Traditional Logic II Validity for Fourth Figure?

[sandydjdm]

Hello,

I'm preparing an intro to Traditional Logic II for my Logic I students (homeschool group), and thought it would be fun to apply the rules of validity to the 64 potential categorical syllogisms. Everything has worked out perfectly, except for the fourth figure (AE and AI). According to Shyreswood's mnemomic:

Quarta insuper addit; BRAMANTIP, CAMENES(AE), DIMARIS, FESAPO, FRESISON,

AE shoud be a valid syllogism.

AE:
All Md is Pu
No Sd is Md
No Sd is Pd

However, it seems to violate Rule III:
If a term is distributed in the conclusion, then it must be distributed in the premises.(Fallacy of Illicit Major)

On the other hand, AI seems to be valid to me:

AI:
All Md is Pu
Some Su is Mu
Some Su is Pu

I cannot find a fallacy. I'm wondering if it's possible that the mnemonic spelling should be CAMINES? Or is there something I'm just plain missing here?

Thanks for your help! Sandy Hollenbeck (CA)

P.S. My plan is to introduce figures/moods and the mnemonic so that they can memorize it over the summer.

[Martin Cothran]

sandydjdm,

In your first question, you said:

AE shoud be a valid syllogism.

AE:
All Md is Pu
No Sd is Md
No Sd is Pd

You are saying here that AE in the fourth figure (CAMENES) should be valid, but that this example of an AE is clearly invalid. You are correct in thinking that this example is invalid, and correct in thinking it is an AE syllogism, but incorrect in thinking it is in the fourth figure. Note that your example is a sub-prae, which means that what you have here is a first, not fourth, figure syllogism. Your example is not a CAMENES, since CAMENES is fourth figure and fourth figure is prae-sub, not sub-prae.

There is no valid AE form in the first figure.

In your second question, you ask:

On the other hand, AI seems to be valid to me:

AI:
All Md is Pu
Some Su is Mu
Some Su is Pu

I cannot find a fallacy. I'm wondering if it's possible that the mnemonic spelling should be CAMINES? Or is there something I'm just plain missing here?

Again, you are mistaking a first for a fourth figure. Your example here is also a first figure sub-prae. It is, in fact, a DARII, and is therefore valid.

Hope this helps!

[sandydjdm]

Thank you so much, Mr. Cothran!

I made charts for all 64 syllogisms so that the kids could apply the rules of validity to eliminate the invalid combinations... They all started to look the same - I didn't realize that the first and fourth charts really were the same!:p

I'm attaching the handout I used with our class. After introducing figure and mood, we reviewed the rules of validity and the distribution of terms. Then we split up into pairs and analyzed the possible combinations. The teams marked their findings on the white board and then explained their reasoning to the class. It turned out to be a nice way to reinforce what we learned this year in Logic I and prepare for Logic II next year. (I had almost twenty 7th and 8th graders this year).

Thanks again for straightening out my reasoning.

Blessings, Sandy Hollenbeck

P.S. If anyone finds errors in the attachment, I would appreciate you letting me know. Thanks!