omega-Circularity of Yablo's Paradox


Cevik M.

LOGIC AND LOGICAL PHILOSOPHY, vol.29, no.3, pp.325-333, 2020 (Journal Indexed in ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 29 Issue: 3
  • Publication Date: 2020
  • Doi Number: 10.12775/llp.2019.032
  • Title of Journal : LOGIC AND LOGICAL PHILOSOPHY
  • Page Numbers: pp.325-333

Abstract

In this paper, we strengthen Hardy's [1995] and Ketland's [2005] arguments on the issues surrounding the self-referential nature of Yablo's paradox [1993]. We first begin by observing that Priest's [1997] construction of the binary satisfaction relation in revealing a fixed point relies on impredicative definitions. We then show that Yablo's paradox is 'omega-circular', based on omega-inconsistent theories, by arguing that the paradox is not self-referential in the classical sense but rather admits circularity at the least transfinite countable ordinal. Hence, we both strengthen arguments for the omega-inconsistency of Yablo's paradox and present a compromise solution of the problem emerging from Yablo's and Priest's conflicting theses.