On 7/31/2015 11:28 PM, Stathis Papaioannou wrote:
On Saturday, August 1, 2015, meekerdb <[email protected]
<mailto:[email protected]>> wrote:
-------- Forwarded Message --------
Michelangelo's Stone: an Argument against Platonism in Mathematics
*ROVELLI, Carlo**Â (2015)Â **/Michelangelo's Stone: an Argument against
Platonism in
Mathematics./**Â [Preprint]*
If there is a /€œplatonic world/€ M of mathematical facts, what does M
contain
precisely? I observe that if M is too large, it is uninteresting,
because the
value is in the selection, not in the totality; if it is smaller and
interesting, it is not independent from us. Both alternatives challenge
mathematical platonism. I suggest that the universality of our
mathematics may
be a prejudice hiding its contingency, and illustrate contingent
aspects of
classical geometry, arithmetics and linear algebra.
*http://philsci-archive.pitt.edu/11595/1/Platonism.pdf*
It's true that the Platonic universe contains all mathematical structures, including
trivial or uninteresting ones,
Not only trivial and uninteresting, but also contrary to the ones that are
interesting.
Brent
and that there is no natural basis for selecting the interesting ones - they are in the
eye of the beholder. However, that is not an argument against the independent reality of
mathematical structures.
--
Stathis Papaioannou
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