We had a sweeping discussion touching upon many issues in the philosophy of mathematics, including the nature of mathematical truth, mathematical abstraction, the nature of mathematical existence, the meaning and role of proof in mathematics, the completeness theorem, the incompleteness phenomenon, infinity, and a discussion about the motivations that one might have for studying mathematics.
This is a graduate seminar in the Philosophy of Logic at the University of Oxford, run jointly by myself and Volker Halbach in Hilary Term 2021.
The theme will be self-reference, truth, and the hierarchy of consistency strength.
A detailed schedule, including the list of topics and readings is available on Volker’s web site.
The seminar will be held Fridays 9-11 am during term, online via Zoom at 812 2300 3837.
The final two sessions of term will be specifically on the hierarchy of consistency strength, based on my current article in progress concerning the possibility of natural instances of incomparability and ill-foundedness in the hierarchy of large cardinal consistency strength.