincides with the truth of what is said. Secondly, consider objective theories of truth, such as standard correspondence theories.A relativist semanticist who believes that ordinary truth is objective will have to say that nonobjective propositions are not apt for evaluation as true or false, that is, that there are truth-value gaps. On this view, truth will coincide with correctness in the objective range, for if it is correct with respect to one standard of taste to believe an objective proposition, then it is correct with respect to all standards. Thus again, it is no accident that semanticists have chosen the word “true,” for as long as we consider an objective fragment of a language, there is a

8. My own view is that there are two ordinary notions of truth that we regularly employ, and that the predicate “true” is ambiguous between a deflationary and an objective-substantial reading. See Kölbel (2008a) for a detailed exposition of this view. 9. See Horwich (1998) for one exposition of such an account.

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straightforward link, in the style of (P) above, between TruthS (and TruthP) and truth.10 In summary, relativistic semantics, just like the standard semantics it hopes to complement or succeed, employs a sentential notion of TruthS. This notion expresses a relation sentences bear to contexts, possible worlds and standards of taste (or whatever else the extra parameter may be in each case). It may also employ a commensurate notion of propositional TruthP, which relates (relativistic) propositions to possible worlds and standards of taste (or whatever else the additional parameter may be in each case). Unlike standard semanticists, relativists should not postulate a straightforward reductive principle that explicates truth in the ordinary sense in terms of TruthS or TruthP. Rather, the relativist should instead ground the semantic truth-predicates “TrueS” and “TrueP” by linking them to a different, individualized, notion of correctness. However, this does not mean that there is no connection at all between ordinary truth and the semantic notions of TruthS and TruthP. Rather, the grounding links exploited by the standard semanticist continue to hold as long as we restrict ourselves to objective propositions only. Thus there remains a sense in which the relativist’s semantic TruthS-predicate can be properly called a “truth-predicate,” and in which the relativist’s semantics can be properly called “truth-conditional.”11 4. ISSUES OF COMMENSURABILITY There is one related issue I would finally like to discuss. This concerns the relationship between the relativist’s semantic notions of sentential TruthS and propositional TruthP on the one hand, and the standard semanticist’s on the other. Let’s introduce new labels to distinguish relativistic and standard notions: “TruthS4” for the relativist’s four-place sentential truth notion and “TruthS3” for the standard theorist’s three-place sentential truth notion. Similarly “TruthP3” for the relativist’s threeplace propositional notion of truth and “TruthP2” for the standard theorist’s twoplace propositional notion of truth. The question I want to address, then, is whether standard semantics and relativistic semantics can in any way be seen as addressing the same topic, that is, whether, when the relativist is specifying conditions for the TruthS4 of some sentence, she can be seen as disagreeing or agreeing with the standard semanticist, who is specifying the conditions for the TruthS3 of the sentence. If there can be no agreement or disagreement, then we may have to conclude that relativistic and standard semantics are incommensurable, and that there is no good sense in which they address the same questions. In that case, the relativist will have to claim that standard semantics is in some sense radically mistaken, in that it 10. My considerations here have concerned the ordinary notion of truth employed by the semanticist herself, that is, expressed by a meta-language truth-predicate. The same accounts can naturally also be applied to a truth-predicate that is part of the object-language, that is, the language the semanticist is describing. One can also introduce an object-language counterpart to the metalinguistic “correct” that I have been discussing. 11. There is of course another sense in which the relativist’s theory is properly truthconditional: it continues to exploit the characteristic truth-conditional formal means of explaining the compositional structure of natural languages.

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employs an empty concept of TruthS3 to which nothing in reality corresponds. I shall be arguing that the relativist need not view standard semantics in this way. Rather, the relativist should view standard semantics as a special case of the more general relativistic semantics. I shall make my case by considering two other cases of potential incommensurability and comparing them to the case at hand. Let us first consider the classic question of the incommensurability between Newton’s mechanics and Einstein’s relativity theory. A good point of comparison are the respective notions of simultaneity: Newton employs a two-place notion of simultaneity, so that it is an absolute matter whether two events are simultaneous, whereas in Einstein’s theory, the simultaneity of two events depends on a further factor, namely on a frame of reference. How does Einstein’s three-place notion of simultaneity3 relate to Newton’s two-place notion of simultaneity2? According to one view, Newton’s notion was empty, because there just is no two-place relationship of simultaneity2. Thus Einstein needed to make a radically new start, introducing a new three-place notion of simultaneity3 that does correspond to a relation that has real instances. Here is an alternative view: what Einstein discovered when he discovered the three-place relation of simultaneity3 was a generalization of Newton’s notion of simultaneity2. Thus, he discovered that mostly, when Newton was speaking about the simultaneity2 of two events, what he meant was that these events were simultaneous3 with respect to this frame of reference. In other words, Newton’s simple two-place notion was discovered by Einstein to be in fact a complex or derived two-place notion. There may well have been isolated cases where Newton was inadvertently employing simultaneity2 when in fact he should have used the more differentiated notion of simultaneity3. In those cases, Newton was simply in error about simultaneity3 with respect to this frame (= simultaneity2). Now, I understand that the problem with the alternative view, as nice as it seems, is that Newton’s notion of simultaneity2 cannot be interpreted as simultaneity3 with respect to some particular frame of reference. The reason for this is that Newton claimed that absolute time flows equably and without relation to anything external, which suggests that there is no more than one legitimate function that gives the temporal relations between events. Thus, Newton at least implicitly assumed simultaneity to be a simple two-place relation. Thus, so the objection goes, it would be a historical distortion to interpret Newton’s claims regarding simultaneity2 to be claims regarding Einstein’s simultaneity3-with-respect-to-this-frame-of-reference. Moreover, it might be argued that the commensurability view outlined above illegitimately plays down those instances where Newton’s employment of simultaneity2 can only be interpreted as simultaneity3-with-respect-to-this-frame-ofreference at the cost of attributing error to Newton. For these cases are not isolated uses. For example, I understand that Newton and contemporaries entertained the possibility of gravity traveling infinitely fast, and that there could be arbitrarily high velocities, possibilities that would be incoherent under an interpretation of simultaneity2 as simultaneity3-with-respect-to-this-frame-of-reference.12 12. This and the previous paragraph draw heavily on help I received from Carl Hoefer, to whom I am very grateful.

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Given that the commensurable interpretation would generate these incoherencies we would need a good reason to say that Newton had the concept of simultaneity3-with-respect-to-this-frame-of-reference but was quite radically mistaken about it, rather than that he had the empty concept of simultaneity2, and was at least conceptually right. What would be the reason for saying that Newton did somehow latch onto simultaneity3-with-respect-to-this-frame-of-reference given that this hypothesis renders him incoherent? This is not the place (or the author) to decide the classic issue concerning the transition from Newton to Einstein. However, I believe it is instructive to compare this case with one that is much closer to the one here under consideration. Consider the transition between an extensional semantic theory for a language and an intensional one that results from adding some intensional operators to the original language and correspondingly expanding the semantics. Let us say that the extensional semantic theory describes extensional language L1, which for simplicity we can assume to be context-insensitive. The extensional semantics thus defines a one-place sentential truth-predicate “TrueS1.” The intensional semantic theory describes a language L2 that results from adding the operators “Necessarily” and “Possibly” to L1. Now, the addition of the intensional operators will require a change in the semantics for all the L1 expressions in L2, which follows the following model. When the intensional semantics has a clause of the following form: (C) For all a, P: if a is a singular term and P is a predicate, then ‘P(a)’ is TrueS1 if and only if the referent of a is a member of the extension of P.13 then the extensional semantics will have a corresponding clause of this form (C*) For all a, P, w: if a is a singular term and P is a predicate and w is a possible world, then ‘P(a)’ is TrueS2 at w if and only if the referent of a is a member of the extension of P in w. The only other change in the extensional semantics will be the addition of clauses for the intensional operators: (Nec) For all a, w, w*: if a is a sentence and w is a possible world, then ‘N(a)’ is TrueS2 at w if and only if a is TrueS2 at all possible worlds w* accessible from w. (Pos) For all a, w: if a is a sentence and w is a possible world, then ‘P(a)’ is TrueS2 at w if and only if a is TrueS2 at some possible world w* accessible from w. Now, what should we say about the relationship between the intensional and the extensional theory? One line of reasoning would lead us to say that despite a certain structural similarity, the two theories are describing completely disjoint 13. Single quotes are used as corner quotes here.

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phenomena. The expressions that are “shared” between L1 and L2 are merely shared in the sense that they are phonetically similar. They are nevertheless different expressions, because their semantic properties are described in incommensurable ways using the predicates “TrueS1” in the extensional case and “TrueS2” in the intensional case. This description of the situation would seem appropriate given what I have said so far, even if it is perhaps in some respects unhelpful. However, let us add the following assumption to our scenario: both the extensional semantics and the intensional semantics were aimed at providing semantic accounts of fragments of the very same language L. The extensional theory made a start with fragment L1, and the intensional theory then attempted a semantics for the slightly greater fragment L2. I believe that in this case the correct view is that the intensional theorist’s TruthS2-predicate is a generalization of the extensional theorist’s TruthS1pedicate, and that the intensional theory merely expands the extensional theory. Here is how TruthS2 can be seen as a generalization of TruthS1: A sentence is TrueS1 just if it is TrueS2 at the actual world. If we read all the occurrences of “TrueS1” in the extensional semantics as “TrueS2 at @,” then we can see the intensional theory as merely adding extra information to the extensional theory—information about the extensions of expressions in non-actual worlds and information about the two new expressions, the operators “N” and “P.” All the information given by the extensional theory is preserved in the intensional theory. In the case of Newton, Newton’s implicit commitment to the absoluteness of simultaneity prevented us from easily interpreting his uses of “simultaneous2” as expressing the complex property of simultaneity3 at this frame of reference. In the case of the extensional theory no analogous commitment prevent us from taking the extensional theorist to be expressing the property of TruthS2 at @ when she uses “TrueS1.” Another reason against this reading of Newton was the attribution of significant error and incoherence engendered by the reading. By contrast, treating the intensional theory as a generalization of the extensional theory does not force us to attribute any errors to the extensional theorist. What I want to suggest is that a benevolent observer will equally view the relativist semanticist’s theory as a mere extension of standard semantic theories, and that TruthS3 at a context c and at a world w should be viewed as TruthS4 at c and at w with respect to some (or all) standards of taste. Such an identification will be completely unproblematic as long as the standard theory does not concern any of the expressions for which the relativist claims to need a relativistic semantics, that is, in this case predicates of personal taste construed as they are construed by the relativist. In this case, the relativist’s theory is plausibly seen as merely adding new information to the standard semantic theory. It may be objected that the standard semanticist’s object language does contain predicates, such as “is tasty,” that the relativist claims to vary in extension not just with possible worlds but also with standards of taste. There is, so the objection goes, genuine disagreement about the best semantics for these expressions, and the relativist cannot be seen as merely adding information to a standard theory, while accepting everything the standard theorist said within her own framework.

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There is some truth to the claim that there is genuine disagreement concerning the disputed range of expressions (here: taste predicates) between the relativist and some proponents of standard semantics, namely those proponents who advocate either an absolutist view of predicates of personal taste, or those who advocate a contextualist view.14 However, this does not prevent the relativist (or a reasonable observer) from viewing the relativist as continuing and expanding the work of standard semantics. For the relativist can simply claim that he rejects those parts of the standard semantics that concern the disputed expressions, and that she agrees with the remainder. The relativist’s theory can then be seen as a mere expansion and generalization of that part of the standard semantics that she agrees with, namely the parts concerning the objective fragment of the language. One final question remains. In the case of Newton, one problem with interpreting his notion of simultaneity2 as simultaneity3 with respect to some particular frame of reference was that Newton had implicit commitments that were in conflict with this. Similarly, it might be claimed that standard semanticists are committed to the absoluteness of propositional truth, so interpreting them as having had in mind a different notion would be inaccurate. I cannot at this moment draw on a comprehensive survey of what standard semanticists have claimed. However, it seems to me unlikely that we will find uniform evidence that the main protagonists of truth-conditional semantics have been taking it as an essential part of their semantic notions of truth that truth-values do not vary with standards of taste. Even in a theorist like Frege, where the commitment to the absoluteness of propositional truth is quite clear, we can find other commitments that might put pressure on the absoluteness of propositional truth, such as the view that propositions (thoughts) are the relata of the belief relation and other propositional attitudes. Kaplan, another important truth-conditional semanticist, who takes himself to be reconstructing a Fregean view, argues against the absoluteness of propositional truth (1977). To conclude this section, there is no need to view the relativist’s semantic project as a radical departure from the project standard semanticists have been pursuing. On the contrary, the most plausible view of relativistic semantics is as a generalization and expansion of non-relativistic semantics.15 REFERENCES Bach, Kent. 2001. “You Don’t Say.” Synthese 128: 15–44. Cappelen, Herman, and Ernie Lepore. 1997. “On an Alleged Connection between Indirect Quotation and Semantic Theory.” Mind and Language 13: 278–96. ———. 2005. Insensitive Semantics. Oxford: Blackwell. 14. There was until recently very little comment by standard semanticists on the proper treatment of taste predicates, so a more realistic description of the dialectical situation would be to say that relativists and contextualists disagree on how to expand a standard semantic theory to accommodate taste predicates. 15. I would like to thank the participants of the workshop on Relativizing Utterance Truth in Barcelona in 2005, where I first presented material on this topic, for their comments and help. I’d also like to thank José Diez, Manuel García-Carpintero, Carl Hoefer, Sanna Hirvonen and Sven Rosenkranz for discussion and/or written comments.

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Carston, Robyn. 2002. “Linguistic Meaning, Communicated Meaning and Cognitive Pragmatics.” Mind and Language 17: 127–48. Egan, A., Hawthorne, J., and Weatherson, B. 2005. “Epistemic Modals in Context.” In Contextualism in Philosophy, ed. G. Preyer and G. Peter. Oxford: Oxford University Press. Grice, H. P. 1975. “Logic and Conversation.” In Syntax and Semantics, vol. 3: Speech Acts, ed. P. Cole and J. Morgan. New York: Academic Press. Reprinted in Grice 1989, 22–40. ———. 1989. Studies in the Way of Words. Cambridge, MA: Harvard University Press. Horwich, Paul. 1998. Truth. Oxford: Oxford University Press. Kaplan, David. 1977. “Demonstratives.” In Themes from Kaplan, ed. Almog et al., 481–563. Oxford: Clarendon Press, 1989. Kölbel, Max. 2002. Truth Without Objectivity. London: Routledge. ———. 2003.“Faultless Disagreement.” Proceedings of the Aristotelian Society 104 (October 2003): 53–73. ———. 2007. “How to Spell out Genuine Relativism and How to Defend Indexical Relativism.” International Journal of Philosophical Studies 15: 281–88. ———. 2008a. “ ‘True’ as Ambiguous.” Forthcoming in Philosophy and Phenomenological Research 77. ———. 2008b. “The Evidence for Relativism.” Forthcoming in Synthese. ———. 2008c. “Motivations for Relativism.” In Relative Truth, ed. Manuel García-Carpintero and Max Kölbel, 1–38. Oxford: Oxford University Press. Lasersohn, Peter. 2005. “Context Dependence, Disagreement, and Predicates of Personal Taste.” Linguistics and Philosophy 28: 643–86. Lewis, David. 1975. “Languages and Language.” Minnesota Studies in the Philosophy of Language 7:3–35. Reprinted in Lewis 1983, 163–88. ———. 1980. “Index, Context, and Content.” In Philosophy and Grammar, ed. Stig Kanger and Sven Öhman, Dordrecht, The Netherlands: Reidel. Reprinted in Lewis 1998, 21–44. ———. 1983. Philosophical Papers, vol. 1. Oxford: Oxford University Press. ———. 1998. Papers in Philosophical Logic. Cambridge: Cambridge University Press. MacFarlane, John. 2003. “Future Contingents and Relative Truth.” Philosophical Quarterly 53: 321–36. ———. 2005a. “Making Sense of Relative Truth.” Proceedings of the Aristotelian Society 105: 321–39. ———. 2005b. “The Assessment Sensitivity of Knowledge Attributions.” Forthcoming In Oxford Studies in Epistemology 1, ed. Tamar Szabo Gendler and John Hawthorne, 197–233. Oxford: Oxford University Press. ———. 2008a. “Nonindexical Contextualism.” Forthcoming in Synthese. ———. 2008b. “Truth in the Garden of Forking Paths.” In Relative Truth, ed. Max Kölbel and Manuel García-Carpintero, 81–102. Oxford: Oxford University Press. ———. Forthcoming. “Epistemic Modals are Assessment-Sensitive.” In Epistemic Modals, ed. Brian Weatherson and Andy Egan. Oxford: Oxford University Press. Recanati, François. 2004. Literal Meaning. Oxford: Clarendon Press. Saul, Jennifer. 2002. “Speaker Meaning, What is Said and What is Implicated.” Nous 36: 228–48. Wilson, Deirdre, and Dan Sperber. 2001. “Truthfulness and Relevance.” Mind 111: 583–632.

Midwest Studies in Philosophy, XXXII (2008)

Being and Truth PAUL HORWICH

1. INTRODUCTION Our belief that Mars is red is true—owing (one might think) to the existence of a certain bit of reality, namely, Mars’ being red. In other words, the belief is made true by something like a fact. And presumably we can generalize—presumably any belief, any statement, and any proposition, if true, is made true by the presence, somewhere in the universe, of the appropriate things, or events, or states of affairs, or facts. Such tempting thoughts are the beginnings of a branch of metaphysics known as truthmaker theory, whose primary aim is to work out, for each of the many kinds of proposition that we believe and assert, which entities would have to exist for such propositions to be true. What makes it true, for example, that either Mars is red or pigs can fly? Is it best to answer by postulating the existence of the complex fact that either Mars is red or pigs can fly, or should we invoke Occam’s razor and make do with Mars’ being red? And what sorts of truthmakers are needed for negative propositions (e.g., that Mars is not inhabited), for general propositions (e.g., that every planet has an elliptical orbit), for conditionals (e.g., that if Mars did have inhabitants, we would be able to detect them), etc.? Those philosophers engaged in this form of inquiry believe that it promises to deliver a rich body of metaphysical knowledge—valuable, not only in itself, but because of its potential to yield a variety of important insights: into, for example, the nature of truth (vindicating a version of the correspondence theory), and into the viability of reductive programs (such as phenomenalism and behaviorism). Midwest Studies in Philosophy: Truth and its Deformities Volume XXXII Editor by Peter A. French and Howard K. Wettstein © 2008 Wiley Periodicals, Inc. ISBN: 978-1-405-19145-6

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My plan for the present paper is to investigate whether these hopes are realistic. For the sake of concreteness and ease of exposition, I will often allude to David Armstrong’s particular execution of the project. But since my appraisal will focus on the fundamentals of truthmaker theorizing, it will bear equally on the many alternative forms of it that can be found in the literature.1 2. TRUTHMAKER THEORY A theory of truthmaking is a theory of the relation ‘x makes y true’. It must therefore address the following questions, among others: (Q1) What are the entities, y, that are made true? (Q2) What are the entities, x, that make things true? (Q3) Under what conditions does something of the latter kind succeed in making true something of the former kind? That is, what is the truthmaking relation? (Q4) What makes true a simple contingent claim, for example, that Mars is red? How about other logical forms such as disjunctions, negations, counterfactuals, etc.? (Q5) Does every truth have at least one truthmaker? And does every statement’s set of potential truthmakers differ from every other statement’s set of potential truthmakers? (Q6) What is it for x to be a minimal truthmaker of y—a truthmaker of y such that nothing less than x will do? And does every truth have a minimal truthmaker? These questions tend to be answered along the following lines: (A1) The entities made true are propositions (or—for those theorists wary of propositions—sentences, utterances, states of believing, or acts of assertion). (A2) The candidate truthmaking entities are ‘things’ in the broadest sense of the word. They may be states of affairs, events, tropes, facts, physical objects, or abstract objects—anything that exists. (A3) x makes y true ≡ x necessitates the truth of y 1. There are too many truthmaker theories for me to consider them all (or even mention them). But some influential contributions to the enterprise have been—Ludwig Wittgenstein’s Tractatus Logico-Philosophicus (London: Routledge & Kegan Paul, 1922); Bertrand Russell’s “The Philosophy of Logical Atomism,” reprinted in Russell’s Logical Atomism, ed. D. Pears (London: Fontana/Collins, 1972); Kevin Mulligan, Peter Simons, and Barry Smith’s “Truth-Makers,” Philosophy and Phenomenological Research 44 (1984): 210–55; John Fox’s “Truthmaker,” Australasian Journal of Philosophy 65 (1987): 188–207; John Bigelow’s The Reality of Numbers (Oxford: Clarendon Press, 1988); Charles Martin’s “How It Is: Entities, Absences and Voids,” Australasian Journal of Philosophy 74 (1996): 57–65; David Armstrong’s A World of States of Affairs (Cambridge: Cambridge University Press, 1997), and his Truth and Truthmakers (Cambridge: Cambridge University Press, 2004). (Armstrong thanks Martin for introducing him to the basic idea at some point in the 1950s).

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≡ x exists & 䊐(x exists → y is true) ≡ x’s existence entails that y is true2 (A4) The atomic proposition, 〈Mars is red〉, is made true by Mars being red (or by the redness of Mars, or by the fact that Mars is red, or simply by Mars itself).3 This instance of ‘being’ also makes true the disjunctive proposition, 〈Mars is red or pigs fly〉. General propositions, such as 〈All men are mortal〉, are made true (arguably) by isomorphic general facts. But such facts serve also as the truthmakers for negative propositions: for example, 〈Mars is not blue〉 is made true by the general fact that every property of Mars differs from blueness.4 (A5) Every truth has many truthmakers. This is the case because, if a certain thing makes a given proposition true, then so does whatever contains that thing. And different necessary truths can have just the same truthmakers. For example, ‘(2+3) = 5’ and ‘(2 ¥ 3) 〉 5’ are (according to Armstrong) both made true by the numbers 2, 3, and 5, and therefore by anything that includes them. (A6) x is a minimal truthmaker of y ≡ x makes y true, and no part of x makes y true ≡ [x makes y true & -($z)(z ⊂ x & z makes y true)] These points convey something of the flavor of the truthmaker research program; but further important features of it will emerge as we proceed to consider its philosophical significance. 3. THE NATURE OF TRUTH Let us begin by looking at the idea that a decent theory of ‘making true’ (incorporating versions of the principles just listed) might lay bare the nature of truth, and might support the intuition that truth is some sort of ‘correspondence with reality.’ The simplest imaginable truthmaker theory (in the sense of ‘the one that is easiest to formulate’) states that the proposition that Mars is red is made true by the fact that Mars is red, the proposition that Mars is red or green is made true by the fact that Mars is red or green, and so on. On this account 〈p〉 is true ↔ The fact that p makes 〈p〉 true5 But, in addition, any truthmaker theorist worth his salt will agree that 〈p〉 is true ↔ ($x)(x makes 〈p〉 true) 2. This gets across Armstrong’s initial suggestion. But, as we’ll see (in footnote 11) he saw subsequently that modifications are needed in order to avoid counterintuitive consequences (e.g., that Mars makes it true that 1 + 2 + 3). 3. I use “〈p〉” as an abbreviation of “The proposition that p.” 4. This is one of Armstrong’s ideas about how to deal with universally quantified propositions and negative propositions. But there are several alternative proposals in the literature. 5. For expository purposes I focus here and later on the idea that propositions are made true by facts. But the points apply equally well (except where explicitly indicated) to theories that focus on different truth bearers (e.g., utterances) and different truthmakers (e.g., states of affairs).

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Therefore, one can arrive at the following definition of truth: 〈p〉 is true ≡ ($x)(x = the fact that p)6 However, there are few advocates of the exceptionally simple truthmaker theory on which this account of truth is based. Armstrong rejects it, and so does almost everyone else in the business. For they regard it as ontologically extravagant—as postulating many more kinds of fact than are needed. For instance, it attributes the truth of 〈Mars is red or green〉 to the existence of a certain disjunctive fact—the fact that either Mars is red or Mars is green. But that’s not called for, they would say. For there is an entity to which we are already committed—namely, the truthmaker for 〈Mars is red〉—which will do a perfectly good job of making the disjunctive proposition true as well. Similarly, it is expected that there will be many other types of proposition whose truth will not require the existence of isomorphic facts, but for which simpler and independently needed truthmakers may be found. For this reason, each of the truthmaker theories favored in the literature is composed of a heterogeneous variety of complex principles. For any given type of proposition—atomic ones, negations, disjunctions, generalizations, counterfactuals, belief attributions, probability claims, etc.—each theory will have its own elaborate story about which alternative aggregations of facts (or entities of other kinds) would make true propositions of that type. Consequently, the account of truth implicit in such a theory—its specification of the conditions necessary and sufficient for different propositions to be true—will be very far from simple. But an ordinary person surely does not understand the word “true” by means of a morass of principles such as these. His mastery of the concept does not require him to deploy a theory of that kind. It seems far more plausible and charitable to regard any such theory as taking for granted our understanding of truth, rather than attempting to supply it, and as proceeding, with the help of that notion, to articulate a body of metaphysical claims. We must first grasp what truth is, and only then can we go on to say which entities are needed to make true all the various kinds of proposition there are. This is a liberating thought. For once we see a truthmaker theory as not aiming to articulate a concept of truth, but as already presupposing one, we are free to invoke the most plausible account of that concept that we can find, and to interpret any proposed truthmaker theory accordingly. And the most plausible account of truth is deflationary:—it’s the idea that there is nothing more to the concept than our taking “〈p〉 is true” to be equivalent to “p.”7 6. One might complain that an adequate theory ought surely to capture such fundamental features of truth as that: 〈Mars is red〉 is true ↔ Mars is red But this demand could be accommodated by adding the following principle concerning facts: ($x)(x = the fact that p) ↔ p 7. It might be thought that even if the deflationary equivalence schema provides the best account of our concept of truth, still, truthmaker theory might supply the best account of the

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An important merit of this idea, besides its theoretical economy, is its capacity to fully explain how we deploy our concept of truth. It takes the primary function of this concept to be that of enabling us to formulate certain generalizations, and it shows us how that function will be fulfilled. Consider, for example, the sentences, “Mars is red or it isn’t,” “If Einstein said that Mars is red, then Mars is red,” and “We should aim to believe that Mars is red, only if Mars is red.” These cannot be generalized in the normal way—merely by substituting a universal quantifier for a singular term.That method can be deployed only after the instances to be generalized have been transformed in light of the above equivalenceschema—into “〈Mars is red or its isn’t〉 is true,” “If Einstein said 〈Mars is red〉, then 〈Mars is red〉 is true,” and “We should aim to believe 〈Mars is red〉, only if 〈Mars is red〉 is true”). For we then are able to quantify, in the normal way, into singular term positions to get: “All instances of 〈p or not-p〉 are true,” “Whatever Einstein said is true,” and “We should aim to believe only what is true.” This is what is meant by calling the concept of truth “a device of generalization.” It follows that, appearances to the contrary, the principles at which we finally arrive are not really about truth. Rather, the substance, in each case, is the collection of its instances—none of which itself involves the notion of truth. From this perspective, the real content of a truthmaker theory lies in specific claims of the form p in virtue of x Truth is brought into the picture merely as an expressive device. It enables us to replace “p” by “〈p〉 is true” to get 〈p〉 is true in virtue of x that is 〈p〉 is made true by x And we can then quantify into the position of the schematic singular terms, “〈p〉” and “x,” in order to formulate such theses as Every proposition is made true by something and

property of truth. It might articulate the fundamental facts about that property—the facts from which all the other facts about truth should be explained. But the same simplicity considerations that favor deflationism with respect to our concept will also favor a deflationary view of the property. Arguably, all facts about truth are satisfactorily explained by a combination of instances of the equivalence schema and facts that do not explicitly concern truth. For elaboration and defense of this point of view, see my Truth, 2nd ed., (Oxford: Oxford University Press, 1998), 50–51.

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A disjunctive proposition is made true by the truth of either one of disjuncts No theory of truth itself is intended here.8 Thus truthmaker theory is not a theory of truth. It relies on that notion as a device of generalization (—thereby presupposing the equivalence schema—) in order to articulate a theory whose real concern is with facts of the form, “p in virtue of x.” 4. METAPHYSICAL KNOWLEDGE Even if we should not look to a truthmaker theory for accounts of either our ordinary conception of truth or of truth’s underlying nature—even if I am right in supposing instead that truth is captured by the schema, “〈p〉 is true ↔ p”—still the explanation of how all the various kinds of proposition are made true might nonetheless be expected to provide a valuable contribution to metaphysical knowledge. Thus the project of truthmaker theory might still seem to be worth pursuing. But even here there are considerable grounds for doubt. One of the central elements of such a theory is that a simple contingent proposition of the form 〈k is F〉 is made true by the fact that k is F.9 This could be extended into a general account,by supposing that any true propositions,〈p〉,is made true by the fact that p. But, as we have seen, truthmaker aficionados tend to reject that approach on grounds of ontological overindulgence. They tend to suppose that there is no need for such weird things as negative facts, or disjunctive facts, or counterfactual facts.And, from this point of view, interesting, nontrivial puzzles arise as to what the truthmakers could be for negations, disjunctions, counterfactuals, etc. Now we might wonder whether intuitions about which kinds of facts are ‘too weird’ to exist, are under rational control; and, if not, whether there could be any objective question as to which is the correct theory of truthmakers. For example, Armstrong cites with approval Greg Restall’s candidate for a truth that has no minimal truthmaker: namely, that there are infinitely many things.10 Here is the argument: Suppose it is true that there are infinitely many things. No totality of these things would be a minimal truthmaker of that proposition; because, in order to be any sort of truthmaker for it, a totality would have to be infinite; but then some of its parts would also be infinite, and would themselves suffice as truthmakers. 8. As noted by Wolfgang Künne (in his Conceptions of Truth (Oxford: Oxford University Press, 2003), 164), the above point was emphasized by one of the early Australian truthmaker theorists—namely, John Bigelow (in his The Reality of Numbers, 1988). The point is also made by David Lewis in his “Forget about ‘The Correspondence Theory of Truth’ ”, Analysis 61 (2001): 275–80. 9. NB footnote 5:—my focus on propositions being made true by facts is just for ease of formulation. The points obviously generalize to other bearers and makers of truth. 10. See G. Restall, “What Truthmakers Can Do for You.” Automated Reasoning Project, Australian National University, Canberra, 1995.

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But this reasoning rests on the assumption that ‘There being infinitely many things’ cannot be a truthmaking fact. (For such a truthmaker would not have any parts—so it would be minimal). And insofar as the assumption of the nonexistence of such a fact is a mere unargued-for intuition, why should we accept it? In response, it will be said—quite reasonably—that such ontological claims are not based on bare intuition. Rather, they are constrained by our concern to provide the best possible explanation of how all the true propositions come to be true—an explanation that will not postulate entities (e.g., negative facts) unless there turns out to be some theoretical need for them. This response is entirely adequate. However, its recognition of the crucial role of the notion of explanation in the foundations of truthmaker theory points us towards a serious defect in Armstrong’s original approach. For the analysis of ‘making k have property F’ that is implicit in his initial truthmaker theory is: k is made F by x ≡ x necessitates the F-ness of k ≡ x exists & 䊐(x exists → k is F) ≡ x’s existence entails that k is F But this cannot be what is really needed. For it fails to capture the idea (which he and the other truthmaker theorists rightly wish to capture) that when k is made F by x, then k is F in virtue of x; that is to say, k is F because of x; or in other words, there is an asymmetric explanatory dependence of k’s being F on the existence of x. Because of this defect, the original account of ‘making’ has various counterintuitive consequences. It entails, for example, that Mars is made red by the fact that Mars is red; that The state of affairs of 〈Mars is red〉’s being true makes it true that Mars is red; and that Mars is made to exist by Mars. These absurdities stem from the supposition that making is a matter of mere necessitation. Clearly, a better definition is needed.And a natural alternative, as just indicated, is to give one in terms of the concept of explanation. Something along the following lines would be a reasonable start: k is made F by x ≡ k is F because of x

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≡ k is F because x exists ≡ x exists, and there is an explanatory deduction from 〈x exists〉 to 〈k is F〉11 In which case—substituting “〈p〉” for “k,” and “true” for “F”—we come to: 〈p〉 is made true by x ≡ 〈p〉 is true because of x ≡ 〈p〉 is true because x exists ≡ x exists, and there is an explanatory deduction from 〈x exists〉 to 〈〈p〉 is true〉. 5. THREE OBJECTIONS This improvement in our account of what truthmaking is puts us in a better position to assess the prospects for a satisfactory truthmaker theory. Indeed it enables us to expose some fundamental difficulties. Earlier we reviewed the reasons of ontological extravagance that are typically cited as grounds for restricting the general schema If 〈p〉 is true, then it is made true by the fact that p But we are now equipped to argue that none of its instances is correct—to argue that it is never possible for the fact that p to make true the proposition that p. And if this conclusion is right, the chances of there being any decent truthmaker theory begin to look rather slim. Three interrelated considerations lead to that potentially devastating conclusion. In the first place, according to our ordinary (and scientific) practice of explanation-giving, if we want to explain, for example, why it is that 〈Mars is red〉 is true, we first deduce that Mars is red from some combination of laws of physics and initial conditions: that is, we establish Mars is red because L1 & . . . & Lj & I1 & . . . & Ik

11. Armstrong has come to appreciate that the familiar notion of necessitation is too weak for his purposes. As mentioned above (in footnote 2), reliance on that notion yields obviously incorrect results; so he proposes (in Truth and Truthmakers, pp. 10–12) to invoke restricted notions of ‘necessitation*’ and ‘entailment*’, for which, by definition, those difficulties (and others) do not arise. But of course this is simply to acknowledge the problem; it does not constitute even the beginnings of a solution to it. My suggestion is that the solution is to define ‘making’ in terms of explanation. Notice, however, that the needed notion is not that of ‘causal explanation’, but rather that of ‘constitutive explanation’. Our concern is with the x that underlies or grounds k’s being F—the x in virtue of which k is F. Notice, also, that in order for x to make k have F-ness it is not enough that k’s being F supervene on the existence of x. For the latter relation (which is a matter of counterfactual dependence) is compatible with x’s existence supervening on k’s being F. Thus the explanatory asymmetry conveyed by ‘making’ is not captured by considerations of supervenience.

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And then—invoking the biconditional 〈Mars is red〉 is true ↔ Mars is red —we go on to deduce that 〈Mars is red〉 is true, and hence to explain why it’s true. Consequently 〈Mars is red〉 is true because Mars is red12 And, in general 〈p〉 is true because p13 Moreover, and for exactly parallel reasons, the schematic relation between p and the fact that p will be There exists such a thing as the fact that p, because p rather than the other way around. For we explain the fact that p exists, not by deducing it directly from laws and initial conditions. But by first deducing that p (thereby explaining why it is that p), and by then invoking the biconditional, ‘The fact that p exists ↔ p,’ to deduce that the corresponding fact exists. Thus ‘the fact that p exists’ is always less fundamental in our explanatory deductive hierarchy than ‘p’ is. Therefore, we have no route from the above-derived 〈p〉 is true because p to 〈p〉 is true because the fact that p exists Yet that is what we would need in order to be able to conclude that 〈p〉 is made true by the fact that p. 12. This paragraph repeats a line of thought from the first edition of my Truth (Oxford: Blackwell, 1990), chap. 7, 110–12. Crispin Wright (in his Truth and Objectivity (Cambridge, MA: Harvard University Press, 1992), p. 27) has objected that the argument shows merely that what explains why Mars is red also explains why it is true that Mars is red—which does not suffice for my conclusion. But the structure of the latter explanation is, first, to deduce that Mars is red (from initial conditions and laws), and only then, in light of that result, to deduce the truth of the proposition, 〈Mars is red〉. And it is this ‘order of deduction’ that is the basis of my conclusion regarding explanatory order. 13. Note that “true” is defined, by the equivalence schema, on the basis of ordinary objectlevel terms that are already understood. Therefore, even when there is no explanation of why it is that p (e.g., when “p” is “1 + 1 = 2”), it is plausible to suppose 〈p〉 is true because p. rather than the other way around.

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So—even in the case of atomic propositions—there is no basis for such a conclusion.14 Proceeding to my second objection: the above problem for truthmaker theory may be deepened, as follows. We saw in section 3 that one ought to construe such a theory as not offering an account of truth, but as deploying an independently explainable concept of truth in order to articulate certain metaphysical theses. For example, the central contention—that each truth has a truthmaker—that is, (y)[y is true → ($x)(y is made true by x)] that is, (y)[y is true → ($x)(y is true because of x)] should be seen as deploying truth merely as a device of generalization in a thesis whose particular implications have the form p → (p because of x) And the idea is that, for certain basic cases of “p,” the x will be the fact that p. But these implications don’t stand up to scrutiny. For, as we have just seen, our explanatory practice is to deduce propositions, such as 〈Mars is red〉, from initial conditions and laws of nature, thereby explaining why, for example, Mars is red—and then to deploy the schema ($x)(x = the fact that p) ↔ p to deduce and explain why the corresponding fact exists. This vindicates the intuition that I believe most of us have: namely, that it is not because of the fact that Mars is red (or the state of Mars being red) that Mars is red. On the contrary, it is because Mars is red that such a fact exists (and such a state is actual). Thus the particular metaphysical claims that truthmaker theory uses the notion of truth to generalize are even less plausible than the (abovecriticized) truth-theoretic reformulations of them.15 A third potential nail in the coffin of truthmaker theory lies in the merits of supposing that what we mean by the word “fact” is simply “true proposition.” For if that is so, then it obviously can never be that 14. Note that the above objection to truthmaker theory is independent of which entities are taken to be the primary bearers of truth and which entities are taken to be their truthmakers. My explicit target in the text is the idea that, in the simplest cases, the fact that p makes true the proposition that p. But instead of propositions one could focus on sentences or believings; and instead of facts one could take the truthmakers to be states, or events, or tropes.The objection, with obvious adjustments, will be no less telling. 15. The present objection (like the previous one) generalizes to all candidate bearers of truth and to all candidate truthmakers.

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〈p〉 is true because the fact that p exists since this would be tantamount to supposing that 〈p〉 is true because the true proposition that p exists that is, 〈p〉 is true because 〈p〉 is true! Thus, if facts are nothing but true propositions, it cannot be that 〈p〉 is made true by the fact that p But what reason is there for identifying facts with true propositions? I think there are four good reasons to do so. First, the objects of belief are propositions; but we can say, “It is a known fact that Mars is red, yet not everyone believes it”; and surely what we are talking about (—that Mars is red—) does not switch from one ontological category to another half way through the sentence. Second, the fact that Mars is red and the proposition that Mars is red have exactly the same structure as one another and involve exactly the same constituents; so it is hard to see what the difference between them could consist in. Third, among possible (i.e. conceivable) states of affairs, some are actual; and it is economical and plausible to identify the actual ones with facts and to identify the possible ones with propositions. And fourth, no compelling motive can be found for expanding our ontology by distinguishing facts (or actual states of affairs) from propositions. Arguably, we need to countenance propositions as the objects of belief, assertion, etc.; but why facts in addition? Only, it would seem, if we feel that something is needed to make the propositions true; but this is precisely what is in dispute. Thus there is ample justification for supposing that “fact” means “true proposition,” and if this is so then the fact that p can never make true the proposition that p.16 16. Let me acknowledge a couple of considerations (brought to my attention by Adolf Rami) that might seem to tend against the identification of facts with true propositions: (i) The subject of the sentence, “What Peter believes is disgraceful”—namely, the expression, “What Peter believes”—surely does not refer to a proposition. Granted. But nor does it refer to the fact of which Peter is aware. It refers, in that context, to Peter’s state of mind, his state of believing what he does. That is the alleged disgrace. (ii) Galileo surely did not discover the proposition that the Earth is round, but rather the fact. Certainly that’s the way we talk. But we are often unable to coherently insert “the proposition” before “that”-clauses—even when they cannot be construed as referring to facts. For example: “I hope that p,” “He conjectured that p,” “You are claiming that p.” This prohibition is admittedly puzzling—but it doesn’t support a distinction between facts and true propositions.

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It may be objected that I have managed to overlook the obvious difference between, for example, (FR) the fact that Mars is red and (RU) the state (or event) of Mars being red and that, although facts of type FR may be the same as true propositions (and hence incapable of making those propositions true), the RU-‘facts’—better called events or states—are concrete entities (quite distinct from propositions which are abstract), and therefore perfectly suitable as truthmakers. But I have not overlooked this distinction. Rather, the above considerations suggest a more illuminating way of articulating it—a way that reveals its inability to aid the cause of truthmaker theory. The fundamental distinction alluded to here is between Fregean propositions and Russellian propositions. On the one hand, we can deploy identity conditions according to which sentences express the same proposition as one another just in case they have the same sense (i.e., meaning). Propositions identified in this Fregean way are the objects of de dicto belief (e.g., the ancient belief that the Morning Star, but not the Evening Star, is visible at dawn).Alternatively—and with equal legitimacy—we can deploy Russellian identity conditions according to which two sentences express the same proposition just in case one may be transformed into the other by substitution of coreferential terms. Such propositions are the objects of de re belief (e.g., the ancient belief, regarding what is in fact the Evening Star, that it’s visible at dawn). Corresponding to each of these kinds of proposition, there is a kind of fact (state, event, condition, etc.) The Fregean facts are the true Fregean propositions (= the actual Fregean states = the occurring Fregean events = the obtaining Fregean conditions). And the Russellian facts are the true Russellian propositions (= the actual Russellian states = the occurring Russellian events = the obtaining Russellian conditions).17 17. Granted, the various nominal constructions (i) (ii) (iii) (iv) (v)

the proposition that k is F the state of k being F the fact that k is F the condition of k being F the event of k being F

exhibit certain syntactic differences and certain differences in meaning. In particular there is variation as to which of the following predicates are appropriately deployed to single out which instances of (i)–(v) entail that k is F: i.e., (i*) (ii*) (iii*) (iv*) (v*)

is true is actual, obtains exists, is real is satisfied, holds occurs, takes place

(footnote continued on p. 270)

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But doesn’t this concede to the truthmaker theorist all he needs? Can his view not be that Fregean propositions are made true by Russellian facts? No, it can’t. For (1) no account would be available of what makes Russellian propositions true; (2) there is no reason to accept the presupposition of this view, that Russellian facts are more fundamental than Fregean facts; and (3) as argued above, neither of these kinds of entity is really at the foundation of things; rather, it is because Mars is red that both of the propositions, 〈Mars is red〉FR and 〈Mars is red〉RU, are true.18 Thus insofar as truthmaker theory aims to get to the metaphysical rockbottom of what is true, it is doomed to failure. For the real foundation is expressed by sentences rather than nominals.19 6. WHAT MIGHT BE SALVAGED FROM TRUTHMAKER THEORY? Most of the hard work within truthmaker theory has been occasioned by the desire to invoke the schema 〈p〉 is made true by the fact that p as little as possible. The struggle has been to account for all truths by showing how they are determined by the truth of the (hopefully) few propositions for which the schema does need to be invoked. Therefore, if, as just suggested, no instances of that schema are correct (—and, for parallel reasons, no instances of analogous schemata concerning, states, events, tropes, etc.—), then one might well conclude However, we need not conclude that the alternate sentence nominals denote different kinds of thing. Such a multiplication of entities would have to be justified in light of explanatory advantages. But it is by no means clear what those would be. Admittedly, events and states stand in causal relations to one another—and that might be thought to distinguish them from propositions which, as abstract entities, may seem incapable of being so related. However, one might respond that true propositions (= actual states of affairs) should not be characterized as “abstract.” Alternatively, one might allow that characterization, but say that such abstracta may indeed cause one another. For the condition for x to cause y would include the condition that x and y be actual (real or true). 18. The present (third) objection—based on the thesis that facts are true propositions—will not count against those theories in which sentences, or believings, are taken to be the fundamental truth bearers. However, as stressed in footnotes 14 and 15, the other two objections apply no matter what the bearers and makers of truth are assumed to be. 19. Why are we prone to confusion on this point? The answer, presumably, is that a natural way of specifying what is fundamental is by saying something of the form, “. . . are the basic elements of reality.” But that sort of claim forces us to supply a subject that will refer to a kind of thing (or to various kinds of thing); the slot must be filled by an expression of the form, “Suchand-such entities”; a list of sentences (—those that we take to articulate our most basic commitments—) won’t do. So we end up with nominalizations of those sentences—referring to facts (states, events, etc.). This result is innocuous if it is taken—as it would ordinarily be taken in nonphilosophical contexts—as nothing more than a loose way of affirming those sentences, a useful approximation to what strictly speaking should be said. The trouble arises when that convenient inaccuracy is not recognized as such—so we wrongly infer that “Such-and-such facts (states, etc.) exist” is the correct form of the most fundamental characterizations of reality.

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that the foundations of truthmaker theory are so radically defective that the ingenious efforts towards erecting the rest of the structure on those foundations are all in vain. But it would be an overreaction to simply throw that work away. For we would be neglecting the possibility of a sanitized version of truthmaker theory—a version that is not focused on truth per se, and that does not attempt to explain everything in terms of what exists, but which is concerned simply with the ways in which various kinds of phenomena are to be explained (i.e., constitutively grounded), and with which of them must (or may, or may not) be regarded as explanatorily basic. Indeed, many of truthmaker theory’s characteristic concerns and claims seem quite reasonable if they are understood as part of such an inquiry. Consider, for example, the idea that there are no negative facts and that the truthmakers of negative propositions are certain nonnegative facts—facts that will make true isomorphic propositions whose truth will then entail negative propositions. We have seen that this formulation is unacceptable as it stands. But it can be regarded as a distorted rendering of something much less implausible:—namely, that no explanatorily fundamental claim can take the form, “k is not F,” that if k is not F then this must be because k is G (or, more generally, because p—where “p” does not express a negative proposition). Such intuitions issue from our concept of “constitutive explanation.” Thus there would appear to be a worthwhile project of elucidating that concept (by articulating our practices of explanation giving), and of drawing conclusions about how facts of various logical types are engendered and about which of them might be fundamental.20 Such conclusions would provide the core of truth within a truthmaker theory. 7. PHILOSOPHICAL IMPORT Armstrong maintains that progress throughout philosophy can be fostered if we keep in mind that each truth must have a truthmaker. And he offers a couple of examples.21 The first concerns phenomenalism—the doctrine that each object consists in how it is experienced—that is, in the existence of certain sense data. Against the objection that we may correctly speak of unperceived objects, the phenomenalist tends to reply that such remarks can be analyzed in terms of counterfactuals— statements of which sense data would exist in various hypothetical circumstances. But, according to Armstrong, the truthmaking intuition gives us a way of articulating what is wrong with this move. For we can raise the question of what could possibly make such counterfactual propositions true; and we can see that no satisfactory answer is available. For, against the strict phenomenalist (who will countenance nothing more than actual sense-data), we can point out that he does 20. Such a project appears to be close what Kit Fine has in mind by an investigation of the grounding relations amongst propositions. See his “The Question of Realism,” Philosophers’ Imprint 1 (2001): 1. 21. See Truth and Truthmakers, pp.1–3.

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not have the resources to provide his counterfactual conditionals with truthmakers. And against the more liberal phenomenalist (who is prepared to expand the universe to include counterfactual facts), we can argue that “surely” no such brute facts can exist. But it’s doubtful whether the characteristic apparatus of truthmaker theory plays any substantial role in this critique. The real objection to the strict phenomenalist is simply that, since his counterfactual propositions are not reducible to what he takes to exhaust the basic elements of reality, no such facts can exist. And the real objection to the liberal phenomenalist is that (allegedly) counterfactuals are never explanatorily fundamental; therefore, deeper elements of reality must be postulated. But this objection stems, not from truthmaker theory properly so-called, but rather from the above-mentioned “sanitized” investigation into our notion of “explanation.” As suggested in section 6, we might think of truthmaker theory as what emerges when one begins with such an entirely legitimate investigation, but then articulates it in light of certain misguided assumptions about truth and existence. A similar dialectic characterizes the discussion of behaviorism (—the doctrine that facts about peoples’ mental states are reducible to facts about their behavior). In response to the objection that someone may be in a certain mental state without revealing it in his behavior, the behaviorist tends to reply by saying that the reducing behavioral propositions may concern mere dispositions to behave in one way or another. But, according to Armstrong, the truthmaking intuition puts us in a position to rebut this response. For what could make true such dispositional propositions? Against the strict behaviorist one can object that actual behavior can’t do that job. And against the liberal behaviorist one might maintain that the postulation of brute dispositional facts is metaphysically bizarre. But again it is perfectly possible to formulate these criticisms without any truthmaking rhetoric. To the hard-line behaviorist one can point out that his hard line has been crossed. In response to the liberal, one can claim that dispositional facts cannot be explanatorily fundamental. As before, it’s not so clear that this is right; but what is clear is that, if it is right, it stems from our view of constitutive explanation. Truthmaker theory merely offers a dressed up way of putting the point. 8. CONCLUSIONS Let me end with a summary of my main objections to truthmaker theorizing: (1) “〈p〉 is made true by x” is most illuminatingly analyzed, not as “x necessitates that 〈p〉 is true,” but rather as “x explains (constitutively) why 〈p〉 is true” or “〈p〉 is true in virtue of x.” (2) The theory of truth supplied by a non-trivial truthmaker theory (of the sort endorsed by Armstrong and other truthmaker enthusiasts) is too long, too complex, too theoretical, and too heterogeneous to be plausibly regarded as an account either of what we mean by “true” or of the nature of truth itself.

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(3) Truthmaker theories are better seen as deploying an independently grasped concept of truth in order to help formulate a body of metaphysical doctrine. More specifically (and bearing in mind the standard role of truth as a device of generalization) we should appreciate that the basic content of a truthmaker theory is formulated by propositions of the form “p because of x” or “p because x exists”—in which the notion of truth plays no role at all. (4) Thus, claims about which kinds of entity (if any) serve as truthmakers boil down to theses about which existential theses are explanatorily fundamental. But it turns out on reflection that fundamental explanatory premises never take the forms “($x)(x = the fact that k is F)” or “($x)(x = the state of affairs of k being F)” or “($x)(x = the F-ness of k).” For such entities exist because k is F. Therefore the truth of 〈k is F〉 is not fundamentally explained by the existence of a fact (or state, or event, etc.).—Rather, it is true because k is F. (5) So it’s a fallacy to presuppose that being is basic—or, in other words, that the world is the totality of ‘things,’ captured by means of singular terms rather than sentences.22 (6) The grains of truth in a truthmaker theory are (i) schematic constitutive theses of the form, “p because q1, q2, . . . and qn”—where “p” ranges over the propositions of a given logical type (e.g. disjunctions, counterfactuals, etc.); and (ii) conclusions to the effect that only certain types of proposition can ever appear in any of the q-positions—that is, can achieve the status of basic facts. The mistakes to beware of are, first, to presuppose that only existential propositions may be given that foundational status; and, second, to think— just because the ‘sanitized’ theses (especially, generalizations of them) are most naturally articulated with the help of our concept of truth—that they concern truth.23

22. This is an observation from the Tractatus. But we shouldn’t be overly surprised that a basic objection to truthmaker theory should emanate from the very work that inspired it. For a fundamental contention of that work is that, like all philosophy, it is itself flawed by the attempt to say what can only be shown. In particular, Wittgenstein’s remark that the world consists of facts rather than things (paragraph 1.1) should not be construed as the proposal of a new sort of world-constituting entity, but precisely the opposite. 23. The present article is an expanded and heavily revised descendant of “Une Critique de la Théorie des Vérifacteurs” (in La Structure du Monde, edited by Jean-Maurice Monnoyer, Vrin, Paris, 2004, 115–27). That paper was the translation of a talk I gave at a conference on Truthmaker Theory at the University of Grenoble in December 1999. I was responding to Armstrong’s “Truths and Truthmakers,” which he had delivered a few days beforehand at Le College de France. I am grateful to those who raised questions on that occasion, especially David Armstrong and Kevin Mulligan; and also to Kit Fine, Adolf Rami, and Jonathan Simon, with whom I have had more recent discussions of the topic.

Midwest Studies in Philosophy, XXXII (2008)

Quine’s Ladder: Two and a Half Pages from the Philosophy of Logic Marian David

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want to discuss, in some detail, a short section from Quine’s Philosophy of Logic. It runs from pages 10 to 13 of the second, revised edition of the book and carries the subheading ‘Truth and semantic ascent’.1 In these two and a half pages, Quine presents his well-known account of truth as a device of disquotation, employing what I call Quine’s Ladder. The section merits scrutiny, for it has become the central document for contemporary deflationary views about truth. 1. REDUNDANCY, UTILITY, AND DISQUOTATION In the passages of Philosophy of Logic—henceforth PL—leading up to the section under discussion, Quine has been engaged in dismissing meanings in general and propositions in particular. Truth enters the scene because the friends of propositions have said propositions are needed as the proper bearers of truth. Quine responds that truth applies to sentences and not to propositions (because there are none). This view of Quine is of course contentious. I will not quarrel with it here. It will turn out that the choice of truth-bearers does not matter all that much as far as my main topic is concerned. Quine’s Ladder can be decoupled from his view that truth applies to sentences: there are friends of propositions who advocate an essentially Quinean account of truth. 1. Quine 1986; the first edition appeared in 1970. Midwest Studies in Philosophy: Truth and its Deformities Volume XXXII Editor by Peter A. French and Howard K. Wettstein © 2008 Wiley Periodicals, Inc. ISBN: 978-1-405-19145-6

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Quine’s preference for sentences as bearers of truth leads him to consider the “deeper and vaguer” worry that truth should hinge on reality, not on language. He fully agrees with the sentiment but thinks that it creates no difficulties for his view. On the contrary, he says: “No sentence is true but reality makes it so” (PL, 10). What comes next is motivated by his desire to show that truth applying to sentences is not in conflict with truth hinging on reality. It is noteworthy that this concern with truth hinging on reality, which surfaces prominently at various points, is the initial motivation for the whole section; indeed, Quine’s account of truth, the disquotational account, emerges eventually as an offshoot from the way in which he addresses this concern.2 The remainder of our section from PL can be divided into three parts, exhibiting a movement of thought somewhat like the movement from thesis to antithesis to synthesis.3 first part: limited redundancy This part is very short, consisting of the last 10 lines of the paragraph that runs from pages 10 to 11. Having embraced the point that sentences are made true by reality, Quine illustrates it by reminding us of Tarski’s biconditional: (1) ‘Snow is white’ is true if and only if snow is white.4 He immediately continues with the words (label added): [A] In speaking of the truth of a given sentence there is only indirection; we do better simply to say the sentence and so speak not about language but about the world. So long as we are speaking only of the truth of singly given sentences, the perfect theory of truth is what Wilfrid Sellars called the disappearance theory of truth. (PL, 11) Later, in Quiddities, Quine disavows this talk of the disappearance (theory) of truth on the grounds that it takes the quotation marks too lightly: after all, ‘is true’ is not all that has disappeared on the right-hand side of (1). Instead: What can justly be said is that the adjective ‘true’ is dispensable when attributed to sentences that are explicitly before us. (Quine 1987, 214) These passages are deliberately phrased to remind us of the so-called redundancy theory of truth, according to which the truth predicate is superfluous and could 2. One usually regards Quine as the father of contemporary deflationism about truth. Yet, serious concern for the idea that truths are made true by reality is often seen as a sign of inflationary thinking about truth. 3. You might want to compare this section from PL with pages 212–15 from Quine’s Quiddities (1987) and, especially, with pages 79–82 from the second edition of his Pursuit of Truth (1992). 4. Actually, he says (PL, 10): “The sentence ‘Snow is white’ is true, as Tarski has taught us, if and only if real snow is really white.” The ‘real’ and ‘really’ are concessions to the made-trueby-reality sentiment.

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simply be erased from our language without loss. But note Quine’s qualifying proviso: so long as we are speaking only of the truth of singly given sentences that are explicitly before us. second part: utility The second part takes up the contrary theme, already foreshadowed by the proviso of the first part. It tells us that the redundancy theory fails because of cases where the truth predicate is used but not used to speak of the truth of singly given sentences explicitly before us: the truth predicate is not dispensable after all. The important cases of this sort—the only ones Quine considers—are generalizations involving the truth predicate. I cite a number of passages in their order of appearance; they are all from page 11 of PL, with labels in brackets added for ease of cross-reference: [B] Where the truth predicate has its utility is in just those places where, though still concerned with reality, we are impelled by certain technical complications to mention sentences . . . The important places of this kind are places where we are seeking generality, and seeking it along certain oblique planes that we cannot sweep out by generalizing over objects. [C] We can generalize on ‘Tom is mortal’, ‘Dick is mortal’, and so on, without talking of truth or of sentences; we can say ‘All men are mortal’. We can generalize similarly on ‘Tom is Tom’, ‘Dick is Dick’, ‘0 is 0’, and so on, saying ‘Everything is itself’. [D] When on the other hand we want to generalize on ‘Tom is mortal or Tom is not mortal’, ‘Snow is white or snow is not white’, and so on, we ascend to talk of truth and of sentences, saying ‘Every sentence of the form ‘p or not p’ is true’, or ‘Every alternation of a sentence with its negation is true’. [E] What prompts this semantic ascent is not that ‘Tom is mortal or Tom is not mortal’ is somehow about sentences while ‘Tom is mortal’ and ‘Tom is Tom’ are about Tom. All three are about Tom. We ascend only because of the oblique way in which the instances over which we are generalizing are related to one another. Passage [B] ties the utility of the truth predicate to generalizations and announces (a bit mysteriously perhaps) that in certain cases and because of certain complications we are impelled to generalize indirectly. [C] provides two contrast cases for comparison, two cases where we can generalize directly. [D] gives an example of a case where we have to generalize indirectly, which is supposed to illustrate the utility of the truth predicate: this passages contains Quine’s Ladder albeit in compressed form. [E] introduces the notion of semantic ascent and promises to tie it in with the initial motivation, showing how truth applied to sentences still hinges on reality. third part: disquotation In the final part of our section, Quine claims that there is a close connection between the utility of the truth predicate in generalizations, emphasized in the second part, and Tarski’s biconditionals from the first

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part—though exactly how this crucial connection works is not spelled out explicitly. The following are from the bottom half of page 12 of PL—skipping one important passage to be mentioned later: [F] This ascent to a linguistic plane of reference is only a momentary retreat from the world, for the utility of the truth predicate is precisely the cancellation of linguistic reference. The truth predicate is a reminder that, despite technical ascent to talk of sentences, our eye is on the world.This cancellatory force is explicit in Tarski’s paradigm: ‘ ‘Snow is white’ is true if and only if snow is white’. [G] By calling the sentence [‘Snow is white’] true, we call snow white. The truth predicate is a device of disquotation. [I] We need it to restore the effect of objective reference when for the sake of some generalization we have resorted to semantic ascent. With the slogan “The truth predicate is a device of disquotation” Quine’s account of truth has emerged. This may not be obvious right away. The slogan is, after all, still talking about the disquotational or cancellatory force of the truth predicate; that is, according to [F] and [I], about the feature responsible for its utility. But, so Quine seems to hold, what accounts for the utility of the truth predicate thereby accounts for truth. This transition from a claim about the utility or function of the truth predicate—about what it can do for us or we can do with it—to a claim purporting to tell us what truth is, is explicit in his later writings: “Attribution of truth to ‘Snow is white’ just cancels the quotation marks and says that snow is white. Truth is disquotation” (1987, 213). “To ascribe truth to the sentence is to ascribe whiteness to snow . . . Ascription of truth just cancels the quotation marks. Truth is disquotation” (Quine 1992, 80). But isn’t it absurd to identify truth itself with a function like disquotation? Isn’t this some sort of category mistake? Quine wouldn’t mind. He has chosen his slogan because it has a paradoxical ring to it. When Quine talks about truth, using the abstract noun, he has in mind the truth predicate ‘is true’ or the adjective ‘true’. So when we think of his account of truth, we should think of it in the first instance as an account of the predicate, which turns out to be an account of the role the predicate plays in our language and, in particular, of its utility. Quine holds that this is all that can be and need be done here by way of an account, at least as far as our ordinary truth predicate is concerned. Compare his slogan with the classic ‘Truth is correspondence’, which is short for ‘Truth is correspondence with a fact’, which expresses an account of truth in the traditional sense, convertible into standard definitional form: ‘x is true iff x corresponds with a fact’. Quine’s slogan, ‘Truth is disquotation’, is short for ‘The truth predicate is a device of disquotation’, which clearly is not supposed to be convertible into: ‘x is true iff x. . . ’. According to Quine, no account of truth taking this traditional form is possible or even desirable: ‘Truth is disquotation’ is cast to look like ‘Truth is

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correspondence’, but it is intended in a spirit of friendly mockery; its paradoxical flair is meant to convey that traditional “theories” of truth are on the wrong track entirely.5 Quine talks throughout as if there were only one way for sentences to be explicitly given: by quotation. This is wrong. A sentence might be spelled out, letter by letter, using proper names of letters instead of quotations; it might then be followed by the words ‘is true’—this was Tarski’s (1935) official way. A sentence might be explicitly given by being uttered, and the speaker might get the response ‘That is true’. Or the speaker herself might continue with the words ‘is true’, resulting in the sounds: ‘Snow is white is true’—we don’t usually mention quotation marks when speaking. Cases of the last sort could be regarded as containing inaudible quotation marks. But cases of the first two sorts are not as easily assimilated. They pose an obvious problem. Since they are examples of truth attributions to explicitly given sentences, they should come out as involving dispensable uses of the truth predicate. But since the sentences are not quoted, the examples are not covered by the claim that truth is disquotation: the disquotational account, taken literally, is too narrow. Quine would regard this as little more than a nuisance, pointing out that Tarski-style biconditionals (modified in minor ways) still hold for such cases: and that’s what really matters. The slogan that truth is disquotation is an oversimplification, justifiable by the need for brevity in advertising. Quine acknowledges that non-eternal sentences cause problems: the biconditional ‘ ‘This is white’ is true iff this is white’ is untrue if ‘This’ denotes something different than ‘this’. He narrows attention to Tarski-biconditionals quoting eternal sentences, free from demonstratives and other context-sensitive ingredients; he defends this move as “the convenient line for theoretical purposes”.6 I will follow Quine and ignore all such problem cases for simplicity’s sake, focusing on Tarski-biconditionals that quote eternal sentences, and equating the explicit giveness of a sentence with its being quoted.

2. LIMITED REDUNDANCY: A DILEMMA Quine moves from Tarski’s biconditionals to the claim that the truth predicate is dispensable when applied to sentences explicitly before us (i.e. to quoted sentences), and from there to the claim that the truth predicate is indispensable for generalizations. These moves rely on the condition contained in passage [A]:

5. Quine remarks that the disquotational account may be said to define truth, but only in a loose sense: “it only tells us how to eliminate [the truth predicate] when it is attached to a quotation” (1987, 215). Definition in the strict sense, explicit definition, would tell us how to eliminate the predicate from every context, replacing it with other terms. This is not forthcoming, and it could not be done consistently, not for our truth predicate applied to our language, as Tarski has shown; cf. Quine 1987, 214–16; 1992, 81–83. 6. Quine 1992, 79; cf. PL, 13–14. Tarski originally used the context-sensitive ‘it is snowing’ for his paradigmatic biconditional; he corrected that later; cf. his 1935, 156, and his 1944 and 1969.

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Quine’s Limited Redundancy Condition (LRC): The truth predicate is dispensable, provided we are speaking only of the truth of singly given sentences that are explicitly before us. The proviso is intended as a necessary and sufficient condition for the dispensability of the truth predicate; and this dispensability is characterized thus (see [A]): “We do better simply to say the sentence”; and in Pursuit of Truth (Quine 1992, 80): “So the truth predicate is superfluous when ascribed to a given sentence; you could just utter the sentence”. Quine’s LRC is supposed to neatly segregate uses of the truth predicate into two camps for separate treatment: (a) the dispensable ones, where the truth predicate is applied to the quotation of a sentence; and (b) the indispensable ones, universal and existential generalizations, where the truth predicate is applied to a quantifier phrase, or rather, in Quine’s canonical notation, to a variable bound by a quantifier, as in: ‘For every x, if x is F then x is true’; and ‘For some x, x is F and x is true’. This segregating role of the LRC comes out quite nicely in the continuation of the passage from Quiddities, cited earlier, which occurs after Quine has already employed Tarski’s paradigm, (1), to make the point that attribution of truth just cancels the quotation marks: What can justly be said is that the adjective ‘true’ is dispensable when attributed to sentences that are explicitly before us. Where it is not thus dispensable is in saying that all or some sentences of such and such specified form are or are not true, or that someone’s statement unavailable for quotation was or was not true . . . (Quine 1987, 214) But there is a difficulty. The uses of the truth predicate do not line up as neatly as Quine wants them to, giving rise to a dilemma. Consider the occurrence of the truth predicate within the biconditional: (1) ‘Snow is white’ is true if and only if snow is white. The sentence ‘Snow is white’ is explicitly before us, explicitly given by quotation, and succeeded by ‘is true’ to make the left-hand side of (1). Does this embedded use of the truth predicate fall under the proviso of the LRC? Say it does, then the truth predicate of the sentence on the left-hand side of (1) is dispensable. Instead of uttering that sentence, Quine, following his own advice, would have done better simply to say: ‘Snow is white’; hence, instead of uttering (1), he would have done better simply to say: ‘Snow is white if and only if snow is white’. This is puzzling: How can the truth predicate in (1) be thus dispensable? Tarski’s biconditionals are at the very heart of Quine’s account of truth: they are supposed to make explicit the disquotational force of the truth predicate, which is wherein the utility of the predicate is supposed to lie. Quine needs the biconditionals to state his own account of truth. Say, alternatively, that the use of the truth predicate in the sentence on the left-hand side of (1) does not fall under the proviso; say the proviso is meant to

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apply only to free-standing sentences—sentences such as ‘ ‘Snow is white’ is true.’—not to embedded ones. The question arises: What will account for the embedded use of the truth predicate in (1)? and: What will account for embedded uses in general, uses within conditionals, disjunctions, conjunctions, negations, where the truth predicate is attached to the quotation of a sentence but the resulting sentence is itself a component of a larger whole? Not the second part of Quine’s story, for that part is designed to cover generalizations involving truth. All such embedded uses of the truth predicate are left in the lurch. The latter option cannot be a live one for Quine. It would leave hosts of uses of the truth predicate unaccounted for. This leads us back to the first horn of the dilemma. Tarski’s biconditionals, as employed by Quine, are exceptions to the LRC. The truth predicate is dispensable whenever it is applied to explicitly given sentences, except for Tarski’s biconditionals used to expound the disquotational account of truth: eliminate ‘ ‘___’ is true’ from them and you have eliminated the disquotational account. When formulating the LRC, Quine uses the phrase ‘speaking of’; he says the truth predicate is dispensable “so long as we are speaking only of the truth of singly given sentences” (see [A]). At other places, quoted earlier, he says the predicate is dispensable when attributed to or ascribed to explicitly given sentences (1987, 214; 1992, 80). These speech-act verbs are naturally taken with assertoric force, so that attributing or ascribing truth to a sentence, and speaking of the truth of a sentence, imply asserting of the sentence that it is true. If so, the LRC’s proviso applies only to cases where we assert the truth of sentences explicitly before us. Tarski’s biconditionals would then not fall under the proviso, since we do not assert the truth of ‘Snow is white’ when asserting (1). But this takes us back to the second horn of the dilemma, leaving hosts of embedded uses of the truth predicate unaccounted for.7 Assertoric force raises a closely related problem for some of Quine’s most central pronouncements. Consider passage [G] from PL, already quoted above, but with the speech-act verb emphasized: [G] By calling the sentence [‘Snow is white’] true, we call snow white. The truth predicate is a device of disquotation. (PL, 12) The first part covers only assertoric uses of ‘ ‘Snow is white’ is true’. When one utters this assertively, one asserts of ‘Snow is white’ that it is true, one calls the sentence ‘Snow is white’ true. But one does not assert ‘ ‘Snow is white’ is true’ when uttering this in the course of uttering a sentence such as (1), even if one utters (1) assertively; hence, in uttering (1), one does not assert of ‘Snow is white’ that it is true, one does not call it true. I do not assert of you that you are a liar, I do not call

7. Though conjunctions could now be handled. An assertion of ‘ ‘Snow is white’ is true and ‘grass is green’ is true’ can be regarded as asserting both, ‘ ‘Snow is white’ is true’ and ‘ ‘Grass is green’ is true’, with each use of the truth predicate coming out as dispensable. But this still leaves us with occurrences of ‘ ‘s’ is true’ within conditionals, disjunctions, and negations, where it remains unasserted even when the embedding sentences are asserted.

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you a liar, when I assert that you are a liar if and only if I am. Since the first part of [G] covers only assertoric uses of the truth predicate, it is ill equipped to support the second part which is supposed to be an entirely general claim about the function of the truth predicate schlechthin.8 [G] suffers from a confusion censured by P. T. Geach: “This whole subject is obscured by a centuries-old confusion over predication embodied in such phrases as “a predicate is asserted of a subject” . . . In order that the use of a sentence in which “P” is predicated of a thing may count as an act of calling the thing “P,” the sentence must be used assertively, and this is something quite distinct from predication, for, as we have remarked, “P” may still be predicated of the thing even in a sentence used non-assertively as a clause within another sentence” (Geach 1960, 253). We can help Quine out if we take Geach’s hint and distinguish more carefully between predicating and asserting. To say that one predicates a predicate of something implies that one utters a truth-evaluable subject-predicate sentence, it does not imply that one asserts the sentence while uttering it. This allows for talk of predication with respect to unasserted clauses. When one asserts a sentence of the form ‘If a is F then b is H’, the predicate ‘is F’ is predicated of a, even though the sentence ‘a is F’ is an unasserted component within the whole: though unasserted, it is still truth-evaluable.9 Normally, a predicate loses its predicative function within quotation marks. The predicate ‘is white’ is not predicated of snow in ‘ ‘Snow is white’ has three words’: the truth-value of ‘Snow is white’ is irrelevant to the truth-value of the whole. ‘ ‘Snow is white’ is true’, however, is special. Here the predicate ‘is white’ does have its predicative function even though it occurs within quotation marks: the truth-value of ‘Snow is white’ is relevant to the truth-value of the whole; indeed, the whole is true if and only if ‘Snow is white’ is. Predicating ‘is true’ of the sentence ‘Snow is white’ restores the predicative function of ‘is white’. Quine’s claim should have been: [G*] By predicating ‘is true’ of ‘snow is white’, we predicate ‘is white’ of snow. Truth is disquotation. Thus reconstructed along non-assertoric lines, the first part of the claim does a better job supporting the general thesis that (the) truth (predicate) is (a device of) disquotation. Moreover, we can now see the first part of Quine’s [G] as being focused more narrowly—too narrowly—on a special subset of the cases covered by

8. Quine’s later variants of [G] exhibit the same problem: “Attribution of truth to ‘Snow is white’ just cancels the quotation marks and says that snow is white. Truth is disquotation” (Quine 1987, 213); “To ascribe truth to the sentence is to ascribe whiteness to snow . . . Truth is disquotation” (1992, 80). The speech-act verbs indicate assertoric force, making the first parts of these claims too narrow to support the thesis that truth is disquotation, which is supposed to hold even when truth is not asserted of anything. 9. Quine (1960, § 20):“Predication joins a general term and a singular term to form a sentence that is true or false according as the general term is true or false of the object, if any, to which the singular term refers.”

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[G*], namely the ones where we not only predicate ‘is true’ of ‘Snow is white’ but, in doing so, assert of ‘Snow is white’ that it is true.10 The move to predication improves on Quine’s [G]. It also helps with LRC whose proviso is naturally taken as covering only assertoric uses of the truth predicate, which makes it too narrow, leaving all non-assertoric uses unaccounted for. Rephrasing LRC, or reinterpreting it, in terms of predication removes this unwanted restriction: the truth predicate is dispensable, provided we are predicating it only of singly given sentences that are explicitly before us. This is good, because Quine surely wants all such uses of the truth predicate to come out as dispensable.All, that is, except the ones within the Tarski-biconditionals he employs when expounding his account of truth. The puzzle posed by them is still with us. Quine, it seems, has failed to notice that Tarski’s biconditionals, which are indispensable to his account of truth, are dispensable on his account of truth. I will return to this point below, suggesting that he should have loosened the tie to the redundancy theory even more than he did. 3. UTILITY AND QUINE’S LADDER The redundancy theory promised a deflationary view of truth. It was designed to deflate especially correspondence theories, but also epistemic and pragmatic theories. As such, it appealed to many. Quine rejects the redundancy theory. We need the truth predicate for generalizations, viz. ‘Everything Archimedes says is true’.11 Evidently, removing ‘is true’ from such sentences will produce nonsense: the truth predicate is not dispensable. Quine stresses this point repeatedly. Nevertheless, his own view retains the deflationary spirit—therein lies its appeal to friends of the late redundancy theory; and it is the Ladder that is supposed to do the trick: the beauty of Quine’s Ladder, in the eyes of deflationists, lies in its power to allow them to reject the redundancy theory, emphasizing that the truth predicate is not redundant (on the contrary, it is useful and needed), without giving succor to advocates of inflationary accounts of truth. In the previous section we looked at one side of the line Quine wants to draw with the LRC, the one concerned with dispensable uses of the truth predicate. We will now look at the other side, the one concerned with indispensable uses, with universal and existential generalizations. Quine is going to take the very feature of the truth predicate that undid the redundancy theory—its utility for expressing

10. Note the difference between predicating, which is semantic, and attaching, which is syntactic. I cannot attach ‘is white’ to ‘snow’ (or to snow) by attaching ‘is true’ to the quotation of ‘snow is white’. But, according to [G*], I can predicate ‘is white’ of snow by attaching ‘is true’ to the quotation of ‘snow is white’, provided that, in doing so, I predicate ‘is true’ of ‘snow is white’. 11. More weighty examples should readily come to mind: ‘No sentence is true but reality makes it so’ (cf. PL: 10); ‘Whatever I perceive very clearly and distinctly is true’; ‘Some of the things we believe are not true’; ‘A belief-producing process is reliable iff it tends to produce true beliefs’; ‘Every significant sentence is either true or false’ (etc.). Note, since the point at hand concerns the expressibility of generalizations involving truth or falsehood, false examples are as relevant as true ones.

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generalizations involving truth—and treat it as the reason why we have the truth predicate. It is the task of Quine’s Ladder to explain how the truth predicate manages to play this role. Before I turn to this, I should address a worry, if only to set it aside. When it comes to uses of the truth predicate not handled by the redundancy theory, Quine focuses on generalizations involving truth. But there seem to be additional cases, viz.‘The first sentence in Quine’s PL is true’, from which the truth predicate cannot simply be removed. Did Quine forget about cases of this sort? No, but for Quine they too are generalizations, because they contain definite descriptions. Following Russell, Quine construes sentences whose grammatical subjects are definite descriptions (including definite descriptions of sentences) as cases of existential generalizations. But what about cases with proper names of sentences say ‘(17) is true’, where some sentence has been baptized with the temporary name ‘(17)’? Quine would say they too can be construed as generalizations via his assimilation of proper names to definite descriptions. Quine is committed to the view that all problem cases for the redundancy theory can be reduced to generalizations of some sort. In any case, Quine’s Ladder is only equipped to handle generalizations. This may be a weak point of his approach, but I will not pursue it here.12 Quine’s Ladder is contained in passage [D], which is at the heart of the second part of our section from PL. In this passage, Quine says that when we want to generalize on sentences like ‘Tom is mortal or Tom is not mortal’ (etc.), we ascend semantically to talk of sentences and of truth. The passage is a bit condensed. It has become customary to fold it out a little so that the crucial rung of the ladder, which Quine oddly suppressed, stands out more prominently.13 quine’s ladder It asks us to consider, for example, the transition from (2) to (3) to (4); it follows this up with some comments connecting these steps: (2) Tom is mortal or Tom is not mortal; Snow is white or snow is not white; All bats are insects or not all bats are insects; . . . and so on. (3) The sentence ‘Tom is mortal or Tom is not mortal’ is true; The sentence ‘Snow is white or snow is not white’ is true; The sentence ‘All bats are insects or not all bats are insects’ is true; . . . and so on. (4) Every sentence of the form ‘p or not p’ is true. 12. See Quine (1960, § 37–38), for his assimilation of proper names to descriptions. Soames (1999, 48f.) points out that proper names of truth-bearers may pose a special problem for redundancy-inspired views because Kripke’s work shows that proper names, being rigid designators, are not easily assimilated to descriptions. But Quine’s strategy seems immune, for he simply proposes to reparse occurrences of a name, ‘Saul’, as occurrences of ‘x =Saul’, where the predicate ‘=Saul’ can be regarded as uniquely and rigidly applying to Saul. There is an irony here. If names are to be reparsed in this manner, then so are quotation names to be reparsed as, say, ‘x =‘Snow is white’ ’, with the predicate ‘=‘Snow is white’ ’ applying uniquely and rigidly to a sentence. But then ‘ ‘Snow is white’ is true’ turns into the generalization ‘($x)(x =‘Snow is white’, and x is true)’, where the truth predicate is not attached to a quoted sentence: the category of quotational, hence disquotational, uses of the truth predicate threatens to dissolve. 13. Compare Leeds (1978, 121–23); Soames (1984, section 1); Horwich (1998b [11990], 3–5, 120–26); Gupta (1993a, 59–63); David (1994, 95–97); Blackburn and Simmons (1999, 11–14); Künne (2003, chap. 4.2.2).

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We want to generalize on the items gestured at in (2). Proceeding from (2) via (3) to (4), we reach a generalization expressing a general law of logic (excluded middle), the one that was in some sense already implicit in the items gestured at by (2). Note the step to (3) and the role played, in the background, by Tarski’s biconditionals, the instances of the disquotation schema: T.

The sentence ‘p’ is true if and only if p,

ingeniously labeled to allude to both, truth and Tarski. The instances of T, looked at from right to left as it were, mediate the semantic ascent from (2) to (3). The items gestured at in (2) do not serve up any objects generalizing over which would take us to the logical law in its full generality (see [B]). But applying the instances of the schema to the items in (2) leads to (3)—the rung not explicitly mentioned by Quine himself—which does serve up the right sort of objects, namely sentences (truth bearers), over which we can generalize to reach (4), the intended law. Quine’s passage [D] does not explicitly mention (3). He talks about generalizing on the items in (2) and ascending semantically to (4), but he leaps over (3) which appears to be an important step. It splits the difference between generalization and semantic ascent: semantic ascent relates (2) to (3); generalization relates (3) to (4). Why did Quine not mention (3) explicitly? I cannot explain it unless he thought that what I am about to say is too obvious for words. The step is not only important, it is all important to Quine’s account. For it is the transition from (2) to (3), semantic ascent, that brings into play the instances of schema T, Tarski’s biconditionals. Without the step to (3), the disquotational feature of truth would not be given any role to play in the account of generalizations involving truth. There would be no ground for saying that the truth predicate is a device of disquotation. I take it for granted, then, that it is obligatory to regard passage [D] as a condensed version of Quine’s Ladder as laid out above. Here we see how Quine takes the very feature of the truth predicate that undid the redundancy theory, its utility for expressing generalizations, and treats it as the reason why we have the truth predicate: the role the predicate plays in these generalizations is its reason for being. The Ladder is designed to show how the truth predicate manages to play this role; and since the Ladder does this on the basis of the instances of the disquotation schema, T, Quine concludes that the truth predicate is a device of disquotation. Note the negative, deflationary, implicature of Quine’s slogan: the truth predicate is a device of disquotation and nothing more; or maybe somewhat more cautiously: the truth predicate is a device of disquotation and no more substantive claim about it is warranted. Whence this negative implicature? The answer, I take it, is this. Quine thinks that generalizations involving truth are the sole reason why we have the truth predicate, the data left unaccounted for by the redundancy theory. The Ladder explains them merely on the basis of the instances of schema T, without appeal to anything more substantive about truth. So the instances of the schema constitute a sufficient account of the truth predicate, allowing us to explain all that needs to be explained. A richer conception of truth is not warranted by the need to explain the data; hence, not warranted.

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It is important to be clear about the difference between (4) and T. T contains the schematic letter ‘p’: T is a schema; it is not a sentence; it does not say anything; only its substitution instances, for example, (1), are sentences and say things. Though (4) also contains the letter ‘p’, (4) is a sentence and not a schema; it says something; it says: ‘For every x, if x is a sentence of the form ‘p or not p,’ then x is true’. Here the ‘p’ is not a schematic letter, instead it is part of the predicate ‘x is a sentence of the form ‘p or not p’ ’, which displays a pattern to specify the logicosyntactic structure or form of a lot of sentences. (Compare Quine’s alternative rendering in [D]: ‘Every alternation of a sentence and its negation is true’.) I will mark such form-terms by use of the formulation ‘is a . . . of the form ___’. In view of the potentially confusing double-use of ‘p’—as part of a form-term and as schematic letter—it might have been better to adopt a notation that marks the difference more boldly; but I don’t like to do so because this double use is fairly standard, for example, in the later Quine.14 Evidently, the Ladder I extracted from our section of PL is an exemplar, a paradigm. Other generalizations involving truth must be accounted for by variations on this theme, including of course existential generalizations (but universal generalizations will give us enough to worry about for the present paper). Above I assumed the Quinean will rely on the (claimed) explanatory power of Tarski’s biconditionals to explain generalizations involving truth. Quine himself does not put that much stress on explanatory considerations in this context, at least not explicitly—compare passages [B] through [G]. Although these passages are obviously intended to give an account of the utility of the truth predicate, explanatory terminology is not at the forefront. The introduction of more overtly explanatory considerations into discussions over deflationary views about truth is largely due to other authors, Hartry Field (1972, 1986), Stephen Leeds (1978), Hilary Putnam (1978), and Paul Horwich (1982, 1998a), among others.15 Giving more weight to explanatory considerations allows for a resolution of the earlier dilemma. Referring to the Ladder, the Quinean can point out that the need for explaining generalizations involving truth generates a need for uses of the truth predicate attached to quoted sentences: according to the Ladder, the disquotation biconditionals, as well as free-standing sentences of the form ‘ ‘p’ is true.’, are needed for the semantic-ascent step from (2) to (3). Hence, in the context of such explanations, the truth predicate is not at all dispensable, even 14. In PL, p. 13, Quine is dismissive of citing schema T itself in addition to sample instances; he complains that its left-hand side merely quotes the sixteenth letter of the alphabet. By the fourth edition of Methods of Logic (1982), he has become much more relaxed about this: both uses of ‘p’ occur there side by side, with schematic uses allowed freely within quotation marks; for comment, see Quiddities, 234–35. By the way, like Quine, I will continue to ignore that ‘Tom is mortal or Tom is not mortal’ does not actually look like it is of the form ‘p or not p’: it is to be regarded as a notational variant of ‘Tom is mortal or (it is) not (the case that) Tom is mortal’— some stratification of natural language is presupposed. 15. Field, Leeds, and Putnam, however, are more concerned with the question whether the concept of truth is really needed for genuine explanations of other things that really need to be explained. This issue is broader than the one under consideration here, which concerns the explanatory role of Tarski’s biconditionals in explanations of our uses of the truth predicate in generalizations.

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though it occurs attached to singly given sentences explicitly before us (quotations). In such contexts, we would not do better simply to utter the quoted sentences, for that would destroy the explanations. Consequently, Quine would do better to drop his LRC and replace it with a weaker, subjunctive formulation— which Quine himself probably wouldn’t approve of, owing to his tendency to be suspicious of subjunctives: LRC*: If we didn’t need the truth predicate to formulate generalizations involving truth, then we wouldn’t need the truth predicate at all, because a need for using the truth predicate outside of generalizations, i.e. for predicating it of a sentence by attaching it to the quotation of the sentence, arises only in the course of explaining our use of generalizations involving truth. This further loosens the tie to the redundancy theory. It admits that predicating the truth predicate of singly given sentences explicitly before us is indispensable in certain contexts, thus making room for acknowledging the crucial explanatory role assigned to Tarski’s biconditionals in Quine’s account of truth. (I have incorporated two simplifying assumptions mentioned earlier into this new formulation: that quotation is the way by which sentences are explicitly given; that all genuine problem cases for the redundancy theory can be reduced to generalizations involving truth.) 4. A VARIANT LADDER AND DIS-THAT-ISM A variant of Quine’s Ladder can be employed by those who hold, pace Quine, that the bearers of truth are propositions. They will work with the propositional variant of schema T, namely schema TP.

The proposition that p is true if and only if p.

Starting from the same place as before, namely (2), they can construct their variant ladder: (2) Tom is mortal or Tom is not mortal; Snow is white or snow is not white; All bats are insects or not all bats are insects; . . . and so on. (3P) The proposition that Tom is mortal or Tom is not mortal is true; The proposition that snow is white or snow is not white is true; The proposition that all bats are insects or not all bats are insects is true; . . . and so on. (4P) Every proposition of the form ‘that p or not p’ is true.16 Deflationists who apply truth to propositions can thus take the Quinean approach on board, modulo their disagreement about the primary bearers of truth.

16. The italics are not meant to carry any secret message; they are there only to help parsing.

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For them the task of explaining how the truth predicate plays its role falls to this variant of Quine’s Ladder. Of course, they would not refer to the transition mediated by the instances of TP, that is, the step from (2) to (3P), as semantic ascent— they might call it intensional ascent instead. If they wanted to have a Quine-style slogan, theirs would not sound quite as colorful: ‘The truth predicate is a device of disthating’. Paul Horwich takes the instances of TP together with this variant of Quine’s Ladder to account for the raison d’être of our notion of truth: he advocates an essentially Quinean deflationary position. Actually, this does not quite do justice to Horwich who consistently highlights explanatory considerations. He never says that ‘is true’ (or ‘the proposition that ___ is true’) is dispensable; he emphasizes the need for instances of TP to explain the facts involving the property of truth as well as our generalizations involving the concept of truth; and he maintains that both our concept and the meaning of the term ‘true’ are constituted by our inclination to accept instances of schema TP which, he says, displays the explanatorily basic regularity underlying our overall employment of the concept and the term.17 I often gloss over the otherwise rather important difference between sententialist and propositionalist Quineans, talking of (2), (3), (4), and T, where what I say might be applied as well to (2), (3P), (4P), and TP, mutatis mutandis: by and large, what goes for semantic ascent and disquotation also goes for intensional ascent and disthating.

5. CLIMBING THE LADDER? Quine’s Ladder is supposed to explain generalizations involving truth.The rungs of the Ladder, (2), (3), (4), together with T, are important ingredients in this explanation, but they are not the whole explanation. For that we must look to the surrounding text. We might, then, ask what sort of explanation Quine is giving us there. Throughout our section from PL, Quine talks in terms of our intending and doing various things, in terms of performing a goal-directed activity or procedure. (I mimicked this talk when laying out the Ladder in Section 3.) He says: “We are seeking generality, and seeking it along certain oblique planes” (see [B]); “we can generalize on ‘Tom is mortal’ . . . without talking about truth” (see [C]); “when on the other hand we want to generalize on ‘Tom is mortal or Tom is not mortal’, ‘Snow is white or snow is not white’, and so on, we ascend [semantically] to talk of truth and of sentences” (see [D]); “to gain our desired generality, we go up one step and talk about sentences” (PL, 12). In Pursuit of Truth, he says: “The truth predicate proves invaluable when we want to generalize along a dimension that cannot be swept out by a general term [of ordinary objects]”; and a little bit later:

17. Cf. Horwich (1998b, section 7; 1998b: chap. 3). An interesting alternative to Horwich’s view can be found in Chris Hill’s (2002, esp. chap. 2).

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“We cleared this obstacle by semantic ascent: by ascending to a level where there were indeed objects over which to generalize, namely linguistic objects, sentences” (1992, 80–81). What is to be made of this talk of our intendings and doings? Should we take it at face value? Say we do: then Quine is giving us a (rough) sketch of a psychological or psycholinguistic account of how we come up with universal generalizations involving truth in language and/or thought, an account of their psychological production history. Spelled out in more detail, the account would proceed along the following lines, if taken literally. infinite In the process of producing a generalization such as (4), so this story has it, we are mentally climbing the Ladder from (2) to (3) to (4): (2) Tom is mortal or Tom is not mortal; Snow is white or snow is not white; All bats are insects or not all bats are insects; . . . and so on. (3) The sentence ‘Tom is mortal or Tom is not mortal’ is true; The sentence ‘Snow is white or snow is not white’ is true; The sentence ‘All bats are insects or not all bats are insects’ is true; . . . and so on. (4) Every sentence of the form ‘p or not p’ is true. We find ourselves entertaining the infinitely many items gestured at by (2). We want to generalize universally over these items. Since we cannot do so directly (by generalizing over the ordinary objects the sentences are about), we entertain infinitely many appropriate substitution instances of the schema, T.

The sentence ‘p’ is true if and only if p,

which we apply to the items gestured at by (2).As a result of this infinite procedure, we come to entertain the infinitely many items gestured at by (3). We then generalize universally over the linguistic objects mentioned in these items, which results in our entertaining and maybe affirming (maybe verbally) the finite generalization (4). But surely, this is absurd—and I have spelled it out in detail just to make clear how absurd it is. We cannot entertain the infinite sequences gestured at by (2) and (3), nor can we make the infinitely many applications of appropriate substitution instances of T. It is absurd to account for our deployment of the truth predicate in terms of our performing a certain procedure if we cannot possibly perform this procedure. Moreover, the account has the paradoxical result that, if we could do what it has us do, then there wouldn’t be any need for the truth predicate after all, not on Quine’s view of truth. Leeds (1978, 121–22) uses language similar to Quine’s, as does David (1994, 96–97), when discussing the Quinean view. It is most prominent, however, in Horwich, where the paradoxical turn the account takes comes out quite starkly: “We may wish to cover infinitely many propositions (in the course of generalizing) and simply can’t have all of them in mind. In such situations the concept of truth is invaluable. For it enables the construction of another proposition, intimately related to the one[s] we can’t identify, which is perfectly appropriate as the alter-

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native object of our attitude” (Horwich 1998a, 2–3). He then illustrates this in terms of our mentally climbing Quine’s Ladder, using constructivist language that implies that we can have in mind all these propositions after all. Truth, he says, “enables the construction” of a generalization like (4), with the help of the instances of T, by which “the infinite series” of items under (2) “may be transformed into another infinite series of claims,” (3), and “the sum of these claims may be captured in an ordinary universally quantified statement,” that is, (4).18 This construction of finite (4) from infinite (3), which in turn is constructed from infinite (2), can hardly be effected without having in mind (impossibly) the infinite sequences that are being constructed and transformed. Note the paradoxical result: the very account of truth as an Ersatz device for something we cannot do is couched in language implying that we can do what, according to the view at hand, we cannot do and need truth as an Ersatz for.19 This paradoxical aspect comes out in finite cases too. We can use the truth predicate to say, for example, ‘Every sentence in book B is true’, when we don’t actually know all the sentences in B. Judging from what he did in PL, Quine would list a few sentences from B—let’s write them as ‘s1’, ‘s2’, ‘s3’, for brevity—and would begin his account with the following claim about our initial intention: “When we want to generalize on ‘s1’, ‘s2’, ‘s3’, and so on, we ascend [semantically] to talk of truth and of sentences” (see [D]). But this very specification of our intention implies that we do not need the truth predicate in this case. If we have this “want”, if we want to generalize on ‘s1’, ‘s2’, ‘s3’, and so on, then we are in a position to affirm each sentence of the book directly. Oddly, the story about how the generalization is useful to those who do not know all the sentences in B presupposes that they do know the sentences in B.20 This way of understanding Quine’s Ladder won’t do. Indeed, this seems so obvious, one might well think that taking Quine’s and Horwich’s words literally, as I have done for the last few paragraphs, is a gross misinterpretation. But what, then, is the literal account? Maybe something like this. Quine is telling us how a being that can form the infinite intention to generalize on ‘Tom is mortal or Tom is not mortal’, ‘Snow is white or snow is not white’, and so on, (or someone who does know each sentence in B), can use the relevant instances of T to formulate a generalization that comes in handy in case the being (or that someone) is too lazy 18. Horwich (1998b, 3–5); he uses the variant Ladder for propositions and a different example. Such constructivist language shows up in all of Horwich’s presentations of the Ladder. He talks of our “wish to generalize”, of our “constructing” or “composing” (4) by “reformulating” (2) as (3), or by “converting” (2) into (3), which “can be generalized” as (4), or from which (4) can be “extracted”; see Horwich (1998b, 122–23; 1998a, 105–56; 2004, 38–39, 72–73, and 141–42). 19. One might object that we can have (2) and (3) in mind, just not directly, item by item, but indirectly, namely by having (4) in mind. Fair enough, but then Quine’s Ladder collapses into (4), repeated three times, which destroys the account it was supposed to provide. 20. In Pursuit of Truth, Quine specifies our intention differently. Looking at another example, namely the conditional ‘If time flies then time flies’, he says: “We want to say that this compound continues true when the clause [‘time flies’] is supplanted by any other; and we can do no better than to say just that in so many words, including the word ‘true’ ” (1992, 81). With this specification of our initial intention, the Ladder does not take on the paradoxical aspect, but it does not get off the ground either.

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to list all those sentences. But on this interpretation the account misses its mark again. It tells us how the truth predicate can be used by a being for whom it is dispensable (or can be used by us at occasions at which it is dispensable to us), instead of making intelligible how we deploy the truth predicate in the sort of generalizations (under circumstances) where it is indispensable to us. Can we find a more plausible interpretation of the account Quine’s Ladder is supposed to provide, one that discards the transfinite aspect and avoids the paradoxical turn, but otherwise manages to stay close to Quine’s actual words? So far I have taken (2) and (3) as abbreviations of infinite lists, gestured at by the phrase ‘ . . . and so on’. Why not take them as abbreviations of finite lists? finite We entertain, so the revised story goes, something much like (2) itself, a finite sequence of disjunctions, capped by our thinking ‘and so on’. We form an intention to generalize. Whatever precisely this intention is, it has a finite content: it is an intention to generalize universally on ‘Tom is mortal or Tom is not mortal’, ‘Snow is white or snow is not white’, ‘All bats are insects or not all bats are insects’, and so on. There might be additional items on the list, the point is: the intention is finite and the ‘and so on’ is now part of its content. Somehow, the intention leads us to apply the appropriate substitution instances of T to the finitely many items in (2); and as a result of this finite procedure, we entertain finitely many items like the ones in (3), capped by our thinking ‘and so on’. Some more steps should now be made explicit to exhibit the contribution of the general term that serves, as Quine puts it, “to sweep out the desired dimension of generality” (1992, 81). In our example, this crucial role is played by the form-term ‘is a sentence of the form ‘p or not p’ ’. Somehow, the intention to generalize also leads us to detect the relevant feature common to the items in (2) and to select that form-term to sweep out the items in (2), thus coming to entertain the finite: (3.1) ‘Tom is mortal or Tom is not mortal’ is a sentence of the form ‘p or not p’; ‘Snow is white or snow is not white’ is a sentence of the form ‘p or not p’; ‘All bats are insects or not all bats are insects’ is a sentence of the form ‘p or not p’; and so on. This is interwoven with (3) to form the equally finite: (3.2) ‘Tom is mortal or Tom is not mortal’ is a sentence of the form ‘p or not p’ and is true; ‘Snow is white or snow is not white’ is a sentence of the form ‘p or not p’ and is true; ‘All bats are insects or not all bats are insects’ is a sentence of the form ‘p or not p’ and is true; and so on. We then generalize universally over the linguistic objects mentioned in (3.2), reaching (4), ‘Every sentence of the form ‘p or not p’ is true’, by way of a leap—a leap akin to induction—from finitely many cases to a universal generalization. The epistemic status of this leap is not under discussion, for we are presently concerned with an account of our deployment of the truth predicate when producing generalizations, however reasonable or unreasonable the result may be epistemically speaking. This remark may strike you as superfluous, thinking that

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we surely won’t go wrong with the generalization ‘Every sentence of the form ‘p or not p’ is true’. But this feature is an artifact of Quine’s choice of a target generalization which happens to be a law of logic. Other universal generalizations we employ in language/thought, taking the form ‘Every sentence that is F is true’, may well be false or, if true, wildly unreasonable, given the startup list from which we generalize.21 This revised account is of course no more than a sketch; fundamental questions remain: How does any of this work in detail? What makes us “select” one rather than another general term to sweep out the desired dimension of generality? What makes us generalize to (4) rather than to: ‘Every true sentence is of the form ‘p or not p’ ’? But these are the sorts of questions that always arise regarding generalizations; they don’t pertain specifically to generalizations involving truth. The revised account (however sketchy) has the considerable merit that it avoids attributing infinite thought processes to us, and it avoids what I called the paradoxical turn taken by the literal reading of Quine’s account. Moreover, it stays faithful to Quine’s (and Horwich’s) words insofar as it construes semantic ascent as a psychological activity or process, or the result of such an activity or process. But the account is incomplete. We can use generalizations like ‘Everything B says is true’, even when we don’t know any of the sentences contained in some book, or uttered by some person, B. In cases of this sort, we seem to have no startup list (along the lines of (2)) from which to generalize at all. One could try to meet this worry with the suggestion that we do have a startup list in such cases after all, namely one that contains (finitely many) conditionals such as: ‘If B says ‘snow is white’ then snow is white’. Applying the relevant instances of T to these conditionals, we produce (finitely many) attributions of truth. Deploying the general formterm ‘is a sentence of the form ‘If B says ‘p’ then p’ ’ to sweep out the desired dimension of generality, we generalize to: ‘Every sentence of the form ‘If B says ‘p’ then p’ is true’. But this points to a shortcoming of the account. It invariably issues universal generalizations beginning with the words: ‘Every sentence of the form . . . ’. Yet there are many universal generalizations involving truth that do not begin with these words. The generalization that was supposed to be explained in the previous paragraph, ‘Everything B says is true’, is a case in point: the account offered there was off target. It seems an extension of the procedure is needed. So far I have assumed, following Quine’s lead, that we always apply T from outside, to whole items on the startup list: call this the outer method. On the extended procedure, we on occasion apply T inside the items on the startup list, to one (or more) of their components: call this the inner method. To illustrate, assume again that the startup list contains such sentences as: 21. Starting from the items in (2), someone might arrive at the false generalization ‘Every sentence of the form ‘p or q’ is true’. An account of the psychological production history of generalizations involving truth must cover this sort of faulty process too. Note that Horwich (1998b) is often concerned with arguing that all facts involving truth, including all general facts involving truth, can be explained on the basis of the instances of T, or rather TP.This is an enterprise different from the one we are presently engaged in; it is not envisaged by Quine. For critical discussion of this enterprise, see Gupta (1993b), and David (2002).

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If B says ‘snow is white’ then snow is white; If B says ‘the earth rests’ then the earth rests. On the inner method, the relevant instances of T are not applied to each conditional as a whole, as in the previous paragraph, but only to their consequents, which yields: If B says ‘snow is white’, then ‘snow is white’ is true; If B says ‘the earth rests’, then ‘the earth rests’ is true. We then quantify-in, thereby generalizing to: ‘For every x, if B says x, then x is true’, that is, ‘Everything B says is true’.22 I have not found any applications of the inner method in Quine. Still, it does seem needed to handle generalizations not beginning with the words ‘Every sentence of the form. . . ’. If so, the paradigm Ladder from our section of PL turns out to be potentially misleading: Quine’s Ladder will have to be understood as being rather more versatile than the paradigm suggests, the inner method counting as one of its variations.23 The account is still not complete. We have not checked whether it can handle more complicated cases; and we have not even glanced at existential generalizations. I will set these aside for now. The envisaged account is at least broadly empirical: it advances an empirical hypothesis, supposed to cover all occasions at which we entertain, and maybe also utter, universal generalizations involving truth.24 According to this hypothesis, our productions of such generalizations are caused or motivated by conscious or, rather more likely, subconscious mental processes that proceed through steps like the ones sketched above for (2), (3), and (4), or some sufficiently close variation thereof—these mental processes should be seen as, or at least modeled as, processes operating on inner sentences, that is, on sentences of the language of thought: we certainly don’t verbally utter the steps of Quine’s Ladder before uttering generalizations involving truth. Since the account offers an empirical hypothesis,

22. The sweeping-out term would in this case be ‘thing’, or better, ‘is a sentence’, which could be regarded as being suppressed in our version of the generalization. 23. It is however not clear how to think of the “intention to generalize” that would trigger application of the inner rather than the outer method. Also, the inner method is less mechanical than the outer, requiring more ingenuity on our part, for it allows that T be applied selectively, to one or more components of the items on the startup list, as the need arises. The method is hinted at in Field (1986, 57), and appears on a few occasions in Horwich (1998a, e.g. 3, 123), who usually employs the outer method even though it frequently issues generalizations that differ from the ones he set out to explain. The inner method appears a bit more prominently in Field (1994), Sections 3 and 5, and Horwich (2004, 42); see also Gupta (1993a) , and McGee (1993, 96–97), who describe Quine’s view in terms of the inner method. 24. On various occasions generalizations involving truth might be entertained on the psychological basis of other generalizations involving truth; the former will then be explained indirectly, via the explanation of the latter which will proceed in terms of the Ladder.

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it needs empirical evidential support. As far as my own conscious processing is concerned, my introspection does not provide much support. When I say or think a universal generalization involving truth, I usually just say or think it. I do not notice going through stages like the ones depicted in Quine’s Ladder. Of course, the processing might not be (easily) accessible to introspection; it might be subconscious processing. I do not know whether support for subconscious processing of this sort can be found in cognitive psychology or psycholinguistics. Quine himself does not provide any (neither does Horwich). Still, the account is at least broadly empirical in nature and it seems to avoid the main problems of the absurd infinite account. But I have glossed over a question concerning the role played by the instances of T, Tarski’s biconditionals. The finite stories outlined above may not require a very large number of them, but these stories account for only three generalizations involving truth. There are very many more such generalizations to be accounted for, each one requiring a finite number of these biconditionals. It is highly likely that the required total number of T-biconditionals that must be available to us, according to the present account, will be very large. The question arises, then, how all these biconditionals are supposed to become available to us. Initially, one might think the account should address this by maintaining that we have a standing belief with a general content, one that subsumes all the particular T-biconditionals, so that various batches of them become available to us by a process of inference (instantiation) from this general belief. But it is hard to see what this belief could be. It should have something to do with schema T; but note that the following, (5) Jane believes that ‘p’ is true if and only if p, does not ascribe any belief to Jane. It is itself a mere schema; each of its substitution instances ascribes a particular belief to Jane: Jane believes that ‘snow is white’ is true if and only if snow is white; Jane believes that ‘Tom is mortal or Tom is not mortal’ is true if and only if Tom is mortal or Tom is not mortal; Jane believes that ‘2 + 2 = 5’ is true if and only if 2 + 2 = 5; and so on to infinity. The following, (6) Jane believes that every instance of the schema ‘ ‘p’ is true if and only if p’ is true, does ascribe a single belief to Jane; but it is of little use to the Quinean. It dethrones the T-biconditionals in favor of the generalization: ‘Every instance of the schema ‘ ‘p’ is true if and only if p’ is true’. Moreover, since this is a generalization involving truth, it is among the items that are supposed to be explained by Quine’s Ladder and cannot be used as part of the explanation the Ladder is supposed to provide. Finally, as Gupta (1993a, 72–73) in effect points out, (6) cannot do its job anyway. To get T-biconditionals from the generalization, Jane needs to apply T-biconditionals, namely to the instances of ‘ ‘p’ is true if and only if p’ is true,

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to get at the instances of ‘p’ is true if and only if p. Calling upon (6) to explain how indefinitely many T-biconditionals become available to us from finite resources would be quixotic. So, how do all these T-biconditionals become available to us? It is tempting to talk of dispositions at this point: each person who can entertain generalizations involving truth has the disposition(s) to employ batches of relevant T-biconditionals as the need arises. Quine might be content to leave this unexplained, as a brute disposition. Other Quineans might want to do a bit better by picking up a suggestion made by Hartry Field and Chris Hill. The idea is, roughly, that we have this disposition because we have schema T itself in our minds, as Hill puts it, we are “cognitively linked” to T: not by way of believing it—as pointed out above, T, being a schema, does not specify the content of any belief—but we nevertheless have T in our minds in some manner which allows us to make inferences from it, so that we can infer sufficiently many of Tarski’s biconditionals from the schema by substitution. This is, again, a broadly empirical hypothesis; I am not aware of any empirical evidence having been cited that speaks for or against it.25 My attempt to understand Quine’s Ladder, taking Quine by his own words, has encountered some difficulties, but they do not seem insurmountable. The resulting account of how we deploy universal generalizations involving truth in language and/or thought is broadly empirical in nature, which seems a good thing. On the other hand, no actual empirical evidence has been cited (from any branch of psychology) supporting the empirical hypotheses advanced by the account. This may well be considered a bit worrisome. You may have been wondering how the psychological story I have outlined, based on Quine’s own words, fits in with his overall views in philosophy of psychology. I am not entirely sure; but at least it is in keeping with his practice. Remember the third chapter of Word and Object, it offered an account of a stage in the child’s linguistic development—an account which Quine himself described as “imagined,” fullness of “experimental detail” not being an objective (Quine 1960, 125). In The Roots of Reference, he expanded on this practice, giving a much longer and more detailed psychological account, couched partly in mentalistic language, supported by little or no empirical evidence. He referred to this as 25. See Field (1994, Section 3, and 2001, Section 1). The way in which Field introduces this idea does not fit smoothly into the present picture. He describes it from the point of view of designing a “formalism” such that T itself is “part of the language, rather than merely having instances that are part of the language”; and he suggests “to incorporate schematic letters for sentences into the language, reasoning with them as with variables” (1994, 115). For our purposes, “the language” in question would be the language of thought. But then talk of “incorporating” schematic letters seems a bit odd: we do not design our language of thought like we design a formalism. Schematic letters, such as ‘p’, and the schema T itself, must have been “incorporated” into our minds for us, say, by mother nature and mother working together. For Hill’s version of the suggestion, see his 2002, 68–69.

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“psychogenetic speculation” and “imaginative reconstruction” (Quine 1973, 92, 101). He also commented on the “mentalistic idiom,” saying that it “has its uses as a stimulant” (Quine 1973, 33): “Conjectures about internal mechanisms are laudable insofar as there is hope of their being supported by neurological findings” (Quine 1973, 37). It appears that, for better or for worse, the account Quine sketches in our section from PL is of this general sort: Quine’s Ladder is an imaginative reconstruction of the psychological processes that lead to generalizations involving truth, couched in mentalistic language, to be born out by future scientific findings. 6. AFFIRMING A LOT OF SENTENCES Quine says we need the truth predicate for generalizations such as (4): ‘Every sentence of the form ‘p or not p’ is true.’ For what do we need such generalizations? Here is an often quoted passage I have not quoted yet, together with its immediate continuation (already quoted as [I]); it is from page 12 of PL: [H] We may affirm the single sentence by just uttering it, unaided by quotation or by the truth predicate; but if we want to affirm some infinite lot of sentences that we can demarcate only by talking about the sentences, then the truth predicate has its use. We need it to restore the effect of objective reference when for the sake of some generalization we have resorted to semantic ascent. Quine’s example of such an infinite lot of sentences we might want to affirm was the one gestured at by: (2) Tom is mortal or Tom is not mortal; Snow is white or snow is not white; All bats are insects or not all bats are insects; . . . and so on.26 Quine’s sample generalization was (4), which I rephrase in a style closer to the notation of first-order predicate logic—the canonical notation, according to Quine: (4) For every x, if x is a sentence of the form ‘p or not p’, then x is true. Quine is telling us in [H] that (4) will give us what we want, if we want to affirm the infinite lot of sentences gestured at by (2). How so? He does not quite say himself, but the natural interpretation is this: We manage to affirm the infinite lot of sentences gestured at in (2) by affirming (4)—slightly more explicitly: CL. By affirming (4) we affirm each of the infinitely many sentences gestured at in (2). 26. Granting Quine that we can want to affirm such an infinite lot of sentences, namely by way of an intention whose content is finite; see the previous section.

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CL functions as a closure principle for affirmation. Apparently, it has to be understood as presupposing a distinction between two kinds or subspecies of affirmation: direct and indirect. For Quine wants to say that we cannot affirm each of the infinitely many sentences gestured at by (2), which is why we need (4) and the truth predicate. CL, on the other hand, says we can affirm each of the infinitely many sentences gestured at by (2). So we have to distinguish between direct and indirect affirmation: we cannot affirm the sentences gestured at by (2) directly; we can affirm them only indirectly, namely by affirming (4), which we can affirm directly. Direct affirmation is a psychological notion: we can actually entertain (4) in our minds and utter it with our mouths. Indirect affirmation, on the other hand, extends the notion of affirmation beyond the psychological: we cannot actually entertain or utter more than a small sample of all the sentences that we can affirm indirectly according to CL.27 CL seems crucial to Quine’s view, for it tells us that the universal generalization involving the truth predicate does indeed serve the kind of need Quine has identified in passage [H]. Without CL, or something very much like it, Quine would be in a rather peculiar position: “We need the truth predicate for generalizations that we need to affirm infinite lots of sentences, though these generalizations do not actually serve this need”—a peculiar position indeed. Let us begin consideration of CL with the following idea (primarily because it helps clarify the situation). Maybe Quine advocates this particular closure principle on the basis of a general closure principle, saying that affirmation is closed under logical consequence: If you affirm x, and if y is a logical consequence of x, then you affirm y; and if y ⫽ x, then you affirm y indirectly. This principle yields the intended result: if you affirm (4), then you affirm (indirectly) each of the infinitely many sentences gestured at by (2). But it yields this result for unintended reasons, simply because the sentences gestured at by (2) are logical truths, hence logical consequences of any arbitrary sentence. It does not matter whether you affirm (4), or (4)’s negation, or something entirely unrelated: according to the present principle, you affirm the infinite lot of sentences gestured at by (2), along with each and every other logical truth, no matter what you affirm. The principle is much too broad. It undermines the idea that affirming (4) is needed for what Quine says it is needed for. It just happens to get the intended result because of the special nature of Quine’s chosen examples, (4) and (2).

27. Think of this in terms of processing sentence-tokens of Mentalese, the language of thought. A person who affirms (4) has a token of (4)—or rather of a Mentalese analogue of (4)—in her belief-box. By CL she thereby affirms each of the infinitely many sentences gestured at by (2); but she does not have Mentalese tokens of all these sentences in her belief-box: the second use of ‘affirms’ projects this term far beyond the first, far beyond what might be underwritten by actual psychological processing going on in the person’s mind or brain. (Our person will have a few samples of the sentences gestured at by (2) in her belief-box: she used those as a finite startup list when generalizing to (4); see the story outlined in the previous section.) One might try to bring indirect affirmation within the ambit of the psychological by suggesting that it involves no more than a disposition to affirm directly. But this is not promising. Very many of the sentences gestured at by (2) are of such mindboggling complexity that we have a disposition to get completely confused (or die) long before we have even processed the first disjunct.

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Quine, writing a book on logic, has understandably chosen a law of logic, the law of excluded middle, (4), as his example of a universal generalization involving truth, which has naturally led him to the infinite lot of logical truths gestured at by (2). But these examples, owing to their special nature, tend to import distracting issues not germane to the topic at hand. Quine’s claims must hold generally and not just with respect to generalizations that are also laws of logic and infinite lots of sentences that are also logical truths. We must bracket these idiosyncratic features of Quine’s examples.28 So let us bracket the fact that the sentences gestured at by (2), being logical truths, are logical consequences of (4) in the trivial sense of being logical consequences of anything. One might next try the idea that Quine advocates CL based on a narrower but still quite general closure principle according to which we affirm (indirectly) the logical consequences, in the nontrivial sense, of what we affirm. But this principle is too narrow. The sentences under (2) are not nontrivial logical consequences of (4). To put this differently, sentences of the form ‘ . . . ’ are not in general logical consequences of generalizations of the form ‘For every x, if x is a sentence of the form ‘ . . . ,’ then x is true’. This fails for two reasons which it will be helpful to distinguish. Remember rung (3) of Quine’s Ladder: (3) The sentence ‘Tom is mortal or Tom is not mortal’ is true; The sentence ‘Snow is white or snow is not white’ is true; The sentence ‘All bats are insects or not all bats are insects’ is true; . . . and so on. We can divide CL into two parts: CL-1. By affirming (4) we affirm each of the infinitely many sentences gestured at in (3). CL-2. By affirming each of the infinitely many sentences gestured at in (3) we affirm each of the infinitely many sentences gestured at in (2). I am mainly interested in CL-1, but let us consider CL-2 first, where for the moment we are not worried about how we manage to affirm each of the infinitely many sentences gestured at by (3). The sentences gestured at by (2) are, of course, logical consequences of the sentences under (3), but only in the distracting, trivial sense which we should bracket as irrelevant for present purposes. They are logical consequences in the nontrivial sense not of the sentences under (3) themselves but of their conjunctions with the relevant instances of schema T, Tarski’s biconditionals. Obviously, Quine subscribes to CL-2 based on his claim that the truth predicate is a device of disquotation. CL-2 is just a collective version of this claim, applied to the sentences gestured at by (3) and (2): By affirming ‘ ‘Tom is mortal or Tom is not 28. It might have been better if Quine had chosen, say, the infinite lot of arbitrary disjunctive sentences and the false generalization ‘Every sentence of the form ‘p or q’ is true’; that might have helped avoiding interference from distracting idiosyncrasies of the examples.

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mortal’ is true’ we affirm ‘Tom is mortal and Tom is not mortal’; By affirming ‘ ‘Snow is white or snow is not white’ is true’ we affirm ‘Snow is white or snow is not white’; and so on. Some would see these pragmatic facts about affirming as flowing from semantic facts about meaning: ‘ ‘Snow is white’ is true’, they would say, means the same as ‘Snow is white’—I am reverting to the standard example for convenience. Advocates of this meaning claim don’t typically argue for it (it is hard to see how one could argue for it); they treat it as intuitively obvious, a datum. Others do not find this so obvious. On the contrary, they find it obvious that ‘ ‘Snow is white’ is true’ does not mean the same as ‘Snow is white’. They point out that the former talks about a sentence and attributes truth to it while the latter only talks about snow and says that it is white. What is Quine’s position? One expects him to say that this is a non-issue because it isn’t really about ‘is true’ but about ‘means the same as’, the clash of intuitions merely reflecting the bankruptcy of our notions of meaning and synonymy. However, at times Quine himself makes pronouncements suggesting an inclination on his part to side with those who have the synonymy intuition: for to say that S is true is simply to say S. (Quine 1951, 4) To say that the statement ‘Brutus killed Caesar’ is true, or that ‘The atomic weight of sodium is 23’ is true, is in effect simply to say that Brutus killed Caesar, or that the atomic weight of sodium is 23. (Quine 1960, 24) Prima facie, such pronouncements suggest that the two sides of Tarski’s biconditionals are taken to say the same thing, to be synonymous or at least to express the same proposition (but Quine rejects propositions). One would like to ask Quine: What is this to say that__is in effect simply to say that . . . relation? and: If it does not indicate that the sentences thus related are synonymous or say the same thing, Why does it hold? Quine doesn’t say. He did, on the other hand, remark “that there is no need to claim, and that Tarski has not claimed, that [Tarski’s biconditionals] are analytic” (Quine 1953, 137). He even said that Church-Langford translation-reasoning “can be used to show that ‘There are no unicorns’ is not strictly or analytically equivalent to ‘There are no unicorns’ is true in English’ ”, adding that Tarski’s paradigm was not intended to assert analytic equivalence (1956, 196). Later he finds that reasoning inconclusive.29 But since this later verdict arises from his misgivings about sameness of meaning, it does not indicate that he would regard Tarski’s biconditionals as 29. Church-Langford translation-reasoning (Church 1950) applied to the case at hand: ‘There are no unicorns’ and ‘ ‘There are no unicorns’ is true in English’ do not mean the same, because their respective German translations, ‘Es gibt keine Einhörner’ and ‘ ‘There are no unicorns’ ist wahr auf Englisch’, do not mean the same: neither provides enough information to enable a German ignorant of English to infer the other. Judging from § 44 of his 1960, Quine would call this

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analytic or would take their two sides to mean the same, the above pronouncements notwithstanding. Concerning CL-2 this is, I think, as far as we can go within Quine’s world. The pragmatic ‘by’-claims about affirmation and truth, claims of the form ‘By affirming ‘ ‘ . . . ’ is true’ we affirm ‘ . . . ’ ’, are almost rock-bottom.We can take one more step and observe that, according to Quine, claims of this form hold because to say that ‘ . . . ’ is true is in effect simply to say that . . . —and now we have really reached rock-bottom. All we are told about this relation is that it should not be taken to indicate that Tarski’s biconditionals are analytic or that their two sides mean the same. On this topic, nothing more is forthcoming from Quine.30 CL-2 is concerned with affirmation and truth; it is crucial to CL, the claim that by affirming (4) we affirm each of the infinitely many sentences gestured at in (2). The other closure principle, CL-1, is equally crucial to this claim: CL-1. By affirming (4) we affirm each of the infinitely many sentences gestured at in (3). This principle is only incidentally concerned with truth, it is essentially concerned with affirmation and universal generalization. Note the division of labor: CL-2 is about semantic descent, it highlights the cancellatory or disquotational force of (4)’s truth predicate; CL-1, on the other hand, highlights the generalizing function of the universal quantifier heading (4).31 inconclusive because it presupposes that the English sentences and their German translations mean the same—a notion not fit for conclusive arguments. 30. Field, who shares Quine’s skepticism about synonymy, holds that, for any utterance u that a person understands, the claim that u is true is cognitively equivalent to u for that person, relative to the existence of u; where cognitive equivalence is an epistemic relation, to be thought of in terms of “fairly direct” and “more or less indefeasible” inferences licensed by the persons “inferential procedures”; see Field’s 1994, 105–6. Horwich holds that the instances of T’s propositional sibling, TP,“implicitly define” the truth predicate and are “necessary”,“a priori”, and “conceptually basic”; he nevertheless maintains that ‘The proposition that snow is white is true’ does not mean the same as ‘Snow is white’; see Horwich (1998b, 120–29). Gupta argues that the Quineans’ account of the role of the truth predicate commits them to making implausibly strong meaning claims about the instances of T and/or TP, even if they don’t like to admit it; see his 1993a. By the way, pace Quine, Tarski himself did make meaning claims about his biconditionals. He said, for example, that they “explain in a precise way, in accordance with linguistic usage, the meaning of phrases of the form ‘x is a true sentence’ ” (Tarski 1935, 187); and many years later:“By saying that S [= ‘Snow is white’] is true we mean simply that snow is white” (Tarski 1969, 103). 31. Some undermine this division of labor, saying that for the Quinean the truth predicate itself is a device of generalization, namely a device of infinite conjunction or disjunction. According to this idea, which relies on formulation T*, foreshadowed by Ramsey (1928, n. 7) and rejected by Tarski (1935, 159), the function of the truth predicate can be exhibited by: T*. x is a true sentence if and only if, for some p, x = ‘p’ and p, where ‘for some p’ is a quantifier of sorts, and the right-hand side can be understood as “encoding” the infinite disjunction: ‘(x = ‘snow is white’ and snow is white) or (x = ‘grass is green’ and grass is green) or (x = ‘snow is green’ and snow is green) or . . .’. T*, so the idea, shows that the truth predicate functions as some sort of quantifier, a device of generalization; see Field (1986, 57–58, and 1994, 120); Horwich (1998b, 104); and David (1994, 97). This construal of the Quinean view is

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Whence CL-1? Consider the following more general claims: (a) By affirming a universal generalization we affirm the conjunction of all of its instances; and (b) By affirming a conjunction we affirm each of its conjuncts. The second seems plausible enough. The first seems rather more worrisome. But let us grant it for now. Putting (a) and (b) together yields: By affirming a universal generalization we affirm each of its instances. Let that be granted: it does not take us to CL-1. The instances of our universal generalization, the law of excluded middle, (4) For every x, if x is a sentence of the form ‘p or not p’, then x is true, are all of them conditionals: If ‘Tom is mortal or Tom is not mortal’ is a sentence of the form ‘p or not p’, then ‘Tom is mortal or Tom is not mortal’ is true; If ‘Snow is white’ is a sentence of the form ‘p or not p’, then ‘Snow is white’ is true; If ‘Snow is green’ is a sentence of the form ‘p or not p’, then ‘Snow is green’ is true; If ‘Snow is white and Snow is not white’ is a sentence of the form ‘p or not p’, then ‘Snow is white and snow is not white’ is true; . . . and so on. They are all true: many talk about sentences of the form ‘p or not p’; many do not—they talk about sentences of all forms. According to (a) & (b), when we affirm (4), we affirm all these conditionals which are (4)’s instances.32 Consider now the sentences gestured at by (3): ‘ ‘Tom is mortal or Tom is not mortal’ is true’, ‘ ‘Snow is white or snow is not white’ is true’, and so on. They are not among the instances of (4). But why go to such length to stress this point? Surely, Quine would not think otherwise; he would not mistake the sentences under (3) for instances of (4). Surely, he would not base CL-1 on the idea that by affirming (4) we affirm all of its instances. I wonder. Remember passage [E]: [E] What prompts this semantic ascent is not that ‘Tom is mortal or Tom is not mortal’ is somehow about sentences while ‘Tom is mortal’ and ‘Tom is Tom’ are about Tom. All three are about Tom. We ascend only because of the oblique way in which the instances over which we are generalizing are related to one another. Three pages later, Quine refers again to the law of excluded middle, our (4), saying: distinctly not Quine’s who would denounce the phrase ‘for some p’ as a pseudo-quantifier not fit for respectable use: generalization, according to Quine, is exclusively a matter of the ordinary, objectual quantifiers, as canonized in the notation of first-order predicate logic. 32. Quine: “An instance of a quantification exactly matches the old open schema that followed the quantifier” (1982, 180); “So a generalized conditional [a universal generalization] can in full accordance with common usage be construed as affirming a bundle of material conditionals” (1982, 22); a universal generalization “is not itself a conditional but has the effect of simultaneous affirmation of a vast array of conditionals” (1951, 18). (This phrase again: “has the effect”—What does Quine mean by it?)

