David Corfield Topos institute

Idea

What philosophy can gain from category theory/type theory. See Philosophical points resolved by categorical logic.

CT for use in maths and physics. Higher gauge theory. $\infty$-category theory.

HoTT

CT as a kind of generalized logic.

See an opportunity to wrap together these interests. Friedman paper.

Summit of what’s happening here. Hypothesis H. QS. Quantum modal logic. One thing I’m convinced is a very good thing: new logic, new maths, new physics.

NLP. No ambiguity in mathematical parsing. We don’t just have a collection of mathematical nouns, and meaningfulness is retained on substitution.

And yet ‘$2+i$ is prime’ ‘the trefoil knot is prime’. Reason Lean is doing well.

Natural language. My approach DTT.

Modal logic: Temporal type theory and Behavioral Mereology: A Modal Logic for Passing Constraints

Posts

• one
• two

Talk

Role of philosophy

1. Precursor thought, anticipating and stimulating through proposed connections.
2. Making sense after the event.

Both arise from wondering how things hang together.

“The aim of philosophy, abstractly formulated, is to understand how things in the broadest possible sense of the term hang together in the broadest possible sense of the term.” (Wilfred Sellars, Philosophy and the Scientific Image of Man, 1962)

Category theory can facilitate this process.

History

1. Maths, physics, logic: Klein 2-geometry;
2. Machine learning; Probability;
3. As a practice: how to write history.

Theme

ACT looking like they do what philosophers do: causality, learning, etc. with a kit of tools.

What’s the difference?

• Different tools, predicate logic, modal logic
• Long history, e.g., causality and Hume.
• Less ambitious: dHoTT and universe.

Worth looking at the critics of predicate logic, such as Rundle and Ryle.