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Thread: syllogistic logic

  1. #1 syllogistic logic 
    Forum Sophomore
    Join Date
    Jan 2008
    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:


    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


    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


    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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