Philosophical Studies:1-38 (forthcoming)

Authors
David Builes
Princeton University
Jessica M. Wilson
University of Toronto at Scarborough
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), Pruss (2020), and Scambler (2021), 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 some 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 in light of its theoretical and explanatory advantages, Countabilism is more likely true than not.
Keywords Infinity  Set Theory  Modality  Ontology
Categories (categorize this paper)
DOI 10.1007/s11098-021-01760-8
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy

 PhilArchive page | Other versions
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

Modal Logic as Metaphysics.Timothy Williamson - 2013 - Oxford, England: Oxford University Press.

View all 95 references / Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles

Making Sense of the Aristotelian Notion of Infinity.Hwan Sunwoo - 2018 - Proceedings of the XXIII World Congress of Philosophy 55:53-71.
Actual Versus Potential Infinity (BPhil Manuscript.).Anne Newstead - 1997 - Dissertation, University of Oxford
The Influence of Spinoza’s Concept of Infinity on Cantor’s Set Theory.Paolo Bussotti & Christian Tapp - 2009 - Studies in History and Philosophy of Science Part A 40 (1):25-35.
Concrete Possible Worlds.Phillip Bricker - 2008 - In Theodore Sider, John Hawthorne & Dean W. Zimmerman (eds.), Contemporary Debates in Metaphysics. Blackwell. pp. 111--134.
Approaching Infinity.Michael Huemer - 2016 - New York: Palgrave Macmillan.

Analytics

Added to PP index
2021-11-18

Total views
436 ( #20,068 of 2,463,235 )

Recent downloads (6 months)
436 ( #839 of 2,463,235 )

How can I increase my downloads?

Downloads

My notes