Philosophy 290-3

Provability logic is the branch of modal logic in which the box operator is interpreted as provability in a formal theory, such as Peano Arithmetic. In this seminar, we will cover the core results of provability logic as presented in The Logic of Provability by George Boolos, including the most famous result in the field: Solovay’s Arithmetical Completeness Theorem for the Gödel-Löb logic GL. Additional material may be drawn from Artemov and Beklemishev’s chapter on provability logic in the Handbook of Philosophical Logic, as well as Verbrugge’s survey in The Stanford Encyclopedia of Philosophy. All enrolled students must give a presentation in at least one seminar session (or more, depending on enrollment) and submit a final paper. Enrollment by undergraduates is subject to consent of the instructors. Class attendance and participation is mandatory.