The move from “No humans are horses” to “Some nonhorses are not nonhumans” uses an existing human as a witness: that human is a nonhorse and is not a nonhuman.
If the original subject has no instances, a universal negative alone does not guarantee a particular existence claim. Modern formal logic often makes this qualification explicit.
The traditional rule must therefore be read with its existential assumption.
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Contraposition: Classical Rules, Validity and the Later Convention
The move from “No humans are horses” to “Some nonhorses are not nonhumans” uses an existing human as a witness: that human is a nonhorse and is not a nonhuman.
If the original subject has no instances, a universal negative alone does not guarantee a particular existence claim. Modern formal logic often makes this qualification explicit.
The traditional rule must therefore be read with its existential assumption.