the.com/law of the excluded middle

means A logical law stating that for any proposition, either it or its negation must be true — there is no middle ground where neither holds.

from The phrase translates the Latin 'principium tertii exclusi' (principle of the excluded third), itself rendering a concept traced to Aristotle's writings on logic, where he argued that of two contradictory statements, one must hold. The Latin scholastic tradition formalized and named it centuries later; the English 'excluded middle' settled in as the standard term once formal logic became an academic discipline, with the 'middle' being the forbidden third truth-value between true and false.