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113Log[p(h/eb)/p(h/b)] is the one true measure of confirmationPhilosophy of Science 63 (1): 21-26. 1996.Plausibly, when we adopt a probabilistic standpoint any measure Cb of the degree to which evidence e confirms hypothesis h relative to background knowledge b should meet these five desiderata: Cb > 0 when P > P < 0 when P < P; Cb = 0 when P = P. Cb is some function of the values P and P assume on the at most sixteen truth-functional combinations of e and h. If P < P and P = P then Cb ≤ Cb; if P = P and P < P then Cb ≥ Cb. Cb – Cb is fully determined by Cb and Cbe – Cbe; if Cb = 0 then Cb + Cbe =…Read more
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79The foundations of probability and quantum mechanicsJournal of Philosophical Logic 22 (2). 1993.Taking as starting point two familiar interpretations of probability, we develop these in a perhaps unfamiliar way to arrive ultimately at an improbable claim concerning the proper axiomatization of probability theory: the domain of definition of a point-valued probability distribution is an orthomodular partially ordered set. Similar claims have been made in the light of quantum mechanics but here the motivation is intrinsically probabilistic. This being so the main task is to investigate what …Read more
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46Disjunction and Disjunctive SyllogismCanadian Journal of Philosophy 28 (1). 1998.The validity of argument by disjunctive syllogism has been denied by proponents of relevant and paraconsistent logic. DS is stigmatised for its role in inferences — most notably C.I. Lewis's derivation of that fallacy of irrelevance ex falso quodlibet — that involve both it and other rules of inference governing disjunction, or, to speak more precisely, other rules of inference taken to apply to the very same disjunction that obeys DS. In avoiding these inferences the road less travelled is to d…Read more
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89Physical probabilitiesSynthese 73 (2). 1987.A conception of probability as an irreducible feature of the physical world is outlined. Propensity analyses of probability are examined and rejected as both formally and conceptually inadequate. It is argued that probability is a non-dispositional property of trial-types; probabilities are attributed to outcomes as event-types. Brier's Rule in an objectivist guise is used to forge a connection between physical and subjective probabilities. In the light of this connection there are grounds for s…Read more
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25From Introduction: In a 1968 article, ‘Probability Measures of Fuzzy Events’, Lotfi Zadeh pro-posed accounts of absolute and conditional probability for fuzzy sets (Zadeh, 1968)
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58On the completeness of non-philonian stoic logicHistory and Philosophy of Logic 16 (1): 39-64. 1995.The majority of formal accounts attribute to Stoic logicians the classical truth-functional understanding of the material conditional and exclusive disjunction.These interpretations were disputed,...
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79A note on scale invarianceBritish Journal for the Philosophy of Science 34 (1): 49-55. 1983.A note on scale invariance.
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209Not every truth has a truthmaker IIAnalysis 73 (3): 473-481. 2013.A proof employing no semantic terms is offered in support of the claim that there can be truths without truthmakers. The logical resources used in the proof are weak but do include the structural rule Contraction
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54Is there a logic of confirmation transfer?Erkenntnis 53 (3): 309-335. 2000.This article begins by exploring a lost topic in the philosophy of science:the properties of the relations evidence confirming h confirmsh'' and, more generally, evidence confirming each ofh1, h2, ..., hm confirms at least one of h1, h2,ldots;, hn''.The Bayesian understanding of confirmation as positive evidential relevanceis employed throughout. The resulting formal system is, to say the least, oddlybehaved. Some aspects of this odd behaviour the system has in common withsome of the non-classic…Read more
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15Science without Unity: Reconciling the Human and Natural SciencesPhilosophical Books 30 (1): 62-63. 1989.
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88Frege, informative identities, and logicismBritish Journal for the Philosophy of Science 40 (2): 155-166. 1989.
