[FOM] Infinity and the "Noble Lie"

joeshipman@aol.com joeshipman at aol.com
Fri Dec 9 15:54:04 EST 2005

Reply to Obua:

You can declare the discussion "doomed" and say some "final words", but 
the rest of us still may have something to say....

It sounds like you are willing to accept axioms about infinite sets in 
proofs of finitary statements. There's nothing inconsistent about that. 
My concern is with those who insist that key statements about infinite 
sets are "meaningless" or "fictitious" and refuse to grant axioms like 
the Axiom of Infinity the status of "True", while continuing to conduct 
or refer to ordinary mathematical research which depends in an 
essential way on such an axiom.

For thosefollowing this discussion who have no problem with the Axiom 
of Infinity in ZFC, and who are comfortable saying that it is a true 
statement and that statements derived from it are therefore also true, 
I'd like to hear what your attitude is to the axiom that an 
Inaccessible Cardinal exists.  Is that statement true, false, one or 
the other but you have no idea which, or neither?  If "neither", why 
exactly does your answer differ from the answer you gave for the Axiom 
of Infinity?

-----Original Message-----
From: Steven Obua <obua at in.tum.de>

I think this whole discussion is doomed. Let me say some final words:
The only thing that needs to be finite is your argumentation to 
me of a theorem. For the rest there is no limit.

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