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Philosophical investigation of the concept of truth is often divided along two dimensions: investigation of the nature of truth and investigation of the semantics of truth claims. This tutorial will focus on the second kind of concern. One key impetus for a philosophical interest in the semantics and definability of truth is the challenge posed by semantic paradoxes such as the Liar paradox and Curry¿s paradox. Despite each having the initial appearance of a parlor trick, philosophers and logicians have come to appreciate the deep implications of these paradoxes. The main goal of this tutorial is to gain an appreciation of the philosophical issues -­ both with respect to formal and natural languages ­¿ which arise from consideration of the paradoxes. To this end, we will study some of the classic contributions to this area including Tarski¿s famous result that, in an important sense, the semantic paradoxes render truth indefinable, and Kripke¿s much later attempt to provide a definition of truth in the face of Tarski¿s limitative result. Further topics include the debate between paracomplete and paraconsistent solutions to the semantic paradoxes (notably defended by, respectively, Field and Priest); the relationship between deflationism about truth and the paradoxes; and the notion of ¿revenge problems¿ (roughly, the claim that any solution to the paradoxes can be used to construct a further paradox).nThe tutorial will avoid excessive technical discussions, but will aim to engender appreciation for some philosophical interesting technical points and will assume a logic background of PHIL150 level.