FOM: Where do mathematical objects exist?
martind at cs.berkeley.edu
Wed Jan 28 01:16:18 EST 1998
This question presupposes that any kind of "existence" must be existence
somewhere. If the real number e exists, and we can't locate it in the
physical world, then where does it exist? In our (inter-subjective)
imagination (Feferman/Hersh)? In some metaphysically difficult-to-swallow
Platonic domain of pure forms?
I am reminded of the nineteenth century quest for the ether. Given the
wave-like character of light, it seemed to follow that there must be some
medium in which light carries out its undulations: the luminiferous ether.
It transpired that experiments required this ether to have remarkable and
very peculiar properties. Finally, after Einstein, it was gradually realized
that the ether was an unnecessary conceptual nuisance.
So I think it will be with the locale of the objects of mathematics. It will
come to be understood that, just as light can undulate perfectly well
without anything to undulate in, so the objects of mathematics can have a
perfectly satisfactory existence without any particular place in which to exist.
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