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ShardPhoenix comments on Unsolved Problems in Philosophy Part 1: The Liar's Paradox - Less Wrong
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I'm not sure if I like this paper (it seems to be trying to do too much), but it did contain something new to me - Yablo's non-self-referential version of the Liar Paradox: for every natural number n, let S(n) be the statement that for all m>n S(m) is false. Also there is a funny non-self-referential formulation by Quine: “Yields falsehood when preceded by its quotation” yields falsehood when preceded by its quotation.
The second has an implied "This sentence ..." so I'd say it's still self-referential.
edit: actually I don't think that's required (the quote is the subject) so it does count I suppose.
If I remember rightly, the process is called "quining" and while it produces similar paradoxes and problems, it is distinct from self-reference. Linguistically, at least - logically one might be a form of the other.
(Upvoted the edit!)