One of the most well-known paraconsistent logics is Logic of Paradox (LP) developed by Graham Priest. As is clear from its name, LP is strongly motivated by the considerations on paradoxes such as the liar paradox and Russell's paradox. And the characteristic aspect of Priest's treatment is that he deals with paradoxes with the metaphysical view known as dialetheism, namely the view that there are true contradictions. The aim of the talk is threefold. First, we review the modern origin of paraconsistency and try to clarify the real challenge of paraconsistency. To this end, we make explicit what we exactly need to justify in defending paraconsistency, and its relation to dialetheism. Second, we focus on the naive set theory which may serve as an example to justify dialetheism. In general, dialetheism is regarded as something hard to swallow, but naive set theory might be a good place to start. Finally, we argue that we need more than paraconsistent logic in developing dialetheic theories, and introduce the notion of dialetheic logic. We will also present an expansion of LP which is dialetheic. Interestingly, this expansion will shed some light on connexive logics.