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54Is every truth knowable? Reply to hand and KvanvigAustralasian Journal of Philosophy 79 (1). 2001.This Article does not have an abstract
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77On Turing machines knowing their own gödel-sentencesPhilosophia Mathematica 9 (1): 72-79. 2001.Storrs McCall appeals to a particular true but improvable sentence of formal arithmetic to argue, by appeal to its irrefutability, that human minds transcend Turing machines. Metamathematical oversights in McCall's discussion of the Godel phenomena, however, render invalid his philosophical argument for this transcendentalist conclusion
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115The full price of truthAnalysis 58 (3). 1998.Some ideas gain currency as soon as there is a linguistic medium of exchange. Truth is one such. Its role in our intellectual economy is much like that of money in the real one. Canonical warrants to make assertions are like gold bars. Truth-claims are like paper money: promises to produce gold bars on demand.
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75Existence and Identity in Free Logic: A Problem for Inferentialism?Mind 116 (464): 1055-1078. 2007.Peter Milne (2007) poses two challenges to the inferential theorist of meaning. This study responds to both. First, it argues that the method of natural deduction idealizes the essential details of correct informal deductive reasoning. Secondly, it explains how rules of inference in free logic can determine unique senses for the existential quantifier and the identity predicate. The final part of the investigation brings out an underlying order in a basic family of free logics
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275Minimal logic is adequate for Popperian scienceBritish Journal for the Philosophy of Science 36 (3): 325-329. 1985.
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60A New Unified Account of Truth and ParadoxMind 124 (494): 571-605. 2015.I propose an anti-realist account of truth and paradox according to which the logico-semantic paradoxes are not genuine inconsistencies. The ‘global’ proofs of absurdity associated with these paradoxes cannot be brought into normal form. The account combines epistemicism about truth with a proof-theoretic diagnosis of paradoxicality. The aim is to combine a substantive philosophical account of truth with a more rigorous and technical diagnosis of the source of paradox for further consideration b…Read more
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11Review: Richard E. Grandy, Advanced Logic for Applications (review)Journal of Symbolic Logic 47 (3): 714-716. 1982.
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152Deflationism and the gödel phenomena: Reply to KetlandMind 114 (453): 89-96. 2005.I am not a deflationist. I believe that truth and falsity are substantial. The truth of a proposition consists in its having a constructive proof, or truthmaker. The falsity of a proposition consists in its having a constructive disproof, or falsitymaker. Such proofs and disproofs will need to be given modulo acceptable premisses. The choice of these premisses will depend on the discourse in question.
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40Conventional Necessity and the Contingency of ConventionDialectica 41 (1‐2): 79-95. 1987.SummaryI defend a conventionalist view of logical and mathematical truths against the criticisms of Quine and Stroud. Conventionalism is best formulated by appealing to sense‐conferring rules governing important logical and mathematical expressions. Conventional necessity can be understood as arising from these rules in a way that is immune to Quine's and Stroud's criticisms of the earlier formulation of conventionalism, in which stress was incorrectly laid on axiomatic systems of logic.RésuméJe…Read more
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100Williamson’s WoesSynthese 173 (1): 9-23. 2010.This is a reply to Timothy Williamson ’s paper ‘Tennant’s Troubles’. It defends against Williamson ’s objections the anti-realist’s knowability principle based on the author’s ‘local’ restriction strategy involving Cartesian propositions, set out in The Taming of the True. Williamson ’s purported Fitchian reductio, involving the unknown number of books on his table, is analyzed in detail and shown to be fallacious. Williamson ’s attempt to cause problems for the anti-realist by means of a suppos…Read more
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82Intuitionistic mathematics does not needex falso quodlibetTopoi 13 (2): 127-133. 1994.We define a system IR of first-order intuitionistic relevant logic. We show that intuitionistic mathematics (on the assumption that it is consistent) can be relevantized, by virtue of the following metatheorem: any intuitionistic proof of A from a setX of premisses can be converted into a proof in IR of eitherA or absurdity from some subset ofX. Thus IR establishes the same inconsistencies and theorems as intuitionistic logic, and allows one to prove every intuitionistic consequence of any consi…Read more
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111Belief-revision, the Ramsey test, monotonicity, and the so-called impossibility resultsReview of Symbolic Logic 1 (4): 402-423. 2008.Peter G¨ ardenfors proved a theorem purporting to show that it is impossible to adjoin to the AGM -postulates for belief-revision a principle of monotonicity for revisions. The principle of monotonicity in question is implied by the Ramsey test for conditionals. So G¨
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58Ultimate Normal Forms for Parallelized Natural DeductionsLogic Journal of the IGPL 10 (3): 299-337. 2002.The system of natural deduction that originated with Gentzen , and for which Prawitz proved a normalization theorem, is re-cast so that all elimination rules are in parallel form. This enables one to prove a very exigent normalization theorem. The normal forms that it provides have all disjunction-eliminations as low as possible, and have no major premisses for eliminations standing as conclusions of any rules. Normal natural deductions are isomorphic to cut-free, weakening-free sequent proofs. …Read more
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67The Law of Excluded Middle Is Synthetic A Priori, If ValidPhilosophical Topics 24 (1): 205-229. 1996.
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26Evolutionary v. Evolved EthicsPhilosophy 58 (225): 289-302. 1983.Kant writes: If … the only aim of Nature regarding some creature possessed of reason and a will were its preservation, its well-being, in a word its happiness, then she would have come to a very bad arrangement in choosing its reason as executor of that aim. For all actions that it had to execute in this her intention, and the whole regulation of its behaviour would have been able to be prescribed to it much more precisely by instinct, and that aim thereby much more certainly maintained, than ev…Read more
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63New Foundations for a Relational Theory of Theory-revisionJournal of Philosophical Logic 35 (5): 489-528. 2006.AGM-theory, named after its founders Carlos Alchourrón, Peter Gärdenfors and David Makinson, is the leading contemporary paradigm in the theory of belief-revision. The theory is reformulated here so as to deal with the central relational notions 'J is a contraction of K with respect to A' and 'J is a revision of K with respect to A'. The new theory is based on a principal-case analysis of the domains of definition of the three main kinds of theory-change (expansion, contraction and revision). Th…Read more
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