The indirect proof shows that conversion is not just a memorized pattern; it is a necessary consequence.
When a universal negative is true, supposing its converse false creates a contradiction with the original. Therefore the converse does not merely happen to be true in the human-and-stone example; its validity follows from complete disjointness between the two classes.
This reasoning generalizes to other true universal-negative propositions.
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Simple Conversion: Definition, Categorical Rules and Reductio
The indirect proof shows that conversion is not just a memorized pattern; it is a necessary consequence.
When a universal negative is true, supposing its converse false creates a contradiction with the original. Therefore the converse does not merely happen to be true in the human-and-stone example; its validity follows from complete disjointness between the two classes.
This reasoning generalizes to other true universal-negative propositions.