This chapter considers two possible explanations for the paradoxes.One is Lawvere’s diagonal theorem from category theory. Theother is the inclosure schema, proposed by Priest as the structureof many paradoxes and a step toward a uniform solution to theparadoxes. Inclosure suggests that paradoxes arise at the limits ofthought because the limits can be surpassed, and also not. Theconsequences of accepting Priest’s proposal are explored, andit is found that, from a thoroughly dialetheic perspective, (i) somelimit phenomena cannot be contradictory, on pain of absurdity, and(ii) true contradictions are better thought of as local, not“limit,” phenomena. Dialetheism leads back from theedge of thought, to the inconsistent in the everyday.

The Sorites Paradox is one of the most venerable and complex paradoxes in the territory of philosophy of logic. Together with the Sorites, the semantic paradoxes also occupy a very prominent place in research in this area. In this chapter we examine the relation between the Sorites and the best-known of the semantic paradoxes: the Liar Paradox. Traditionally, the Sorites and the Liar have been considered to be unrelated. Nevertheless, there have been several attempts to uniformly cope with them. This chapter begins by examining when and why in general, a uniform solution to more than one paradox should be expected and, in particular, why a uniform solution to the Liar and the Sorites should be expected. Subsequently the chpater focuses on the work of Paul Horwich, who has used epistemicist ideas that were first applied to solve the Sorites in order to attempt to give a solution to the Liar. It shows in some detail, as a particular example of the influence that the Sorites has had over the semantic paradoxes, whether the epistemicist approach Horwich presents in order to face the Sorites can be successfully applied to his theory of truth.