Source: A Concise Introduction to Logic (12 Ed, 2014), by Patrick J. Hurley.
Please observe my amelioration (and so change) of Hurley's notation;
I use MIN, MAJ, and MID to abbreviate the Minor, Major, and Middle Terms.
[p 287:] Rule 4: [...] a Negative Conclusion Requires a Negative Premise.
Fallacy: [...] Drawing a negative conclusion from affirmative premises
[p 288:] Conversely, a negative conclusion asserts that the MIN class is separate either wholly or partially from the MAJ class. But if both premises are affirmative, they assert class inclusion rather than separation. Thus, a negative conclusion cannot be drawn from affirmative premises.
I seek only intuition; so please do not answer with formal proofs or arguments.
The bolded sentence does not convince me. The only affirmative Categorical Propositions are A (in which only the Subject is distributed) and I (in which neither the Subject nor Predicate is distributed). So for any Affirmative Proposition, at least one term is not distributed and we know nothing about this one term. Then how is the bolded true?
How can you assert something about a term about which you know nothing?