Must One of Two Contradictory Claims Be False?

In Book IV of the Metaphysics, Aristotle formulates the principle of non-contradiction: the same thing cannot, at the same time and in the same respect, both have and not have the same attribute. In classical logic, if “the door is open” and “the door is not open” really are a claim and its negation, they cannot both be true; at least one must be false.

The difficulty often lies in whether there is a genuine contradiction. A door left five centimetres ajar may be called open by someone who means “not fully shut”, while another calls it not open because nobody can pass through. The surface opposition hides two standards. Changes in time, subject or meaning create similar false conflicts. The principle does not say that reality never changes. It asks us to hold the relevant conditions fixed while making the judgement.

Contemporary dialetheism argues that at least some contradictions are true, with familiar debates involving the liar paradox and systems that must reason despite inconsistent information. This does not mean that anything goes: associated paraconsistent logics are designed to prevent one contradiction from entailing every claim. It is a genuine challenge to the classical framework, not Aristotle's own view.

My judgement is that everyday reasoning should begin by preserving non-contradiction, because correction and commitment become unstable without a reliable difference between assertion and denial. Yet when statements clash, the first task is not to declare the other person absurd. It is to check whether both sides mean the same subject, time and sense. Most disputes need ambiguity removed, not a true contradiction accepted.

Sources: https://plato.stanford.edu/entries/aristotle-noncontradiction/
https://plato.stanford.edu/entries/dialetheism/