Date(s) - 26/10/2016
2:15 pm - 3:15 pm
SICSA DVF Professor Philip Scott from the University of Ottawa will be giving a talk entitled “From Goedel to Lambek: studies in the foundations of logic and computation” on Wednesday 26 October at Heriot-Watt University.
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 early work with my late colleague Joachim Lambek (McGill).
P. J. Scott is a mathematical logician working in category theory, proof theory, and theoretical computer science. In 1986 he published the book Introduction to Higher Order Categorical Logic (Cambridge University Press) with J. Lambek, which has been highly inuential both in the development of categorical logic, and in its applications in theoretical computer science. In particular, the book establishes the close connections between various type theories, categories, and logics. It thus motivated later works on using category theory and related machinery in programming languages, as well as operational and denotational semantics.
Professor Scott is currently Associate Editor of the Cambridge journal Mathematical Structures in Computer Science, and a Coordinating Editor of the North-Holland journal Annals of Pure and Applied Logic. In Canada, his research funding comes from NSERC (Natural Sciences and Engineering Research Council of Canada). Since the early 1990s, Prof. Scott has published foundational papers in areas relating categorical logic to theoretical computer science.
The host of Professor Philip Scott visit to Scotland is Chris Heunen.