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10Mathematics in philosophy, Selected essays, by Charles Parsons, Cornell University Press, Ithaca, N.Y., 1983, 365 pp (review)Journal of Symbolic Logic 53 (1): 320-329. 1988.
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8Varieties of Pluralism and Relativism for LogicIn Steven D. Hales (ed.), A Companion to Relativism, Wiley‐blackwell. 2011.This chapter contains sections titled: Abstract Introduction Defining Terms: Relativism, Pluralism, Tolerance What Is Logic? One Route to Pluralism: Logic ‐ as ‐ Model The Boundary Between Logical and Non ‐ Logical Terminology Vagueness Relativity to Structure References.
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7Review of Michael D. Resnik: Mathematics as a Science of Patterns_; Stewart Shapiro: _Philosophy of Mathematics: Structure and Ontology (review)British Journal for the Philosophy of Science 49 (4): 652-656. 1998.
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7Vagueness in ContextOxford University Press. 2006.Stewart Shapiro's aim in Vagueness in Context is to develop both a philosophical and a formal, model-theoretic 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 with such contextual factors as the comparison class and paradigm cases. A person can be tall with respect to male accountants and not tall with respect to professionalbasketball players. The main feature of Sh…Read more
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6An Introduction to Non-classical Logic (review)Review of Metaphysics 56 (3): 670-671. 2003.This book is just what its title says: an introduction to nonclassical logic. And it is a very good one. Given the extensive interest in nonclassical logics, in various parts of the philosophical scene, it is a welcome addition to the corpus. Typical courses in logic, at all levels and in both philosophy departments and mathematics departments, focus exclusively on classical logic. Most instructors, and some textbooks, give some mention to some nonclassical systems, but usually few details are p…Read more
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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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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.
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5Mathematics in Philosophy, Philosophy in Mathematics: Three Case StudiesIn Francesca Boccuni & Andrea Sereni (eds.), Objectivity, Realism, and Proof. FilMat Studies in the Philosophy of Mathematics, Springer International Publishing. 2016.The interaction between philosophy and mathematics has a long and well articulated history. The purpose of this note is to sketch three historical case studies that highlight and further illustrate some details concerning the relationship between the two: the interplay between mathematical and philosophical methods in ancient Greek thought; vagueness and the relation between mathematical logic and ordinary language; and the study of the notion of continuity.
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5Computability, Proof, and Open-TextureIn Adam Olszewski, Jan Wolenski & Robert Janusz (eds.), Church's Thesis After 70 Years, Ontos Verlag. pp. 420-455. 2006.
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3Necessity, Meaning, and Rationality: The Notion of Logical ConsequenceIn Dale Jacquette (ed.), A Companion to Philosophical Logic, Blackwell. 2006.This chapter contains sections titled: Modality Semantics Form Epistemic Matters Recapitulation Mathematical Notions.
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2Simple truth, contradiction, and consistencyIn Graham Priest, J. C. Beall & Bradley Armour-Garb (eds.), The Law of Non-Contradiction, Oxford University Press. 2004.
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2Vagueness and ConversationIn J. C. Beall (ed.), Liars and Heaps: New Essays on Paradox, Clarendon Press. 2004.
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2Mathematical StructuralismCambridge University Press. 2018.The present work is a systematic study of five frameworks or perspectives articulating mathematical structuralism, whose core idea is that mathematics is concerned primarily with interrelations in abstraction from the nature of objects. The first two, set-theoretic and category-theoretic, arose within mathematics itself. After exposing a number of problems, the book considers three further perspectives formulated by logicians and philosophers of mathematics: sui generis, treating structures as a…Read more
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1Burali-Forti's revengeIn J. C. Beall (ed.), Revenge of the Liar: New Essays on the Paradox, Oxford University Press. 2007.
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1Properties and predicates, objects and names : impredicativity and the axiom of choiceIn Ivette Fred Rivera & Jessica Leech (eds.), Being Necessary: Themes of Ontology and Modality from the Work of Bob Hale., Oxford University Press. 2018.
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1Objectivity, explanation, and cognitive shortfallIn Annalisa Coliva (ed.), Mind, meaning, and knowledge: themes from the philosophy of Crispin Wright, Oxford University Press. 2012.
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1Review: Constructibility and mathematical existence by Charles Chihara (review)Mind 101 361-364. 1992.
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 |