Can a sentence be both true and false in the same sense? - Dialetheism
It might seem nonsensical until one sees the liar’s paradox:
This sentence is false.
Using classical logic, this sentence seems to be both true and false. Due to the explosion rule, that implies every sentence. This is absurd, but philosophers don’t agree on what has gone wrong here.
Dialetheism is the solution that accepts that it is both true and false and modifies logic to exclude the principle of explosion
Under classical logic, a paradox is a result of faulty premises, and proof that the premises cannot be true. It’s how you make any logical proof, by assuming the null hypothesis, and showing how it implies A and ¬A. It’s true for the liar’s paradox, and for Russell’s paradox (sorry Russell).
So my conclusion is “This sentence is false” is false. If it was true, then the sentence would be both true and not true. By the contrapositive, “This sentence is false” cannot be true, and cannot be a logical premise.
Never heard of dialetheism.
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