How to Test Validity using Reductio ad Absurdum

[StevieTNZ]

Hi there,

I'm quite interested in propositional logic. Can anyone point me to a document out there (preferably from a university website, e.g. a lecturer/Professor etc. of Philosophy's personal webpage) that explains, in a clear manner, how to test for validity using the Reductio ad Absurdum method.

Many thanks,
Stevie

 

[ImaLooser]

Hi there,

I'm quite interested in propositional logic. Can anyone point me to a document out there (preferably from a university website, e.g. a lecturer/Professor etc. of Philosophy's personal webpage) that explains, in a clear manner, how to test for validity using the Reductio ad Absurdum method.

Many thanks,
Stevie

Start with a self-consistent system. This means that (A and not A) is false for all A.

Let's say that the truth value of X is unknown. Assume X is true. If you can deduce for some A that (A and not A) is true, then you have done the impossible. Since it is not possible to do the impossible, something is wrong. You've reduced the system to an absurdity. The only possible thing that could be wrong is your assumption that X is true. So X must be false.

 

[Akshay_Anti]

a very elementary example could be proving that √2 is irrational