[FOM] Infinity and the "Noble Lie"

[Giovanni Lagnese]

> 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