Substance and what it means to be › Why Contradiction Needs Qualifications

The inquiry also concerns principles used across different subjects. In IV.3, Aristotle formulates noncontradiction: an attribute cannot both belong and fail to belong to the same subject at the same time and in the same respect. The qualifications matter as much as the prohibition. Someone can be tired now and rested tomorrow. A surface can be warm on one side and cold on another without the same part being both in the same respect. Neither example violates the principle he states.

In IV.4 Aristotle denies that every principle can receive a demonstration from more basic premises. An unlimited demand for prior demonstration would prevent demonstration from getting started. Instead, he offers a refutative defense against someone who rejects noncontradiction while still saying something definite. The interlocutor must make a meaningful distinction if a word is to signify something determinate in the discussion. Aristotle tries to show that unrestricted denial undermines the distinctions required for the denial itself.

This is a defense through the conditions of intelligible argument, rather than a proof from a supposedly more certain axiom. One can assess whether each step succeeds without confusing the strategy with a refusal to give reasons. For present purposes, its practical use is modest: specify the subject, time, and respect before declaring two claims inconsistent. That habit can expose a verbal dispute before anyone mistakes it for a discovery about reality.