Morals and aesthetics are not legitimately subject to reasoning, based as they are on unreasoned (although not unreasonable) emotion.

That was the logical positivist claim, which has been completely rejected by every school of philosophy in the world for the past fifty years. Indeed, now it held as an object of ridule - a position I find a little unkind because it did provide some useful starting points for Karl Popper's falsification theory.

Universal pragmatics provides a rational basis for moral and aesthetic reasoning.

Thanks for relinquishing "fundamentalist", however reluctantly

It wasn't reluctant at all. Checking the thread it is worth noting that I only applied it in the most tentative sense anyway.