CHALLENGE THE INFINITE SPEAKERS

Tim Button

Tim Button is Head of the Philosophy Department, and a Professor of Philosophy & Logic, at UCL.

Before joining UCL in 2019 Tim was at Cambridge: as a PhD student (2006-10), a research fellow (2010-2012) and a faculty member (2012-2019).

He works at the intersection of philosophy, logic and mathematics.

Tim's numerous publications include a recently published trilogy on Level Theory that challenges the benefits of Modal Potentialism.

Title: Why I am not a (Height-)Potentialist

Abstract:

Actualists have a coherent story about the sets. If they speak modally at all, they claim that any set which could exist do exist. You might reject actualism because you reject objects-platonism; but if you are onboard with objects-platonism, actualism seems a good buy.

Potentialists don't like actualism. They like to speak modally, and they think that (necessarily) any things could form a set. I contend that there's no good reason to think this. I'll show this, by running through a few things potentialists might mean by "could".

If "could" is understood naively, then the potentialists' own arguments against actualism typically recoil against them. If "could" is understood interpretationally, then this opens several disastrous cans of worms. If "could" is understood in terms of priority, then they have a coherent view; but it's hard to see why it's better than (or indeed very different from) actualism.