On 13/04/2013 1:07 PM, Peter Percival wrote: > > > 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?
That's a pathetic response from Peter on multiple accounts:
(a) Def-1 and Def-2 were given by Nam on Peter's specific request on the the phrase relativity and Def-1 and Def-2 are _not_ dependent on any version of the language of arithmetic.
(b) In this thread _Nam has clarified already_ what language he has been using for cGC, and the like.
(c) It does _NOT_ matter at all that Godel's language of arithmetic used for the naturals number doesn't include the symbol '<'. The argument about the relativity of the truth value of cGC rests with the fact a certain predicate/function _set_ of 2-tuples can't be defined in a finite manner or inductively, as Def-2 mentions.
Your (as well as fom's and Frederick's) insistence on the clarity of which of the 2 languages "S,+,x,0 or <,S,+,x,0" is only a buzzword smokescreen hiding the ignorance on the "_NOT_ matter at all" I've pointed out. But in any case, I've clarified in many occasions the language I used is FOL L(PA), of which the signature you do know (right?).
Now that you understand which of L(S,+,x,0) and L(<,S,+,x,0) I've been using for years, would you answer my question about Def-1, Def-2?
-- ---------------------------------------------------- There is no remainder in the mathematics of infinity.