> modifying the LEM to permit Unknowable as a third category LEM doesn't need to be modified, and it's not a third category. In classical logic (with LEM), unl

> modifying the LEM to permit Unknowable as a third category LEM doesn't need to be modified, and it's not a third category. In classical logic (with LEM), unlike in constructive/intuitionistic logic (no LEM), truth and provability are simply not the same -- in fact, it is LEM that creates that difference. > Instead we maintain that it has a truth value one way or the other, but that it happens to be both unknowable and of no consequence. Precisely! That is the difference between classical and constructive logic. In constructive logic truth and provability are the same, and something is neither true nor false until it has been proven or refuted. But before you conclude that this kind of logic, without LEM, is obviously better (philosophically), you should know that any logic has weirdnesses. What happens without LEM, for example, is that it is not true that every subset of a finite set is necessarily finite. ¯\_(ツ)_/¯