What Paradoxes Depend on

Synthese:1-27 (2018)
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Abstract

This paper gives a definition of self-reference on the basis of the dependence relation given by Leitgeb (2005), and the dependence digraph by Beringer & Schindler (2015). Unlike the usual discussion about self-reference of paradoxes centering around Yablo's paradox and its variants, I focus on the paradoxes of finitary characteristic, which are given again by use of Leitgeb's dependence relation. They are called 'locally finite paradoxes', satisfying that any sentence in these paradoxes can depend on finitely many sentences. I prove that all locally finite paradoxes are self-referential in the sense that there is a directed cycle in their dependence digraphs. This paper also studies the 'circularity dependence' of paradoxes, which was introduced by Hsiung (2014). I prove that the locally finite paradoxes have circularity dependence in the sense that they are paradoxical only in the digraph containing a proper cycle. The proofs of the two results are based directly on König's infinity lemma. In contrast, this paper also shows that Yablo's paradox and its nested variant are non-self-referential, and neither McGee's paradox nor the omega-cycle liar paradox has circularity dependence.

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reprint Hsiung, Ming (2020) "What paradoxes depend on". Synthese 197(2):887-913

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Author's Profile

Ming Hsiung
Zhongshan University

Citations of this work

Unwinding Modal Paradoxes on Digraphs.Ming Hsiung - 2020 - Journal of Philosophical Logic 50 (2):319-362.
Notes on Leitgeb’s What Truth Depends on.Edoardo Rivello - 2020 - Studia Logica 108 (6):1235-1262.
From Paradoxicality to Paradox.Ming Hsiung - 2024 - Erkenntnis 89 (7):2545-2569.
The Elimination of Direct Self-reference.Qianli Zeng & Ming Hsiung - 2023 - Studia Logica 111 (6):1037-1055.

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References found in this work

Paradox without Self-Reference.Stephen Yablo - 1993 - Analysis 53 (4):251-252.
Axiomatic Theories of Truth.Volker Halbach - 2010 - Cambridge, England: Cambridge University Press.
Truth and paradox.Anil Gupta - 1982 - Journal of Philosophical Logic 11 (1):1-60.
Axiomatic theories of truth.Volker Halbach - 2008 - Stanford Encyclopedia of Philosophy.

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