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9II—Patrick Greenough: Contextualism about Vagueness and Higher‐order VaguenessAristotelian Society Supplementary Volume 79 (1): 167-190. 2005.To get to grips with what Shapiro does and can say about higher-order vagueness, it is first necessary to thoroughly review and evaluate his conception of (first-order) vagueness, a conception which is both rich and suggestive but, as it turns out, not so easy to stabilise. In Sections I–IV, his basic position on vagueness (see Shapiro [2003]) is outlined and assessed. As we go along, I offer some suggestions for improvement. In Sections V–VI, I review two key paradoxes of higher-order vagueness…Read more
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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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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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6Vagueness 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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6Varieties 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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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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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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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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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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2Necessity, 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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1Review: Constructibility and mathematical existence by Charles Chihara (review)Mind 101 361-364. 1992.
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1Vagueness, Metaphysics, and ObjectivityIn Richard Dietz & Sebastiano Moruzzi (eds.), Cuts and Clouds: Vaguenesss, its Nature and its Logic, Oxford University Press. 2010.
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1""Bertrand Russell," On Denoting"(1905) and" Mathematical Logic as Based on the Theory of Types"(1908)In Jorge J. E. Gracia, Gregory M. Reichberg & Bernard N. Schumacher (eds.), The Classics of Western Philosophy: A Reader's Guide, Blackwell. pp. 460. 2003.
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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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1Objectivity, explanation, and cognitive shortfallIn Annalisa Coliva (ed.), Mind, meaning, and knowledge: themes from the philosophy of Crispin Wright, Oxford University Press. 2012.
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 |