An earlier lesson established the valid exceptive form: denying the consequent of a conditional denies its antecedent. The final step of qiyās al-khalf uses that pattern.
Conditional: If the contradictory is true, impossibility follows.
Exception: But impossibility does not hold.
Conclusion: Therefore the contradictory is not true.
The original claim then follows by the impossibility of both contradictories being false. Thus reductio combines previously studied forms of reasoning.
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Qiyās al-Khalf: Compound Reductio, Impossibility and Proof of the Claim
An earlier lesson established the valid exceptive form: denying the consequent of a conditional denies its antecedent. The final step of qiyās al-khalf uses that pattern.
Conditional: If the contradictory is true, impossibility follows.
Exception: But impossibility does not hold.
Conclusion: Therefore the contradictory is not true.
The original claim then follows by the impossibility of both contradictories being false. Thus reductio combines previously studied forms of reasoning.