David Corfield book outline

Book sketch

Book sketch

  • Friedman's Dynamics of Reason

  • New exemplar: new logic for a new geometry for a new physics.

  • Type theory: Husserl; Constructive type theory, Martin-Löf

  • Category theory: Lawvere; universal properties; adjunctions

  • Higher toposes

  • Modal type theory

  • Geometry: supergeometry + homotopy

  • Cohomology in mathematics

  • differential cohomology in mathematics

  • differential cohomology in physics

  • Gauge field theory

  • Quantum field theory: “three pillars of modern QFT (it’s a) local b) Lagrangian c) gauge field theory) translating into three reasons why one needs to pass from plain linear type theory to a linear version of dependent homotopy-type theory.”

  • M-theory: Hypothesis H

  • Philosophy: Carnap, Cassirer, Kuhn, Brandom, …

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