Roberts, Chapter 12: How to reject objections
Roberts, Ch. 12 -- Jerz: American Lit II (EL 267)
The situation to imagine is that someone is raising objections to your solution to the problem. It is then your task to show that the objections (1) are not accurate or valid, (2) are not strong or convincing, or (3) are based on unusual rather than usual conditions (on an exception and not the rule).
I found this passage to be particularly helpful, because I have often wondered how one disproves an antithesis satisfactorily, or more to the point, how much and what kind of evidence one must provide in order to prove such a thing.