 How to allow inconsistency without incoherence is one of the main topics of dialetheim. A standard solution consists in subscribing to the view that deductive logical consequence is  paraconsistent.  A logical consequence relation \(\vdash\) is explosive if, according to it, a contradiction entails everything (ex contradictione quodlibet: for all \(A\) and \(B\): \(A,\neg A \vdash B\)). It is paraconsistent if and only if (iff) it is not explosive. By adopting a paraconsistent logic, a dialetheist can countenance some contradictions without being thereby committed to countenancing everything and, in particular, all contradictions. The development of paraconsistent logics has contributed to the most recent developments (and acceptance of the legitimacy) of dialetheism.