Modal Homotopy Type Theory: The Prospect of a New Logic for Philosophy

ISBN : 9780198853404

David Corfield
192 ページ
156 x 234 mm

"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.


1 A path to a new logic

2 Dependent types

3 Homotopy types

4 Modal types

5 Spatial types

6 Conclusion


David Corfield has been a Senior Lecturer since 2009 in the Department of Philosophy at the University of Kent, which he joined in 2007. His principal areas of research are philosophy of mathematics and philosophy of medicine. As regards to the former, his work has not only been closely studied by other philosophers, but has also been appreciated by some of the world's leading mathematicians internationally recognised as an exponent of a new style of work which pays much closer attention to the practice of mathematicians.