In defense of Countabilism

David Builes, Jessica M. Wilson

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

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, initially 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.

Original languageEnglish (US)
Pages (from-to)2199-2236
Number of pages38
JournalPhilosophical Studies
Volume179
Issue number7
DOIs
StatePublished - Jul 2022

All Science Journal Classification (ASJC) codes

  • Philosophy

Keywords

  • Cantor’s theorem
  • Cardinality
  • Countabilism
  • Diagonalization
  • Indefinite extensibility
  • Infinity
  • Metaphysics
  • Modality
  • Ontology
  • Philosophy of mathematics
  • Russell’s paradox
  • Set theory

Fingerprint

Dive into the research topics of 'In defense of Countabilism'. Together they form a unique fingerprint.

Cite this