[FOM] Infinity and the "Noble Lie"

[A. Mani]

On Thursday 08 December 2005 00:36, joeshipman at aol.com wrote:

> In reply, Derbyshire was asked whether the explanation of Infinity
> given by mathematical philosophers was any better.
>
There is no comparison. In the philosophy of mathematics we are on exact 
terrain, given a materialistic conception of reality.
> 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.
>
The axiom of infinity in ZFC has the same status as the concept of a point in 
geometry. ...it has probably more real realizations.
> 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.
>
Axioms are not lies. Take it or leave it... of course if you can stand up with 
it.
> Does anyone perceive an ethical issue here?
>
No I do not see any. Doing comparisons between two concepts one in a 
speculative 'idealist' domain and another in a real domain is more 
questionable and unjustifiable. This is a huge subject.


A. Mani
Member, Cal. Math. Soc