Let the claim be A, and its contradictory not-A.
Reductio rejects not-A, leaving not-not-A. In standard classical two-valued logic, eliminating this double negation gives A.
The step requires the assumption to be the actual contradictory. Refuting a merely contrary or loosely opposing statement does not necessarily prove the initial claim.
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Qiyās al-Khalf: Compound Reductio, Impossibility and Proof of the Claim
Let the claim be A, and its contradictory not-A.
Reductio rejects not-A, leaving not-not-A. In standard classical two-valued logic, eliminating this double negation gives A.
The step requires the assumption to be the actual contradictory. Refuting a merely contrary or loosely opposing statement does not necessarily prove the initial claim.