[FOM] Infinity and the "Noble Lie"
joeshipman at aol.com
Wed Dec 7 14:06:08 EST 2005
In a recent online discussion at nationalreview.com, John Derbyshire
(author of the excellent pop-math book "Prime Obsession") complained
about how some political philosophers seem to think it a good thing for
society that the masses believe in a religion they (the political
philosophers) don't themselves believe in. This tradition of a "noble
lie" goes back to Plato.
In reply, Derbyshire was asked whether the explanation of Infinity
given by mathematical philosophers was any better.
It is certainly true that the Axiom of Infinity is a tenet of our "ZFC
religion", and we are all encouraged to use it when formalizing -- but
at the same times many mathematical philosphers (either mathematicians
on their day off, or philosphers writing about mathematics) claim to
disbelieve in actual infinities.
It seems to me that there is a bit of the "noble lie" here -- because
these finitists (and also the agnostics about infinity) are benefiting
from the use of the Axiom of Infinity by the entire society of
mathematicians, even when they don't use it in their own work, because
the Axiom of Infinity has been so useful in the development of
mathematics as a whole. And of course those skeptics who DO nonetheless
use the axiom are in an even less defensible position.
Does anyone perceive an ethical issue here?
-- Joe Shipman
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