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Modal Homotopy Type Theory

Modal Homotopy Type Theory

Publisher Oxford University Press
Year 01/02/2020
Edition First
Pages 192
Version hardback
Readership level Professional and scholarly
Language English
ISBN 9780198853404
Categories Philosophy: logic, Philosophy of mathematics, Calculus, Mathematical modelling
Delivery to United States

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Book description

"The old logic put thought in fetters, while the new logic gives it wings." For the past century, philosophers working in the tradition of Bertrand Russell - who promised to revolutionise philosophy by introducing the 'new logic' of Frege and Peano - have employed predicate logic as their formal language of choice. In this book, Dr David Corfield presents a comparable revolution with a newly emerging logic - modal homotopy type theory. Homotopy type theory has recently been developed as a new foundational language for mathematics, with a strong philosophical pedigree. Modal Homotopy Type Theory: The Prospect of a New Logic for Philosophy offers an introduction to this new language and its modal extension, illustrated through innovative applications of the calculus to language, metaphysics, and mathematics. The chapters build up to the full language in stages, right up to the application of modal homotopy type theory to current geometry. From a discussion of the distinction between objects and events, the intrinsic treatment of structure, the conception of modality as a form of general variation to the representation of constructions in modern geometry, we see how varied the applications of this powerful new language can be.

Modal Homotopy Type Theory

Table of contents

1: A path to a new logic
2: Dependent types
3: Homotopy types
4: Modal types
5: Spatial types
6: Conclusion

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