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Math Help - Logical Argument #2 Valid or not.

  1. #1
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    Logical Argument #2 Valid or not.

    Explicitly identify the component statements that are part of the argument and show the symbolic form of the argument.

    Decide whether the argument is valid or invalid. Here you may use truth tables, standard forms, Euler diagrams, and/or logical manipulation. If the argument is invalid, point to its logical fallacy.

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    Taken from Lewis Carroll's Symbolic Logic (1896):

    "Babies are illogical. Nobody is despised who can manage a crocodile. Illogical persons are despised. Hence, babies cannot manage crocodiles."

    P - Babies are illogical
    Q - Nobody is despised who can manage a crocodile (just "manage a crocodile" ??)
    R - Illogical persons are despised
    S - babies cannot manage crocodiles? (very lost here)

    Symbolically - (P ^ Q)--> (R --> S) I have a feeling I am doing something very wrong.
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  2. #2
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    At the risk of having emakarov breathing down my neck, I'll risk an opinion or two. I think your variable assignments aren't granular enough. I would do something more like this:

    D = despised
    B = babies
    M = manage a crocodile
    I = illogical.

    Translations:

    All B are I.
    No M are D.
    All I are D.
    Hence, no B are M.

    This is a syllogistic argument, or at least can be thought of that way, so I would probably use those concepts to determine the validity.
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  3. #3
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    Quote Originally Posted by stueycal View Post
    Taken from Lewis Carroll's Symbolic Logic (1896):"Babies are illogical. Nobody is despised who can manage a crocodile. Illogical persons are despised. Hence, babies cannot manage crocodiles."
    In my view, this is exactly like the first argument you posted.
    It reads like this.
    All babies are illogical.
    No one who is despised can manage a crocodile.
    All illogical persons are despised

    Therefore: No baby can manage a crocodile.

    Draw the Venn diagrams for this.
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  4. #4
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    I am having the most trouble drawing venn diagrams because we hardly discussed it in class, is there perhaps an online resource I could view? Or maybe someone could explain that it should look like.
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  5. #5
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    Quote Originally Posted by stueycal View Post
    I am having the most trouble drawing venn diagrams because we hardly discussed it in class, is there perhaps an online resource I could view? Or maybe someone could explain that it should look like.
    Unfortunately this forum is having image problems.
    The statement If P then Q or All P is Q can be drawn as two circles.
    The circle P is completely interior to the circle Q.

    Whereas, If P then not Q or No P is Q are two disjoint circles.
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  6. #6
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    I agree that this can be proved using Venn diagrams. I also agree with Adrian that this statement cannot be written symbolically in propositional logic, like the previous one about pigs. There, one did not need to go break apart the proposition "pigs understand logic."

    The translation of "Nobody is despised who can manage a crocodile" is ∀x (M(x) -> ~D(x)). I also agree that these statements can be written as syllogisms, but syllogisms, unlike first-order logic, are mostly studied for historic reasons, and I don't know much about them.
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  7. #7
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    So I am still lost on if this is a valid statement or not :/

    I drew the two diagrams, still sort of confused.
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  8. #8
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    Babies is a subset of Illogical, which in turn is a subset of Despised because of the first and third assumptions, respectively. Manages a crocodile is disjoint with Despised because of the second assumption, i.e., ∀x (M(x) -> ~D(x)). It follows that Babies and Manages a crocodile are disjoint, so the argument is valid.
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  9. #9
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    Thank you for breaking it down for me, I feel that my brain evolved slower then my peers when it comes to math.
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