January 26, 2018,
Professor of Philosophy, University of California, Berkeley
Is Logic a Normative Discipline?
Various philosophers, including Kant, Frege, and more recently Hartry Field and Greg Restall, have held that logic is in some interesting sense a normative discipline. Field, in particular, has argued that we need a normative characterization of logical validity in order to understand what proponents of alternative logics are disagreeing about. I will discuss what one needs to say in order to sustain an interesting version of this claim, and I will consider whether Field gives good reasons for accepting it.
February 09, 2018,
Professor Emeritus, San Jose State University
We used computer proof-checking methods to verify the correctness of our proofs of the propositions in Euclid Book I. We used axioms as close as possible to those of Euclid, in a language closely related to that used in Tarski’s formal geometry. We used proofs as close as possible to those given by Euclid, but filling Euclid’s gaps and correcting errors. Then we checked those proofs in the well-known and trusted proof checkers HOL Light and Coq. The talk will contain many geometrical diagrams and discuss both the geometry and the proof-checking. (This is joint work with Julien Narboux and Freek Wiedijk.)