[ted.macinnes]

I just took the test and got one question wrong, technically, though I think my answer works just as well, I just added an unnecessary step. It was the last question, 6b, where we are asked to provide the conclusion to the syllogism GIR GEP(comp) -> ?

I used obversion to change GEP(comp) to GAP, and did the rest of the work using that, which gave me 2 possible answers, RIP and PIR. Those two answers are essentially the same, as they can be converted by simple conversion, and I believe they can be obverted to arrive at the answer provided in the course.

My question is twofold, 1 – is my answer correct? and 2, is there a reason why one should not convert a premise with a compliment if, including that premise there are only 3 terms?

I hope that made sense! Thanks, Ted

[gerard.casey]

Ted: Sorry for the delay in responding. I’ve only just seen your post.

In answer to the first part of you question: yes, PIR or RIP is correct. As you note, they are effectively the same proposition (by conversion) and are also equivalent to POR(complement) and ROP(complement) by obversion.

I’m not quite sure what you intend by the second part to your question. Did you miswrite ‘convert’ for ‘obvert’? Because what you did was to obvert the second premise, thereby getting rid of the complement on its predicate. You weren’t wrong to do this – it just wasn’t absolutely necessary as the two premises as they stood contained three and only three terms.

If I haven’t understood the second part of your question correctly, come back to me again.

I hope this helps somewhat.

[dmdavidmann]

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
[Lists possibilities]
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.

[gerard.casey]

Thank you, David. This came up before and I posted a correction in the thread ‘Errata’ but since someone might miss the correction, I’m redoing the lesson and it will be reposted. Here’s what I said in the Errata thread:

“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.”

[dmdavidmann]

Also in the video ‘how much do you know?’ At 11.00 when referring to question 6. Gerard makes the same mistake
a) BAC, ???, BID

“Of the four remaining candidates, the only one in which C is distributed is CAD, since rule six is vacuously satisfied, the proposition CAD satisfies all the rules and will give us a valid syllogism. ”
However this is not a valid syllogism because the B term is distributed being the subject term in the universal affirmative proposition yet the B term is undistributed as the subject term in the particular affirmative proposition that is the conclusion to the syllogism. Rule six is not satisfied (no term can be distributed in the conclusion that is not distributed in the premise) and since all six rules must be satisfied in order for a syllogism to be valid, this syllogism is invalid.

[dmdavidmann]

“Thank you, David. This came up before and I posted a correction in the thread ‘Errata’ but since someone might miss the correction, I’m redoing the lesson and it will be reposted. Here’s what I said in the Errata thread:”

Thank you for the response, I’m brand-new to liberty classroom and so have not had a chance to check out all the threads, I’m sure I would have come across this if I had done some digging.
Having spotted the mistake I thought it a good excuse to make my first contribution to the forum.

All the best.

[gerard.casey]

David, the second case you mention [BAC, ????, therefore BID] is in fact a valid syllogism if you add, as the second premise, CAD.

Rule 6 on distribution goes from bottom (conclusion) to top (premises), not the other way around. What rule 6 prohibits is having a term distributed in the conclusion and not distributed in the premise in which it occurs. There’s no problem having a term distributed in a premise and not distributed in the conclusion. Roughly, the idea is this.
If in my premises I haven’t been using a term to refer to all the things that it can refer to, it’s hard to see how I can start doing so in my conclusion. On the other hand, it’s perfectly in order to use a term to refer to all of the things it can refer to in a premise, and then not to do so in the conclusion. You can validly go from all to some, but not from some to all.

So, if you check the complete syllogism according to the six rules, you get:

BAC
CAD
therefore, BID

Rule 1 satisfied (at least one universal)
Rule 2 satisfied (vacuously – no particular premise so no need to check further)
Rule 3 satisfied (at least one affirmative premise)
Rule 4 satisfied (vacuously – no negative premise so no need to check further)
Rule 5 is satisfied (the middle term, C, is distributed in the second premise)
Rule 6 is satisfied (vacuously, since no term in the conclusion is distributed)

I hope this clears things up?

If you have any other queries or questions, please do let me know. And if you start a thread, please send your initial post directly to me, otherwise I might not see it for some time.

Best wishes,

GC

[dmdavidmann]

So if the propositions were switched around to make the new order:
BIC
CAD
therefore, BAD

Then that would be a violation of rule six because we are moving from an undistributed term [B] in one of the premises [BIC] to a distributed term [B^] in the conclusion [BAD]
so whenever you’re limiting the scope (going from a full scope [in one or more of the premises] to smaller scope [in the conclusion)) then that’s cool/valid, but when you’re enlarging the scope (going from a smaller scope [in one or more of the premises] to full scope/extension [in the conclusion]) then that’s not cool/invalid
am I on the right track?
I just realise that this is a bad example because it violates rule 2

Is there any chance that you might be able to come up with some better examples than the one I just gave which would explain the point more accurately and help make it a little clearer?

“If you have any other queries or questions, please do let me know. And if you start a thread, please send your initial post directly to I might not see it for some time.”
How would I go about sending a link/message directly to you?

[gerard.casey]

David,

Switching them around as you did:

BIC
CAD
therefore BAD

would give you an invalid syllogism as it would fail rule 6. As you noticed, it also fails rule 2! Are you on the right track? Yes. You put the essential point very well – using your language, you can go from large to small (validly) but not from small to large.

Here’s an example of an invalid syllogism that fails only rule 6:

PEQ
QIR
therefore POR

If you run the six rules over this, you’ll see that if passes the first 5 but fails no. 6.

If you start a new thread, email me at gerard.casey@ucd.ie to let me know.

Keep up the good work.

Best wishes,

GC

[dmdavidmann]

Thank you for your help and patience.

And wow, that is a really good example that you just gave. Exactly what I was after

“PEQ
QIR
therefore POR”

It fails to satisfy rule six not because the P is undistributed in the conclusion and distributed in the major premise but because the R term is distributed in the conclusion and undistributed in the minor premise. Have I understood once and for all?

[gerard.casey]

Yes, you’ve got it. Well done and well put. Logicians don’t mind if your evidence is about everything but your conclusion only about some things; but they get very upset if from a limited range of evidence you start drawing conclusions about everything.

GC

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