FOM: More on the astonishing dictum
rhersh at math.unm.edu
Mon Dec 29 14:42:37 EST 1997
On Fri, 26 Dec 1997, Neil Tennant wrote:
> Reuben Hersch calls it an "astonishing dictum" when I claim that the
> history of social-institutional practices surrounding mathematics is
> irrelevant to the truth of Platonism. Why so astonishing? Surely it's
> just part and parcel of a Platonist account. I was simply pointing out
> an obvious consequence of Platonism for a Platonist, so that the
> social constructivists on this list would be minded of it, and be
> prepared to take it into account
when trying to argue their Platonist colleagues out of their Platonism.
I'M NOT! rh
> To a Platonist, it would be even more astonishing if, in the absence
> of an objective, mathematical realm somehow accessible to
> intellection, we managed to achieve such unanimity on long and
> difficult proofs, choice of axiom systems, etc. *through social forces
> alone*. THAT would be the truly astonishing dictum: namely, that the
> appearance of objectivity in mathematics was nothing more than an
> appearance---both socially contrived and utterly misleading as to the
> true nature of the subject matter of mathematical discourse.
> The social constructivist owes us, at the very least
Wow! And at the very most, I wonder?
, a fully
> naturalized account of the provenance of the *norms* governing our
> mathematical reasoning; and of the source of our intuitions as to what
> is mathematically true. Can they do that? WE'RE WORKING ON IT.
SEE DEHAENE AND LAKOFF
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