АПАГОГИЧЕСКОЕ ДОКАЗАТЕЛЬСТВО

Apagogic Proof

A form of indirect proof, also known as reductio ad impossibile or proof by opposites. The following is a typical apagogic proof. Let B be the thesis to be proved and A₁, A₂...Aₙ the true facts by means of which the thesis is proved. It is agreed to consider that non-B, the logical opposite of B, is true and it is included in the facts of the proof.

From the series of facts thus obtained—A₁, A₂...Aₙ, and non-B—conclusions are formed until a situation is arrived at which logically contradicts one of the facts of the evidence. This contradiction of the original facts, provided the conclusion is correct, is possible only if the facts of the proof are false. Since A₁, A₂...Aₙ are undoubtedly true, the assumption of the truth of non-B was false; hence B is true.

Апагогическое доказательство

(От греч. apagogys - отводящий) то же, что Доказательство от противного.