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    Please help - number of valid syllogisms

    Hello,

    I admit that this is a repost but I truly need help on this question. I have waited for months but no one has replied. Perhaps my questions is confusing. If so, please advise!

    I am a beginning logic teacher. I noticed on page 10 of Cothran's *Traditional Logic book II* that he says there are 19 valid syllogisms. But, if the conclusion of the syllogism is included as part of the mood then there are 5 more syllogisms that are valid, namely, AEO-2, AII-1, EAO-1, EAO-2, and AEO-4 for a total of 24. These are legitimately valid syllogisms but don't seem to be accounted for.

    What am I missing?

    Thanks for helping.

    #2
    I'm not sure about the extra 5 syllogisms you mention. Are they syllogisms where there is an alternate possibility for the conclusion? I would say that since mood is defined with reference to the disposition of the premises (without mention of the conclusion), any alternate conclusions would not be considered a new syllogism.
    Does this help?

    Comment


      #3
      Are there more than 19 valid syllogism forms?

      Sorry for missing your original post. Your question seems to be whether there are not more than 19 valid syllogism forms.

      The answer is yes and no. Yes, in the sense that the additional syllogism forms you identify are valid (with some qualification here--see below). No, in the sense that they are not really different from certain forms already included in the original listing of 19.

      Let me explain why the ones you listed, although valid, are not really different from the ones already listed. AEO-2 is really just CAMESTRES with a particular conclusion. EAO-1 is really CELARENT with a particular conclusion. EAO-2 is CESARE and AEO-4 is CAMENES for the same reason. You also listed AII-1, but I think you must have meant AAI-1, which is a BARBARA with a particular conclusion.

      All of the additional ones you listed are syllogisms that, in the original 19, have universal conclusions that you have made particular without changing the quality. You might think that these are really different than the original ones, since their conclusions are, in fact, different statements. That is because the assumption is that in any case where a syllogism is listed with a universal conclusion, the same syllogism with a particular conclusion (of the same quality) will also be valid.

      But these syllogisms are not really a different form of reasoning, since they say the same thing, just in a weaker form. If I say:

      All men are mortal
      All Romans are men
      Therefore, some Romans are mortal

      that is not really different from saying:

      All men are mortal
      All Romans are men
      Therefore, all Romans are mortal.

      The first is just a weaker form of the latter.

      I hope this helps.

      Martin



      Originally posted by weatherhogge
      Hello,

      I admit that this is a repost but I truly need help on this question. I have waited for months but no one has replied. Perhaps my questions is confusing. If so, please advise!

      I am a beginning logic teacher. I noticed on page 10 of Cothran's *Traditional Logic book II* that he says there are 19 valid syllogisms. But, if the conclusion of the syllogism is included as part of the mood then there are 5 more syllogisms that are valid, namely, AEO-2, AII-1, EAO-1, EAO-2, and AEO-4 for a total of 24. These are legitimately valid syllogisms but don't seem to be accounted for.

      What am I missing?

      Thanks for helping.

      Comment


        #4
        Outstanding. I obviously didn't study my own examples enough as I hadn't noticed the pattern in the 5 "extra" valid syllogisms, that is, they have particular conclusions. I also appreciate your characterization of these 5 syllogisms as weaker. And yes, I had meant AAI-1 as one of the five.

        Thank you. You have been most kind to reply.

        Comment

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