High Quality Content by WIKIPEDIA articles! Consequentia mirabilis (Admirable consequence), also known as Clavius's Law, is used in traditional and classical logic to establish the truth of a proposition from the inconsistency of its negation. It is thus similar to reductio ad absurdum, but it can prove a proposition true using just its negation. It states that if a proposition is a consequence of its negation, then it is true, for consistency. It can thus be demonstrated without using any other principle, but that of consistency. The most famous example is perhaps the Cartesian "cogito ergo sum": Even if one can question the validity of the thinking, no one can deny the existence of thought. Children have an uncanny appreciation for this law, and use it unwittingly on a regular basis: "I'm not talking to you" proves that, in saying this, the person is in fact talking to the other.

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