[FOM] Falsify Platonism?
Timothy Y. Chow
tchow at alum.mit.edu
Fri Apr 23 16:10:33 EDT 2010
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?
> 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.
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