What is proof by Reductio Ad Absurdum?
  • TheMadFool
    13.8k
    1. P > Q..............premise
    2. P.....................premise......./Q
    3. ~Q..................assume for reductio ad absurdum
    4. Q.....................1, 2 Modus Ponens
    5. Q & ~Q............3, 4 Conjunction
    6. Q......................2 to 5 reductio ad absurdum

    I know the rules but I don't understand why it works.

    What I think is happening:

    1. ~Q > (Q & ~Q)...from 3-5 in the above argument
    But we know: 2. ~(Q & ~Q)...from law of noncontradiction
    3. ~~Q......1, 2 Modus Tollens
    4. Q............3 Double Negation

    Am I right?
    TheMadFool Options
  • Srap Tasmaner
    4.6k
    ↪TheMadFool

    That's basically it.

    One conceptual step that might help:
    If you have premises ¶ and want to derive the conclusion Q, then you want to show that the conditional ¶→Q is true. Assuming that conditional is false should lead to a contradiction. As it happens, ~(¶→Q) is ¶ & ~Q. So if you show that the conclusion Q being false leads to a contraction, then you've shown that the premises do imply the conclusion.
    Srap Tasmaner Options
  • TheMadFool
    13.8k
    ↪Srap Tasmaner
    (Y)
    TheMadFool Options
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