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Math Help - Suppes' Logic of Identity Exercise Question

  1. #1
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    Question Suppes' Logic of Identity Exercise Question

    Hi,

    And again, I'm stuck with an exercise in Suppes' Introduction to Logic. The exercise is:

    Some members of the swimming team have not lost a race. Jones is on the swimming team; furthermore he's the fastest man on the team. Therefore, Jones has not lost a race. (Mx, Lx, j, f)

    So I know that (Ex)(Mx & ~Lx), Mj. Jones is the fastest, so I guess I can say that j = f. But, how can I conclude that he hasn't lost a race?

    Thanks in advance,

    Mirko
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  2. #2
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    Frankly, taken at face value this does not seem to be a valid argument.
    I think that one needs to add some premises the to given. Such as, “the fastest member on the team would not have lost to others on the team”.

    I wish I could locate my copy of Suppes’s. There may be some hints in the section where this exercise appears.
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  3. #3
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    Quote Originally Posted by Plato View Post
    Frankly, taken at face value this does not seem to be a valid argument.
    I think that one needs to add some premises the to given. Such as, “the fastest member on the team would not have lost to others on the team”.
    Yes exactly, that's what I thought too.. it's just not enough information. Well, it might be that that's the whole point of the exercise, but that wouldn't be very nice of Suppes, to make the first exercise unsolvable.

    Quote Originally Posted by Plato View Post
    I wish I could locate my copy of Suppes’s. There may be some hints in the section where this exercise appears.
    Google has the whole book online.
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  4. #4
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    Quote Originally Posted by mirko View Post
    Hi,

    And again, I'm stuck with an exercise in Suppes' Introduction to Logic. The exercise is:
    Some members of the swimming team have not lost a race. Jones is on the swimming team; furthermore he's the fastest man on the team. Therefore, Jones has not lost a race. (Mx, Lx, j, f)
    So I know that (Ex)(Mx & ~Lx), Mj. Jones is the fastest, so I guess I can say that j = f. But, how can I conclude that he hasn't lost a race?

    Thanks in advance,

    Mirko

    I have right in front of me a the book of PATRICK SUPPES ,INTRODUCTION TO LOGIC,Dover publication.

    Please tell me where i will find the said problem
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  5. #5
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    Quote Originally Posted by triclino View Post
    Please tell me where i will find the said problem
    It's on page 107, the second exercise. Thanks for taking a look at it!
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  6. #6
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    Fastest Swimmer

    My apologies for coming in on this late (I've been noodling off and on with the Suppes volume myself, and just stumbled on this thread).

    Jones might be the fastest swimmer on his team, but that doesn't make him the fastest swimmer. Suppose each meet pits the best against the best, the second best against the second, etc. Then one can readily come up with an interpretation that shows that the conclusion can not be proven. Let Jones' team be "A", and rank the members of "A" according to their speed: {10 (Jones), 7, 5, 4, 2}. Clearly Jones is the fastest on his team. But if team "B" is {11, 6, 3, 1, 1} then Jones will lose his heat, while everyone else on his team will win theirs.

    In terms of fairness, I would note that this is actually the second exercise on pg. 107, not the first. But it also shows some signs of poor editing; the actual task before us is not explicitly set out either at the start of the exercises or in #2 itself (compare, for instance, the instructions on #1 and #3.)

    Anyway, that's my "read" on it.
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