The argument at the moment seems to be "define a problem that a computer can't do that a human brain can"... "I can't because expressing that problem is beyond the machinery I have developed for cognition, and it may always be".

What is certain is that there are uncomputable problems, but are any of the problems that humans solve in order to speak, act, socialise uncomputable? Some people think that because they are solved within the physical universe then they must be computable but that implies that the physical universe can be simulated (in principle) by a universal turing machine, since we can express problems (using the machinary of the universe) that a universal turing machine can't do then there is a gap that permits the possibility that there may be some process which is not simulatable by a universal turing machine.

In my belief free will/autonomy/initaitive/creativity are expressions of that process, but belief is not an argument.