[FOM] Infinity and the "Noble Lie"

[Andrew Boucher]

On  14 Dec 2005, at 7:20 PM, joeshipman at aol.com wrote:
>
> can you provide an example of a statement whose proof requires the
> Axiom of Infinity, but which you regard as having a higher
> epistemological status than the Axiom of Infinity, and explain why you
> accord it such a status?
>
> --

To be honest, I'm not really in the habit of according higher (or  
lower) epistemological statuses, since I think most statuses are  
incomparable.  But putting that to one side, for the sake of  
argument, take your own example of Con(PA).  One could argue that  
this proposition has received real-world confirmation by the absence  
of a contradiction derived in PA after all these years and  
centuries.  That is, it has some kind of support from our experience  
in the real-world.

As to the other part of your message, I appreciate your interests,  
and find them of value, but obviously they are not the same as mine.   
In the systems that I look at the Completeness Theorem is equivalent  
to the Successor Axiom, so it is infinitary.

Regards