Dialetheism

Abstract

A contradiction is any sentence of the form “P and not P,” a sentence together with its negation. Dialetheism is the thesis that some contradictions are true: some true sentences have true negations. It is the claim that there are truth-value gluts. It is a thesis about truth and sharply at odds with a lot of philosophy going back to Aristotle. The term “dialetheic” was invented in the late 1970s by Graham Priest and Richard Sylvan (Routley at the time). This neologism was to replace the term “dialectical,” which had been in use from Hegel. The word is intended to mean something like “two-way truth” and is sometimes spelled “dialethism.” The idea that there are truth-gluts has been advocated by Richard Routley/Sylvan, Graham Priest, J. C. Beall, and others. If there are any true contradictions (or dialetheias) they could be in anything from natural language to arithmetic to the structure of reality. So dialetheism has reverberations throughout logic, language, mathematics, and metaphysics. Dialetheism is motivated largely by logical paradoxes in truth theory and set theory, apparently unsolvable contradictions that heavily influenced logical research in the early 20th century. As such, dialetheism is deeply tied to technical issues in logic—and particularly paraconsistent logic—formal systems that allow for contradictions. Unlike classical logic, a theory in a paraconsistent logic can be inconsistent but non-trivial, so that not every sentence is a part of the theory. Some scholars have traced the idea of dialetheism in works and traditions around the world going back thousands of years. Nevertheless, for the sake of focus, in this article dialetheism per se is conceived of as a contemporary phenomenon in modern philosophical logic.