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Math Help - Silly question

  1. #1
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    Silly question

    A = X
    B = X

    =>

    A = B


    John = human
    Steve = human
    => John = Steve

    obviously wrong, but how exactly?
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  2. #2
    MHF Contributor Unknown008's Avatar
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    In terms of human, yes, John and Steve are both human.

    If you were considering the characteristics of each of John and Steve, then surely you will get different ones, where some might not be equal to the other.
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  3. #3
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    Quote Originally Posted by meathead View Post
    A = X
    B = X

    =>

    A = B


    John = human
    Steve = human
    => John = Steve

    obviously wrong, but how exactly?
    Whether that is obviously wrong or obviously right depends upon what you mean by "=". If you meant the usual meaning for "=", "these are names for the same thing", all three statements would be wrong. But if you mean "=" as an equivalence relation, by saying "Steve= human" you are asserting that being "human" is the only trait you are looking at here- two things are equivalent if and only if they are both human. In that case the three statements are true, the last statement simply saying that John and Steve share the trait of being human.

    But in either case the argument would be valid (not "true", "valid"). If it were true that "John" and "human" were names for the same thing, and that "Steve" and "human" were names for the same thing, then "John" and "Steve" would both be names for that same thing.

    Now, is your question whether that argument is "true" (the conclusion is true argument) or "valid" (the conclusion is true if the premises are true).
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