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.


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.

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Kurt Gödel Research Center for Mathematical Logic. Währinger Straße 25, 1090 Wien, Austria. Phone +43-1-4277-50501. Last updated: 2017-05-08, 14:34.