The Logic and Metaphysics Workshop will meet on March 24th from 2:00-4:00 in-person at the Graduate Center (Room 7395) for a talk by Davide Sutto (Oslo).
Title: The iterative conception of pluralities
Abstract: Georg Cantor informally distinguished between “consistent” and “inconsistent” multiplicities as those many things that, respectively, can and cannot be thought of as one, i.e., as a set. In this talk I propose a framework that clarifies the distinction through a contemporary development of the iterative conception of set. Reshaping Tim Button’s Level Theory by means of plural logic, I define and axiomatize the notion of a plural level. This provides an explanation of Cantor’s consistent multiplicities as level-bound pluralities, namely as those pluralities that appear at some level of the plural cumulative hierarchy of sets. Furthermore, it also yields a development of set theory from plural logic that retains the full power of the comprehension axiom schema. This feature is especially relevant as it enables a parallel understanding of inconsistent multiplicities as those pluralities that are not level-bound, that is, as proper classes.