Applicability of Maths to the Universe

[The Grand Nudger]

And I would say that this is directly contradicted by Godel's results. There are *always* questions that cannot be answered. it isn't simply a matter of not knowing, but that the issue cannot be resolved without making an arbitrary choice in our axioms.

Are there?  To whom or what?  Godel?  Math?  It doesn't seem like we've exhausted the full list of knowers or knowledge.  This would not be enough to reject platonism as a metaphysical stance.  If we assumed that there were some mathematical objects that demonstrably proved mathematical platonism false (and much more from doing it purely by axiom, as we address below) then a platonist can simply concede that mathematical objects are mental objects (and this isn't the only concession that can be made).  It may be the case that there are not always cognitive answers for mental objects.  This would surprise no one.  Satisfied expressions of taste, like "yum" are not cognitive objects, they cannot be true or false, though we've been known to mistake them as such - on account of being satisfied pattern seekers.  

However, in an effort to maintain the position, it will always be posited first and foremost, that we've got something wrong, perhaps as a consequence of our axioms...and what we've got wrong may be godels results.  

Well, we *know* that set theory isn't complete in the sense that all meaningful questions have answers that can be proven. And, in any supplemental system, there will ALWAYS be new questions that cannot be answered.

And the *only* real way to resolve such questions is to *arbitrarily* choose which way we want the axioms to go.

Now, we can make such choices based on things like aesthetics, but there is no way to determine the truth or falsity without making additional assumptions.

Which is a leveler for platonism.  If it's just a disagreement over axioms, and if the things that are taken to be indicative that platonism might be false are merely products of differing axioms or aesthetics.....