[FOM] Infinity and the "Noble Lie"

joeshipman@aol.com joeshipman at aol.com
Sat Jan 7 16:32:14 EST 2006


I wonder whether everyone here is using the notion of "an axiom of
infinity" in the same sense.

I reply:

I am using THE "Axiom of Infinity" in the specific formal system ZFC.

It is possible to express, and prove, the Paris-Harrington Theorem in 
many other formal systems, but any such proof will, I contend, at some 
point invoke an axiom which cannot be justified without reference to 
actually infinite sets, or structures of other types whose domain is 
necessarily infinite.

-- JS

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