The uses of categorical logic in philosophy:
Types, Dependent types, Quotient types, Modality applied to philosophy, especially metaphysics and philosophy of language.
Learning/probability/causality/modelling
Philosophy of mathematics: everyday mathematical discourse, structuralism, topology/geometry.
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
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.
See here
Book example (physical object/info source) via quotient types.
See here
Following @andrejbauer’s response (https://twitter.com/andrejbauer/status/1450181993187233801) to @evanewashington on variables, how about we set up a grand challenge?
Ryle’s type-pranking
Multi-indexing
Dan Shiebler, Bruno Gavranović, Paul Wilson, Category Theory in Machine Learning
Spivak et al.
Paterson
Last revised on December 9, 2022 at 15:37:05. See the history of this page for a list of all contributions to it.