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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory,sci.logic
Subject: Re: H(D,D) cannot even be asked about the behavior of D(D) --- Truth
 Itself is not Broken. (Just misunderstood)
Date: Sat, 15 Jun 2024 09:44:15 -0500
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On 6/15/2024 8:52 AM, Richard Damon wrote:
> On 6/15/24 8:26 AM, olcott wrote:
>> On 6/15/2024 6:48 AM, joes wrote:
>>> Am Fri, 14 Jun 2024 21:39:50 -0500 schrieb olcott:
>>>
>>>> The key aspect of all of this is that if the halting problem is correct
>>>> then truth itself is fundamentally broken. Since truth itself cannot
>>>> possibly be fundamentally broken it must be fallible human 
>>>> understanding
>>>> of truth that is actually broken.
>>> I've got bad news for you, and you're a century late. Gödel proved that
>>> not all true statements are provable. It sure would have been nice.
>>>
>>
>> He didn't even prove this.
>> He proved that a statement that can be expressed in PA
>> cannot be proving in PA that is not true in PA yet can be
>> proved in matamath thus is true in metamath.
> 
> No, you are just showing you don't know what you are talking about.
> 
> You have admitted that you don't even understand the actual statement he 
> was using, but can only understand it as the simplication through 
> implication in the meta-thoery.
> 
> G, the statement about the non-existance of a Natural Number 'g' that 
> satisfied the specified relationship.
> 
> It can be shown (in the meta-theory) that no such number can exist, so G 
> must be true. Either the number 'g' exists or it doesn't so their can be 
> no middle ground, and it if is shown (in the meta theory) that if such a 
> number 'g' existed, then we could build a proof (as encoded in the 
> finite number 'g') in PA that PROVES CONCLUSIVELY no such number exist. 

*This is the crux of your correct insight*
> There can not be a number that proves that itself doesn't exist, so 
> there must not be such a number.
> 

There can be no proof in PA that G cannot be proven in PA
because such a proof in PA requires a sequence of inference
steps in PA that prove that they themselves do not exist.

*To sum this up in my terminology G has no truthmaker in PA*

-- 
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer