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341How we learn mathematical languagePhilosophical Review 106 (1): 35-68. 1997.Mathematical realism is the doctrine that mathematical objects really exist, that mathematical statements are either determinately true or determinately false, and that the accepted mathematical axioms are predominantly true. A realist understanding of set theory has it that when the sentences of the language of set theory are understood in their standard meaning, each sentence has a determinate truth value, so that there is a fact of the matter whether the cardinality of the continuum is א2 or …Read more
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248Inscrutability and its discontentsNoûs 39 (3). 2005.That reference is inscrutable is demonstrated, it is argued, not only by W. V. Quine's arguments but by Peter Unger's "Problem of the Many." Applied to our own language, this is a paradoxical result, since nothing could be more obvious to speakers of English than that, when they use the word "rabbit," they are talking about rabbits. The solution to this paradox is to take a disquotational view of reference for one's own language, so that "When I use 'rabbit,' I refer to rabbits" is made true by …Read more
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197A puzzle about de rebus beliefsAnalysis 60 (4). 2000.George Boolos (1984, 1985) has extensively investigated plural quantifi- cation, as found in such locutions as the Geach-Kaplan sentence There are critics who admire only one another, and he found that their logic cannot be adequately formalized within the first-order predicate calculus. If we try to formalize the sentence by a paraphrase using individual variables that range over critics, or over sets or collections or fusions of critics, we misrepresent its logical structure. To represent plural…Read more
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196Timothy Williamson, vagueness: London and new York: 1994 (review)Linguistics and Philosophy 21 (2): 221-235. 1998.
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195Conditional probabilities and compounds of conditionalsPhilosophical Review 98 (4): 485-541. 1989.
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177Logical operationsJournal of Philosophical Logic 25 (6). 1996.Tarski and Mautner proposed to characterize the "logical" operations on a given domain as those invariant under arbitrary permutations. These operations are the ones that can be obtained as combinations of the operations on the following list: identity; substitution of variables; negation; finite or infinite disjunction; and existential quantification with respect to a finite or infinite block of variables. Inasmuch as every operation on this list is intuitively "logical", this lends support to …Read more
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175KilimanjaroCanadian Journal of Philosophy 27 (sup1): 141-163. 1997.This is not an overly ambitious paper. What I would like to do is to take a thesis that most people would regard as wildly implausible, and convince you that it is, in fact, false. What's worse, the argument I shall give is by no means airtight, though I hope it's reasonably convincing. The thesis has to do with the fuzzy boundaries of terms that refer to familiar middle-sized objects, terms like ‘Kilimanjaro’ and ‘the tallest mountain in Africa.’ It is intuitively clear that Kilimanjaro has a f…Read more
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165Thought, thoughts, and deflationismPhilosophical Studies 173 (12): 3153-3168. 2016.Deflationists about truth embrace the positive thesis that the notion of truth is useful as a logical device, for such purposes as blanket endorsement, and the negative thesis that the notion doesn’t have any legitimate applications beyond its logical uses, so it cannot play a significant theoretical role in scientific inquiry or causal explanation. Focusing on Christopher Hill as exemplary deflationist, the present paper takes issue with the negative thesis, arguing that, without making use of …Read more
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153Logical commitment and semantic indeterminacy: A reply to WilliamsonLinguistics and Philosophy 27 (1): 123-136. 2004.
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145Maximal consistent sets of instances of Tarski’s schemaJournal of Philosophical Logic 21 (3). 1992.
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143How truthlike can a predicate be? A negative resultJournal of Philosophical Logic 14 (4). 1985.
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141There's Something about Gödel is a bargain: two books in one. The first half is a gentle but rigorous introduction to the incompleteness theorems for the mathematically uninitiated. The second is a survey of the philosophical, psychological, and sociological consequences people have attempted to derive from the theorems, some of them quite fantastical.The first part, which stays close to Gödel's original proofs, strikes a nice balance, giving enough details that the reader understands what is go…Read more
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136Learning the ImpossibleIn Ellery Eells & Brian Skyrms (eds.), Probability and Conditionals: Belief Revision and Rational Decision, Cambridge University Press. pp. 179-199. 1994.
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118We Turing machines aren't expected-utility maximizers (even ideally)Philosophical Studies 64 (1). 1991.
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113Truth by defaultPhilosophia Mathematica 9 (1): 5-20. 2001.There is no preferred reduction of number theory to set theory. Nonetheless, we confidently accept axioms obtained by substituting formulas from the language of set theory into the induction axiom schema. This is only possible, it is argued, because our acceptance of the induction axioms depends solely on the meanings of aritlunetical and logical terms, which is only possible if our 'intended models' of number theory are standard. Similarly, our acceptance of the second-order natural deduction r…Read more
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110An Epistemic Principle Which Solves Newcomb's ParadoxGrazer Philosophische Studien 40 (1): 197-217. 1991.If it is certain that performing an observation to determine whether P is true will in no way influence whether P is tme, then the proposition that the observation is performed ought to be probabilistically independent of P. Applying the notion of "observation" liberally, so that a wide variety of actions are treated as observations, this proposed new principle of belief revision yields the result that simple utihty maximization gives the correct solution to the Fisher smoking paradox and the tw…Read more
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106XIII*—Two Problems with Tarski's Theory of ConsequenceProceedings of the Aristotelian Society 92 (1): 273-292. 1992.Vann McGee; XIII*—Two Problems with Tarski's Theory of Consequence, Proceedings of the Aristotelian Society, Volume 92, Issue 1, 1 June 1992, Pages 273–292, htt.
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86The Revision Theory of Truth (review)Philosophy and Phenomenological Research 56 (3): 727-730. 1996.
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81If P, then Q: Conditionals and the Foundations of ReasoningPhilosophy and Phenomenological Research 53 (1): 239-242. 1992.
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