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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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358How 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 Bradley P. Armour-Garb & J. C. Beall (eds.), Deflationary Truth, Open Court Press. 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 Jarvis 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, Jc Beall & Bradley P. Armour-Garb (eds.), The law of non-contradiction : new philosophical essays, Oxford University Press. 2004.
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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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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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62Awarded the 1988 Johnsonian Prize in Philosophy. Published with the aid of a grant from the National Endowment for the Humanities.
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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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13The Complexity of the Modal Predicate Logic of "True in Every Transitive Model of ZF"Journal of Symbolic Logic 62 (4): 1371-1378. 1997.
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45On the degrees of unsolvability of modal predicate logics of provabilityJournal of Symbolic Logic 59 (1): 253-261. 1994.
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