 Much of the ongoing discussion about dialetheism involves not just the LNC but its dual, the Law of Excluded Middle (LEM). (See  section 3.2  below.) The LEM says (informally) that for every sentence \(A\), either \(A\) or \(\neg A\) is true (we bracket here views that disentangle the LEM from Bivalence). Dialetheism is the thesis that there are truth value gluts, challenging the LNC; the dual position, challenging the LEM, is that there are truth value gaps. It is a subtle issue, which we will not discuss here, whether a gap should count as lacking any  truth value,  or as having a non-classical value distinct from both truth and falsity, and similarly whether a glut has two truth values, or some third ‘glutty’ value. In any case, these dual approaches are nowadays labelled paracomplete versus (paraconsistent) dialetheic theories of truth. (The paraconsistent/paracomplete terminology is not entirely happy: see Ripley 2015a, footnote 1; but is now standard.) Priest’s logic includes the LEM and he rejects the existence of gaps in Priest 1987/2006, ch.1. Other approaches are both paracomplete and paraconsistent; they include a place for both gaps and gluts. The case for and against dialetheism turns as much on the status of the LEM as the LNC; see Beall and Ripley 2018.