Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Really simple question

  1. Mar 25, 2005 #1
    I didn't want to post this in the logic subforum, because it's really basic...

    I know that when proving mathematical statements, one can't assume what he/she is trying to prove. But can one assume its converse?

    - Kamataat
    Last edited: Mar 25, 2005
  2. jcsd
  3. Mar 25, 2005 #2


    User Avatar
    Science Advisor
    Homework Helper

    You mean like reductio ad absurdum...?It's by far the most elegant method of mathematics...

  4. Mar 25, 2005 #3

    matt grime

    User Avatar
    Science Advisor
    Homework Helper

    The constructivists may disagree that it is the most elegant, and indeed proofs by contradiction are to be frowned upon if they are unnecessary - often doing a proof by contradiction merely shows what we first started with to be true directly, and we've jist added pointless length to it.

    You may assume not(X) is true and show that if so then we derive a logical contradiction, hence not(X) is false, X is true. Is that what you're getting at?
  5. Mar 25, 2005 #4


    User Avatar
    Gold Member

    Do you mean converse or negation? I've only seen converse applied to conditionals: (Q -> P) is the converse of (P -> Q). Note that the reason you "can't" assume the proposition you're trying to prove is only that such an argument is circular; Circular arguments are still valid- they just don't tell you anything new. With one exception- when P and Q are equivalent- you can assume the converse of a proposition without being circular, since [(Q -> P) -> (P -> Q)] is a contingent proposition, i.e., [(Q -> P) therefore (P -> Q)] is an invalid argument; Its counterexample is [Q is false, P is true]).
    Last edited: Mar 25, 2005
  6. Mar 26, 2005 #5
    Yeah, that's what I meant. Thanks!

    - Kamataat
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Really simple question
  1. Really basic question (Replies: 8)

  2. Simple Question (Replies: 4)

  3. A simple question (Replies: 3)