Unfolding the Content of the Concept of Set

Talk held by Zeynep Soysal (Harvard University, Cambridge, Massachusetts, USA) at the KGRC Friday seminar on 2016‑11‑25.


In his famous paper on the continuum problem, Kurt Gödel states that there are some axioms of set theory "which a more profound understanding of the concepts underlying logic and mathematics would enable us to recognize as implied by these concepts" (Gödel, 1964, 477.). He states that such axioms "only unfold the content of the concept of set" (Gödel, 1964, 476f.). These statements are remarkable in part because they suggest that mere understanding of concepts is sufficient for knowing some axioms of set theory. This is to say that some axioms of set theory are, in some sense, analytic or conceptually true. In this paper, I propose two ways of defending this Gödelian unfolding claim. First, I argue for it on the basis of our ordinary practice of ascribing mathematical concepts. Second, I argue for it from a theoretical point of view; I examine three main accounts of concept possession, and argue that the Gödelian unfolding claim is true on these accounts if these accounts are to be in line with the way people actually possess the concept of set.

Bottom menu

Kurt Gödel Research Center for Mathematical Logic. Währinger Straße 25, 1090 Wien, Austria. Phone +43-1-4277-50501. Last updated: 2016-11-25, 21:24.