[gerard.casey]

You may have noticed some minor errors in the slides, most spelling, such as ‘and’ for ‘an’ or eccentric punctuation, such as missing a closing apostrophe. These are the result of my fingers being too fast for my brain! While regrettable, they shouldn’t cause any confusion as the accompanying narration is usually correct.

If I notice anything I think might cause a problem, I’ll post it under this topic. If you think you notice something problematic, could I ask you to let me know, not under this topic, but by email to me at gerard.casey@ucd.ie. If I agree that it is or might be problematic, I’ll reply under this topic in a new post.

Thank you.

[susan]

Hello! My home-schooled teenage sons and I are enjoying the logic class. We are wondering about one of the exercises, though, since we all got a different answer than you. It is the Exercises in Construction set, number 5. We obverted the second premise to get NAR, as you did. But in your answer you said that neither premise distributes the middle term (Rule 5), thus there was no valid conclusion. Isn’t the middle term (N) distributed in NAR because it’s an “A” type? Are we missing something? Thanks!
Susan in New Hampshire

[gerard.casey]

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)
[Conclusion] ???

By obverting our 2nd premise, we get as our fragment,

MIN
NAR
???

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.

[Author]

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