CHALLENGE THE INFINITE SPEAKERS

Zeynep Soysal

Zeynep is an Associate Professor of Philosophy at the University of Rochester.

Prior to that, she attained her phD from Harvard in May 2017, and was an Andrew W. Mellon Postdoctoral Associate at Boston University.

Zeynep's research and publications focus primarily on foundational issues at the intersection of philosophy of language, philosophy of mathematics, metaphysics, and (social) epistemology.

Her 2020 paper 'Why is the Universe of Sets Not a Set?' contains some of the most important challenges to the viability and purported benefits of Modal Potentialism.

Title: Why Be a Height Potentialist?

Abstract

According to height potentialism, the height of the universe of sets is “potential” or “indefinitely extensible,” and this is something that a (formal) theory of sets should capture. Height actualism is the rejection of height potentialism: on this view, the height of the universe of sets isn't potential or indefinitely extensible, and our standard non-modal theories of sets don't need to be either supplemented with or reinterpreted in a modal language. In this paper, I examine and (mostly) criticize arguments for height potentialism. I first argue that arguments for height potentialism that appeal to its explanatory powers are unsuccessful. I then argue that the most promising argument for height potentialism involves the claim that height potentialism follows from an intuitive conception of sets. But, as I explain, this argument from intuitive conception, if sound, entails that whether height potentialism or height actualism is true is a verbal dispute, i.e., a matter of what meanings we choose to assign to our set-theoretic expressions. I explain that only pragmatic considerations can settle such a dispute. Finally, I suggest that these pragmatic considerations weigh in favor of actualism over potentialism. My discussion is intended to serve two broader aims, which are to develop what I take to be the most promising line of argument for height potentialism, and to elaborate the height actualist position in greater detail than is standardly done.