-
56Modal metaphysics and comparativesAustralasian Journal of Philosophy 70 (3). 1992.This Article does not have an abstract
-
16Review of Roy Weatherford: Philosophical foundations of probability theory (review)British Journal for the Philosophy of Science 35 (1): 95-100. 1984.
-
83II—Peter Milne: What is the Normative Role of Logic?Aristotelian Society Supplementary Volume 83 (1): 269-298. 2009.
-
41I examine the ideas leading up to Wittgenstein's pronouncement at Tractatus 5.4611 that signs for logical operations are punctuation marks
-
56Existence, freedom, identity, and the logic of abstractionist realismMind 116 (461): 23-53. 2007.From the point of view of proof-theoretic semantics, we examine the logical background invoked by Neil Tennant's abstractionist realist account of mathematical existence. To prepare the way, we must first look closely at the rule of existential elimination familiar from classical and intuitionist logics and at rules governing identity. We then examine how well free logics meet the harmony and uniqueness constraints familiar from the proof-theoretic semantics project. Tennant assigns a special ro…Read more
-
89Schlesinger On Justified Belief And ProbabilityAnalysis 49 (January): 11-16. 1989.George schlesinger has characterized justified belief probabilistically. I question the propriety of this characterization and demonstrate that with respect to it certain principles of epistemic logic that he considers plausible are unsound.
-
99Algebras of intervals and a logic of conditional assertionsJournal of Philosophical Logic 33 (5): 497-548. 2004.Intervals in boolean algebras enter into the study of conditional assertions (or events) in two ways: directly, either from intuitive arguments or from Goodman, Nguyen and Walker's representation theorem, as suitable mathematical entities to bear conditional probabilities, or indirectly, via a representation theorem for the family of algebras associated with de Finetti's three-valued logic of conditional assertions/events. Further representation theorems forge a connection with rough sets. The r…Read more
-
16Operations are punctuation marks'In Peter M. Sullivan & Michael D. Potter (eds.), Wittgenstein's Tractatus: history and interpretation, Oxford University Press. pp. 97. 2013.
-
-
61Verification, falsification, and the logic of enquiryErkenntnis 34 (1). 1991.Our starting point is Michael Luntley's falsificationist semantics for the logical connectives and quantifiers: the details of his account are criticised but we provide an alternative falsificationist semantics that yields intuitionist logic, as Luntley surmises such a semantics ought. Next an account of the logical connectives and quantifiers that combines verificationist and falsificationist perspectives is proposed and evaluated. While the logic is again intuitionist there is, somewhat surpri…Read more
-
105Harmony, Purity, Simplicity and a “Seemingly Magical Fact”The Monist 85 (4): 498-534. 2002.In his penetrating and thought-provoking article “What Is Logic?” Ian Hacking flags an issue that he leaves undiscussed
-
64The design inference: Eliminating chance through small probabilitiesBritish Journal for the Philosophy of Science 52 (4): 801-808. 2001.
-
65Russell's completeness proofHistory and Philosophy of Logic 29 (1): 31-62. 2008.Bertrand Russell’s 1906 article ‘The Theory of Implication’ contains an algebraic weak completeness proof for classical propositional logic. Russell did not present it as such. We give an exposition of the proof and investigate Russell’s view of what he was about, whether he could have appreciated the proof for what it is, and why there is no parallel of the proof in Principia Mathematica
-
104Probability as a Measure of Information AddedJournal of Logic, Language and Information 21 (2): 163-188. 2012.Some propositions add more information to bodies of propositions than do others. We start with intuitive considerations on qualitative comparisons of information added . Central to these are considerations bearing on conjunctions and on negations. We find that we can discern two distinct, incompatible, notions of information added. From the comparative notions we pass to quantitative measurement of information added. In this we borrow heavily from the literature on quantitative representations o…Read more
-
308Not every truth has a truthmakerAnalysis 65 (3). 2005.First paragraph: Truthmaker theory maintains that for every truth there is something, some thing, some entity, that makes it true. Balking at the prospect that logical truths are made true by any particular thing, a consequence that may in fact be hard to avoid (see Restall 1996, Read 2000), this principle of truthmaking is sometimes restricted to (logically) contingent truths. I aim to show that even in its restricted form, the principle is provably false
-
25Minimal doxastic logic: probabilistic and other completeness theoremsNotre Dame Journal of Formal Logic 34 (4): 499-526. 1993.
-
77Scotching the dutch book argumentErkenntnis 32 (1): 105--26. 1990.Consistent application of coherece arguments shows that fair betting quotients are subject to constraints that are too stringent to allow their identification with either degrees of belief or probabilities. The pivotal role of fair betting quotients in the Dutch Book Argument, which is said to demonstrate that a rational agent's degrees of belief are probabilities, is thus undermined from both sides.
-
52Conditionalisation and quantum probabilitiesAustralasian Journal of Philosophy 69 (2). 1991.This Article does not have an abstract
-
51Bets and Boundaries: Assigning Probabilities to Imprecisely Specified EventsStudia Logica 90 (3): 425-453. 2008.Uncertainty and vagueness/imprecision are not the same: one can be certain about events described using vague predicates and about imprecisely specified events, just as one can be uncertain about precisely specified events. Exactly because of this, a question arises about how one ought to assign probabilities to imprecisely specified events in the case when no possible available evidence will eradicate the imprecision (because, say, of the limits of accuracy of a measuring device). Modelling imp…Read more
-
114Log[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