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Theoremizing Yablo's Paradox

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arxiv 1406.0134 v1 pith:QB5YPIAF submitted 2014-06-01 math.LO cs.ITcs.LOmath.IT

Ahmad Karimi , Saeed Salehi This is my paper · ORCID
classification math.LOcs.ITcs.LOmath.IT
keywords paradoxyablologicself--referencesometheoremsversionsargument
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To counter a general belief that all the paradoxes stem from a kind of circularity (or involve some self--reference, or use a diagonal argument) Stephen Yablo designed a paradox in 1993 that seemingly avoided self--reference. We turn Yablo's paradox, the most challenging paradox in the recent years, into a genuine mathematical theorem in Linear Temporal Logic (LTL). Indeed, Yablo's paradox comes in several varieties; and he showed in 2004 that there are other versions that are equally paradoxical. Formalizing these versions of Yablo's paradox, we prove some theorems in LTL. This is the first time that Yablo's paradox(es) become new(ly discovered) theorems in mathematics and logic.

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  1. Sometime a Paradox, Now Proof: Non-First-Order-izability of Yablo's Paradox

    math.LO 2019-08 conditional novelty 5.0 of 10

    Yablo's paradox, formalized as a monadic second-order sentence, is provably not equivalent to any first-order sentence or any first-order theory.

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