Consider the claim “Every intelligent student finishes first in an examination.” Its contradictory is “Some intelligent student does not finish first.”
That exception is entirely possible and may occur for many reasons. It does not entail a logical contradiction. Saying that intelligent students “ought” to finish first is not a reductio proof.
Reductio requires a genuine impossibility entailed by the contradictory assumption, not an expectation or preference.
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Qiyās al-Khalf: Compound Reductio, Impossibility and Proof of the Claim
Consider the claim “Every intelligent student finishes first in an examination.” Its contradictory is “Some intelligent student does not finish first.”
That exception is entirely possible and may occur for many reasons. It does not entail a logical contradiction. Saying that intelligent students “ought” to finish first is not a reductio proof.
Reductio requires a genuine impossibility entailed by the contradictory assumption, not an expectation or preference.