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Logic, Mathematics, Philosophy, Vintage EnthusiasmsLogic in Category Theory

Logic, Mathematics, Philosophy, Vintage Enthusiasms: Logic in Category Theory [Logic already spanned a great range of topics before the birth of categorical logic. Some celebrated results achieved in logic during the first half of the twentieth century are milestones in the understanding of mathematical relations between syntactic, semantic and algorithmic aspects of the structure of language and reasoning. Logical tools have been exploited in a variety of applications: from linguistics to computer science, from methodology of science to specific physical theories. The very formulation of questions and answers concerning the foundations of mathematics relies on such tools. Finally, mathematical logic has altered the face of philosophy. In view of such outcomes, it is all the more appropriate to consider the impact of categorical methods on logic, since they affect the study of proofs and models, by forging a stricter relationship between a theory and its models, and by enlarging the range of possible models beyond the universe of sets in a way that leads to a substantial refinement of the status ascribed to logic itself.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

Logic, Mathematics, Philosophy, Vintage EnthusiasmsLogic in Category Theory

Part of the The Western Ontario Series in Philosophy of Science Book Series (volume 75)
Editors: DeVidi, David; Hallett, Michael; Clarke, Peter

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References (67)

Publisher
Springer Netherlands
Copyright
© Springer Science+Business Media B.V. 2011
ISBN
978-94-007-0213-4
Pages
287 –324
DOI
10.1007/978-94-007-0214-1_15
Publisher site
See Chapter on Publisher Site

Abstract

[Logic already spanned a great range of topics before the birth of categorical logic. Some celebrated results achieved in logic during the first half of the twentieth century are milestones in the understanding of mathematical relations between syntactic, semantic and algorithmic aspects of the structure of language and reasoning. Logical tools have been exploited in a variety of applications: from linguistics to computer science, from methodology of science to specific physical theories. The very formulation of questions and answers concerning the foundations of mathematics relies on such tools. Finally, mathematical logic has altered the face of philosophy. In view of such outcomes, it is all the more appropriate to consider the impact of categorical methods on logic, since they affect the study of proofs and models, by forging a stricter relationship between a theory and its models, and by enlarging the range of possible models beyond the universe of sets in a way that leads to a substantial refinement of the status ascribed to logic itself.]

Published: Jan 27, 2011

Keywords: Category Theory; Intuitionistic Logic; Left Adjoint; Indispensability Argument; Categorical Logic

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