Content Implication and Yablo's Sequence of Sentences

Piotr Łukowski

DOI: http://dx.doi.org/10.12775/LLP.2019.012

Abstract


This paper is a continuation of [Łukowski, 2019], where it is shown that just like sets, sentences can also be understood in two ways: distributively or collectively. A distributive understanding of sets leads to the Russell antinomy, and a distributive understanding of sentences to liar antinomy. A collective understanding of sets frees up the set theory from Russell’s antinomy. Taking a similar approach to sentences no liar like paradoxes appear. The aim of the paper is to examine Yablo’s problem from this collective perspective. Given its nature, by using the content implication connective it becomes possible to assign logical values to all Yablo’s sentences. Moreover, it seems that Yablo’s problem is not a case of circularity.


Keywords


Yablo’s paradox; paradox; self-reference; circularity; content implication

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References


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