[FOM] The lure of the infinite
Mark Steiner
marksa at vms.huji.ac.il
Sun Feb 19 02:40:38 EST 2006
Berkeley did not deny that the infinitesmal calculus gives the right
numerical answers to questions in physics. He even had a theory to account
for it, having to do with one error cancelling another (sort of reminds me
of today's "renormalization"). He did not advocate not using the calculus.
His point was that there was no intellectual rigor in this branch of
mathematics, that it was only a tool for number crunching, and that its
practitioners should not pretend to more than practical, rather than
theoretical, knowledge. But he also argued that classical geometry is also
only a useful tool, and not knowledge, since space is in fact discrete and
thus the axioms of Euclid are not "true."
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