LessonsQiyās al-Khalf: Compound Reductio, Impossibility and Proof of the ClaimQuiz

First stage: If “Every human is an animal” were false, “Some human is not an animal” would be true. Under the assumed genus relation, that supposed exception would contradict an established feature of being human.

Second stage: Such a contradiction cannot hold. Hence “Some human is not an animal” is false. That proposition is the contradictory of the original claim.

Conclusion: Every human is an animal.

The argument first derives the unacceptable consequence and then denies it to recover the claim.

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Completing the textbook inference

Qiyās al-Khalf: Compound Reductio, Impossibility and Proof of the Claim

First stage: If “Every human is an animal” were false, “Some human is not an animal” would be true. Under the assumed genus relation, that supposed exception would contradict an established feature of being human.

Second stage: Such a contradiction cannot hold. Hence “Some human is not an animal” is false. That proposition is the contradictory of the original claim.

Conclusion: Every human is an animal.

The argument first derives the unacceptable consequence and then denies it to recover the claim.