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
The sentence refers to a fact that can be true or false, but doesn’t refer to any fact in and of itself. Nobody would ever use this sentence outside of grading papers. So the one sentence is grammatically incorrect because it refers to nothing. It’s a waste of thought.