How about a little absurdity?

Assume you want to prove a Theorem X. If you’re a fan of reductio ad absurdum (RAA), you start by saying “Assume that Theorem X is false. Hence…” and after some reasoning, you reach a contradiction.  You write as a closing sentence, “This contradiction shows that Theorem X must be true.”

I want to argue about the following questions: Do we need only one use of the rule of contradiction? Can we start a proof as above and not use an argument by contradiction but at the end? Continue reading