What is proof by Reductio Ad Absurdum?
TheMadFool 2017-07-30
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?
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?
Comments (2)
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.