Minor: Some reciters are teachers.
Major: No poet is a reciter.
Target: Some teachers are not poets.
Assume the contradictory of the target: “All teachers are poets.” The minor supplies reciters who are teachers; under the assumption, they are also poets. But the major excludes every poet from reciters. This is a contradiction.
The assumption is false; hence some teachers are not poets. Reductio succeeds only when the true contradictory, not merely another negative sentence, is assumed.
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The Fourth Figure: Productive Conditions, Moods and Proofs
Minor: Some reciters are teachers.
Major: No poet is a reciter.
Target: Some teachers are not poets.
Assume the contradictory of the target: “All teachers are poets.” The minor supplies reciters who are teachers; under the assumption, they are also poets. But the major excludes every poet from reciters. This is a contradiction.
The assumption is false; hence some teachers are not poets. Reductio succeeds only when the true contradictory, not merely another negative sentence, is assumed.