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We saw why it was phrased in linguistic terms: its instances differ from one another in a manner other than simple variation of reference. The reason for the semantic ascent was not that the instances themselves, e.g. ‘Tom is mortal or Tom is not mortal’, are linguistic in subject matter . . . (PL, 15) It seems Quine does, after all, mistake the sentences from (3) for instances of (4). Admittedly, what he is referring to here as an instance of (4) is one of the items from (2) rather than (3)—I assume this is because he has silently disquoted the relevant item from (3), that is, disquoted ‘ ‘Tom is mortal or Tom is not mortal’ is true’ to ‘Tom is mortal or Tom is not mortal’. It does not matter: the sentences from (2) are just as much not among the instances of (4) as the sentences from (3). The problem may derive from Quine’s choice of examples. (4) is a law of logic, the law of excluded middle. But one also hears ‘p or not p’ referred to as the law of excluded middle. Quine taught us that this is a mistake: the latter is no law; it is a mere schema; it says nothing. Still, ‘Tom is mortal or Tom is not mortal’ is a substitution instance of that schema: maybe Quine, despite his better self, has slipped into thinking of the schema as the law, thus slipping into thinking of ‘Tom is mortal or Tom is not mortal’ as an instance of (4).33 The problem also shows up in Horwich. Supposing that we wish to state the law of excluded middle, he presents us with: Everything is red or not red, and happy or not happy, and cheap or not cheap, . . . and so on, and says our task is “to find a single, finite proposition that has the intuitive logical power of the infinite conjunction of all these instances” (Horwich 1998b, 3; my emphases). The concept of truth, he continues, provides the solution, namely by way of the universal generalization: Every proposition of the form: 〈everything is F or not F〉 is true. (Horwich 1998b, 4) But the conjuncts of the infinite conjunction are not among the instances of this generalization, and the generalization does not have the logical power of the infinite conjunction: it is much weaker; its instances are all conditionals of the form ‘if x is of the form 〈everything is F or not F〉, then x is true’. At another point Horwich says that from the generalization “we can derive (given the truth schemata) all the statements we initially wished to generalize” (1998b, 123). But the statements we initially wished to generalize were the ones from the conjunction above; they are not derivable from the universal generalization, not without appropriate true premises of the form ‘x is of the form 〈everything 33. Quine once suggested that ‘p or not p’ might be said “to illustrate” the law of excluded middle, pointing out of course that it must not be identified with it; cf. Quine (1951, 51). Note, by the way, that a logical truth, according to Quine, is (roughly) a sentence that is true and remains true under all substitutions of its non-logical constituents; cf. PL, 50. So ‘Tom is mortal or Tom is not mortal’ is a logical truth: (4), although a law of logic, is not.

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is F or not F〉’. Well, actually, they are derivable from the generalization because they are all logical truths: they are trivially derivable from anything. Again the special nature of the chosen examples intrudes to confuse things. We have to keep bracketing the examples’ idiosyncrasies and remember that the derivability claim will fail as soon as we switch to alleged “generalizations” of conjunctions of items other than logical truths.34 Let us return to Quine. The instances of (4) are conditionals of the form ‘if x is a sentence of the form ‘p or not p,’ then x is true’. The sentences gestured at by (3) are not among them. How do they relate to (4)? They are the consequents of just those instances of (4) whose antecedents are true, that is, whose antecedents say of a sentence that actually is of the form ‘p or not p’ that it is of the form ‘p or not p’. To get to CL-1, Quine needs the following closure principle for affirmation: CL-0. By affirming (4) we affirm each of the infinitely many consequents of those instances of (4) whose antecedents are true, i.e. by affirming (4) we affirm ‘is true’ of each of the infinitely many sentences that are of the form ‘p or not p’. In terms of more general principles, Quine needs not only the two mentioned earlier: (a) by affirming a universal generalization we affirm the conjunction of all of its instances; (b) by affirming a conjunction we affirm each of its conjuncts; he also needs: (c) by affirming a conditional whose antecedent is true we affirm its consequent. Putting these together gives a generalized version of CL-0: by affirming a universal generalization, we affirm each of the consequents of those of its instances whose antecedents are true, that is, if you affirm ‘Everything that is F is G’, then everything that is in fact F is such that you affirm of it that it is G. The new principles make highly questionable claims about affirming. Take (c). When one affirms a conditional, one does not thereby affirm its consequent, and the issue of whether its antecedent is true or not does not seem to enter into it at all. You affirm ‘If I have the winning ticket, then I am rich’. As luck would have it, you do indeed have the winning ticket, though you have no idea that it is the winning ticket, you think it isn’t, and you have lots of reasons for thinking that it isn’t. Did you affirm ‘I am rich’, or at least that you are rich? It seems not. Take the generalized version of CL-0. Ralph affirms ‘Everyone working for the CIA is a spy’. Entirely unbeknownst to him, his neighbor, Sally Ortcutt, is in fact working for the CIA. Did he affirm ‘Sally is a spy’, or affirm of Sally that she is a spy, or at least affirm that Sally is a spy? It seems not. 34. An epistemic version of the same confusion shows up in Leeds (1978, 121): “It is not surprising that we should have use for a predicate P with the property that ‘ “____” is P’ and ‘____’ are always interdeducible. For we frequently find ourselves in a position to assert each sentence in a certain infinite set z (for example when all the members of z share a common form); lacking the means to formulate infinite conjunctions, we find it convenient to have a single sentence which is warranted precisely when each member of z is warranted. A predicate P with the property described allows us to construct such a sentence: (x)(x ∈ z → P(x)).” Gupta (1993a) argues that the Quineans confuse universal generalizations with their instances. It seems, rather, that they confuse non-instances of universal generalizations with instances.

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Quine once observed that there are two readings of ‘Ralph believes that someone is a spy’: the notional reading, viz. ‘Ralph believes there are spies’, and the relational reading, viz. ‘There is someone whom Ralph believes to be a spy’. He pointed out that the difference between them “is vast” (1956, 186). The difference between the notional ‘Ralph believes that everyone who works for the CIA is a spy’ and the relational ‘Everyone who works for the CIA is such that Ralph believes him/her to be a spy’ is just as vast. Note that switching from ‘affirms’ to ‘believes’ is not beside the point at this point. The former talk is prominent in my discussion merely because Quine uses it in our section from PL, taking sentences as the vehicles of truth. In a broader setting, there would be a parallel discussion conducted in terms of believing propositions. For those who do not share Quine’s aversion to such talk but are otherwise Quineans about truth, for example, Horwich, principles (a) through (c) would be rephrased accordingly, resulting in a general principle that gives license to systematic confusion of notional or de dicto belief attributions and relational or de re belief attributions. The objections just canvassed seem quite decisive as long as affirming (and believing) has its ordinary sense. There is, however, a complication. When introducing CL, the affirmation-closure principle that occasioned this whole discussion, I pointed out that it requires drawing a distinction between affirming something directly and affirming something indirectly—because Quine wants to say that we cannot affirm (directly) the sentences gestured at by (2) but can affirm them (indirectly) by affirming (4). One might now try to defend our new closure principles by appeal to this distinction: if we affirm (directly) ‘Everything that is F is G’, then everything that is in fact F is such that we affirm (indirectly) of it that it is G; and: if we affirm (directly or indirectly) a conditional whose antecedent is true, then we affirm (indirectly) its consequent. It is hard to argue with this because of the unexplained nature of indirect affirmation. Is it merely stipulated to be any relation R such that, when we affirm a conditional whose antecedent is in fact true, we stand in R to its consequent? We might also ask, again rhetorically: According to Quine what we wanted was to affirm an infinite lot of sentences: Why does affirming a universal generalization involving truth count as getting what we wanted, if by doing so we merely “indirectly affirm” each of those sentences? Why does that show that the truth predicate serves the need Quine has identified? Maybe one could construe this “indirect affirmation” as some sort of commitment, broadly conceived: by affirming a universal generalization we are committed to those consequents of its instances whose antecedents are in fact true; by affirming a conditional whose antecedent is in fact true we are committed to its consequent.35 But again this commitment, for example, to the consequent of an affirmed conditional, without any sort of cognitive attitude on our part to the antecedent, is a strange affair. Quine, albeit in another context, seems to agree: “An affirmation of the form ‘if p then q’ is commonly felt less as an affirmation of a conditional than as a conditional affirmation of the consequent. If, after we have 35. Of course, on this proposal we don’t, strictly speaking, get what we wanted. According to Quine, what we wanted was to affirm an infinite lot of sentences, what we get is a commitment to the sentences we wanted to affirm.

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made such an affirmation, the antecedent turns out true, then we consider ourselves committed to the consequent, and are ready to acknowledge error if proven false” (1982, 21; my emphasis).What Quine means here, I take it, is that we are committed to the consequent of an affirmed conditional, if the antecedent turns out true as far as we can tell, if we believe it or assent to it. What is missing from these closure principles is a clause adding that we stand in an appropriate cognitive relation to the antecedent of the conditional, or to the relevant antecedents of the conditionals that are the instances of a universal generalization. However, if such a clause is added, Quine’s project runs into difficulties. Consider CL-1 which said: CL-1. By affirming (4) we affirm each of the infinitely many sentences gestured at in (3). If we expand this in the manner that seems to be required, adding a clause to the effect that we at least believe or affirm the relevant antecedents of the conditionals that are the instances of (4), we get the following: By affirming (4), i.e. by affirming ‘For every x, if x is a sentence of the form ‘p or not p’ then x is true’, and affirming each true sentence of the form ‘x is a sentence of the form ‘p or not p’ ’, we affirm each of the infinitely many sentences gestured at in (3). Sadly, the clause introduced by ‘and’ takes us back where Quine started from. There are infinitely many true sentences of the form ‘x is a sentence of the form ‘p or not p’ ’, one for each of the infinitely many sentences of the form ‘p or not p’. How do we manage to affirm this infinite lot of sentences? So far I have concentrated on the more general claims, (a) through (c), that seem to stand behind CL-1. One might, however, think that I should have paid closer attention to CL-1 itself. The general closure principles, especially (c) and the general principle that resulted from putting (a) through (c) together, are indeed not to be accepted, so the suggestion, but CL-1 and its ilk are more specific: they have a special subject matter. Maybe that makes a difference. What is special about the subject matter of CL-1—other than the distracting fact that it happens to talk of a universal generalization, (4), that is a law of logic? Well, (4)’s antecedent is a form-term. CL-1 is of course only a sample principle; its closest relatives talk of other universal generalizations whose antecedents are form-terms, the sort of generalizations issued by the original model of Quine’s Ladder according to the procedure I called the outer method in Section 5: For every x, if x is a sentence of the form ‘p or not p’, then x is true; For every x, if x is a sentence of the form ‘p or q’, then x is true; For every x, if x is a sentence of the form ‘If B says ‘p’ then p’, then x is true. Here are examples of true instances of their antecedents: ‘ ‘Tom is mortal or Tom is not mortal’ is a sentence of the form ‘p or not p’ ’; ‘ ‘Tom is mortal or snow

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is green’ is a sentence of the form ‘p or q’ ’; ‘If B says ‘snow is white’ then snow is white’ is a sentence of the form ‘If B says ‘p’ then p’. They are indeed somewhat special: they are truths, but not any old truths; they are truths about sentence-forms, truths about the logico-syntactic structure of sentences of our language. But does this make a difference to the issue at hand? Consider an argument from one of the generalizations to one particular item on a list à la (3)—but let us take the second generalization instead of the first to avoid distraction from irrelevant side issues: (7) For every x, if x is a sentence of the form ‘p or q’, then x is true. (8) ‘Tom is mortal or snow is white’ is a sentence of the form ‘p or q’. (9) ‘Tom is mortal or snow is white’ is true. There has been a tendency in the (relatively) recent history of logic to talk of sentences such as (8), truths from the theory of the syntax of a language, as if they were logical truths: almost-logical truths.36 If they were logical truths, one could say simply that (9) is a logical consequence of (7); by the principle that, if C is a logical consequence of A&B, then C is a logical consequence of A, if B is a logical truth. But almost-logical truths are not logical truths. There is no good reason for saying that (9) is a logical consequence of (7); it is not: it is a logical consequence of the conjunction of (7) with (8).This is not to deny that sentences such as (8) are special. One might plausibly hold, for example, that the proposition expressed by (8) is a necessary truth, so that the proposition expressed by (9) can be said to be entailed by the one expressed by (7), where a proposition C is entailed by a proposition A iff it is not possible that A is true and C false—the proposition expressed by (8), being necessary, drops from consideration on this understanding of entailment.37 But how does any of this help with CL-1, or with CL-1’s sibling which says that by affirming (7) we affirm each of the infinitely many sentences that are like (9)? It does not, unless the formal nature of sentences like (8) is claimed to have some extravagant epistemological benefits, unless it is claimed that form-truths such as (8) are a priori or analytic in a such a manner that anyone who has the

36. Tarski said (roughly) that a definition of ‘true’ is an adequate definition of truth (for a formalized language) iff it has the instances of his biconditionals as consequences (1935, 187–88). It turns out that these instances are not logical consequences of the definition he proposes; they are, at best, logical consequences of the conjunction of his definition with (logical consequences of) various principles, referred to as “the specific axioms of the metalanguage”, detailing the syntactic makeup of the formalized language under consideration. (cf. 1935, 173). When he simply calls the instances of his biconditionals “consequences” of his definition, not mentioning the syntax principles, he treats these principles as if they were logical truths. I should point out that this tendency of authors such as Tarski (and Carnap) to treat truths about syntax as if they were logical truths is limited to truths about the syntax of formalized languages. 37. Horwich maintains that, relative to the instances of T, or rather TP, “any generalization of the form ‘All instances of [the form] S are true’ will entail all the instances of S—which are precisely the statements we need to generalize” (1998b, 124; my emphasis). This seems right if Horwich means ‘entails’ as defined in the text; however, he said on the previous page, that we can “derive” the alleged “instances” from the generalization, which is wrong. Note also that formclaims about propositions are quite different from form-claims about sentences: there is no such thing as a syntactic metatheory for propositional forms.

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cognitive wherewithal to affirm (7) thereby implicitly knows or believes or affirms each one of the infinitely many sentences such as (8)—this would give us all the additional premises needed for CL-1 and its siblings for free. There is, however, not much to be said for that claim, especially considering that very many of (8)’s siblings are of such mindboggling complexity that any being remotely like us is entirely unable to even begin to grasp them.38 Moreover, focusing on generalizations such as the ones listed above, that is, universal generalizations whose antecedents are form-terms, is in any case too narrow. These are the sort of generalizations issued by the original paradigm of Quine’s Ladder which implements the outer method. As pointed out in Section 5, that paradigm is incomplete. Many universal generalizations involving the truth predicate do not take this special form. They require a variation on Quine’s Ladder proceeding in accordance with the inner method; for example: ‘For every x, if B says x then x is true’. The true antecedents of the instances of this sort of generalizations are not form-truths, not truths about the logico-syntactic structure of our language: they cannot lay claim to any such special status. Consequently, the recent suggestion to focus narrowly on CL-1 and its closest relatives, because of their special subject matter, is off the mark—we were led to CL-1 with its reference to (4) merely because we adopted Quine’s sample generalization. To handle all universal generalizations involving the truth predicate, Quine needs a more general principle, a principle saying that by affirming such generalizations we affirm each of the consequents of those of their instances whose antecedents are true; and that is the sort of closure principle that makes a highly questionable claim about affirmation. 7. NEEDING THE TRUTH PREDICATE? Quine says the utility of the truth predicate lies in the role it plays in generalizations. This raises two questions: Is the truth predicate really needed for what Quine says it is needed for? and: Does it really serve this need? The previous section was concerned with the second question. In this section, I address, more briefly, the first. According to the redundancy theory, the truth predicate is dispensable. According to Quine, it is indispensable because of the role it plays in generalizations: generalizations involving the truth predicate are the counterexamples that undo the redundancy theory, the data the redundancy theory cannot handle. Quine then develops his disquotational account of truth which, in spite of the disagreement over indispensability, retains quite a bit of the deflationary spirit of the redundancy theory. Quine’s brand of deflationism is canonical deflationism: it conforms with the language of first-order predicate logic, which Quine (1960) taught us to call the canonical notation. Consider a universal generalization containing the truth

38. It would be somewhat ironic if Quine’s view about how the truth predicate serves the need he has identified were to ultimately depend on the idea that the infinitely many true antecedents of the instances of generalizations such as (4) and (7) are “implicitly affirmed” by us, as soon as we affirm (4) or (7), on the grounds that all these antecedents are a priori or analytic.

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predicate and a partial paraphrase into canonical notation—suppressing the details of ‘F’ for simplicity’s sake: (10) Every sentence that is F is true. (10.1) For every x, if x is a sentence that is F, then x is true. Quine’s objection to the redundancy theory is this: “In such contexts [(10)], when paraphrased to fit predicate logic [(10.1)], what stands as subject of the truth predicate is not a quotation but a variable. It is there that the truth predicate is not to be lightly dismissed” (Quine 1987, 214). That is, ‘is true’ cannot be removed from (10.1); the remainder is not a well-formed sentence of the canonical language; hence, ‘is true’ is not dispensable. Noting Quine’s reliance on paraphrase into canonical notation, one might take him to have established a conditional conclusion: if paraphrase into canonical notation gives the correct analysis of generalizations involving truth, then the redundancy theory fails—and this conditional might suggest trying an alternative paraphrasing strategy with an eye towards helping the redundancy theory to a comeback. ‘If ‘p’ is F then ‘p’ is true’, looks promising at first, because the last part seems reducible to ‘p’—the truth predicate being dispensable when we are predicating it only of quoted sentences. But this is not a paraphrase of (10) at all; it is just a schema while (10) is a universal generalization. The next move is simply to “quantify over” the schematic sentence letter, as in (10A), and then disquote the truth predicate to reach (10B): (10A) For every p, if ‘p’ is F, then ‘p’ is true; (10B) For every p, if ‘p’ is F, then p. This is uncanonical deflationism—uncanonical because (10A) and (10B) are not well-formed expressions of the canonical language. In the notation of firstorder predicate logic the variables of the expression following the quantifier phrase have to be in name position; they function much like pronouns. In (10A) and (10B) the variables following the quantifier phrase are in sentence position; consequently, the quantifier notation employed in these formulations is not the quantifier notation canonized in first-order predicate logic.39 According to uncanonical deflationists, the truth predicate is dispensable after all: it is not needed for what Quine says it is needed for. The heretics aim to uphold the dispensability thesis, in the face of Quine’s objection, by reconstruing the data Quine said cannot be handled by the redundancy theory, so that they can be handled by the redundancy theory. Here we have a challenge to Quine’s claim that the truth predicate is needed for expressing generalizations. The ensuing debate turns on the question whether the canonical paraphrasing strategy provides the correct analysis of truth-involving

39. ‘For every sentence, if it is F, then it is true’ is a close reading of (10.1). Trying to read (10B) along the same canonical lines produces nonsense: ‘For every sentence, if ‘it’ is F then it’.

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generalizations (not much to discuss there for Quine: of course it does, it is the correct analysis of all generalizations); and on the question whether the uncanonical paraphrases make any sense at all and/or make sufficient sense to serve the heretics’ purposes. The issue has been much discussed, though not always with direct reference to Quine.40 A second challenge can be made. Quine says in passage [H] we need the truth predicate if we want to affirm a lot of sentences that we can demarcate only by talking about the sentences. To do so, we select an appropriate general term, ‘F’, to sweep out the desired dimension of generality and affirm: (10) Every sentence that is F is true. But if we can do that, if we can thus sweep out the desired dimension of generality, why not adopt a more “pragmatic” strategy? Instead of affirming (10), so the suggestion, I could just as well affirm a generalized explicit performative: (11) I hereby affirm every sentence that is F, thereby affirming every sentence that is F. No need for the truth predicate. Such a performative will be available whenever Quine’s preferred universal generalization is available, that is, whenever we have a general term, ‘F’, to sweep out the desired dimension of generality. Quine does not consider this strategy, even though it seems suggested by the very formulation he uses in passage [H]. To get a better grip on this performative strategy, consider a singular explicit performative such as: (12) I hereby affirm ‘snow is white’. When I affirm (12), I affirm that I affirm ‘snow is white’, so that my affirmation is automatically true: (12), when affirmed, is self-verifying. But that is not all I affirm when affirming (12): I also affirm that snow is white. Say I state in court: ‘I hereby state that I have never engaged in the act of flag-burning’. Photographs are then produced showing me engaged in the act of flag-burning. I will not evade a charge of perjury arguing that I did not state that I was never so engaged, but that I merely stated that I stated that I was never so engaged.41 So, when I affirm (12), I affirm that I affirm ‘snow is white’, and I thereby also affirm that snow is white. We can even put it like this: I affirm directly that I affirm ‘snow is white’, and I affirm indirectly that snow is white. Similarly for (11)—so the suggestion: when I affirm (11), I affirm directly that I affirm every sentence that is F, and I thereby indirectly affirm every sentence that is F—and I don’t need the truth predicate for it.

40. See Field (1986, Section 1, and 1994). David (1994, chap. 4), and Künne (2003, chaps. 2 and 4), provide more discussion and most of the relevant references. Hill (2002) and Künne (2003, chap. 5), are two recent defenses of the heretical point of view. 41. See Lycan (1984, chap. 6), which contains more discussion and references. I have updated his example which is: ‘I state that I have never been a Communist’.

