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Math Help - Arguments: order of premises and conclusion

  1. #1
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    Arguments: order of premises and conclusion

    I have to rearrange these premises and decide what the conclusion is.

    a) All writers who understand human nature are clever
    b) No one is a true poet unless he can stir the human heart
    c) Shakespeare wrote Hamlet
    d) No writer who does not understand human nature can stir the human heart
    e) None but a true poet could have written Hamlet

    I figured the conclusion is 'Shakespeare was a true poet"

    and order.

    a, d, b,e, c

    thanks
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  2. #2
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    Re: Arguments: order of premises and conclusion

    Propositions c and e are alone sufficient to deduce your proposed conclusion. So the full sequence must be designed to reach another conclusion.

    I think the sequence starts c e rather than ends c e.
    Thanks from topsquark
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    Re: Arguments: order of premises and conclusion

    Quote Originally Posted by JeffM View Post
    Propositions c and e are alone sufficient to deduce your proposed conclusion. So the full sequence must be designed to reach another conclusion.

    I think the sequence starts c e rather than ends c e.
    Start with c?

    I thought more along the lines of

    All men are mortal
    Socrates was a man
    therefore, socrates was mortal

    and for conclusion:

    Shakespeare was a clever true poet who could stir the human heart.
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    Re: Arguments: order of premises and conclusion

    The format of major premise, minor premise, conclusion is fine and very intuitive. Unfortunately, this problem is not designed in a way that makes it obvious how to use that format.

    You are correct that you can deduce several conclusions from these premises and that you can summarize them into one compound conclusion. Frankly, I am not sure what answer is expected. But I think the problem teaches you the most if you deduce multiple simple conclusions (rather than one compound conclusion).

    Shakespeare wrote Hamlet.
    None but a true poet could have written Hamlet.
    Thus, Shakespeare was a true poet. This is your first, non-compound conclusion.

    Now look for a premise involving true poets.

    No one is a true poet unless he can stir the human heart.
    From above: Shakespeare was a true poet.
    Thus, Shakespeare could stir the human heart.

    Second non-compound conclusion.

    Now look for a premise about stirring the human heart, and so on.
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    Re: Arguments: order of premises and conclusion

    Shakespeare was a writer who understood human nature making him a clever true poet who could stir a human heart. ??
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    Re: Arguments: order of premises and conclusion

    The first thing I would do is rephrase the negative statements in (b), (d), and (e) "positively":
    (b) "If a person is a true poet then he can stir the human heart", (d) "If a person can stir the human heart then he understands human nature", (e) If a person wrote Hamlet then he is a true poet.

    The statements can now be written in a more direct form:
    (a)If a person can understand human nature then that person is clever.
    (b)If person is a true poet then he can understand the human heart.
    (c)If a person is Shakespeare then that person wrote Hamlet.
    (d)If a person can stir the human heart then he understands human nature.
    (e) If a person wrote Hamlet then he is a true poet.

    I notice is that "Shakespeare" is the hypothesis in statement (c) but appears in no other. That tells me that "Shakespeare" (more precisely "if a writer is Shakespeare" as in "if a writer is Shakespeare then that writer wrote Hamlet") must be the hypothesis in the entire argument. The rest is easy- The conclusion of (c) is "wrote Hamlet" which is the hypothesis of (e). The conclusion of (e) is "is a true poet" which is the hypothesis of (b). The conclusion of (b) is "can understand the human heart" but now we run into a problem.

    (d) was, initially, "No writer who does not understand human nature can stir the human heart" which I put into "positive" form as "If a writer can stir the human heart then he understands human nature". That's the wrong way around. It is NOT the same as "If a writer understands human nature then he can stir the human heart"! We cannot go any further and these statements do NOT imply any one statement.

    IF statement "No writer who cannot stir the human heart understands human nature", the converse of (d) as it is given, THEN we could write it as "if a write understand human nature then he can stir the human heart" and continue to (a) "If a writer understands human nature then he is clever".

    With that proviso, we have (c), (e), (b), (d) (a) leading to the conclusion "If a writer is Shakespeare then he is clever" or "Shakespeare is clever".
    Thanks from JeffM and Jonroberts74
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    Re: Arguments: order of premises and conclusion

    ah, thanks

    d) was a ~q --> ~ P and you changed it to p --> q which is equivalent
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