I guess the sarcasm of my post flew over your head<quoted text>
Mockery doesn't solve the purpose; on the contrary, it may aggravate the atmosphere since the other person involved in the debate may think that you're not serious in debating the issue in depth and seeing it from various angles including his own and so he may be put off and so mockery could create misunderstanding.
Mockery should be used sparingly.
If the other person cannot see the light of reason despite giving him the entire logic supported by evidence, well, then, you can't do anything and so better tell him to be free to follow what he wishes to without imposing his ideas or thoughts on others since the evidence doesn't support his views and wrap up the debate at that point. But, always keep communication lines open with him and if he at some point has a rethink then analyze what he has to say and further the debate from there by closely analyzing his point for what it's worth.