In a conditional inference, this pattern is valid:
1. If the antecedent holds, the consequent holds.
2. The consequent does not hold.
3. Therefore the antecedent does not hold.
Symbolically: P ⇒ Q; ¬Q; therefore ¬P.
In reductio, the antecedent is the contradictory of the claim and the consequent is an impossibility. Denying the impossible rejects the contradictory.
Affirming an antecedent merely from the truth of its consequent would be a different, invalid form.
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Qiyās al-Khalf: Compound Reductio, Impossibility and Proof of the Claim
In a conditional inference, this pattern is valid:
1. If the antecedent holds, the consequent holds.
2. The consequent does not hold.
3. Therefore the antecedent does not hold.
Symbolically: P ⇒ Q; ¬Q; therefore ¬P.
In reductio, the antecedent is the contradictory of the claim and the consequent is an impossibility. Denying the impossible rejects the contradictory.
Affirming an antecedent merely from the truth of its consequent would be a different, invalid form.