Speaker: Thomas Schindler (ILLC)
Date and Time: Thursday, May 16th 2019, 16:30-18:00
Venue: ILLC Seminar Room F1.15, Science Park 107.
Title: Unrestricted quantification and universal classes.
Abstract. According to the naive comprehension schema, an object belongs to the class of Fs iff that object is an F. Here, by class I simply understand the extension of some predicate. Due to Russell’s paradox, the naive comprehension schema is inconsistent. The orthodox solution to the class-theoretic paradoxes is found in the theory of types. However, this theory comes with severe expressive limitations, e.g. there can be no universal class (i.e. a class containing all objects). Based on some ideas of Gödel, I present a type-free theory of classes according to which there is a universal class containing all objects, including itself. I have published the basic ideas of my theory in my paper “Classes, why and how” (Phil Studies 2019). In this talk, I will survey the main ideas of this paper and also present some more recent, unpublished work on this topic.