[FOM] Infinity and the "Noble Lie"

Norman Wildberger wildberger at pacific.net.au
Thu Dec 8 14:09:26 EST 2005

I am one of those errant mathematicians who happen to not only believe 
that the Axiom of Infinity does not make proper sense, but worse, that 
the wholescale adoption and uncritical acceptance of this kind of 
dubious reasoning has not done mathematics any good at all.

Mathematics would be much better served by people restricting themselves 
to talking about things which actually make mathematical sense, as 
opposed to things which perhaps make grammatical sense. Show me an 
infinite set, either in mathematics, or in physics! And I`ll show you 
some unsubstantiated claims.

Norman Wildberger

joeshipman at aol.com wrote:

>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
>FOM mailing list
>FOM at cs.nyu.edu

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