Proof by contrapositive = modus tollens?

[Ryker]

I was just looking at the 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]

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]

Yeah, it does make sense, quite a bit actually. Thanks!