David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Key words: liar paradoxes, propositions, definite descriptions A Liar would be a sentence or sentence-token that expresses a proposition that is both true and not true. A Liar Paradox is reasoning that would do the impossible and demonstrate the reality of a Liar. It is sufficient, fully to resolve a Liar Paradox, to turn its purported demonstration that some sentence or sentence-token expresses a proposition that is both true and not true into a reductio of the existence of the proposition that would be expressed, while ‘explaining away’ the particular tricks and charm of the purported demonstration of paradox. The interest of these exercises lies in the seductiveness of the would be demonstration of a Liar Paradox, and in the depth and subtlety of logical/grammatical resources that can be tapped and fashioned to dispel it. The Liar taken on in this paper occasions especially seductive reasoning that exploits ‘scope-ambiguities’ of definite descriptions that, not incidentally, survive unscathed when its argument is symbolized in a Fregean description theory in which scopes of definite descriptions are not discriminated. Symbolizing this argument in a Russellian description theory in which scopes are discriminated makes unavoidable that its scope-ambiguities be settled one way or another, and reveals that however the scope ambiguity of a certain premise is settled the resultant unambiguous argument is unsound, either because it is invalid, though this premise comes out true, or because, though it is valid, this premise comes out not true. These results of Russellian analysis pave the way to a formal demonstration, from premises to which a monger of the paradox would be committed, that contrary to his case the Liar of this paper does not express a proposition. This conclusion is confirmed in the Appendix to this paper by a demonstration from a single empirical premise that no one can deny, in a Russellian calculus enhanced for truth of propositions expressed by tokens of sentences..
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