Logique et Analyse

TitleLeitgeb, ``about'', Yablo
Publication TypeJournal Article
Year of Publication2009
AuthorsUrbaniak, R
JournalLogique et Analyse
Volume52
Number207
Pagination239-254
Abstract

Leitgeb (2002) objects against the clarity of the debate about the alleged (non-)circularity of Yablo’s paradox, arguing that there actually are at least two notions of self-reference and circularity at play.One, on which Yablo’s paradox is not circular, is defined via thereference of the constituents of a sentence, and another, on which the paradox is circular, is defined via syntactic mappings and fixedpoints. More importantly, Leitgeb argues that both definitions aren’t satisfactory and that before we can undertake a serious debate about the circularity of Yablo’s paradox we first need to clarify the notions involved. I will focus on Leitgeb’s criticism of the first definition1and will argue that the problems arise not as much on the level of our definition of circularity as on the level of our definition of reference of sentences (aboutness). Leitgeb’s main worry is the failure of a requirement called ‘Equivalence Condition’, which says that if a formula is self-referential, any formula logically equivalent to it should also be self-referential. I will argue that preservation under logical equivalence is unreasonable with respect to self-reference,but is indeed needed with respect to aboutness. Since Leitgeb’ sown tentative notion of aboutness doesn’t satisfy the requirement, I will suggest another approach which fixes this problem. I also explain why the intuitions that circularity should satisfy the equivalence condition are misled. Next, I argue that the new notion of aboutness is not susceptible to slingshot arguments. Finally, I compare it with Goodman’s notion of absolute aboutness, emphasizing those features of Goodman’s approach that make his notion inapplicable in the present discussion. [1]I would like to express my gratitude to all the people who discussed earlier versions of this paper with me: Hannes Leitgeb, Jeffrey Ketland, Karl Georg Niebergall, Diderik Batens, Joke Meheus, Maarten Van Dyck, Stefan Wintein, Martin Bentzen, Christian Straßer, Ghent Centre for Logic and Philosophy of Science members, and the participants of PhDs in Logic workshop (Gent 2009)

Citation KeyUrbaniak2009b
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