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Math Help - logic

  1. #1
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    logic

    Suppose the time is before symbolic logic was discovered and you were asked to prove:

    That Antony is a funny guy ,given that:

    If anyone is funny ,then he is happy. And ,there is someone who is funny but not happy.
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  2. #2
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    Re: logic

    Quote Originally Posted by alexandros View Post
    If anyone is funny ,then he is happy. And ,there is someone who is funny but not happy.
    Those two assertions together are absurd. So anything follows from them.
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  3. #3
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    Re: logic

    Quote Originally Posted by MoeBlee View Post
    Those two assertions together are absurd. So anything follows from them.
    That is what symbolic logic concerns.BUT the time is before symbolic logic was discovered.
    How would we tackle the problem then??
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  4. #4
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    Re: logic

    Quote Originally Posted by alexandros View Post
    the time is before symbolic logic was discovered.
    How would we tackle the problem then??
    If I'm not mistaken, the idea that an absurdity implies anything precedes the invention of symbolic logic. Unless you define 'symbolic logic' otherwise, I take it to be a nineteenth century invention.
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  5. #5
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    Re: logic

    Hello, alexandros!

    Where did this question come from?
    It's badly written and it really doesn't make sense.
    (Well, it does . . . but the conclusion is rather silly.)


    Suppose the time is before symbolic logic was discovered
    and you were asked to prove:

    . . [1] If anyone is funny, then he is happy.
    . . [2] There is someone who is funny but not happy.
    . . [3] Therefore, Antony is a funny guy.

    I have to resort to symbolic logic to make my point.

    We have: . \text{(premise)}\:\to\:\text{(conclusion)}

    That is:. = . . . . . . p\;\to\;q


    Statement [1] says: All funny people are happy.

    Statement [2] says: There is one person who is funny but is not happy.
    . . That is, it is not true that all funny people are happy.

    The two statements contradict each other.
    . . Hence, the premise is false.

    So we have: . F\;\to\;q
    And a false premise can imply anything.

    Therefore: Antony is a funny guy.

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  6. #6
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    Re: logic

    You don't have to use any special symbols.

    The statements "any person who is funny is happy" and "there is a funny but unhappy person" are contradictory, since they imply that there is a person who is happy and unhappy. And a contradiction implies any statement. So the statements "any person who is funny is happy" and "there is a funny but unhappy person" imply the statement "Antony is a funny person".
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  7. #7
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    Re: logic

    Quote Originally Posted by MoeBlee View Post
    If I'm not mistaken, the idea that an absurdity implies anything precedes the invention of symbolic logic. Unless you define 'symbolic logic' otherwise, I take it to be a nineteenth century invention.
    .

    How can we explain ,that from absurdity we can imply anything
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