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57The 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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18Logic, logic, and logic, by Boolos George, with introductions and afterword by John P. Burgess, edited by Jeffrey Richard, Harvard University Press, Cambridge, Mass., and London, 1998, ix+ 443 pp (review)Bulletin of Symbolic Logic 7 (1): 58-62. 2001.
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2Universal Universal Quantification: Comments on Rayo and WilliamsonIn Jc Beall (ed.), Liars and Heaps: New Essays on Paradox, Clarendon Press. pp. 357-364. 2003.
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143How truthlike can a predicate be? A negative resultJournal of Philosophical Logic 14 (4). 1985.
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5There's a Rule for EverythingIn Agustín Rayo & Gabriel Uzquiano (eds.), Absolute Generality, Oxford University Press. pp. 179--202. 2006.
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23
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29Review: John Etchemendy, The Concept of Logical Consequence (review)Journal of Symbolic Logic 57 (1): 254-255. 1992.
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145Maximal consistent sets of instances of Tarski’s schemaJournal of Philosophical Logic 21 (3). 1992.
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Structures and the Hyperarithmetical Hierarchy. Knight has directed or co-directed seven doctoral dissertations in mathematics and one in electrical engineering. She served on selection panels for the NSF Postdoctoral Fellowships, on program committees of numerous meetings, and as an editor of The Journal of Symbolic Logic (1989-1995) (review)Bulletin of Symbolic Logic 6 (1). 2000.
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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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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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11Ramsey and the Correspondence TheoryIn Leon Horsten & Volker Halbach (eds.), Principles of Truth, De Gruyter. pp. 153-168. 2003.
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1Universal Universal QuantificationIn J. C. Beall (ed.), Liars and Heaps: New Essays on Paradox, Clarendon Press. 2004.
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342How 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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