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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