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41Conventional 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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101Williamson’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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83Intuitionistic 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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59Ultimate 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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64New 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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BOSTOCK, D. "Logic and Arithmetic, Vol. II-Rational and Irrational Numbers" (review)Mind 90 (n/a): 473. 1981.
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68The Law of Excluded Middle Is Synthetic A Priori, If ValidPhilosophical Topics 24 (1): 205-229. 1996.
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27Evolutionary 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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