Who Needs a Proof of the Principle of Non-Contradiction?

This article examines Aristotle's "proof by refutation" (elenctic proof) of the Principle of Non-Contradiction (PNC), focusing on its dialectical effectiveness against opponents who tolerate true contradictions. Aristotle addresses interlocutors who both claim contradictions can be true and demand a demonstration (apodeixis) of the PNC. While the PNC cannot be demonstrated in the strict Aristotelian sense, Aristotle offers a refutation-based proof that proceeds from premises the opponent accepts, aiming to show why they must accept the PNC. The article argues that Aristotle’s goal is constructive—to meet the demand for a proof and secure assent—rather than to force opponents to abandon their contradictory views, resolving concerns about the argument’s persuasive power. This approach relies on the opponent’s willingness to engage in meaningful dialogue, highlighting Aristotle’s belief in the possibility of rational exchange even with those holding contradictory positions.