the.com/law of noncontradiction

means The basic logical rule that a statement and its exact opposite cannot both be true at the same time and in the same sense.

from The principle itself traces to ancient Greek philosophy, most famously formulated by Aristotle, who argued in the Metaphysics that the same thing cannot both belong and not belong to the same subject at the same time and in the same respect — he treated it as the firmest of all principles, the bedrock any argument must stand on to mean anything at all. The English name is a straightforward Latin-flavored label (from Latin contradictio, 'speaking against') built to describe exactly that rule: no speaking against yourself and staying true.