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93Vagueness, Open-Texture, and RetrievabilityInquiry: An Interdisciplinary Journal of Philosophy 56 (2-3): 307-326. 2013.Just about every theorist holds that vague terms are context-sensitive to some extent. What counts as ?tall?, ?rich?, and ?bald? depends on the ambient comparison class, paradigm cases, and/or the like. To take a stock example, a given person might be tall with respect to European entrepreneurs and downright short with respect to professional basketball players. It is also generally agreed that vagueness remains even after comparison class, paradigm cases, etc. are fixed, and so this context sen…Read more
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52Life on the Ship of Neurath: Mathematics in the Philosophy of MathematicsCroatian Journal of Philosophy 26 (2): 11--27. 2012.Some central philosophical issues concern the use of mathematics in putatively non-mathematical endeavors. One such endeavor, of course, is philosophy, and the philosophy of mathematics is a key instance of that. The present article provides an idiosyncratic survey of the use of mathematical results to provide support or counter-support to various philosophical programs concerning the foundations of mathematics
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14Arithmetic Sinn and EffectivenessDialectica 38 (1): 3-16. 1984.SummaryAccording to Dummett's understanding of Frege, the sense of a denoting expression is a procedure for determining its denotation. The purpose of this article is to pursue this suggestion and develop a semi‐formal interpretation of Fregean sense for the special case of a first‐order language of arithmetic. In particular, we define the sense of each arithmetic expression to be a hypothetical process to determine the denoted number or truth value. The sense‐process is “hypothetical” in that t…Read more
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27I—Stewart ShapiroSupplement to the Proceedings of the Aristotelian Society 79 (1): 147-165. 2005.
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38Comparing implicit and explicit memory for brand names from advertisementsJournal of Experimental Psychology: Applied 2 (2): 147. 1996.
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130The guru, the logician, and the deflationist: Truth and logical consequenceNoûs 37 (1). 2003.The purpose of this paper is to present a thought experiment and argument that spells trouble for “radical” deflationism concerning meaning and truth such as that advocated by the staunch nominalist Hartry Field. The thought experiment does not sit well with any view that limits a truth predicate to sentences understood by a given speaker or to sentences in (or translatable into) a given language, unless that language is universal. The scenario in question concerns sentences that are not under…Read more
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148‘Neo-logicist‘ logic is not epistemically innocentPhilosophia Mathematica 8 (2): 160--189. 2000.The neo-logicist argues tliat standard mathematics can be derived by purely logical means from abstraction principles—such as Hume's Principle— which are held to lie 'epistcmically innocent'. We show that the second-order axiom of comprehension applied to non-instantiated properties and the standard first-order existential instantiation and universal elimination principles are essential for the derivation of key results, specifically a theorem of infinity, but have not been shown to be epistemic…Read more
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290Epistemology of mathematics: What are the questions? What count as answers?Philosophical Quarterly 61 (242): 130-150. 2011.A paper in this journal by Fraser MacBride, ‘Can Ante Rem Structuralism Solve the Access Problem?’, raises important issues concerning the epistemological goals and burdens of contemporary philosophy of mathematics, and perhaps philosophy of science and other disciplines as well. I use a response to MacBride's paper as a framework for developing a broadly holistic framework for these issues, and I attempt to steer a middle course between reductive foundationalism and extreme naturalistic quietis…Read more
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44On the notion of effectivenessHistory and Philosophy of Logic 1 (1-2): 209-230. 1980.This paper focuses on two notions of effectiveness which are not treated in detail elsewhere. Unlike the standard computability notion, which is a property of functions themselves, both notions of effectiveness are properties of interpreted linguistic presentations of functions. It is shown that effectiveness is epistemically at least as basic as computability in the sense that decisions about computability normally involve judgments concerning effectiveness. There are many occurrences of the pr…Read more
Columbus, Ohio, United States of America
Areas of Specialization
Philosophy of Language |
Logic and Philosophy of Logic |
Philosophy of Mathematics |
Areas of Interest
Philosophy of Language |
Logic and Philosophy of Logic |
Philosophy of Mathematics |