Dialetheism:
It feels like common sense to say that all statements must be true or false. Aristotle called it “the most certain of principles”. But is it? Some philosophers hold the radical view that statements can be both true and false, which is called dialetheism. This view is gaining traction among logicians because of the way it can help with paradoxes.
What are we to make of this strange idea? One big problem for dialetheism is that it allows direct contradictions to exist and this leads to a well-known difficulty in logic called the problem of explosion. If it is fine to say it is raining and not raining, then our entire basis for belief and action blows up. [“A new way to solve paradoxes can help you think more clearly,” Professor Margaret Cuonzo, NewScientist (8 January 2022, paywall)]
