Editing Gödel's incompleteness theorems (section)

=== Paraconsistent logic ===

Although Gödel's theorems are usually studied in the context of classical logic, they also have a role in the study of [[paraconsistent logic]] and of inherently contradictory statements (''[[dialetheia]]''). {{harvs|last=Priest|year=1984|year2=2006|txt}} argues that replacing the notion of formal proof in Gödel's theorem with the usual notion of informal proof can be used to show that naive mathematics is inconsistent, and uses this as evidence for [[dialetheism]].{{sfnm
 | 1a1 = Priest | 1y = 1984
 | 2a1 = Priest | 2y = 2006
}} The cause of this inconsistency is the inclusion of a truth predicate for a system within the language of the system.{{sfn|Priest|2006|p=47}} {{harvtxt|Shapiro|2002}} gives a more mixed appraisal of the applications of Gödel's theorems to dialetheism.{{sfn|Shapiro|2002}}