To everyone else, see
meta.math.stackexchange.com/q/2831. After I have wasted many days attempting to explain some things in logic to him, I'm forced to conclude that he is at best willfully misguided and at worst a troll. It seems he has a rudimentary grasp of basic propositional logic and some non-classical logics, but he is
totally incompetent in proof theory, model theory, computability theory and programming, and if he assumes you are wrong he will never admit otherwise.