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Star Test for Syllogisms

  1. Sep 30, 2014 #1
    I'm reading a book by Harry J. Gensler in which he introduces his 'star test' for checking whether or not a syllogism is valid. According to the star method the premises;

    all A is B
    all A is C

    has no valid conclusion. But wouldn't;

    some B is C

    be a valid conclusion?
    Sorry if this is kind of a silly question, I'm just starting to learn this stuff.
  2. jcsd
  3. Sep 30, 2014 #2


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    Are you sure that you've copied it correctly? The closest that I could find was this fallacy - Undistributed Middle Term.

    If the example is correct, perhaps the answer is elsewhere on that site.
  4. Sep 30, 2014 #3
    I'm pretty sure. Gensler says the star test works by putting a star above any distributed letters in the premises and any non-distributed letters in the conclusion. The test says it is valid only if:
    1) each capital letter is starred exactly once and
    2) there is exactly one letter on the right hand side that is starred.
    In the premises of the examples I listed 'A' would be starred twice, once in each premise, so that should make it invalid but I don't see why 'some B is C' isn't a valid conclusion.

    The example I gave wasn't from the book, it was something I though up which fails the test but appears to have a valid answer.
    Last edited: Sep 30, 2014
  5. Sep 30, 2014 #4
    Never mind, I think I figured it out. Is it because there isn't necessarily anything in A?
  6. Sep 30, 2014 #5


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    My first thought when I read your example was the following:

    A = Ford
    B = vehicle
    C = 4 wheels

    Substituting, using your example:
    all Fords are vehicles
    all Fords have 4 wheels

    It looks like some vehicles have 4 wheels would be true.
  7. Sep 30, 2014 #6
    But if we take:

    A = fairies
    B = things that have wings
    C = things that have magic wands

    then some B is C only if fairies exist, if they don't then there isn't necessarily something that's common to both B and C so I can't say with certainty that some B is C.
  8. Sep 30, 2014 #7
    Wow, after I just posted I literally read two more pages and Gensler started to go into this, turns out it is because A may be empty.
  9. Sep 30, 2014 #8


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    Looks like we both learned something. :)
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