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“Too Many” Yabloesque Paradoxes

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The Yablo Paradox (due to Stephen Yablo and Albert Visser) consists of an infinite sequence of sentences of the following form: S1: For all m > 1, Sm is false. S2: For all m > 2, Sm is false. S3: For all m > 3, Sm is false. : : : Sn: For all m > n, Sm is false. Sn+1: For all m > n+1, Sm is false. Hence, the nth sentence in the list ‘says’ that all of the sentences below it are false. The sequence is genuinely paradoxical – there is no way to assign truth and falsity to each of the sentences in this list so that a sentence is true if and only if what it says is the case and a sentence is false if not. For some background on the Yablo paradox and variations on it, see my previous discussion here. There are numerous variations on the Yablo Paradox. Many of these proceed by varying the quantifier used at the beginning of each of the sentences. For example, we obtain the Dual of the Yablo Paradox by considering an infinite sequence of sentences of the form: Sn: There exists. . .

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News source: OUPblog » Philosophy

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