FOM: More on the astonishing dictum
neilt at hums62.cohums.ohio-state.edu
Fri Dec 26 14:16:58 EST 1997
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.
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, 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?
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