Kurt Gödel Research Center

The iterative conception of properties and comprehension

Talk held by Sam Roberts (University of Oslo, Norway) at the KGRC Friday seminar on 2017‑05‑05.

Abstract

Mathematicians appeal to proper classes: that is, collections too large to form sets. But what are classes if not sets? One response is that classes are properties. Properties are sharply distinguished from sets: they are intensional whereas sets are extensional. Fine and Linnebo have proposed theories on which properties are “built up” in a series of stages. Unfortunately, neither of these theories imply that there are very many properties. In this talk, I will propose an improvement of these theories. More precisely, by ensuring that the stages extend far enough, I will show that the they can be modified to interpret Morse-Kelly class theory, which implies the existence of a plethora of classes.