Logos and episteme
Adam BRAUS
ABSTRACT: Dialetheists claim that some statements are dialetheia or true contradictions and are both true and false. This challenges the classical understanding of the law of non-contradiction (LNC). Dialetheists claim there are at least three types of dialetheia: contradictory concepts, sorites paradoxes, and self-referential paradoxes. Attempts to argue that these contradictions are merely semantic have not succeeded entirely, and dialetheists reject this as begging the question. My goal here is to show that these cited dialetheias are not true contradictions at all, thus preempting motivations for dialetheism (and paraconsistent logics). I argue that contradictory concepts and sorites paradoxes are not dialetheias but rather distinguos—apparent contradictions where each side takes place in a different metaphysical respect. Next, I argue that contradictions of self-reference, such as the liar paradox, are also not dialetheias but a special sort of distinguo I call a quatology—a statement whose metaphysical respect necessarily entails the opposite of its predicated attribute. I argue that neither distinguos nor quatologies violate the classical understanding of the LNC and thus demotivate dialetheism and paraconsistent logics. Finally, I discuss various implications this view might have for logic, mathematics, and physics.
