> > In my original thread that I'm certain Frederick is aware of: > > http://groups.google.com/group/comp.ai.philosophy/msg/58615203416c4d7e?hl=en > > Twice I clearly indicate what language I've been using in my > effort about cGC: > > <quote> > > Arithmetic truths of the natural numbers (written in the language of > arithmetic L(PA)) are supposed to be absolute, in the sense that they > can NOT be undecidable,
The Paris-Harrington Ramsey-like theorem can be stated in the language of first order PA (FOPA) but it is not provable in FOPA. Nevertheless it is true. See the last chapter of Barwise's Handbook.
> can NOT be chosen at discretion, can NOT be > of the nature "it's impossible to know".
So, when you write not undecidable, do you mean in FOPA, or some larger theory (like ZF)? As for chosen at discretion and impossible to know, I do not know what they mean in the context of mathematics.
> [...] > > Def-00: The natural numbers collectively is a language model > [of L(PA)] of which the universe U is non-finite. > </quote> > > So your complaint about me never letting Frederick know the language > (hence its signature)
Is it S,+,x,0 or <,S,+,x,0? Just say yes to one or the other, or no to both.