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Trying to better understand the reductio ad absurdum

  1. Nov 3, 2012 #1
    I've just started studying college math.

    I read the proof by contradiction is based on the law of excluded middle. So i tried
    to make a general logic structure of this kind of demonstration to see how it could use
    this law. If i'm right, of course.

    Let X and Y be propositions.

    1. X -> Y
    2. ~Y
    3. X v ~X ¹
    By 1 and 3 we have:
    4. Y v ~X
    By 2 and 4 we have:

    ¹ - Law of excluded middle

    Is this how reductio ad absurdum is made?

    I mean, generally the following statement is used:
    "Suppose X is true. Then Y is true. But Y is false. So X is false."

    But isn't it the same thing i just did above?

    I know that, probably, i'm just talking non-sense. But even so, i think this non-sense
    can help you guys to help me out with my doubts.

    Anyway, thank you for the attention.

    My first language is portuguese and i'm not a good english writer. So if i made any english mistakes, i apologize.
  2. jcsd
  3. Nov 3, 2012 #2


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    Science Advisor

    Hi, Charlie Sheep: ( I liked your work on two and a half mep ;) )

    This is my perspective: truth-tables for connectives like & , \/ , are defined so that

    they are truth-preserving. An argument is valid if, by definition, whenever the

    premises are true, the conclusion cannot be false. Now, if you start with a true

    premise and arrive --using truth-preserving rules --to a false statement , i.e.,

    a contradiction-- then your initial premise must not have been true to start with.
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