Loving the universe

Tim Button (Cambridge University)

Abstract 

I want to introduce you to a new set theory. (The theory is my own, but it builds on work by many other people.) According to this theory, the sets are arranged into well-ordered stages, but every set has an absolute complement. Since the absolute complement of the empty set is the universal set, this theory puts the empty set and the universal set on a par. Just how 'on a par' they are will emerge during the talk. But in the end, this theory has convinced me that the claim ‘there is no universal set’ is not just an unjustified dogma; it is a dogma without determinate content. (The talk won't be too technical; it should be accessible to anyone who has ever read Boolos's 'The iterative conception of set'.)