Speaker: Salvatore Florio and Nicholas Jones (Birmingham)
Title: Unrestricted Quantification and the Structure of Type Theory
Semantic theories based on a hierarchy of types have prominently been used to defend the possibility of unrestricted quantication. However, they also pose a prima facie problem for it: each quantier ranges over at most one level of the hierarchy and is therefore not unrestricted. We examine this problem in a range of dierent type-theoretic settings, and assess the prospects for unrestricted quantication in each.