```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.-- ----------------------------------------------------There is no remainder in the mathematics of infinity.                                       NYOGEN SENZAKI----------------------------------------------------
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