
Re: Matheology § 224
Posted:
Apr 13, 2013 5:18 PM


Nam Nguyen wrote:
> 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 ParisHarrington Ramseylike 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. > >>> > >>>> [...] > >>>> > >>>> Def00: The natural numbers collectively is a language model > >>>> [of L(PA)] of which the universe U is nonfinite. > >>>> </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 Def1 and Def2, 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) Def1 and Def2 were given by Nam on Peter's specific request > on the the phrase relativity and Def1 and Def2 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 2tuples > can't be defined in a finite manner or inductively, as Def2 > 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?).
No, I know of more than one signature for PA (and I wouldn't be surprised if there are others) so I'm asking you which of them you are using.
> Now that you understand which of L(S,+,x,0) and L(<,S,+,x,0)
I don't know.
> I've been > using for years,
I haven't been reading your posts for years.
> would you answer my question about Def1, Def2?

