TheLawOfNoncontradiction

Variously formulated, the gist of the Law of Noncontradiction is that a proposition and its denial cannot both be true at the same time and "in the same respect." If we're being careful, we won't formulate it this way, in terms of truth (it might then might be confused with ThePrincipleOfBivalence). Instead, we'll say the law is: for any proposition P, it is not both the case that P and not-P. In Aristotle's formulation: "One cannot say of something that it is and that it is not in the same respect and at the same time."

The Law of Noncontradiction is almost universally affirmed by philosophers. See also TheLawOfExcludedMiddle and ThePrincipleOfBivalence.