Nam Nguyen wrote: > > On 13/04/2013 12:47 PM, Peter Percival wrote: > > Nam Nguyen wrote: > > > >> > >> 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. > > Please, Peter. Before we go further discussing, would you let me know > if you understand my definitions Def-1 and Def-2, which would be > important in this debate about cGC?
Please, Nam. Before we go further discussing, would you let me know if the signature is S,+,x,0 or <,S,+,x,0, which would be important in this debate about cGC?