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Math Help - Categorical Logic

  1. #1
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    Categorical Logic

    Is this right,

    Translate into standard form:
    The only boys who deserve cake are good ones.
    answer: Some B are G
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  2. #2
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    Hello, Amber!

    You'll have to explain what concepts you've been taught already.
    To me this is a strange problem . . .


    Translate into standard form:
    The only boys who deserve cake are good ones.

    Answer: Some B are G . . . . . I don't agree
    First of all, I'm not sure what "standard form" means in your course.


    The statement itself is an unusual one to translate.

    It says: Only good boys deserve cake.

    We can translate this a number of ways:
    . . "If a boy deserves cake, then he must be a good boy."
    . . "A boy deserves cake only if he is good."
    . . "Bad boys do not deserve cake."

    It does not say: "If a boy is good, then he deserves cake."

    It does not even say that there are any good boys.

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  3. #3
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    Reply

    Standard form right now is just simply stating the names of the classes for example.....
    Every good boy deserves cake
    answer All G are C

    Only good boys deserves cake
    answeer All G are C
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  4. #4
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    Quote Originally Posted by ambergarrett955 View Post
    Standard form right now is just simply stating the names of the classes for example.....
    Every good boy deserves cake
    answer All G are C YES

    Only good boys deserves cake
    answeer All G are C NO
    This problem has a long history. Irving Copi set of quite a discussion of a similar problem in his symbolic logic text. We were to quantify the following: Only the brave deserve the fair. The key to it turns on a simple fact. P only if Q is equivalent to If P then Q. Anyone deserving the fair must be among the brave:  \left( {\forall x} \right)\left[ {F(x) \to B(x)} \right].

    Now you apply that bit of history to your problem.
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  5. #5
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    Quantifier

    Could someone please explain what a quantifier of a preposition is....in categorical logic...Thank You
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  6. #6
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    Quote Originally Posted by ambergarrett955 View Post
    Could someone please explain what a quantifier of a preposition is....in categorical logic...
    First, please start a new thread when posting a new question.

    Do you have a textbook? Do you have an instructor?
    Because, the question you have posed takes up an entire chapter is most logic texts. It is a huge question.

    If you have a particular problem to work, post it exactly as written. Maybe we can help.
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