[FOM] Infinity and the "Noble Lie"
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
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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