omega-Circularity of Yablo's Paradox
LOGIC AND LOGICAL PHILOSOPHY, vol.29, no.3, pp.325-333, 2020 (ESCI, Scopus)
- Publication Type: Article / Article
- Volume: 29 Issue: 3
- Publication Date: 2020
- Doi Number: 10.12775/llp.2019.032
- Journal Name: LOGIC AND LOGICAL PHILOSOPHY
- Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, Linguistic Bibliography, Philosopher's Index, zbMATH
- Page Numbers: pp.325-333
- Middle East Technical University Affiliated: No
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.