In this talk I revisit some famous logical paradoxes, and consider the possibility that they are utterly ordinary. To do this, I look at the inclosure schema, proposed by Graham Priest as the underlying structure of many paradoxes. The picturesque idea behind the inclosure schema is that paradoxes arise at limits, whichcan both be surpassed and not; this in turn is an argument for dialetheism—the thesis that some contradictions are true—and the adoption of a paraconsistent logic. What are the consequences of taking this route into dialetheism/paraconsistency? I will show how, from a thoroughly dialetheic perspective, the import of the inclosure schema changes dramatically. When reconceived from within a purely paraconsistent framework, many of the motivating arguments and proofs around inclosures break down. For the arguments that remain paraconsistently valid, I argue that any true contradictions turn out to be better thought of as local, not global ‘limit’ phenomenon. The paradoxes point back from the edge of the universe, to the inconsistent in the everyday.