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Topic: Matheology § 224
Replies: 84   Last Post: Apr 20, 2013 4:43 PM

 Messages: [ Previous | Next ]
 namducnguyen Posts: 2,777 Registered: 12/13/04
Re: Matheology § 224
Posted: Apr 13, 2013 5:02 PM

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:
>>>>
>>>>
>>>> Twice I clearly indicate what language I've been using in my
>>>>
>>>> <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

--
----------------------------------------------------
There is no remainder in the mathematics of infinity.

NYOGEN SENZAKI
----------------------------------------------------

Date Subject Author
4/12/13 Alan Smaill
4/12/13 namducnguyen
4/12/13 Frederick Williams
4/12/13 fom
4/13/13 namducnguyen
4/13/13 fom
4/13/13 namducnguyen
4/13/13 fom
4/13/13 namducnguyen
4/13/13 Peter Percival
4/13/13 namducnguyen
4/13/13 Peter Percival
4/13/13 namducnguyen
4/13/13 Peter Percival
4/13/13 namducnguyen
4/13/13 Jesse F. Hughes
4/14/13 namducnguyen
4/14/13 namducnguyen
4/14/13 namducnguyen
4/14/13 Peter Percival
4/14/13 fom
4/14/13 namducnguyen
4/14/13 fom
4/14/13 namducnguyen
4/14/13 namducnguyen
4/14/13 fom
4/14/13 namducnguyen
4/14/13 namducnguyen
4/14/13 namducnguyen
4/14/13 Jesse F. Hughes
4/14/13 namducnguyen
4/14/13 Jesse F. Hughes
4/14/13 namducnguyen
4/16/13 namducnguyen
4/16/13 namducnguyen
4/16/13 Jesse F. Hughes
4/16/13 namducnguyen
4/16/13 fom
4/17/13 namducnguyen
4/17/13 fom
4/17/13 namducnguyen
4/17/13 Jesse F. Hughes
4/17/13 Jesse F. Hughes
4/17/13 namducnguyen
4/20/13 namducnguyen
4/17/13 Frederick Williams
4/17/13 Frederick Williams
4/17/13 fom
4/17/13 Frederick Williams
4/17/13 fom
4/17/13 fom
4/18/13 namducnguyen
4/18/13 Frederick Williams
4/18/13 namducnguyen
4/19/13 Frederick Williams
4/19/13 namducnguyen
4/20/13 Frederick Williams
4/19/13 Frederick Williams
4/19/13 namducnguyen
4/20/13 Frederick Williams
4/14/13 Jesse F. Hughes
4/14/13 namducnguyen
4/14/13 namducnguyen
4/14/13 Jesse F. Hughes
4/14/13 namducnguyen
4/14/13 Peter Percival
4/15/13 Peter Percival
4/14/13 namducnguyen
4/14/13 namducnguyen
4/13/13 Frederick Williams
4/13/13 Peter Percival
4/13/13 Peter Percival
4/13/13 namducnguyen
4/15/13 Peter Percival
4/13/13 fom
4/13/13 namducnguyen
4/13/13 Peter Percival
4/13/13 namducnguyen
4/13/13 Frederick Williams
4/14/13 Frederick Williams
4/14/13 namducnguyen
4/13/13 Peter Percival
4/13/13 namducnguyen
4/13/13 namducnguyen