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Admittedly, (12) does not mean the same as ‘Snow is white’, and (11) does not mean the same as the conjunction of the sentences that are F; they both have surplus meaning, saying something about the speaker in addition. But on the face of it the point does not appear to bear on the issue at hand.42 Quine claims that by affirming ‘ ‘snow is white’ is true’ we affirm ‘snow is white’. He does not claim that these sentences mean the same: we saw in the previous section that he does not take the two sides of Tarski’s biconditionals to mean the same, and he is anyway skeptical about sameness of meaning. Our performative strategist simply points out that by affirming ‘I hereby affirm ‘snow is white’ ’ I affirm ‘snow is white’; she does not need to claim that the two sentences mean the same. In fact, she may share Quine’s views about the truth-predicate when applied to quoted sentences, concentrating exclusively on his thesis that we need the truth predicate when we want to affirm a lot of sentences that are F. She claims I can affirm this lot of sentences, without the truth predicate, by affirming (11), never mind that in doing so I also affirm something additional. How could Quine respond to this challenge? There is a curious difference between some of the performatives and Quine’s generalizations, owing to the formers’ surplus meaning. When I affirm ‘I hereby affirm every sentence of the form ‘p and q’ ’, what I affirm directly is true, whereas what I thereby affirm indirectly, the conjunction of sentences of the form ‘p and q’, is false: I affirm a truth to a affirm a falsehood. Not so with ‘Every sentence of the form ‘p and q’ is true’.43 This generalization is true only if what we affirm indirectly by affirming it, the conjunction (of conjunctions), is true too, that is, the generalization is false, just like the conjunction (of conjunctions). So, the performative functions differently than the truth involving generalization it aims to supplant. Does this show that we need the generalization? It does, if one grants Quine the following addendum to his view: When we want to affirm a batch of sentences that are F, we also want to affirm them by something satisfying the condition: it is true, only if the sentences that are F are true. This condition is not satisfied by the explicit performative ‘I hereby affirm every sentence of the form ‘p and q’, because of its curious self-verifying feature, when affirmed. There is a second response to the performative challenge: Explicit performatives do not behave properly in embedding contexts.44 Let us see what happens when a performative like (11) is embedded in a conditional such as: ‘If I hereby affirm every sentence that is F, then. . .’. The first thing to note is that, in this

42. It would be relevant if the Quinean view did require that the two sides of Tarski’s biconditionals mean the same and that universal generalizations such as (4) mean the same as the conjunctions of sentences like the ones gestured at in (2). Gupta (1993a) argues that the Quineans must ultimately fall back on such meaning claims, to their disadvantage. I have tried to present the Quinean view without committing it to these meaning claims. 43. For argument’s sake, I am now granting Quine that by affirming this generalization we affirm the infinite lot of sentences of the form ‘p and q’; see the previous section for criticism. 44. The performative strategy under consideration is somewhat reminiscent of Strawson’s first paper entitled “Truth” (1949), but Strawson did not pay much attention to generalizations. Ever since Geach (1960), objections from embedding have become the standard objections to performative accounts in general.

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context, the performative is not affirmed. But this means that it is not true in this context: ‘I hereby affirm every sentence that is F’ is true when it is affirmed, and false when it is not affirmed, for it says that I hereby affirm every sentence that is F. Now, if unaffirmed performatives are always false, they cannot play the role played by Quine’s truth-involving generalizations, because they make too many conditionals true. Compare ‘If I hereby affirm every sentence of the form ‘p or not p’, then snow is green or grass is white’ with ‘If every sentence of the form ‘p or not p’ is true, then snow is green or grass is white’. The former is true, having a false antecedent, while the latter is false. Moreover, they make too many conditionals false, namely conditionals in which they appear as (unaffirmed) consequents. Compare ‘If snow is white, then I hereby affirm some sentence of the form ‘p or q’ ’ with ‘If snow is white, then some sentence of the form ‘p or q’ is true’. While the latter is true, the former is false, having a true antecedent and a false consequent. The explicit performatives cannot do the work of the truth-involving generalizations they aim to supplant. This objection to the performative strategy seems telling, but it also points to a lacuna in Quine’s own account, which harks back to Section 2. There we saw that Quine gets into some trouble by focusing too narrowly on occurrences of ‘ ‘Snow is white’ is true’ that carry assertoric force, leaving non-assertoric, embedded occurrences in the lurch. I tried to show that we can get Quine out of this trouble. Later we saw Quine claiming, for example, in passage [H], that we need the truth predicate for generalizations that we need if we want to affirm lots of sentences that we can demarcate only through semantic ascent. Again the focus on assertoric uses, though this time on assertoric uses of generalizations involving ‘is true’. This raises the question how Quine himself would account for non-assertoric uses of such generalizations; in particular, how he would account for embedded uses where such a generalization appears unasserted as a clause within another sentence. To my knowledge, Quine addresses this issue nowhere. Consider especially multiple embedded uses, for example: (13) Every sentence of the form ‘p and q’ is true if and only if some sentence of the form ‘p and not p’ is true. Application of Quine’s Ladder to such cases is by no means straightforward —and there are of course considerably more complicated cases with multiple embedded truth-involving generalizations waiting in the wings. What would the first rung of Quine’s Ladder for (13), the startup list, look like? What about the initial intention to generalize (“we are seeking generality”; see [B]):What would be its content? It is fairly clear that Quine’s original model of the Ladder, the one proceeding mechanically in accordance with the outer method, cannot handle such examples (cf. Section 5): it issues only free-standing generalizations: ‘Every sentence of the form F is true.’—period. Maybe the more versatile, because less regimented (more ad hoc?), variant of Quine’s Ladder that employs the inner method is more promising. But even there it is not obvious how to construct a Ladder leading up to a sentence such as (13). I leave this to the reader as a homework exercise.

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REFERENCES Blackburn, S. and Simmons, K. 1999. “Introduction.” In Truth, eds. S. Blackburn and K. Simmons, 1–28, Oxford: Oxford University Press. Church, A. 1950. “On Carnap’s Analysis of Statements of Assertion and Belief.” Analysis 10: 97–99. David, M. 1994. Correspondence and Disquotation: An Essay on the Nature of Truth. New York: Oxford University Press. ———. 2002. “Minimalism and the Facts about Truth.” In What is Truth? ed. R. Schantz, 161–75. Berlin & New York: Walter de Gruyter. Field, H. 1972. “Tarski’s Conception of Truth.” Reprinted in Truth and the Absence of Fact, 3–26. Oxford: Clarendon Press, 2001. ———. 1986. “The Deflationary Conception of Truth.” In Fact, Science and Morality: Essays on A. J. Ayer’s “Language, Truth & Logic,” ed. G. Macdonald and C. Wright, 55–117. Oxford: Basil Blackwell. ———. 1994. “Deflationist Views of Meaning and Content.” Reprinted in Truth and the Absence of Fact, 104–40. Oxford: Clarendon Press, 2001. ———. 2001. Postscript to “Deflationist Views of Meaning and Content.” In Truth and the Absence of Fact, 141–56. Oxford: Clarendon Press. Geach, P. T. 1960. “Ascriptivism.” Reprinted in Logic Matters, 250–54. Oxford: Basil Blackwell, 1981. Gupta, A. 1993a. “A Critique of Deflationism.” Philosophical Topics 21: 57–81. ———. 1993b. “Minimalism.” Philosophical Perspectives 7: 359–69. Hill, C. 2002. Thought and World: An Austere Portrayal of Truth, Reference, and Semantic Correspondence. Cambridge: Cambridge University Press. Horwich, P. 1982. “Three Forms of Realism.” Reprinted in Horwich 2004: 7–31. ———. 1998a (11990). Truth, 2nd ed. Oxford: Clarendon Press (1st ed. Oxford: Basil Blackwell, 1990). ———. 1998b. Meaning. Oxford: Clarendon Press. ———. 2004. From a Deflationary Point of View. Oxford: Clarendon Press. Künne, W. 2003. Conceptions of Truth. Oxford: Clarendon Press. Leeds, S. 1978. “Theories of Reference and Truth.” Erkenntnis 13: 111–29. Lycan, W. G. 1984. Logical Form in Natural Language. Cambridge, MA: The MIT Press. McGee, V. 1993. “A Semantic Conception of Truth?” Philosophical Topics 21: 83–111. Putnam, H. 1978. Meaning and the Moral Sciences. Boston: Routledge. Quine, W. V. 1951. Mathematical Logic, revised ed. Cambridge, MA: Harvard University Press. ———. 1953. “Notes on the Theory of Reference.” In From a Logical Point of View, 2nd revised ed., 130–38. Cambridge, MA: Harvard University Press, 1980. ———. 1956. “Quantifiers and Propositional Attitudes.” Reprinted in The Ways of Paradox, 185–96. Cambridge, MA: Harvard University Press, 1976. ———. 1960. Word and Object. Cambridge, MA: The MIT Press. ———. 1973. The Roots of Reference. La Salle, IL: Open Court. ———. 1982. Methods of Logic, 4th ed. Cambridge, MA: Harvard University Press. ———. 1986. Philosophy of Logic, 2nd revised ed. Cambridge, MA: Harvard University Press. (1st ed., Englewood Cliffs, NJ: Prentice Hall, 1970.) ———. 1987. Quiddities: An Intermittently Philosophical Dictionary. Cambridge, MA: Harvard University Press. ———. 1992. Pursuit of Truth. 2nd revised ed. Cambridge, MA: Harvard University Press. (1st ed., Harvard University Press, 1990.) Ramsey, F. P. 1928. “The Nature of Truth.” Episteme 16 (1990): 6–16. Soames, S. 1984. “What Is a Theory of Truth?” The Journal of Philosophy 81: 411–29. ———. 1999. Understanding Truth. New York: Oxford University Press. Strawson, P. F. 1949. “Truth.” Analysis 9: 83–97.

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Tarski, A. 1935. “The Concept of Truth in Formalized Languages.” In Logic, Semantics, Metamathematics, 2nd ed., trans. J. H. Woodger, ed. J. Corcoran, 152–278. Indianapolis, IN: Hackett 1983. ———. 1944. “The Semantic Conception of Truth.” Philosophy and Phenomenological Research 4: 341–76. ———. 1969. “Truth and Proof.” Scientific American 220; reprinted in A Philosophical Companion to First-order Logic, ed. R. I. G. Hughes, 101–25. Indianapolis, IN: Hackett Publishing Company, 1993.

Midwest Studies in Philosophy, XXXII (2008)

Truth-definitions and Definitional Truth DOUGLAS PATTERSON

T

arski’s procedure for defining truth is often criticized for turning contingent truths about meaning into necessary or even logical or mathematical truths. The criticism is widely accepted, but I will argue that it is misguided because it rests on confusions about definition, in particular confusions about what is supposed to be preserved by the substitutions licensed by a definition. The result, I hope, will be a vindication of Tarski as well as a clarification of what is involved in evaluating semantic definitions, claims, and theories. I intend the discussion, however, to be of interest not just to those with a scholarly interest in Tarski, and not just to those engrossed in the minutiae of the truth literature, but to anyone who has ever taken an interest in definitions and the relation of definitional truth to other sorts of truth, for instance, logical truth, mathematical truth, and necessary truth. The more general thesis of this paper is that definitions, in the familiar sense of explanations of the meanings of words, need not be logically or even necessarily true. As is well known, Tarski’s way of defining truth relative to a language L is intended (the famous “Convention T”) to result in the implication of lists of “T-sentences,” sentences of the form

s is true in L if and only if p

where what is substituted for “p” translates s. The effect of the procedure is, as Tarski notes, to treat the T-sentences as definitional truths: explanations of the Midwest Studies in Philosophy: Truth and its Deformities Volume XXXII Editor by Peter A. French and Howard K. Wettstein © 2008 Wiley Periodicals, Inc. ISBN: 978-1-405-19145-6

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meaning of “is true” (1983b, 187).1 As such, they allow the elimination of sentences containing “is true” against the background of the mathematical and logical theories which are required for their formulation. As Tarski grants (1983b, 188), the sort of definition he requires could simply take the form of a list of T-sentences if only the language for which truth was defined had a finite number of sentences. For a hypothetical one-sentence language L with “snow is white” (meaning what it means in English) as its only sentence, the truth definition would come to: (1) for all x, x is true in L if and only if x = “snow is white” and snow is white. With respect to the T-sentence (2) “Snow is white” is true in L if and only if snow is white substituting “ = ‘snow is white’ and snow is white” for “is true in L”, as the definition allows, gives (3) “Snow is white” = “snow is white” and snow is white iff snow is white. Many commentators find a gross error in this procedure, on the grounds that Tarski’s definitions allow the T-sentences to be transformed into logical, mathematical or necessary truths like (3) despite the fact that the T-sentences themselves are not truths of these sorts. Here are three versions of the argument. The first is from Putnam: Since (2) is a theorem of logic in meta-L (if we accept the definition, given by Tarski, of “true-in-L”) since no axioms are needed in the proof of (2) except axioms of logic and axioms about spelling, (2) holds in all possible worlds. In particular, since no assumptions about the use of the expressions of L are used in the proof of (2), (2) holds true in worlds in which the sentence “Snow is white” does not mean that snow is white. . . . all a logician wants of a truth definition is that it should capture the extension (denotation) of “true” as applied to L, not that it should capture the sense—the intuitive notion of truth (as restricted to L). But the concern of philosophy is precisely to discover what the intuitive notion of truth is. As a philosophical account of truth, Tarski’s theory fails as badly as it is possible for an account to fail. A property that the sentence “Snow is white” would have (as long as snow is white) no matter how we might use or understand that sentence isn’t even doubtfully or dubiously “close” to the property of truth. It just isn’t truth at all. (1994, 333) 1. In order to set aside complications arising from the semantic paradoxes, I ignore problems that arise from the worry that the truth-definition for a language might be translatable into that language. I have commented on the paradoxes elsewhere (2007a, 2007b, forthcoming a) and what I say here could easily be extended in terms of the view I have developed. Since all the problems covered in this paper arise even if we consider definitions for languages free of semantic vocabulary and other paradox-inducing features, no harm is done in leaving the issue aside.

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The second comes from John Etchemendy: Consider a trivial example, just to drive the point home. Suppose we are dealing with a finite language, say one that contains just the two sentences “S” and “R,” meaning, respectively, that it is snowing and that it is raining. Before we give a Tarskian definition of truth, it is natural to think of the two instances of schema T, (4) “S” is true if and only if it is snowing, (5) “R” is true if and only if it is raining, as expressing important semantic facts about the language. In particular, it is natural to think of these as describing the truth-conditions of our two sentences. Intuitively, (4) and (5) hold because of the meanings of “S” and “R”; a semantic fact, if ever there was one. But when we give a Tarskian definition of “is true,” these become the following truths of logic and syntax: (4′) [(“S” = “S” and it is snowing) or (“S” = “R” and it is raining)] iff it is snowing; (5′) [(“R” = “S” and it is snowing) or (“R” = “R” and it is raining)] iff it is raining; The latter sentences clearly carry no information about the semantic properties of our language, not even about the truth-conditions of its sentences. There are various ways to emphasize this; we might note, for example, that a person could know what is expressed by (4′) and (5′) without knowing anything whatsoever about the meanings of sentences “S” and “R” or that (4′) and (5′) would remain true even if all the semantic properties of this language were to change. But, however, we emphasize it, the point remains the same: the semantic facts about a language, those we aim to characterize in formal semantics, are not simply facts of logic, syntax, and set theory. Yet these facts are the only kind that can possibly follow from a Tarskian definition of truth. (1988, 57) Richard Heck adds his agreement: Note, however, that the T-sentences come out as theorems of the meta-theory, in this case, say, of second-order arithmetic plus certain definitions: the T-sentences are definitional transcriptions of theorems of second-order arithmetic . . . This is a point it took some time to get across: that it is now so widely accepted is due entirely to the heroic efforts of Etchemendy, Soames, Putnam, and others. But once it has been made, it follows immediately that Tarski’s definition is, by itself, no good as a semantic theory. No way is it a theorem of arithmetic that “2 + 2 = 4” is true if and only if 2 + 2 = 4; it’s an empirical fact about what expressions of the language of arithmetic mean.

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(1997, 537) The basic claim, then, is this. Tarski’s definitions allow substitution of the defined expression “is true” for other expressions of the theory to which the definition is added and vice versa. Since in the case at hand the theories are logical or mathematical—“logic, syntax, and set” theory, as Etchemendy has it—this means that if Tarski’s definition is good, semantic truths, namely the T-sentences, are, in Heck’s phrase, “definitional transcriptions” of theorems of logic, syntax, and set theory, which, as Heck has it, comes to second order arithmetic. But, now the objection comes, obviously semantic truths aren’t logical or mathematical truths; for instance, as Putnam and Etchemendy explicitly put it, semantic truths are contingent but the result of replacing “is true” with Tarski’s definition in a T-sentence is clearly a necessary truth, since it is a logical or mathematical truth. So Tarski’s definition is no good: if it were good, claims that are clearly not logical or mathematical or even necessary truths—for example, “ ‘snow is white’ is true if and only if snow is white”—would have to be truths of these varieties. These arguments assume that substitution of definitional equivalents preserves certain sorts of truth, for example, logical truth, mathematical truth or necessary truth. For instance, Etchemendy’s initial version of the complaint is that (4′) is a logical truth while (4) isn’t, and he emphasizes this by pointing out that (4′) is a necessary truth while (4) isn’t. Yet, the suggestion is, by Tarski’s definition (4) “becomes” (4′),2 and, since Etchemendy thinks this is objectionable precisely on the grounds that (4) isn’t necessary or logical while (4′) is, he assumes in taking the difference to show that something is wrong with Tarski’s definitions that substitution of genuine definitional equivalents will preserve necessary truth. Putnam runs through roughly the same points. Heck isn’t as explicit about necessity (except perhaps in the implied contrast with “empirical”) but he is still committed to the claim that substitution of definitional equivalents preserves “arithmetic” truth, since the blunder is supposed to be that Tarski’s definition makes a T-sentence into a truth of arithmetic when one substitutes in accord with it. Thus Putnam, Etchemendy, and Heck all assume that substitution of definitional equivalents preserves logical, mathematical, and necessary truth, and on this ground object to the idea that a Tarskian definition of truth could be a good one. The assumptions, however, are false: substitution in accord with a good definition preserves neither logical, nor mathematical, nor even necessary truth, as I will now argue. I will keep the discussion as non-technical as possible, though at times I will note the fact that definitions rigorously considered are to be taken against the background of a theory and a set of contexts. (The reader wanting a good introduction to the formal theory of definition should consult Belnap 1993.) Let us begin with logical truth. Consider a familiar definition: (6) Bachelors are unmarried men. 2. The whole problem, really, as we’ll see, is packed into this seductive but literally false “becomes.”

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Is (6), with the obvious first order translation “("x)(Bx iff (Ux and Mx) ),” a truth of logic? Of course not. Consider the absurdities that would follow if it were: that dictionaries are catalogues of logical truths, that Quine’s criticism of analyticity, which left the notion of logical truth unchallenged, was radically misguided since there is no difference between logical truth and logical truth plus substitution of synonyms for synonyms, and so on. Notice also that it makes no difference whether definition is stipulative or not: (7) Wrinks are wild elephants. This isn’t a logical truth either, or nobody would have to stipulate it. Again, absurdities follow if one assumes that it is a logical truth, for instance that matters of logic can be stipulated. However, if we accept (6) and (7), substitution in accord with them in some cases results in logical truths, turning, for instance, the non-logical (8) Bachelors are unmarried. into the logical (9) Unmarried men are unmarried. Since (8) is definitionally equivalent to (9), but (9) is a logical truth and (8) isn’t, substitution in accord with a good definition doesn’t preserve logical truth: the trip from (9) to (8) is an example of definitionally licensed substitution that doesn’t do so. I suppose this might seem to some to motivate reconsidering the claim that (6) is really a correct definition, but then the stipulative (7) makes the point even more clearly: “wild elephants are elephants” is a logical truth, but since (7) is stipulative, the failure of preservation of logical truth when substitution gives “wrinks are elephants” can’t be blamed on (7) somehow having been faulty as an account of what “wrink” already meant. For any good definition, there are non-logical truths that become logical truths when we substitute the definiens for the definiendum— in the limit the definition itself will always be an example.3 One can therefore accept Tarski’s definition of truth while maintaining that Etchemendy’s (4) is not a logical truth. Given this, we may note in his defense that Tarski himself never says that a T-sentence like (4) is a logical truth. Since substitution of definitional equivalents doesn’t preserve logical truth, we can only conclude that Tarski quite rightly didn’t think that giving a definition that showed (4′) to be equivalent to (4) relative to his meta-theory somehow made (4) into a logical truth or assumed that it was one.

3. Note that the point also disarms any inclination to say that definitions are the sort of thing that can’t be true (or false): if that were so, then substituting definiens for definiendum from (6) would turn the truth “Unmarried men are unmarried men” into the “untruth” (6). But then substitution of definitional equivalents wouldn’t even preserve truth.

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Let us now consider the claim that substitution of definitional equivalents preserves mathematical truth. (I take “mathematical” to stand in for various terms taken from the quotations above—“arithmetic,” “set-theoretic,” “formalsyntactic.”) Consider the following familiar points of chemistry.4 First, a version of the standard IUPAC definition of valence (Muller et al. 1994, 1175), clarified and simplified for the sake of example:5 (10) The valence of an element is either the negation of number of hydrogen atoms that can stably combine with an atom of it, or the number of hydrogen atoms for which it can be substituted to form a stable compound. Second, a simplified version of the law of valences is (11) In a stable compound the valences of the components sum to zero. (10) is simply a definition that reports the usage of “valence” and (11) is a basic empirical truth of chemistry. But the effect, in concert, of (10), (11) and the obvious claims about the valence of hydrogen and oxygen is to allow us to inter-derive claims like (12) Two atoms of hydrogen combine stably with one atom of oxygen and (13) 2(1) + (-2) = 0 Given basic chemistry and the definition of valence, empirical claims about the combinations of elements to form molecules such as (12) are transformable into arithmetic claims such as (13) and vice versa. This doesn’t make (12) a mathematical truth. Hence, substitution of definitional equivalents doesn’t preserve mathematical truth. Indeed, as the example indicates, if substitution of definitional equivalents preserved mathematical truth, there would be no such thing as applied mathematics: it’s essential to the application of mathematics that empirical terms can be defined with the help of mathematical terms, so that empirical claims can be transformed into mathematical equivalents, calculations done, new empirical equivalents be derived by the same definitions and then put to empirical use as predictions, engineering specifications, and so on. 4. The comparison is of course inspired by Field (1972). 5. The actual definition is in terms of the maximal number of hydrogen atoms that can combine with something and it also interposes a notion of “univalence” so as not to define valence directly in terms of any particular element. I also modify things to involve negatives to simplify the interaction with the law of valences. Comments on the IUPAC definition sometimes say that it ignores or “simplifies” some chemical facts, but one could also read it as leaving valence somewhat indeterminate when there is corresponding indeterminacy about “maximal” or “combine” for various chemical compounds.

