In the video ‘exercises in construction’ at 5.42 (when discussing the solution to question 5) Gerard makes a mistake.
“5. MIN, NER, conclusion?
Let’s eliminate the compliment in the second premise by using obversion, giving us NAR
our fragment is now: MIN NAR, conclusion?
The middle term is N, so the terms in the conclusion must be M and R
Since we have no negative premises we can rule out a negative conclusion; and since one of our premises is particular, we can rule out a universal conclusion, leaving us with MIR/RIM
However, the middle term is N and N is distributed in neither premise so no valid conclusion is possible”
This last sentence is false (this is where the mistake occurred) N is in fact distributed in the proposition NAR, this being a universal affirmative proposition it distributes its subject term, which in this case is N. So the assertion that “and N is distributed in neither premise” is false.
MIR is in fact a valid conclusion to the syllogism since it accords with all six rules.