This class will address different aspects of the justification of deduction, including classic papers by Lewis Carroll and Arthur Prior, and more recent work of Crispin Wright and Paul Boghossian. We will also cover a scholarly debate about the status of the justification of deduction in Frege and recent scholarly investigations of Hilbert’s program. Some attention will be given to Gödel’s first and second theorems, and perhaps the Gentzen, Gödel and Kleene consistency arguments for arithmetic. As a specific application of the issues, we will consider debates over the logical character of “abstraction principles”.
The class will presuppose some familiarity with quantificational logic. Familiarity with elementary number theory and basic computation theory (Turing machines, etc.) would be helpful but will not be presupposed.