“It is impossible for the same thing to belong and not to belong at the same time to the same thing and in the same respect.” – Aristotle
“A is not non-A” – Classical Logic’s Formulation of the Above
Is it possible that this formulation of the Law of Non-Contradiction, set forth by Aristotle and unquestioned ever since, is missing something? Are there some contradictions, however few, that can be said to be true?
Enter dialetheism, which, if you have been living under a philosophical rock like me, you have probably never heard of. According to Wikipedia:
Dialetheism is the view that some statements can be both true and false simultaneously. More precisely, it is the belief that there can be a true statement whose negation is also true. Such statements are called “true contradictions”, dialetheia, or nondualisms.
One dialetheia is said to be the Liar’s Paradox, a logical problem which has stumped philosophers for ages. Is the statement “this sentence is false” true or false? If it’s true, the sentence is false. If the sentence is false, then it’s true. We’re left in a conundrum. Dialetheism seeks to address this paradox head on by suggesting the possibility of true contradictions. (See one attempt at a refutation of the dialetheist view on the Liar’s Paradox).
For the most recent of our regular philosophy night discussions in the Praxis participant and alumni group, we talked to one of dialetheism’s leading lights, Graham Priest.
The idea of true contradictions may strike you as immediately absurd. It did to me, too, but give Priest a shot. In this discussion, I thought he held his own pretty well. He explained his position enough for me to ditch some of my preconceptions about dialetheism.
I still hold to the law of noncontradiction, and I’m still rather fuzzy on some of Priest’s definitions – but that’s my fault for not asking. After this call, I do appreciate that dialetheism is a pretty limited and humble approach. It doesn’t cast aside the law of noncontradiction – which Priest seems to think holds in almost every case, particularly with matter itself. However, dialetheism does honestly try to address some of the paradoxes of syllogism and mathematics which other philosophers might toss aside as irrelevant.
The logicians of dialetheism ask an open question: have we come to the end of our work in formulating logic and precision in language? I would say not.