[FOM] Infinity and the "Noble Lie"

[joeshipman@aol.com]

To "justify" a theorem which has been proven in some formal system 
means to "give an explanation why we should accept the axioms the 
therem is proved from".

-- JS

-----Original Message-----
From: Giovanni Lagnese <lagnese at ngi.it>
To: Foundations of Mathematics <fom at cs.nyu.edu>
Sent: Sun, 8 Jan 2006 05:30:59 +0100
Subject: Re: [FOM] Infinity and the "Noble Lie"

> 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.

So, you think the Paris-Harrington statement itself cannot be 
"justified"
without reference to actually infinite sets?
What does "justify" mean?

GL