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217Classical harmony: Rules of inference and the meaning of the logical constantsSynthese 100 (1). 1994.The thesis that, in a system of natural deduction, the meaning of a logical constant is given by some or all of its introduction and elimination rules has been developed recently in the work of Dummett, Prawitz, Tennant, and others, by the addition of harmony constraints. Introduction and elimination rules for a logical constant must be in harmony. By deploying harmony constraints, these authors have arrived at logics no stronger than intuitionist propositional logic. Classical logic, they maint…Read more
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152Bruno de finetti and the logic of conditional eventsBritish Journal for the Philosophy of Science 48 (2): 195-232. 1997.This article begins by outlining some of the history—beginning with brief remarks of Quine's—of work on conditional assertions and conditional events. The upshot of the historical narrative is that diverse works from various starting points have circled around a nexus of ideas without convincingly tying them together. Section 3 shows how ideas contained in a neglected article of de Finetti's lead to a unified treatment of the topics based on the identification of conditional events as the object…Read more
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234On Gödel Sentences and What They SayPhilosophia Mathematica 15 (2): 193-226. 2007.Proofs of Gödel's First Incompleteness Theorem are often accompanied by claims such as that the gödel sentence constructed in the course of the proof says of itself that it is unprovable and that it is true. The validity of such claims depends closely on how the sentence is constructed. Only by tightly constraining the means of construction can one obtain gödel sentences of which it is correct, without further ado, to say that they say of themselves that they are unprovable and that they are tru…Read more
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4Review of Ralph Charles Sutherland Walker: Kant: the arguments of the philosophers (review)British Journal for the Philosophy of Science 34 (3): 312-313. 1983.
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27Annabel and the bookmaker: An everyday tale of bayesian folkAustralasian Journal of Philosophy 69 (1). 1991.This Article does not have an abstract
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14Languages of Possibility: An essay in Philosophical LogicPhilosophical Books 31 (4): 222-224. 1992.
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155Tarski on truth and its definitionIn Timothy Childers, Petr Kolft & Vladimir Svoboda (eds.), Logica '96: Proceedings of the 10th International Symposium, Filosofia. pp. 198-210. 1997.Of his numerous investigations ... Tarski was most proud of two: his work on truth and his design of an algorithm in 1930 to decide the truth or falsity of any sentence of the elementary theory of the high school Euclidean geometry. [...] His mathematical treatment of the semantics of languages and the concept of truth has had revolutionary consequences for mathematics, linguistics, and philosophy, and Tarski is widely thought of as the man who "defined truth". The seeming simplicity of his famo…Read more
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101Indicative conditionals, conditional probabilities, and the “defective truth-table”: A request for more experimentsThinking and Reasoning 18 (2): 196-224. 2012.While there is now considerable experimental evidence that, on the one hand, participants assign to the indicative conditional as probability the conditional probability of consequent given antecedent and, on the other, they assign to the indicative conditional the “defective truth-table” in which a conditional with false antecedent is deemed neither true nor false, these findings do not in themselves establish which multi-premise inferences involving conditionals participants endorse. A natural…Read more
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119Subformula and separation properties in natural deduction via small Kripke models: Subformula and separation propertiesReview of Symbolic Logic 3 (2): 175-227. 2010.Various natural deduction formulations of classical, minimal, intuitionist, and intermediate propositional and first-order logics are presented and investigated with respect to satisfaction of the separation and subformula properties. The technique employed is, for the most part, semantic, based on general versions of the Lindenbaum and Lindenbaum–Henkin constructions. Careful attention is paid to which properties of theories result in the presence of which rules of inference, and to restriction…Read more
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42Existence and Identity in Free Logic: Two CommentsMind 116 (464): 1079-1082. 2007.Professor Tennant and I agree on much regarding the proof-theoretic semantics of free logic. Here I point to two issues, one on which we disagree, the other on which I find it hard to say how closely we may agree. The first concerns the exact content of Tennant's Rule of Atomic Denotation. The second concerns the nature of assumptions whose formal counterparts contain parametric occurrences of names