Date: Apr 6, 2013 2:34 PM
Author: namducnguyen
Subject: Re: Matheology § 224

On 06/04/2013 12:27 PM, WM wrote:
> On 6 Apr., 19:53, Nam Nguyen <namducngu...@shaw.ca> wrote:
>> On 06/04/2013 11:38 AM, WM wrote:
>>
>>
>>
>>
>>

>>> On 6 Apr., 19:23, Nam Nguyen <namducngu...@shaw.ca> wrote:
>>
>>>> In details:
>>
>>>> We do have the logical equivalence:
>>
>>>> ~Ax[P(x)] <-> Ex[~P(x)]
>>
>>>> But we don't have this equivalence:
>>
>>>> ~P(SS.....S0) <-> Ex[~P(x)].
>>
>>>> Right?
>>
>>> No. Unless SS...S0 is fixed it is the same as x for x in |N. Different
>>> notation does not make different meaning.

>>
>> It was just unclear to you. In my presentation above SS.....S0 is
>> a _fixed_ constant, _not_ a variable.

>
> Every counterexample of GC, if existing, is a fixed natural number.
> But I do not pretend that I know such an SS...S0. And that statement
> with, say 42, does not play a role in my arguing.

>>
> ~GC <==> Counter example with a fixed n in |N exists. <==>
> Fixed n in |N can be found. ==> Goldbach conjecture is decidable.


You're incorrect in that:

~GC is syntactically of the form Ex[P(x)]. No "fixed n" is required. Period.

Nor is "fixed n" grammatically correct in FOL.

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There is no remainder in the mathematics of infinity.

NYOGEN SENZAKI
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