[FOM] Infinity and the "Noble Lie"

[joeshipman@aol.com]

Raatikainen:

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