Léon Probst (Recognised Student: Università della Svizzera Italiana): 'Interpreting Gödel's second incompleteness theorem'
Abstract: Gödel's second incompleteness theorem roughly says that any consistent and sufficiently strong theory cannot prove its own consistency. This is not a mathematical claim, but rather a philosophical interpretation of some metamathematical theorems. Are we then justified in accepting this standard interpretation of Gödel's second incompleteness theorem? More specifically, what do we mean by a sufficiently strong theory, and what is it to prove (or not) a consistency statement? Although this standard interpretation is widely accepted and used in various philosophical fields, answering these questions and thus justifying this important philosophical claim is quite difficult.
In this talk, I examine some of the common justifications for the standard interpretation of Gödel's second incompleteness theorem, and argue against them. I then propose an alternative, more promising approach.
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.
