David Corfield MHTT2

The sequel to MHTT. Two versions.

Updates on each chapter + Friedman chapter.

Chapter 1: Types

Any mentions in types in philosophical literature, much here that’s not dependent?, Lotze, fundamental categories. Univocality/equivocality. $Type$ and $Type^+$ (pointed types), account on ‘Modal type’ of green, but now via $1 \to Type$, filtering out of $Entities$ those that are $X-Entities$.

Chapter 2: Dependent types

Mike’s $n$-theories; questions; extended anaphora case.

Chapter 3: Homotopy types

Equivalence relation, book up to identity; Univalence for structures;

Chapter 4: Modal type

Graded modalities; Leverhulme application; temporal modality; Peirce – coloured modes; inductive, probabilistic; equivariant.

Chapter 5: Spatial types

condensed vs cohesive;

Chapter 6: Friedman

See here.

Alternative scheme

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

2. Learning/probability/causality: https://arxiv.org/abs/2111.14293

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

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

How do these relate?

How does continuous give rise to discrete 2 to 1?

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

4 to 3, the new geometry.