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What Paradoxes Depends on

Hsiung, Ming (2018) What Paradoxes Depends on. [Preprint]

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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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Item Type: Preprint
Hsiung, Mingmingshone@163.com0000-0001-9037-2024
Keywords: Circularity, Dependence, Paradox, Self-reference, Truth
Subjects: Specific Sciences > Mathematics > Logic
Specific Sciences > Mathematics > Proof
Depositing User: Dr. Ming Hsiung
Date Deposited: 24 Feb 2018 17:33
Last Modified: 24 Feb 2018 17:33
Item ID: 14403
DOI or Unique Handle: SYNT-D-17-00814R3
Subjects: Specific Sciences > Mathematics > Logic
Specific Sciences > Mathematics > Proof
Date: 23 February 2018

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