David Corfield Philosophical points resolved by categorical logic

Contents

Contents

Idea

The uses of categorical logic in philosophy:

  1. Types, Dependent types, Quotient types, Modality applied to philosophy, especially metaphysics and philosophy of language.

  2. Learning/probability/causality/modelling

  3. Philosophy of mathematics: everyday mathematical discourse, structuralism, topology/geometry.

  4. Physics: MHoTT to capture higher supergeometry and so quantum gauge field theory. Friedman story.

How do these relate?

How does the continuous give rise to discrete, so 2 to 1?

4 to 2 Learning and physics. E.g., arxiv:2202.11104

Metaphysics/Philosophy of language

Any phenomenon in philosophy of language or metaphysics that philosophers treat is at least as well explained, and generally better explained, with the resources of category-theoretic logic/type theory.

Brandom on contradictory qualities

See here

Magidor on copredication

Book example (physical object/info source) via quotient types.

Magidor on arbitrary reference

See here

Following @andrejbauer’s response (https://twitter.com/andrejbauer/status/1450181993187233801) to @evanewashington on variables, how about we set up a grand challenge?

Questions

Jokes

Ryle’s type-pranking

2-D semantics

Multi-indexing

Learning/probability/causality/modelling

Learning

  • Dan Shiebler, Bruno Gavranović, Paul Wilson, Category Theory in Machine Learning

  • Spivak et al.

Causality

Modelling

Paterson

Mathematics

Structuralism

Geometry

Physics

MHoTT to capture higher supergeometry and so quantum gauge field theory.

Friedman story

Last revised on December 9, 2022 at 15:37:05. See the history of this page for a list of all contributions to it.