[FOM] Infinity and the "Noble Lie"
Helene.Boucher at wanadoo.fr
Wed Dec 14 18:14:39 EST 2005
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.
More information about the FOM