Philosophy of Mathematics Seminar (Monday - Week 4, HT26)

Abstract: Mathematical conventionalism claims that mathematical truth is determined by linguistic conventions, but it faces the problem of explaining the existence of mathematical entities. Jared Warren (2020) considers existence to be trivial: if a conventionally adopted theory of arithmetic contains existence claims, then numbers exist. Zeynep Soysal (2025), drawing on a descriptivist account about set-theoretic expressions, argues that more is required. In her view, not every theory—such as an inconsistent one—describes an existing entity. To address this, she links existence to consistency. Like Warren’s, her account is naturalistic in that it is based on the actual linguistic conventions of mathematical practice. Using a dataset from interviews with 28 practicing set theorists, we studied set-theoretic practice with a focus on consistency beliefs and forms of pluralism. Our findings confirm Soysal’s view: set theorists reject inconsistent theories, and the consistency of their associated theory is evidence enough to use phrases like “sets exist.” Two complications emerged, however. First, our findings reveal divergences among speakers that make it difficult to determine what all set theorists accept no matter what. Second, Soysal’s descriptivism explicitly includes informal descriptions. Yet our data show that informal ways of talking about sets are not always consistent. We will present examples of this phenomenon and offer some preliminary conclusions.

Registration: Online only.

Please note: A notice will be sent out for each talk with the Zoom link.