Sets as properties
University of Oslo
09 / 09 / 2023

According to the iterative conception of set, sets are “built in stages” in a process to be pursued “as far as possible”. It is notoriously difficult to make sense of the “building” analogy unless the mind-dependence of sets is accepted. In this talk I will sketch the sets as properties view, according to which set theory is nothing but a part of cumulative (modal) type theory, and sets are just a specific kind of properties. I will offer some reasons for thinking that the sets as properties view, broadly based on (Linnebo & Rayo 2012, Degen & Johannsen 2000) delivers a more satisfactory and realist understanding of the iterative conception than those presently available. In addition, I will address Button and Trueman’s (2022) “no bootstrapping” objection to the sets as properties view. Finally, I will show how this reply paves the way to a modal and neoRussellian form of logicism which is thoroughly contingentist.

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