[FOM] Falsify Platonism?

[Timothy Y. Chow]

Bill Taylor <W.Taylor at math.canterbury.ac.nz> wrote:
> Lucas Kruijswijk <L.B.Kruijswijk at inter.nl.net> wrote:
> 
> -> Hilbert's program contains hard tests, which are mostly
> -> proven to be impossible. Is there any hard test that can
> -> falsify Platonism?
> 
> Yes.
> 
> If a contradiction is derived from PA, that will falsify Platonism.

I used to think this too, but I no longer believe that it is quite 
correct.  A platonist could react to such a contradiction by concluding 
that not all first-order sentences of arithmetic can be meaningfully 
asserted of the natural numbers.  The platonist could still continue to 
believe that the natural numbers exist objectively, and that every 
sentence from a more restricted class of sentences is either true or false 
when asserted of the integers.

This attitude is roughly analogous to the attitude that the liar paradox 
does not demonstrate the incoherence of the notion of truth, but shows 
only that certain classes of sentences are not meaningful.

Tim