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49Perfect validity, entailment and paraconsistencyStudia Logica 43 (1-2). 1984.This paper treats entailment as a subrelation of classical consequence and deducibility. Working with a Gentzen set-sequent system, we define an entailment as a substitution instance of a valid sequent all of whose premisses and conclusions are necessary for its classical validity. We also define a sequent Proof as one in which there are no applications of cut or dilution. The main result is that the entailments are exactly the Provable sequents. There are several important corollaries. Every un…Read more
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47Sex and the evolution of fair-dealingPhilosophy of Science 66 (3): 391-414. 1999.Brian Skyrms has studied the evolutionary dynamics of a simple bargaining game. Fair-dealing is the strategy 'demand 1/2', competing with the more modest strategy 'demand 1/3' and the greedier strategy 'demand 2/3'. Individuals leave offspring in proportion to their accumulated payoffs. The rules for payoffs from encounters penalize low- and high-demanders. The result is a significant basin of attraction for fair-dealing as an evolutionarily stable strategy. From these considerations Skyrms conc…Read more
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46Game theory and conventiontNordic Journal of Philosophical Logic 6 (1): 3-19. 2001.This paper rebuts criticisms by Hintikka of the author's account of game-theoretic semantics for classical logic. At issue are (i) the role of the axiom of choice in proving the equivalence of the game-theoretic account with the standard truth-theoretic account; (ii) the alleged need for quantification over strategies when providing a game-theoretic semantics; and (iii) the role of Tarski's Convention T. As a result of the ideas marshalled in response to Hintikka, the author puts forward a new c…Read more
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42Rule-Irredundancy and the Sequent Calculus for Core LogicNotre Dame Journal of Formal Logic 57 (1): 105-125. 2016.We explore the consequences, for logical system-building, of taking seriously the aim of having irredundant rules of inference, and a preference for proofs of stronger results over proofs of weaker ones. This leads one to reconsider the structural rules of REFLEXIVITY, THINNING, and CUT. REFLEXIVITY survives in the minimally necessary form $\varphi:\varphi$. Proofs have to get started. CUT is subject to a CUT-elimination theorem, to the effect that one can always make do without applications of …Read more
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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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40The Taming of the TruePhilosophical Review 109 (2): 290. 2000.The Taming of the True continues the project Neil Tennant began in Anti-realism and Logic of investigating and defending anti-realism. Tennant’s earlier book anticipated a second volume, in which issues related to empirical discourse would be addressed in greater detail. The Taming of the True provides this sequel. It also attempts a ground-clearing project, by addressing challenges to some of the presuppositions and implications of Tennant’s anti-realist position. Finally, it takes an opportuni…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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36On the Degeneracy of the Full AGM-Theory of Theory-RevisionJournal of Symbolic Logic 71 (2). 2006.A general method is provided whereby bizarre revisions of consistent theories with respect to contingent sentences that they refute can be delivered by revision-functions satisfying both the basic and the supplementary postulates of the AGM-theory of theory-revision
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35Games some people would have all of us play: A critical study of J. Hintikka, The Principles of Mathematics Revisited (review)Philosophia Mathematica 6 (1): 226-241. 1998.
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35Transmission of VerificationReview of Symbolic Logic 1-16. forthcoming.This paper clarifies, revises, and extends the account of the transmission of truthmakers by core proofs that was set out in chap. 9 of Tennant. Brauer provided two kinds of example making clear the need for this. Unlike Brouwer’s counterexamples to excluded middle, the examples of Brauer that we are dealing with here establish the need for appeals to excluded middle when applying, to the problem of truthmaker-transmission, the already classical metalinguistic theory of model-relative evaluation…Read more
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34Does Choice Really Imply Excluded Middle? Part I: Regimentation of the Goodman–Myhill Result, and Its Immediate Reception†Philosophia Mathematica 28 (2): 139-171. 2020.The one-page 1978 informal proof of Goodman and Myhill is regimented in a weak constructive set theory in free logic. The decidability of identities in general (|$a\!=\!b\vee\neg a\!=\!b$|) is derived; then, of sentences in general (|$\psi\vee\neg\psi$|). Martin-Löf’s and Bell’s receptions of the latter result are discussed. Regimentation reveals the form of Choice used in deriving Excluded Middle. It also reveals an abstraction principle that the proof employs. It will be argued that the Go…Read more
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32Theory-Contraction is NP-CompleteLogic Journal of the IGPL 11 (6): 675-693. 2003.I investigate the problem of contracting a dependency-network with respect to any of its nodes. The resulting contraction must not contain the node in question, but must also be a minimal mutilation of the original network. Identifying successful and minimally mutilating contractions of dependency-networks is non-trivial, especially when non-well-founded networks are to be taken into account. I prove that the contraction problem is NP-complete.1
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32Changes of mind: an essay on rational belief revisionOxford University Press. 2012.An account of how a rational agent should revise beliefs in the light of new evidence.
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31Inferential semantics for first-order logic : motivating rules of inference from rules of evaluationIn T. J. Smiley, Jonathan Lear & Alex Oliver (eds.), The Force of Argument: Essays in Honor of Timothy Smiley, Routledge. pp. 223--257. 2010.
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31Core GödelNotre Dame Journal of Formal Logic 64 (1): 15-59. 2023.This study examines how the Gödel phenomena are to be treated in core logic. We show in formal detail how one can use core logic in the metalanguage to prove Gödel’s incompleteness theorems for arithmetic even when classical logic is used for logical closure in the object language.
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29Core LogicOxford University Press. 2017.Neil Tennant presents an original logical system with unusual philosophical, proof-theoretic, metalogical, computational, and revision-theoretic virtues. Core Logic is the first system that ensures both relevance and adequacy for the formalization of all mathematical and scientific reasoning.
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27Does Choice Really Imply Excluded Middle? Part II: Historical, Philosophical, and Foundational Reflections on the Goodman–Myhill Result†Philosophia Mathematica 29 (1): 28-63. 2021.Our regimentation of Goodman and Myhill’s proof of Excluded Middle revealed among its premises a form of Choice and an instance of Separation.Here we revisit Zermelo’s requirement that the separating property be definite. The instance that Goodman and Myhill used is not constructively warranted. It is that principle, and not Choice alone, that precipitates Excluded Middle.Separation in various axiomatizations of constructive set theory is examined. We conclude that insufficient critical attentio…Read more
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26Revamping the restriction strategyIn Joe Salerno (ed.), New Essays on the Knowability Paradox, Oxford University Press. 2009.This study continues the anti-realist’s quest for a principled way to avoid Fitch’s paradox. It is proposed that the Cartesian restriction on the anti-realist’s knowability principle ‘ϕ, therefore 3Kϕ’ should be formulated as a consistency requirement not on the premise ϕ of an application of the rule, but rather on the set of assumptions on which the relevant occurrence of ϕ depends. It is stressed, by reference to illustrative proofs, how important it is to have proofs in normal form before ap…Read more
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