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59Intentional mathematics (edited book)Sole distributors for the U.S.A. and Canada, Elsevier Science Pub. Co.. 1985.Among the aims of this book are: - The discussion of some important philosophical issues using the precision of mathematics. - The development of formal systems that contain both classical and constructive components. This allows the study of constructivity in otherwise classical contexts and represents the formalization of important intensional aspects of mathematical practice. - The direct formalization of intensional concepts (such as computability) in a mixed constructive/classical context.
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Anti-realism and modalityIn J. Czermak (ed.), Philosophy of Mathematics, Hölder-pichler-tempsky. pp. 269--287. 1993.
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85Introduction II: The George Boolos memorial symposium: Dedicated to the memory of George Boolos (1940 9 4-1996 5 27)Philosophia Mathematica 7 (3): 244-246. 1999.
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201Foundations without foundationalism: a case for second-order logicOxford University Press. 1991.The central contention of this book is that second-order logic has a central role to play in laying the foundations of mathematics. In order to develop the argument fully, the author presents a detailed description of higher-order logic, including a comprehensive discussion of its semantics. He goes on to demonstrate the prevalence of second-order concepts in mathematics and the extent to which mathematical ideas can be formulated in higher-order logic. He also shows how first-order languages ar…Read more
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78Regions-based two dimensional continua: The Euclidean caseLogic and Logical Philosophy 24 (4). 2015.
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219Do not claim too much: Second-order logic and first-order logicPhilosophia Mathematica 7 (1): 42-64. 1999.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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22Review of P. Benacerraf and H. Putnam (eds.) Philosophy of Mathematics (review)Philosophy of Science 52 (3): 488-. 1985.
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211Mathematical structuralismPhilosophia Mathematica 4 (2): 81-82. 1996.STEWART SHAPIRO; Mathematical Structuralism, Philosophia Mathematica, Volume 4, Issue 2, 1 May 1996, Pages 81–82, https://doi.org/10.1093/philmat/4.2.81.
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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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80Classical LogicIn Edward N. Zalta (ed.), The Stanford Encyclopedia of Philosophy, The Metaphysics Research Lab. 2014.Typically, a logic consists of a formal or informal language together with a deductive system and/or a model-theoretic semantics. The language is, or corresponds to, a part of a natural language like English or Greek. The deductive system is to capture, codify, or simply record which inferences are correct for the given language, and the semantics is to capture, codify, or record the meanings, or truth-conditions, or possible truth conditions, for at least part of the language.
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84Varieties of LogicOxford University Press. 2014.Logical pluralism is the view that different logics are equally appropriate, or equally correct. Logical relativism is a pluralism according to which validity and logical consequence are relative to something. Stewart Shapiro explores various such views. He argues that the question of meaning shift is itself context-sensitive and interest-relative.
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 |