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
When I consider if the sentence is true, it claims to be false which is exclusive with truth, therefore the sentence is not true.
When I consider if the sentence is false, the claim is inverted, so the sentence has to be not false.
I arrived at a conclusion that is the opposite of Dialetheism, with the sentence being neither true nor false.