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Modal Homotopy Type Theory - The Prospect of a New Logic for Philosophy (Hardcover)
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Modal Homotopy Type Theory - The Prospect of a New Logic for Philosophy (Hardcover)
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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.
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