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Valid Syllogism?

  1. Feb 14, 2009 #1
    Is this a valid syllogism?

    O: Some A's are not B's.
    O: Some C's are not B's.
    I: Therefore: Some A's are C's.

    For some reason this doesn't look correct. When I tried to put an example of this syllogism, I got a conclusion that was false, from two premises which are true. Here is that example:

    Some reptiles are not lizzards.
    Some warm-blooded-animals are not lizzards.
    Therefore: Some reptiles are warm-blooded-animals?

    Why doesn't this work? Because it seems to me that if the O-claim has a distributive predicate then the above example should work. Or perhaps one of my premises are wrong. Does anyone see what the problem is?
  2. jcsd
  3. Feb 14, 2009 #2


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    I don't understand your problem. Your example shows that the syllogism is invalid. What more can be said?
  4. Feb 14, 2009 #3
    Perhaps I was subtle in my actual question (bad title name). I wanted to see if the O-claim really is distributed, as my textbook says it is. I don't believe it is. So, I set up a syllogism to test it. The syllogism is made to have the O-claim's predicate distribute the middle term. So, if the O-claim's predicate is distributed, then the middle term is distributed and my syllogism should be valid. But it clearly isn't valid. So, I am forced to conclude that the O-claim's predicate is not distributive.

    But that goes against what my textbook says. Either my textbook is wrong or something else is wrong with my syllogism (other than an undistributed middle). Which is it?
  5. Feb 15, 2009 #4


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    I'll have to leave your question to someone else. I have no formal background in this subject (as a mathematician, we didn't get much into this area). Specifically I have no idea what the following sentence means.
  6. Feb 15, 2009 #5
    I see. Any other takers?
  7. Feb 22, 2009 #6
    One of the basic rules of syllogistic logic is that from two particular premises nothing can be concluded.
  8. Feb 22, 2009 #7


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    Your logical statements can be replaced by set statements: A is not a subset of B, C is not a subset of B. The conclusion you give would be "A and B have non-empty intersection" which is certainly not true. We can say nothing about the relationship between A and B.
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