Synthese:1-27 (2018)

Authors
Ming Hsiung
Zhongshan University
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.
Keywords Circularity  Dependence  Paradox  Self-reference  Truth
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DOI 10.1007/s11229-018-1748-1
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References found in this work BETA

Paradox Without Self-Reference.Stephen Yablo - 1993 - Analysis 53 (4):251.
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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Citations of this work BETA

Paradoxes and Contemporary Logic.Andrea Cantini - 2008 - Stanford Encyclopedia of Philosophy.
Notes on Leitgeb’s What Truth Depends on.Edoardo Rivello - 2020 - Studia Logica 108 (6):1235-1262.
Unwinding Modal Paradoxes on Digraphs.Ming Hsiung - 2021 - Journal of Philosophical Logic 50 (2):319-362.

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