Curry paradox cycles

A 'Liar cycle' is a finite sequence of sentences where each sentence in the sequence except the last says that the next sentence is false, and where the final sentence in the sequence says that the
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A Liar cycle is a finite sequence of sentences where each sentence in the sequence except the last says that the next sentence is false, and where the final sentence in the sequence says that the first sentence is false. Thus, the 2-Liar cycle (also known as the No-No paradox or the Open Pair) is: S1:        Sentence S2 is false. S2:        Sentence S1 is false. And the 3-Liar cycle is: S1:        Sentence S2 is false. S2:        Sentence S3 is false. S3:        Sentence S1 is false. The Liar paradox itself is just the 1-Liar cyle (where the Liar sentence plays the role of both the first sentence and the last sentence in the sequence of length one): S1:        Sentence S1 is false. We can prove, for any finite number n, that if n is odd then there is no stable assignment of truth and falsity to each sentence – that is, that the sequence is paradoxical, and if n is even then there are exactly two distinct stable assignments of truth and falsity (the trick is noticing that any stable. . .

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News source: OUPblog » Philosophy

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