-
37Comparing implicit and explicit memory for brand names from advertisementsJournal of Experimental Psychology: Applied 2 (2): 147. 1996.
-
128The 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
-
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
-
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
-
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
-
131Mathematics and philosophy of mathematicsPhilosophia Mathematica 2 (2): 148-160. 1994.The purpose of this note is to examine the relationship between the practice of mathematics and the philosophy of mathematics, ontology in particular. One conclusion is that the enterprises are (or should be) closely related, with neither one dominating the other. One cannot 'read off' the correct way to do mathematics from the true ontology, for example, nor can one ‘read off’ the true ontology from mathematics as practiced.
-
138Second-order languages and mathematical practiceJournal of Symbolic Logic 50 (3): 714-742. 1985.
-
5Webb Judson Chambers. Mechanism, mentalism, and metamathematics. An essay on finitism. Synthese library, vol. 137. D. Reidel Publishing Company, Dordrecht, Boston, and London, 1980, xiii + 277 pp (review)Journal of Symbolic Logic 51 (2): 472-476. 1986.
-
146Reasoning with Slippery PredicatesStudia Logica 90 (3): 313-336. 2008.It is a commonplace that the extensions of most, perhaps all, vague predicates vary with such features as comparison class and paradigm and contrasting cases. My view proposes another, more pervasive contextual parameter. Vague predicates exhibit what I call open texture: in some circumstances, competent speakers can go either way in the borderline region. The shifting extension and anti-extensions of vague predicates are tracked by what David Lewis calls the “conversational score”, and are regu…Read more
-
174Vagueness in contextOxford University Press. 2006.Stewart Shapiro's ambition in Vagueness in Context is to develop a comprehensive account of the meaning, function, and logic of vague terms in an idealized version of a natural language like English. It is a commonplace that the extensions of vague terms vary according to their context: a person can be tall with respect to male accountants and not tall (even short) with respect to professional basketball players. The key feature of Shapiro's account is that the extensions of vague terms also var…Read more
-
138Logical consequence, proof theory, and model theoryIn Oxford Handbook of Philosophy of Mathematics and Logic, Oxford University Press. pp. 651--670. 2005.This chapter provides broad coverage of the notion of logical consequence, exploring its modal, semantic, and epistemic aspects. It develops the contrast between proof-theoretic notion of consequence, in terms of deduction, and a model-theoretic approach, in terms of truth-conditions. The main purpose is to relate the formal, technical work in logic to the philosophical concepts that underlie reasoning.
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 |