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Modal Homotopy Type TheoryThe Prospect of a New Logic for Philosophy$
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David Corfield

Print publication date: 2020

Print ISBN-13: 9780198853404

Published to Oxford Scholarship Online: March 2020

DOI: 10.1093/oso/9780198853404.001.0001

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PRINTED FROM OXFORD SCHOLARSHIP ONLINE (oxford.universitypressscholarship.com). (c) Copyright Oxford University Press, 2021. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in OSO for personal use. date: 18 January 2022

A Path to a New Logic

A Path to a New Logic

(p.1) 1 A Path to a New Logic
Modal Homotopy Type Theory

David Corfield

Oxford University Press

This chapter explains how modal homotopy type theory combines ideas from two currents of thought: type theory and category theory. Despite what might appear to be rather different philosophical starting points, there has emerged an intrinsically structuralist language of great interest to computer scientists, mathematicians and physicists. This in itself should be enough to interest philosophers in the language, but further motivation is provided by addressing some of the kinds of objection raised to formalization in philosophy; in particular, those from ordinary language philosophy which emphasize the elasticity and context-dependence of natural language. We see that several of their concerns, such as that the definitional and descriptive uses of ‘is’ are conflated in logic, are addressed by the type theory. The prospect is then presented of an opportunity to use the new language to explore key issues in philosophy of mathematics, philosophy of language and metaphysics.

Keywords:   Computational trinitarianism, metaphysics, category theory, type theory, intuitionism, William Lawvere, categorification, topos, groupoid

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