Premises:
All teachers are human.
Some calligraphers are not teachers.
Target conclusion: Some humans are not calligraphers.
Build a countermodel: all teachers are human, all humans are calligraphers, and some additional non-teachers are calligraphers. Both premises hold, but the conclusion is false because every human is a calligrapher.
The failure of entailment is established. One explicit counterexample teaches more than merely labeling the mood unproductive.
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The Fourth Figure: Productive Conditions, Moods and Proofs
Premises:
All teachers are human.
Some calligraphers are not teachers.
Target conclusion: Some humans are not calligraphers.
Build a countermodel: all teachers are human, all humans are calligraphers, and some additional non-teachers are calligraphers. Both premises hold, but the conclusion is false because every human is a calligrapher.
The failure of entailment is established. One explicit counterexample teaches more than merely labeling the mood unproductive.