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Equiparadoxicality of Yablo’s Paradox and the Liar

Ming Hsiung

Journal of Logic, Language and Information 22 (1):23-31 (2013)

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The Elimination of Direct Self-reference.Qianli Zeng & Ming Hsiung - 2023 - Studia Logica 111 (6):1037-1055.details This paper provides a procedure which, from any Boolean system of sentences, outputs another Boolean system called the ‘_m_-cycle unwinding’ of the original Boolean system for any positive integer _m_. We prove that for all \(m>1\), this procedure eliminates the direct self-reference in that the _m_-cycle unwinding of any Boolean system must be indirectly self-referential. More importantly, this procedure can preserve the primary periods of Boolean paradoxes: whenever _m_ is relatively prime to all primary periods of a Boolean paradox, this (...) Download Export citation Bookmark
Some Open Questions about Degrees of Paradoxes.Ming Hsiung - manuscriptdetails We can classify the (truth-theoretic) paradoxes according to their degrees of paradoxicality. Roughly speaking, two paradoxes have the same degrees of paradoxicality, if they lead to a contradiction under the same conditions, and one paradox has a (non-strictly) lower degree of paradoxicality than another, if whenever the former leads to a contradiction under a condition, the latter does so under the same condition. In this paper, we outline some results and questions around the degrees of paradoxicality and summarize recent progress. Download Export citation Bookmark
(1 other version)What Paradoxes Depend on.Ming Hsiung - 2018 - Synthese:1-27.details 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 (...) Download Export citation Bookmark 7 citations
Tarski's theorem and liar-like paradoxes.Ming Hsiung - 2014 - Logic Journal of the IGPL 22 (1):24-38.details Tarski's theorem essentially says that the Liar paradox is paradoxical in the minimal reflexive frame. We generalise this result to the Liar-like paradox $\lambda^\alpha$ for all ordinal $\alpha\geq 1$. The main result is that for any positive integer $n = 2^i(2j+1)$, the paradox $\lambda^n$ is paradoxical in a frame iff this frame contains at least a cycle the depth of which is not divisible by $2^{i+1}$; and for any ordinal $\alpha \geq \omega$, the paradox $\lambda^\alpha$ is paradoxical in a frame (...) Download Export citation Bookmark 4 citations
Content Implication and the Yablo’s Sequent of Sentences.Piotr Łukowski - forthcoming - Logic and Logical Philosophy:1.details Download Export citation Bookmark
Boolean Paradoxes and Revision Periods.Ming Hsiung - 2017 - Studia Logica 105 (5):881-914.details According to the revision theory of truth, the paradoxical sentences have certain revision periods in their valuations with respect to the stages of revision sequences. We find that the revision periods play a key role in characterizing the degrees of paradoxicality for Boolean paradoxes. We prove that a Boolean paradox is paradoxical in a digraph, iff this digraph contains a closed walk whose height is not any revision period of this paradox. And for any finitely many numbers greater than 1, (...) Download Export citation Bookmark 13 citations
Guest Editors’ Introduction.Riccardo Bruni & Shawn Standefer - 2019 - Journal of Philosophical Logic 48 (1):1-9.details Download Export citation Bookmark 5 citations

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