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.