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Logic II Workbook, Ch. 6 Question

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    Logic II Workbook, Ch. 6 Question

    Hi. The exercises for day 2 in ch. 6 require the student to state what order each of the listed enthymemes is. The Teacher Key states that letter h is a SECOND order enthymeme; hence, the minor premise is missing. This means that the premise of the enthymeme is the major premise.

    However, minor premise is the premise that has as its subject the subject of the conclusion (All S is M; Therefore all S is P). In this case, the subject of the premise, "proof," is also the subject of the conclusion. This would make the premise the minor premise, and the enthymeme a FIRST order enthymeme, missing its major premise.

    Conversely, the predicate of the conclusion is "poverty causes crime," This should also be the predicate of the major premise. If the enthymeme is of the second order, including the major premise, the predicate of the premise should be the same as the predicate of the conclusion. But there is nothing about poverty causing crime in the premise.

    So, would this not be a FIRST order premise? Thanks for helping us out. We have been trying to crack this nut for a while.


    The nut you are trying to crack appears to be a mistake in the answer key. I'm surprised no one has caught this until now. It is indeed a first order enthymeme, not a second order. Sorry for the inconvenience, but congratulations for catching it!

    Mr. Cothran


      Actually, now that I've thought about it a little more, it can be either a first or second order, depending on which kind of syllogism you resolve it into.

      The key is correct in stating that it could be resolved into a CAMENES:

      cAm All proof must be a convincing thing
      En No convincing thing is a proof that poverty causes crime
      Es No proof that poverty causes crime is a proof

      This is done by interpreting the conclusion so that the term "proof" is in the predicate and then adding a minor premise.

      But the key is incomplete because it could also be resolved into a CESARE:

      cEs No proof that poverty causes crime is convincing
      Ar All proof must be convincing
      E No proof is a proof that poverty causes crime

      Here the conclusion a little differently, but it a way that logically means the same thing as the conclusion in the CAMENES. You can do either one because it is an E statement and E statements can be simply converted, so that the subjects and predicates are interchangeable. The conclusion given ("There is no proof that poverty causes crime" could be stated either way). In this case, it is the major premise that is missing.

      But it could also be a CELARENT!

      cE No convincing thing is a proof that poverty causes crime
      lAr All proof must be convincing
      Ent Therefore, no proof is a proof that poverty causes crime

      Why? Because, remember from ch. 3 that CAMENES and CESAREs both reduce to a CELARENT! It all has to do with those tricky E statements which can be simply converted by switching the subject and predicate and coming up with a logically equivalent statement. If you interpret the conclusion one way, you get a first order. If you interpret it the other way you get a second order.

      That's what makes logic so fun--and so frustrating.


        Thank you very much for that discussion. It was very helpful.