The no-no paradox is a paradox

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Abstract

The No-No Paradox consists of a pair of statements, each of which 'says' the other is false. Roy Sorensen claims that the No-No Paradox provides an example of a true statement that has no truthmaker: Given the relevant instances of the T-schema, one of the two statements comprising the 'paradox' must be true (and the other false), but symmetry constraints prevent us from determining which, and thus prevent there being a truthmaker grounding the relevant assignment of truth values. Sorensen's view is mistaken: situated within an appropriate background theory of truth, the statements comprising the No-No Paradox are genuinely paradoxical in the same sense as is the Liar (and thus, on Sorensen's view, must fail to have truth values). This result has consequences beyond Sorensen's semantic framework. In particular, the No- No Paradox, properly understood, is not only a new paradox, but also provides us with a new type of paradox, one which depends upon a general background theory of the truth predicate in a way that the Liar Paradox and similar constructions do not.

Original languageEnglish (US)
Pages (from-to)467-482
Number of pages16
JournalAustralasian Journal of Philosophy
Volume89
Issue number3
DOIs
StatePublished - Sep 2011

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