Modal Homotopy Type Theory

Modal Homotopy Type Theory
Author: David Corfield
Publisher: Oxford University Press
Total Pages: 208
Release: 2020-02-06
Genre: Philosophy
ISBN: 0192595032


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"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
Language: en
Pages: 208
Authors: David Corfield
Categories: Philosophy
Type: BOOK - Published: 2020-02-06 - Publisher: Oxford University Press

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"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 - wh
Homotopy Type Theory: Univalent Foundations of Mathematics
Language: en
Pages: 484
Authors:
Categories:
Type: BOOK - Published: - Publisher: Univalent Foundations

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Categories for the Working Philosopher
Language: en
Pages: 486
Authors: Elaine M. Landry
Categories: Mathematics
Type: BOOK - Published: 2017 - Publisher: Oxford University Press

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This is the first book on category theory for a broad philosophical readership. There is no other discussion of category theory comparable in its scope. It is d
Temporal Type Theory
Language: en
Pages: 235
Authors: Patrick Schultz
Categories: Mathematics
Type: BOOK - Published: 2019-01-29 - Publisher: Springer

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This innovative monograph explores a new mathematical formalism in higher-order temporal logic for proving properties about the behavior of systems. Developed b
Categorical Logic and Type Theory
Language: en
Pages: 784
Authors: B. Jacobs
Categories: Computers
Type: BOOK - Published: 2001-05-10 - Publisher: Gulf Professional Publishing

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This book is an attempt to give a systematic presentation of both logic and type theory from a categorical perspective, using the unifying concept of fibred cat