وفي مانعة الخلو القسم الثاني دون الأول
In a disjunction excluding emptiness, the second kind of inference works, but not the first.
Exclusion of emptiness means the alternatives cannot both be false; they may both be true. Example: “This number is at least 5 or at most 5.” At 5, both statements are true; at other values, at least one is true.
Therefore denying either side establishes the other. But affirming one does not rule out the other, since both may hold.
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Exceptive Syllogism: Valid Inferences from Connected and Disjunctive Conditionals
وفي مانعة الخلو القسم الثاني دون الأول
In a disjunction excluding emptiness, the second kind of inference works, but not the first.
Exclusion of emptiness means the alternatives cannot both be false; they may both be true. Example: “This number is at least 5 or at most 5.” At 5, both statements are true; at other values, at least one is true.
Therefore denying either side establishes the other. But affirming one does not rule out the other, since both may hold.