In this talk, I want to re-examine some foundations of mathematics and computability theory, based on more recent results in type theory and categorical logic. We shall focus on some themes surrounding computability: What is a computable function? What are "natural" theories of computable functions? What is truth and what are Goedel’s Incompleteness Theorems? Finally, if time permits, I would like to discuss a candidate for an "ideal" model for a moderate constructivist, allowing us to reconcile various competing foundational philosophies. Many of these issues come from my work with my late colleague Joachim Lambek (McGill).
Philip Scott is a professor in the Department of Mathematics and Statistics at the University of Ottawa, Canada. His research interests include mathematical logic, category theory, foundations of mathematics and computing, theoretical computer science, and programming language theory.