وإن كان زيد حمارا كان ناهقا لكنه ليس بناهق.
And if Zayd were a donkey he would bray, but he does not bray.
Here the conditional is granted and the consequent is denied. It follows that Zayd is not a donkey: if he were, the assumed conditional would require braying.
This is the valid pattern “If A then B; not B; therefore not A.” Simply denying A, by contrast, does not establish not B.
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Proof: Syllogism, Induction, Analogy and the Four Figures
وإن كان زيد حمارا كان ناهقا لكنه ليس بناهق.
And if Zayd were a donkey he would bray, but he does not bray.
Here the conditional is granted and the consequent is denied. It follows that Zayd is not a donkey: if he were, the assumed conditional would require braying.
This is the valid pattern “If A then B; not B; therefore not A.” Simply denying A, by contrast, does not establish not B.