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The point here has nothing to do with mathematics in particular. Consider two theories, T and T′, with distinguished vocabularies involving terms a1, . . . , an of T and b1, . . . , bm of T′ respectively and perhaps distinguished axioms. It might be a substantial fact about T 艛 T′ that every sentence j involving some given bi is equivalent in T 艛 T′ to a substitution instance j′ in T, where bi is replaced by some of the terms a1, . . . , an. It might be the case that for all bi any j in T 艛 T′ involving them is equivalent in T 艛 T′ to a sentence involving only terms from a1, . . . , am so that all theorems of T 艛 T′ containing b1, . . . , bm are definitionally equivalent to theorems of T alone. In such a case, T can be extended to T 艛 T′ by means of definitions. It doesn’t follow that truths of T 艛 T′ have all of the features enjoyed by truths of T alone. We can see this in at least two ways, which simply reflect a basic point about the theory of definitions. (1) Distinguished Vocabulary. Suppose a1, . . . , an from the previous paragraph are nifty terms, and b1, . . . , bm are keen terms. The fact that T can be extended to T 艛 T′ doesn’t show that all terms of T′ are nifty, or that some terms of T are keen. That one can define a long word in terms of short ones does not show that short words are actually long or long words are actually short. Perhaps this looks uninteresting, but consider in this connection how easily debates over logicism degenerate into seemingly verbal quibbles over whether or not certain expressions are “logical”: the philosophical significance of a definition turns crucially on the categories into which the definiendum and definiens fall. (2) Intensional Differences. Suppose T 艛 T′ is extensional and suppose some terms can be eliminated by a definition that extends T to T 艛 T′. Suppose, however, that in fact the eliminated term has some intensional feature not expressed in T 艛 T′—for example, it’s a predicate such that everything that falls under it falls under it essentially, or as a fact of mathematics. If T itself doesn’t have the resources to express this modality, we shouldn’t expect definitions of terms in T to track the modality, which could, however, be revealed by a further extension of the theory to one that included a context producing sentences the truth value of which was sensitive to this intensional feature of terms. The chemical example above has this feature: the IUPAC definition of valence works against an assumed background theory that doesn’t include an “it is a mathematical truth that” operator; extend the theory to include this context and substitution in accord with the definition no longer preserves truth, as witnessed by the embedding of (12) and (13) in this context. The points just made are directly relevant to the views expressed by Putnam, Etchemendy and Heck, since the charge against Tarskian definitions is that though they map truths to truths against his chosen background theories, they don’t map mathematical truths to mathematical truths: (4) contains non-mathematical vocabulary and doesn’t follow from any mathematical theory, while (4′) is fully mathematical. What we have seen, though, is that there is simply no reason to think that substitution of definitional equivalents preserves mathematical truth or any other distinguished sort of truth attributed to the theorems of a certain theory, precisely because definability is a matter of preservation of consequence in a

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certain theory and doesn’t require preservation of consequence in a sub-theory thereof. What we should not do here is be seduced into overgeneralizing on the special case where we add a symbol to a theory via a stipulative definition in which we also stipulate that the added symbol belongs to some category to which the symbols of the definiens also belong. In such cases, of course, what follows from a sub-theory plus a definition and makes up the remainder of the full theory under discussion has the same status as the theorems of the sub-theory. But this is only because we’ve stipulated as much. And notice that we aren’t always free even to do that: one can’t stipulate that a long word defined in terms of short ones is itself thereby short. Furthermore, almost no interesting case of definition falls into the purely stipulative category where we specify ab initio both the meaning of a term and the categories to which it belongs. Interesting definitions, whether in the dictionary, in chemistry, or in philosophy and formal semantics, are specifications of the meaning of a definiendum already in use. They don’t merely introduce a string of symbols as an “abbreviation” for something else, but rather amount to substantial claims about intersubstitutibility.6 When a definition establishes that a term already in use in a theory can be eliminated in favor of other terms from a distinguished sub-theory, this is always an important fact about the theory and the relevant sub-theory; it isn’t a mere typographical addition to the sub-theory. For comparison, consider the evaluation of logicist attempts to “reduce arithmetic to logic” in this regard.7 The logicist goal is to show that two extant theories— arithmetic and logic—are in fact such that definitions of terms of arithmetic allow every theorem of arithmetic to be intersubstituted with a theorem that uses only the vocabulary of the designated logic. Were this to be done convincingly, it would remain the case that it is a substantial fact about two theories and their terms already in use that they are related in the manner the logicist demonstrates. Most of the issues here go missing from view if one thinks of the definitions as stipulative. Though a stipulated abbreviation of a logical truth is (by stipulation) a logical truth with all the features of logical truths, a proof that a definition will allow us to intersubstitute arithmetic theorems with logical ones relative to the background logic doesn’t show that arithmetic theorems are just abbreviations of logical theorems. Of course they could be such, but the mere possibility of definition doesn’t show this, any more than the equivalence, given (6), of “bachelors are unmarried” and “unmarried men are unmarried” shows that “bachelors are unmarried” is a logical truth.8 The logicist project is to reduce arithmetic to logic plus 6. That is, though not metalingusitic themselves, they’re true if and only if certain expressions in fact are intersubstitutible salva veritate relative to all models of the background theory to which the definition is added. 7. Obviously Frege is the classic example here, but I won’t wade into Frege scholarship in this short paper. 8. At some point one realizes that “just abbreviations” and related locutions are troublemakers. Is “bachelors are unmarried” “just an abbreviation” of a logical truth? Well, it’s definitionally equivalent to one. But the definition isn’t a logical truth, and neither is “bachelors are unmarried.” If “just an abbreviation” or “transcription” encourages us to forget this, these expressions should simply be dropped.

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definitions. This claim is still significant, since it comes to the idea that arithmetic amounts to nothing more than logic plus what one has to know to understand arithmetic terms. If true this would be an important feature of arithmetic, since nobody, by contrast, thinks that chemistry just comes to logic plus what one needs to know to understand chemical terms. Nevertheless, extra theses are required to turn this into an argument that the ontological commitments of arithmetic aren’t what one thought they were, or that no “faculty of intuition” of abstract objects need be postulated to explain mathematical knowledge. The logicist’s definitions can only show that arithmetic reduces to logic plus what you have to know in order to understand arithmetic terms. They don’t show that understanding such terms doesn’t require a relation to a range of problematic objects by means of a faculty of intuition. For that, substantial claims about understanding arithmetic terms are required. To put it another way, a successful definitional project of the sort the logicist would require would show that arithmetic theorems are true if and only if an assumed set of logical theorems is and if the facts expressed by the definitions obtain. What it would not show, all by itself, is that these facts can (or do) obtain without the existence of a range of problematic objects.9 I won’t attempt to comment decisively here because, whatever the fate of logicism, the point stands that logic alone is not the same as logic plus what one has to know to understand arithmetic terms. The same goes for Tarski: his goal wasn’t to reduce semantics to mathematics; it was to reduce semantics to mathematics plus definitions. The claim isn’t, then, the amazing one that somehow facts of English usage are determined eternally by the structure of the natural numbers, it is, rather, that a mere report on the proper usage of certain semantic terms allows a mathematical syntactic theory to be extended to a semantic theory. What Tarski’s definitions establish is that given a semantic theory for a language and a formal syntax that incorporates some mathematics, there is a mapping from sentences of the first to sentences of the second that preserves truth in models of their axioms. If, however, it isn’t established by other means that semantic truths are “really” mathematical truths, the mere existence of such a mapping doesn’t itself suffice to establish that semantic truths are really mathematical truths. They simply show that in certain cases semantic truths follow from mathematical truths plus what one has to know to understand semantic terms. In this connection, it is therefore important historically that Tarski nowhere declares that the T-sentences are logical or mathematical truths, or that substitution of definitional equivalents preserves mathematical truth. In fact, his discussions give the contrary impression: he often talks about defining truths of one theory in terms of those of another (semantics in terms of formal syntax in 1983b, mechanics in terms of geometry in 1983a) but never suggests that the availability of such definitions would mean that mechanical truths are really geometric truths, or semantic truths are really formal-syntactic truths. He says exactly what he says and 9. Most of the work of contemporary neo-logicists such as Hale and Wright (2001) is concerned to address such issues. Of course the “neo” in “neo-logicism” has to do with the fact that abstraction principles aren’t definitions, which magnifies the problems. The point in the text, though, is that even if definitions proper were available, this alone wouldn’t settle the epistemic and metaphysical issues.

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no more: certain theories can be extended to other theories by means of definitions. Heck allows for this point when he says “the T-sentences come out as theorems of the meta-theory, in this case, say, of second-order arithmetic plus certain definitions” but he then sweeps the crucial point under the rug with the comment that according to Tarski, “the T-sentences are definitional transcriptions of theorems of second-order arithmetic”. “Transcriptions” is crafted to suggest something like writing the theorems out in a different notation, and this impression then makes the subsequent emphatic “No way is it a theorem of arithmetic that ‘2 + 2’ = 4 is true if and only if 2 + 2 = 4” go down smoothly as a criticism of Tarski. Tarski, however, does not say that the T-sentence is “a theorem of arithmetic”; he says, as Heck notes earlier, that it is a theorem of arithmetic plus definitions. Since it is patent that “ ‘2 + 2 = 4’ is true if and only if 2 + 2 = 4” is a contingent, empirical truth that depends on the meaning and ultimately the use among groups of speakers of the expressions in “2 + 2 = 4,” there is no reason to think that Tarski ever thought otherwise.10 Again, he nowhere says anything of the sort, and he in some places takes explicit note of the fact that what words mean depends on how people use them (e.g. 1983b, 164). Surely it would be incredible if Tarski didn’t know that people might have used symbols differently from how they in fact have. Furthermore, as we’ve established, substitution of definitional equivalents doesn’t preserve mathematical truth, so even one who accepts that Tarski’s truth-definitions are good can perfectly well accept that the T-sentences are not “theorems of arithmetic”; they are, rather, theorems of “scientific semantics,” a discipline in which mathematics is applied in semantic claims. I turn now to necessary truth. Here the fact that Tarski’s definitions are semantic and thereby metalinguistic is crucially relevant. For consider (6) Bachelors are unmarried men again. (6) seems to be not just true, but necessarily true. Supposing it’s a necessary truth that all men are mammals, substitution into (14) unmarried men are mammals in accord with (6) seems to preserve necessary truth. Furthermore, it can look as though substitution in accord with a good definition ought to preserve necessary truth; this answers, ultimately, to the apparently plausible idea that in order to know a definitional truth you don’t need to know “how things are” or “how the world is,” you just need to know what words mean. However, if substitution in accord with a good definition preserves necessary truth, then Tarski is guilty of at least one charge: on the assumption that a Tarskian 10. Note that Putnam et al.’s confusion about Tarski is the same as the common confusion about logicism that specifies the logicist goal as to reduce arithmetic to logic, rather than logic plus definitions: in both cases it’s assumed, wrongly, that if one theory follows from another plus some definitions, then all theorems of the larger theory have some special status attributed to those of the sub-theory. The difference is that Putnam et al. see the consequence they wrongly discern as a bad one, while proponents of logicism tend to like the result of their form of the confusion.

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definition is good, the fact that Etchemendy’s (4′) is necessarily true implies that (4) should be necessarily true. But (4) isn’t necessarily true, so, if substitution of genuine definitional equivalents preserves necessary truth, we have to conclude that Tarski’s definition is no good. (We could also bite the bullet and cook up a reading of (4) on which it is necessarily true but this is acceptable. This is the strategy of the standard defenses of Tarski on this issue: just take him to have taken it to be a necessary truth about a language properly individuated that its words have the meaning they in fact actually have. I think this defense overlooks the real error in the arguments against Tarski and can’t be squared with passages like Tarski (1983b, 164) as mentioned above, so I won’t have anything to do with it here.) Does, however, substitution of definitional equivalents preserve even necessary truth? Not always. Consider: (15) “Socrates” refers to Socrates or, to make it more explicit, take (16) What “Socrates” refers to = Socrates. Is this a definitional truth? Of course: it’s true in virtue of the meaning of the word “Socrates,” and anyone who doesn’t know that what “Socrates” refers to is Socrates fails to understand “Socrates.” Is it a necessary truth? Of course not: if our language had been used differently, “Socrates” might have referred to something other than what it currently refers to.11 Call a definition that, like (16), explicitly specifies the semantic properties of an expression a semantic definition.12 Semantic definitions are true, when true, in virtue of the meanings of words they mention: it’s because “Socrates” means what it does that (16) is true. Semantic definitions may even be knowable a priori, at least on a conception of a priority where being a priori knowable is a matter of being knowable on the basis solely of what needs to be known to understand the terms involved. They are not, however, necessary truths. (16) is true in virtue of the fact that “Socrates” refers to Socrates. Anyone who understands “Socrates” knows what’s stated by (16). (16) is true in virtue of meaning. But (16) is not necessarily true: “Socrates” might have been used to refer to something else. Semantic definitional truths are another category of Kripke’s contingent a priori.13 When Socrates

11. Kripke (1980), using the example of Socrates and his name, mentions the interest of sentences like (15) in a discussion of the sorts of issues raised here. 12. See Hodges (forthcoming) on Kotarbinski’s use of this terminology and its influence on Tarski. 13. So are some analytic truths contingent? Kripke (1980, 122 note 63) prefers to hold that analytic truths are necessarily true. Kripke seems unsympathetic to holding that analytic truths could be contingent, alluding to a difference between fixing of reference as in (15) and (16) and genuine fixing of “sense”, which he associates with definition proper. I leave the fraught topic of

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was given his name, it was known in advance that this name would refer to him, but it doesn’t follow that the name couldn’t have been given to someone else. Here as in the previous cases the example might tempt one to raise the standards for definition: the very failure of (16) to be necessarily true could be seen to disqualify it. If so tempted, we should remind ourselves what we want of a definition. Definitions are supposed to explain the meanings of words. The interaction of quotation and semantic attribution in a semantic definition singles out the meaning of an expression for a special kind of attention: semantic properties, rather than remaining in the inferential background of a semantic definition, are explicitly ascribed. The result will always be a contingent truth about the quoted expression as long as expressions have their meanings contingently. It may be, nevertheless, perfectly complete as an attribution of the meaning the expression in question actually has. Even if one holds that (16) isn’t a complete definition of “Socrates” on the grounds that the meaning of a name is something more than its referent that for the sake of this discussion we can just call “sense,” an explicit ascription of this extra meaning to “Socrates” will still not be a necessary truth. Such an ascription will take the form: (17) The sense of “Socrates” = x where x is the sense of “Socrates.” The result, just as much as (16), would be a contingent truth about “Socrates,” even if it were the whole truth.14 As long as expressions have their meanings contingently, it will be possible completely to ascribe their meanings to them with claims that are nevertheless contingently true. One should therefore expect no connection between “giving the meaning” of an expression and saying something necessarily true as long as direct semantic attributions (which, after all, are our concern in semantics) are permitted. In particular, then, one should positively expect some definitional truths to be merely contingent. The same goes for the T-sentences as for (16): they are contingent. They are, however, also true in virtue of meaning: it’s because “snow is white” means what it does that it is true if and only if snow is white. They’re definitional in that they are true, when true, because the terms involved mean what they do. Plausibly, anyone who denies (2) doesn’t understand at least one of the expressions it contains. Despite all of this, the T-sentences are not necessary truths: the meaning of “snow is white” might have been different so that it had a different truth-condition. As with (17), as well, even if there is more to the meaning than mere truth-conditions, an explicit attribution of this more to “Snow is white” will be a contingent truth.

analyticity, and especially “analyticity”, aside here. It’s obvious, though, that if (16) states an “analytic” truth, then according to my view some analytic truths are contingent. 14. I suspect that adherence to the view that genuine definitions cannot be contingently true may behind early Wittgensteinian doctrines to the effect that sense can only be shown and cannot be said: sense has to be shown because anything that says what the sense of a term is will obviously be only contingently true and thus (here’s the confusion) unsuited to play the role of a definition of sense.

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Semantic definitional truths are both definitional and contingent, because they involve a special—and especially straightforward—sort of truth in virtue of meaning: they state the very meaning facts in virtue of which they are definitional. It’s because of this that they can be true in virtue of meaning in such an unproblematic way: in general, sentences are true when what they say is the case, and semantic definitional truths state things about the meanings of expressions they contain. They’re thus true in virtue of meaning, but they’re no more made necessarily true by this than any other sentences are made necessary truths just because what they state to be the case is in fact the case. Here as above, then, it is important to note that Tarski nowhere says that the T-sentences are necessarily true, that his definitions are necessarily true, or that substitution in accord with his definitions preserves necessary truth. Treating the T-sentences as definitional truths—as “explaining the meaning . . . of the sentences of the form ‘x is a true sentence’ that occur in them” (1983b, 187)—did not commit Tarski to the view that they were necessarily true, or that substitution in accord with them would preserve necessary truth. Since it’s so obvious that they aren’t necessarily true, there is no reason to think anything other than that he didn’t think they were necessarily true. Of course, I am not suggesting that Tarski anticipated Kripke’s remarks on the contingent a priori. I am saying only that he assumed that the T-sentences could function as definitions but that there is no evidence that he assumed that they weren’t contingent. Given a proper grasp, aided by Kripke, on the contingent a priori, one is in a position to see that Tarski’s assumptions, though inarticulate, were perfectly acceptable. Why, then, is it so easy for commentators to think that Tarski thought that the T-sentences expressed necessary truths, or that his use of them as partial definitions, or his method of defining truth so as to imply them, committed him to their being necessary truths? This is because he treated them as definitional truths in defining semantic notions within mathematical theories. We tend to think that mathematical truths are necessary truths, and hence we are easily lulled into the idea that when someone adds a definition to a mathematical theory he intends what he uses it to prove to have the same necessary status as the theorems of the theory had before it was added. Now Tarski doesn’t deny that mathematical truths are necessary truths, but it is of importance here to note that he doesn’t assert it either. This is because, coming out of the Polish philosophical tradition, Tarski was intensely skeptical about the possibility of making any good sense of any intensional notions at all. (For just one example, see the comments on the intensionality of the quotation function at 1983b, 161.) Tarski’s aim was to add definitions of semantic notions to extensional formulations of mathematical theories. Since the theories were extensional, and since the definitions he added to them were extensionally correct, the result was a seamless reduction of semantics to mathematics plus definitions relative to the contexts in which Tarski was interested, namely, extensional contexts. Later commentators, like Putnam, Etchemendy and Heck, are willing to say that mathematical truths are necessary, since they don’t share his aversion to such talk, but also assume that substitutions licensed by a definition preserve necessary truth—among other reasons since they are attracted to the idea that such substitutions preserve

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logical or mathematical truth.15 This generates the impression that Tarski must have thought that the T-sentences were necessary truths, or at least that his procedure committed him to as much. Nothing of the sort is the case. The criticisms we have rejected here are misguided, but they appeal no doubt in part because they answer to the impression that something is seriously wrong with Tarski’s way of defining truth. We should, then, consider whether alternative diagnoses of the problem with Tarski’s procedure are available. I believe, in fact, that at least one superior criticism of Tarski is available. Tarski appears to want to tell us what truth is—witness his many claims about the philosophical interest of his formal work (1983b, 154, 266)—but he does so by generating lists of conditions under which things are true. Something about this strikes many philosophers as misguided—surely, it is thought, there is more to truth than that. (Of course others come along to defend the view—this is the position of certain kinds of deflationists and minimalists about truth; e.g. Field 1994 and Horwich 1998.) At this juncture, the prejudice that definition somehow amounts to “transcription” enters the scene to suggest that Tarski’s idea that semantic claims could be reduced by definitions to mathematical claims is the problem: if the “transcriptional” conception of definition were right, Tarski’s definitional project would be seriously misguided. But the problem doesn’t lie where Putnam, Etchemendy and Heck seek it.The T-sentences are definitional truths, in the sense that they are truths in virtue of meaning, that lack of assent to them manifests linguistic ignorance, and so on.There is nothing wrong with accepting this. The problem, rather, is this: Tarski maintains that the T-sentences are definitional truths about truth. It follows from this view that (2) “snow is white” is true in English if and only if snow is white is a definitional truth about truth, and this has unacceptable consequences that have often been noted: if the T-sentence is a definitional truth about truth, then one who fails to accept it can be accused of not knowing what truth is, or what “true” means. All it takes is to think of a monolingual speaker of something other than English to realize that this has to be wrong, or at least that we need to weld “in English” to “is true” in (2) so that the claim is merely that the monolingual speaker of, say, Chinese, doesn’t understand “truth-in-English”. The latter, however, is never very plausible, despite how often interpreters of Tarski—or those who support related forms of deflationism and minimalism about truth—are driven to it. Since it seems so obvious that there actually is something common to truths across languages, one is left with the sense that there must be something going on that Tarski’s procedure omits or obscures, and at this point the assumption appeals that what is wrong in Tarski’s procedure is the proposed definitional equivalence of semantic and mathematical terms.16 15. Indeed, I suspect that if it weren’t for the prevalence of the latter prejudice the straightforward extension of Kripke’s ideas about contingent a priori truth to semantic claims like “ ‘Socrates’ refers to Socrates”—one to which Kripke himself alludes—would have become a staple of the literature on Tarski and semantics long ago. 16. I discuss Tarski’s own views about what is common to his defined truth predicates across languages in my forthcoming b.

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However, there is another way out: accept that T-sentences like (2) are definitional truths not about truth, but about exactly what they appear to be about: they are definitional truths about the conditions under which the sentences they mention are true, since, when true, they ascribe to sentences precisely the truthconditions that the meanings of these sentences determine them to have. As such they are contingent truths in virtue of meaning. There is, moreover, no reason to expect substitution in accord with them to preserve logical, mathematical, or necessary truth. One who doesn’t believe that “snow is white” is true if and only if snow is white can rightly be accused of failing to understand “snow is white.” This doesn’t, however, impugn the person’s understanding of truth, or even of truth in English (though it does, of course, impugn the person’s understanding of English). This is the view defended in Davidson (1990) and Patterson (2002), but I think it has yet to get a fair hearing, largely because the Tarskian view—the real source of the problem—that the T-sentences are definitional truths about truth continues uncritically to be accepted. If we hold, rather, that the T-sentences are definitional truths about truth-conditions, we can account for the facts, as well as for our sense that there is something wrong with Tarski’s way of doing things, all without falling into the trap of accepting the standard criticism of Tarski. Just as Tarski assumed, the T-sentences, though definitional truths, are not logical, mathematical or even necessary truths. REFERENCES Belnap, Nuel. 1993. “On Rigorous Definitions.” Philosophical Studies 72: 115–46. Davidson, Donald. 1990. “The Structure and Content of Truth.” Journal of Philosophy 87: 279– 328. Etchemendy, John. 1988. “Tarski on Truth and Logical Consequence.” The Journal of Symbolic Logic 53: 51–79. Field, Hartry. 1972. “Tarski’s Theory of Truth.” The Journal of Philosophy 69: 347–75. ———. 1994. “Deflationist Views of Meaning and Content.” Mind 103: 249–85. Hale, Bob and Wright, Crispin. 2001. The Reason’s Proper Study: Essays towards a Neo-Fregean Philosophy of Mathematics. New York: Oxford University Press. Heck, Richard G. Jr. 1997. “Tarski, Truth and Semantics.” The Philosophical Review 106: 533–54. Hodges, Wilfrid. Forthcoming. Tarski’s Theory of Definitions. In Patterson forthcoming c. Horwich, Paul. 1998. Truth, 2nd ed. New York: Oxford University Press. Kripke, Saul. 1980. Naming and Necessity. Cambridge, MA: Harvard University Press. Muller, P. et al. 1994. “Glossary of Terms Used in Physical Organic Chemistry.” Pure and Applied Chemistry 66 (5): 1077–1184. Patterson, Douglas. 2002. “Theories of Truth and Convention T.” Philosophers’ Imprint 2: 5. ———. 2007a. “Understanding the Liar.” In Revenge of the Liar: New Essays on Paradox, ed. JC Beall, 197–224. New York: Oxford University Press. ———. 2007b. “Inconsistency Theories: The Significance of Semantic Ascent.” Inquiry 50, 6. ———. Forthcoming a. “Inconsistency Theories of Semantic Paradox.” Philosophy and Phenomenological Research. ———. Forthcoming b. “Tarski’s Conception of Meaning.” In Patterson forthcoming c. ———. Forthcoming c. New Essays on Tarski and Philosophy. New York: Oxford University Press. Putnam, Hilary. 1994. “A Comparison of Something with Something Else.” In Words and Life, ed. Conant, 330–50. Cambridge, MA: Harvard University Press. Quine, W. v O. 1953. “Two Dogmas of Empiricism.” In From a Logical Point of View, 20–46. Cambridge, MA: Harvard University Press.

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Tarski, Alfred. 1983a. “Some Methodological Investigations on the Definability of Concepts.” In Logic, Semantics, Metamathematics, 2nd ed., trans. Woodger, ed. Corcoran, 296–319. Indianapolis, IN: Hackett. ———. 1983b. “The Concept of Truth in Formalized Languages.” In Logic, Semantics, Metamathematics, 2nd ed., trans. Woodger, ed. Corcoran, 152–278. Indianapolis, IN: Hackett.

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