Metaphysics and Logic Seminar Jann Paul Engler (University of St. Andrews)
September 26 @ 3:00 pm - 5:00 pm
Title: Sheaves for Intuitionistic Logic
Abstract: Somewhat simplified, the ‘traditional’ intuitionistic conception of logic evaluates the judgement ‘that p’ not as “p is true” but as “p is verifiable” or “there is a proof of p”. This talk is concerned with finding an adequate formal semantical framework that reflects central aspects of the meaning of the logical constants under this conception. It has two parts. Based on historical writings and on systematic grounds, I will first review a number of desiderata that such a semantical framework has to fulfil. I will then observe that none of the common semantics for intuitionistic logic manages to account for all of them. In the second part, I will introduce a version of sheaf semantics for intuitionistic logic, for which I argue that it does (if it works the way that I hope it does). This semantics differs in some respects from already known sheaf models. It is a bit more complex than the semantics that are more familiar to philosophers, but it manages to integrate all the other formal approaches that I will discuss, and each of its components also permits an intuitive understanding.