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62IntroductionPhilosophia Mathematica 16 (1): 1-3. 2008.Christopher Peacocke, in A Study of Concepts, motivates his account of possession conditions for concepts by means of an alleged parallel with the conditions under which numbers are abshacted to give the numerosity of a predicate. There are, however, logical mistakes in Peacocke's treatment of numbers, which undermine his intended analogy. Nevertheless Peacocke's account of possession conditions for concepts is not rendered inadequate simply by virtue of being deprived of the intended analogy an…Read more
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40Contracting Intuitionistic TheoriesStudia Logica 80 (2-3): 369-391. 2005.I reformulate the AGM-account of contraction (which would yield an account also of revision). The reformulation involves using introduction and elimination rules for relational notions. Then I investigate the extent to which the two main methods of partial meet contraction and safe contraction can be employed for theories closed under intuitionistic consequence.
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39What might logic and methodology have offered the Dover School Board, had they been willing to listen?Public Affairs Quarterly 21 (2): 149-167. 2007.
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37The relevance of premises to conclusions of core proofsReview of Symbolic Logic 8 (4): 743-784. 2015.
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72Normalizability, cut eliminability and paradoxSynthese 199 (Suppl 3): 597-616. 2016.This is a reply to the considerations advanced by Schroeder-Heister and Tranchini as prima facie problematic for the proof-theoretic criterion of paradoxicality, as originally presented in Tennant and subsequently amended in Tennant. Countering these considerations lends new importance to the parallelized forms of elimination rules in natural deduction.
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1064Aristotle’s Syllogistic and Core LogicHistory and Philosophy of Logic 35 (2): 120-147. 2014.I use the Corcoran–Smiley interpretation of Aristotle's syllogistic as my starting point for an examination of the syllogistic from the vantage point of modern proof theory. I aim to show that fresh logical insights are afforded by a proof-theoretically more systematic account of all four figures. First I regiment the syllogisms in the Gentzen–Prawitz system of natural deduction, using the universal and existential quantifiers of standard first-order logic, and the usual formalizations of Aristo…Read more
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12The future with cloningIn James H. Fetzer (ed.), Consciousness Evolving, John Benjamins. pp. 34--223. 2002.
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