>Enderton told me, when I was his TA for set theory at UCLA, that most mathematicians were Platonists. I was absolutely stunned.

He would probably say that I am a Platonist.  I prefer to consider myself a fictionalist.  The idea of a platonic reality seems absurd.

An actual Platonist would say that the continuum hypothesis is either true or false (as a fact of the matter in Platonic reality), and that the Cohen/Goedel result doesn't settle anything.  By contrast, I doubt that there is an fact of the matter and it all depends on the constraints of our assumed axioms.

However, except for a few such special cases, it is hard to distinguish the way I do mathematics from the way a Platonist does it.  I'm inclined to say that the real distinguishing feature of Platonism is the use of what I am calling geometric methodology, and that a belief in a Platonic reality isn't actually important.

Regards,
Neil