SusanB_NH: You are absolutely right! I’d like to pretend I put that error in deliberately just to check if people were paying attention but the truth is that Homer nodded. Well spotted! I don’t quite know why that error happened – I can only think that I must have been looking at the MIR/RIM on the line immediately before the erroneous statement.
Here’s the situation.
In lesson 13, problem 5 (starting at 6.04 on the video) asks you to find (if possible) a conclusion that, if added to the syllogism fragment, would give you a valid syllogism.
The fragment is
[1st premise] MIN
[2nd premise] NER(complement)
By obverting our 2nd premise, we get as our fragment,
At 6.36, having shown that the premises as they now are together with MIR or RIM as a conclusion will satisfy the first four rules of the syllogism, I go on to say:
“However, the middle term is N and N is distributed in neither premise so no valid conclusion is possible”
This, of course, is incorrect! The middle term is ‘N’ and ‘N’ is distributed in the second premise. That satisfies rule 5.
Rule 6 requires that any term distributed in the conclusion be distributed in the premise in which it occurs. As we have seen, the only possible candidates for a conclusion are:
MIR or RIM (which, by conversion, are the same proposition)
As this is an ‘I’ type proposition, neither term is distributed so that rule 6 is vacuously satisfied.
So, MIR or RIM will, if added to the fragment, give us a valid syllogism.
So, thank you SusanB_NH for bringing this to my attention. If you notice anything else of significance, please do let me know.
I hope you and your sons continue to enjoy the logic lessons.