The source appeals to the impossibility of both contradictories being false (irtifāʿ al-naqīḍayn).
If “Every human is an animal” and “Some human is not an animal” were both false, the universal affirmative and its genuine contradictory would both have been denied. Classical logic excludes that possibility.
Thus, refuting the true contradictory establishes the original proposition. Do not confuse contradictories with propositions that are merely contraries.
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Qiyās al-Khalf: Compound Reductio, Impossibility and Proof of the Claim
The source appeals to the impossibility of both contradictories being false (irtifāʿ al-naqīḍayn).
If “Every human is an animal” and “Some human is not an animal” were both false, the universal affirmative and its genuine contradictory would both have been denied. Classical logic excludes that possibility.
Thus, refuting the true contradictory establishes the original proposition. Do not confuse contradictories with propositions that are merely contraries.