Philosopher Stephen Read on non-classical logic, Curry’s paradox, and modus ponens
How can something be both true and false at the same time? What are dialetheic solutions? How do classical and non-classical logic differ? These and other questions are answered by Professor Emeritus of History and Philosophy of Logic in the Arché Research Centre for Logic, Language, Metaphysics and Epistemology, Stephen Read.
The liar paradox arises when someone tries to say that what they were actually saying at that time is false. They say ‘I’m lying, in this very utterance I’m lying’, or ‘This utterance is false’. This seems rather strange: why would someone even want to do this? But if they do, that’s going to undermine our theory of truth, or so it would seem. And the other aspect goes like this: supposing what I say is true, but I say that what I say is false. Then if it’s true, it’s surely how things are, but I’ve said that it’s false, so if it’s true, it’s false.
Why do philosophers emphasize non-contradiction? What’s so bad about contradictions? There is an argument that goes a very long way in the history of philosophy that states that contradictions are a very bad thing, that if we admitted contradictions into our theory, we could admit anything into our theory. For example, take the proposition we just discussed, suppose we admitted that this sentence I came up with is both true and not true, then it would seem that it’s true. Then if it true, it is either not true or the Moon is made of green cheese.
Dialetheic solutions to the liar paradox accept everything there is about the theory of truth that other philosophers accept, plus they add to it the basic principle that it’s possible for some things to be both true and false for them to be true contradictions. But to do that it means that they have to revise logic, they find that the basic principles that have been around for thousands of years – it doesn’t mean they are right, but logicians have embraced these principles like disjunctive synergism and the contraction of antecedents – they have to produce a logic that doesn’t use those principles.