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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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44
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11Ramsey and the Correspondence TheoryIn Volker Halbach & Leon Horsten (eds.), Principles of truth, Hänsel-hohenhausen. pp. 153-168. 2002.
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1Universal Universal QuantificationIn J. C. Beall (ed.), Liars and Heaps: New Essays on Paradox, Oxford University Press Uk. 2003.
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350How 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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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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34Review: James Van Aken, Axioms for the Set-Theoretic Hierarchy; Stephen Pollard, More Axioms for the Set-Theoretic Hierarchy; Michael D. Potter, Sets. An Introduction (review)Journal of Symbolic Logic 58 (3): 1077-1078. 1993.
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22Afterword: Trying (With Limited Success) to Demarcate the Disquotational-Correspondence DistinctionIn J. C. Beall & B. Armour-Garb (eds.), Deflationary Truth, Open Court. pp. 143-152. 2005.
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15[Omnibus Review]Journal of Symbolic Logic 56 (1): 329-332. 1991.Reviewed Works:S. N. Artemov, B. M. Schein, Arithmetically Complete Modal Theories.S. N. Artemov, E. Mendelson, On Modal Logics Axiomatizing Provability.S.N. Artemov, E. Mendelson, Nonarithmeticity of Truth Prdicate Logics of Provability.V. A. Vardanyan, E. Mendelson, Arithmetic Complexity of Predicate Logics of Provability and Their.S. N. Artemov, E. Mendelson, Numerically Correct Provability Logics
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16The Philosophical Review: Vol. 106, No.1, January 1997Review of Metaphysics 51 (1): 208-208. 1997.
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2There are many thingsIn Judith Thomson & Alex Byrne (eds.), Content and Modality: Themes From the Philosophy of Robert Stalnaker, Oxford University Press. pp. 93--122. 2006.
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1Ramsey's DialetheismIn Graham Priest, J. C. Beall & Bradley Armour-Garb (eds.), The Law of Non-Contradiction, Clarendon Press. 2004.
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178Logical 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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119We Turing machines aren't expected-utility maximizers (even ideally)Philosophical Studies 64 (1). 1991.
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50The degree of the set of sentences of predicate provability logic that are true under every interpretationJournal of Symbolic Logic 52 (1): 165-171. 1987.
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76How 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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62Awarded the 1988 Johnsonian Prize in Philosophy. Published with the aid of a grant from the National Endowment for the Humanities.
Cambridge, Massachusetts, United States of America