Logic in Category Theory

Chapter
Part of the The Western Ontario Series in Philosophy of Science book series (WONS, volume 75)

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.

Keywords

Category Theory Intuitionistic Logic Left Adjoint Indispensability Argument Categorical Logic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Department of Theoretical PhilosophyUniversity of FlorenceFlorenceItaly

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