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The Yablo ParadoxAn Essay on Circularity$
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Roy T Cook

Print publication date: 2014

Print ISBN-13: 9780199669608

Published to Oxford Scholarship Online: September 2014

DOI: 10.1093/acprof:oso/9780199669608.001.0001

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The Yablo Paradox and Circularity

The Yablo Paradox and Circularity

(p.71) 2 The Yablo Paradox and Circularity
The Yablo Paradox

Roy T Cook

Oxford University Press

This chapter addresses the Circularity Question. Several scholars have claimed that the Yablo paradox is, in fact, circular. The first critical task is thus to distinguish between a number of different senses in which a linguistic construction might be circular. We then examine extant arguments for and against the circularity of the Yablo construction. Prominent amongst these are Graham Priest’s argument that the use of diagonalization in the construction of the Yablo paradox smuggles in problematic circularity, and Hannes Leitgeb’s suggestion that non-well-founded sets can be used to model the referential structure of various semantic puzzles and thus settle this question. After deciding that the Yablo paradox is circular, but in a rather benign sense, the chapter concludes with the construction of a version of the paradox using infinitary connectives, a proof that this infinitary variant is genuinely non-circular, and a discussion and pre-emption of objections to the construction in question.

Keywords:   Yablo paradox, diagonalization, non-well-founded sets, infinitary connectives, circularity

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