ω-Circularity of Yablo's Paradox
DOI:
https://doi.org/10.12775/LLP.2019.032Keywords
self-reference, Yablo's paradox, ω-circularity, ω-inconsistent theories, impredicativityAbstract
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 ‘ω-circular’, based on ω-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 ω-inconsistency of Yablo’s paradox and present a compromise solution of the problem emerged from Yablo’s and Priest’s conflicting theses.References
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