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View Full Version : Proof by contrapositive = modus tollens?


Ryker
Dec10-10, 10:57 AM
I was just looking at the Wikipedia page for modus tollens (http://en.wikipedia.org/wiki/Modus_tollens) and found the line "Modus tollens is sometimes confused with proof by contradiction or proof by contrapositive." I thought proof by contrapositive and modus tollens are one and the same though. Is that then not the case or is Wikipedia wrong?

someperson05
Dec10-10, 11:07 AM
I'm not too sure on this, but it seems to be it may just be a logical nuance.

In Modus tollens proper, I believe (If p, then q), is made as an assumption. Or another way, I think the validity of the statement If p then q is already assumed in Modus tollens.
Versus when performing a proof by contrapositive, we don't know that the statement (If p then q) is actually valid, so we proceed to try to derive q after assuming only p. (We can't assume the entire implication to perform a proof, there would be nothing to prove.) Proof by Contrapositive we assume not q and then derive not p.

Did any of that make sense or did I just make up a whole bunch of stuff?

Ryker
Dec10-10, 11:37 AM
Yeah, it does make sense, quite a bit actually. Thanks!