[FOM] Infinity and the "Noble Lie"

joeshipman@aol.com 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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