Paradox Revisited I: Truth

Abstract

In this pair of essays, I revisit the logical paradoxes. In the present essay I discuss the most famous of the so-called semantical paradoxes, the paradox of the Liar, the sentence that says of itself that it is not true, and in the essay that follows (Paradox Revisited II) I shall consider whether we should really accept a view once expressed by Godel, the view that the paradoxes of set theory are ones that we can see through, can definitely and satisfactorily resolve, even if (as he conceded) the same cannot be said for the semantical paradoxes. The Liar Paradox The best presentation I know of the Liar Paradox is Charles Parsons', and in the end the view I shall defend is, I believe, an elaboration of his. In “The Liar Paradox,” a paper I have thought about for almost twenty years, the paradox is stated in different ways. One of these ways is in terms of three alternatives: either a sentence expresses a true proposition, or it expresses a false proposition, or it does not express a proposition at all. A second way mentioned in that paper is the one I followed in my presentation of the Liar paradox in Realism with a Human Face , in which talk of propositions is avoided, and I mostly employ that way here in order to facilitate comparison with Tarski's work.