Date: Apr 6, 2013 12:25 PM
Author: namducnguyen
Subject: Re: Matheology § 224
On 06/04/2013 9:03 AM, Nam Nguyen wrote:

> On 06/04/2013 8:35 AM, WM wrote:

>> On 6 Apr., 16:13, Nam Nguyen <namducngu...@shaw.ca> wrote:

>>> On 06/04/2013 7:32 AM, Peter Percival wrote:

>>>

>>>> Nam Nguyen wrote:

>>>

>>>>> But if GC is undecidable in PA, there's no proof left in

>>>>> FOL but

>>>>> _structure theoretically verifying_ the truth value of

>>>>> GC in

>>>>> this structure.

>>>

>>>> If the Goldbach conjecture is undecidable in PA then it is true.

>>>

>>> Care to verify (prove) your claim here?

>>

>> Goldbach conjecture is false. <==> Counter example exists. <==>

>> Counter example can be found. <==> Goldbach conjecture is decidable.

>>

>> The second equivalence requires to neglect reality. But in mathematics

>> this is standard.

>

> But, to start with, how would one _structure theoretically prove_ the

> 1st equivalence:

>

> "Goldbach conjecture is false. <==> Counter example exists."

>

> ?

>

> Logically:

>

> (A _specific_ counter example exists) => (Goldbach conjecture is false).

>

> How would one _prove_ ( i.e. _structure theoretically verify_ ) the

> other-way-around?

>

> Consider:

>

> (P(0) -> Ex[P(x)]) <-> (Ex[P(x)] -> P(0))

>

> Is this a logical equivalence?

Iow, the meta statement:

"This.specific_counter_example exists"

is not of the same semantics as:

"There exists a counter example".

And this is logically true, hence uncontroversial.

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There is no remainder in the mathematics of infinity.

NYOGEN SENZAKI

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