Philosophy of Physics Seminar (Thursday - Week 5, HT26)

Abstract: Model Theory, a part of mathematical logic, has been surprisingly effective in its applications to core areas of mathematics. This success is based on an analysis of the formalism of a given area and on the efficient use of Classification Theory, which determines various degrees of “tameness’’ of formal theories. We will discuss a similar approach to the foundations of physics. This includes the question of the choice of language, the interpretation of that language in a structure, approximation, and related issues.

I will argue that the appropriate language for both quantum and statistical mechanics is that of Continuous Logic, and I will explain how the Hilbert‑space formalism emerges within the abstract CL setting. In this context one can speak of CL‑models of Dirac’s axioms, which are geometric universes equipped with continuous predicates and transformations. Finally, I will present a theorem showing that the Dirac–von Neumann axioms have, in addition to continuous models, approximate (huge) finite models.

Registration: If you do not hold a university card, please contact the seminar convenor or admin@philosophy.ox.ac.uk at least two working days before a seminar to register your attendance.