Countabilism is the view according to which every infinite collection is countable. We discuss this view in an online workshop.
Speakers: Jessica Wilson (University of Toronto), David Builes (Princeton University), Stewart Shapiro (Ohio State University), Chris Scambler (Oxford University), Øystein Linnebo (University of Oslo), Laura Crosilla (University of Oslo).
Schedule (all times are CET)
15:00 -- 15:50: Chris Scambler, Two Paths to Countabilism
16:00 -- 16:50: Jessica Wilson and David Builes, In Defense of Countabilism
17:00 -- 17:50: Laura Crosilla, Øystein Linnebo and Stewart Shapiro, Predicativity and Countabilism
18:00 -- 18:30: General discussion
The workshop will be held on Zoom. You need to register to attend the workshop.
Registration deadline: 8 November 2021. Please fill in this form to register.
Titles and Abstracts:
Abstract: Inspired by Cantor's Theorem (CT), orthodoxy takes infinities to come in different sizes. The orthodox view has had enormous influence in mathematics, philosophy, and science. We will defend the contrary view---Countablism---according to which, necessarily, every infinite collection (set or plurality) is countable. We first argue that the potentialist or modal strategy for treating Russell's Paradox, first proposed by Parsons 2000 and developed by Linnebo 2010, 2013 and Linnebo and Shapiro 2019, should also be applied to CT, in a way that vindicates Countabilism. Our discussion dovetails with recent independently developed treatments of CT in Meadows 2015, Scambler 2021, and Pruss 2020, aimed at establishing the mathematical viability, and therefore epistemic possibility, of Countabilism. Unlike these authors, our goal isn't to vindicate the mathematical underpinnings of Countabilism. Rather, we aim to argue that, given that Countabilism is mathematically viable, Countabilism should moreover be regarded as true. After clarifying the modal content of Countabilism, we canvas certain of Countabilism's many positive implications, including that Countabilism provides the best account of the pervasive independence phenomena in set theory, and that Countabilism has the power to defuse several persistent puzzles and paradoxes found in physics and metaphysics. We conclude that the theoretical advantages of Countabilism far outweigh its potential downsides.
Organisers: Neil Barton, Laura Crosilla and Øystein Linnebo