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228Higher-Order Logic or Set Theory: A False DilemmaPhilosophia Mathematica 20 (3): 305-323. 2012.The purpose of this article is show that second-order logic, as understood through standard semantics, is intimately bound up with set theory, or some other general theory of interpretations, structures, or whatever. Contra Quine, this does not disqualify second-order logic from its role in foundational studies. To wax Quinean, why should there be a sharp border separating mathematics from logic, especially the logic of mathematics?
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15Essay ReviewHistory and Philosophy of Logic 6 (1): 215-221. 1985.D. GABBAY and F. GUENTHNER (eds.), Handbook of philosophical logic. Volume 1: Elements of classical logic. Dordrecht, Boston, and Lancaster: D. Reidel Publishing Company, 1983. xiv + 497 pp. Dfl225/$98.00
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182So truth is safe from paradox: now what?Philosophical Studies 147 (3): 445-455. 2010.The article is part of a symposium on Hartry Field’s “Saving truth from paradox”. The book is one of the most significant intellectual achievements of the past decades, but it is not clear what, exactly, it accomplishes. I explore some alternatives, relating the developed view to the intuitive, pre-theoretic notion of truth.
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16Do Not Claim Too Much: Second-order Logic and First-order LogicPhilosophia Mathematica 6 (3): 42-64. 1998.The purpose of this article is to delimit what can and cannot be claimed on behalf of second-order logic. The starting point is some of the discussions surrounding my Foundations without Foundationalism: A Case for Secondorder Logic.
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6Classical logic II: Higher-order logicIn Lou Goble (ed.), The Blackwell Guide to Philosophical Logic, Blackwell. pp. 33--54. 2001.A typical interpreted formal language has (first‐order) variables that range over a collection of objects, sometimes called a domain‐of‐discourse. The domain is what the formal language is about. A language may also contain second‐order variables that range over properties, sets, or relations on the items in the domain‐of‐discourse, or over functions from the domain to itself. For example, the sentence ‘Alexander has all the qualities of a great leader’ would naturally be rendered with a second‐…Read more
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111Why anti-realists and classical mathematicians cannot get alongTopoi 20 (1): 53-63. 2001.Famously, Michael Dummett argues that considerations concerning the role of language in communication lead to the rejection of classical logic in favor of intuitionistic logic. Potentially, this results in massive revisions of established mathematics. Recently, Neil Tennant (“The law of excluded middle is synthetic a priori, if valid”, Philosophical Topics 24 (1996), 205-229) suggested that a Dummettian anti-realist can accept the law of excluded middle as a synthetic, a priori principle groun…Read more
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2Vagueness and ConversationIn J. C. Beall (ed.), Liars and Heaps: New Essays on Paradox, Clarendon Press. 2004.
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 |