
718

239How we learn mathematical languagePhilosophical Review 106 (1): 3568. 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

163Inscrutability 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

120Logical 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

113Conditional probabilities and compounds of conditionalsPhilosophical Review 98 (4): 485541. 1989.

110Logical commitment and semantic indeterminacy: A reply to WilliamsonLinguistics and Philosophy 27 (1): 123136. 2004.

110How truthlike can a predicate be? A negative resultJournal of Philosophical Logic 14 (4). 1985.

100Thought, thoughts, and deflationismPhilosophical Studies 173 (12): 31533168. 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

89Maximal consistent sets of instances of Tarski's schema (t)Journal of Philosophical Logic 21 (3). 1992.

85There'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

78Learning the ImpossibleIn Ellery Eells & Brian Skyrms (eds.), Probability and Conditionals: Belief Revision and Rational Decision, Cambridge University Press. pp. 179199. 1994.

78XIII—Two Problems with Tarski's Theory of ConsequenceProceedings of the Aristotelian Society 92 (1): 273292. 1991.

76Timothy Williamson, vagueness: London and new York: 1994 (review)Linguistics and Philosophy 21 (2): 221235. 1998.

68Truth by defaultPhilosophia Mathematica 9 (1): 520. 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 secondorder natural deduction r…Read more

67We Turing machines aren't expectedutility maximizers (even ideally)Philosophical Studies 64 (1). 1991.

52If P, then Q: Conditionals and the Foundations of Reasoning (review)Philosophy and Phenomenological Research 53 (1): 239242. 1993.

45The complexity of the modal predicate logic of "true in every transitive model of ZF"Journal of Symbolic Logic 62 (4): 13711378. 1997.

41How We Learn Mathematical LanguagePhilosophical Review 106 (1): 3568. 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
Cambridge, Massachusetts, United States of America