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Thread: syllogistic logic

  1. #1 syllogistic logic 
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    Jan 2008
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    Hi there,

    I'm learning syllogistic logic (am reading "Introduction to logic" by Harry Gensler). I've come across his excercises, and the answers to only odd numbered ones are given. I was hoping some of you could verify my answers?

    I'll give a quick review of what I've read so far:

    Syllogistic language uses capital letters for general categories (like "logician") and small letters for specific individuals (like "Gensler"). For example:

    B = a cute baby
    C = charming
    D = drives a Buick

    b = the world's cutest baby
    c = this child
    d = David


    Five words exist in the grammar:

    all
    no
    some
    is
    not


    The grammatical sentences are called wffs (well-formed-formulas). Wffs are sequences having any of these eight forms:

    all A is B
    some A is B
    x is A
    x is y
    no A is B
    some A is not B
    x is not A
    x is not y


    Exercises:

    2.1a
    Which of the following are wffs?

    1. no e is f

    Not a wff. We can't put "no" before a specific individual.

    2. g is H
    This is a wff. We can verify that an individual IS one of a general category.

    3. J is K
    This is a wff.

    4. all M is not Q
    This is not a wff. But why?

    How about:

    All guns are not good.
    All G is not G

    Does that clarify as a wff? Apparently not according to the above, but why?

    Does it go to say that we can put:

    All guns are not good

    into the sentence

    All guns are evil (replace "not good" with "evil")

    to give us

    All G is E

    which is definitely a wff?


    5. some L is m
    Not a wff. We can't classify some general things as being specific indivdiuals.

    6. p is not Q
    Is a wff. We can classify a specific individual as being one of a category.

    7. R is not S
    Not a wff. Again why? See below number 4.

    8. not all T is U
    Not a wff. Why not? This is certainly valid:

    all T is U

    Why?


    9. some X is not Y
    This is a wff. We can certainly say that some of a category are not of another category.

    I guess I'm a little confused on some aspects of the language.

    I can certainly understand that we can't put "all","no" or "some" before a specific individual because it's well I guess unique. To that tune, we can't say:

    A is B

    because we are saying everything in a category is everything of another category? Is that correct?

    Looking forward to a response!


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