Re: H(D,D) cannot even be asked about the behavior of D(D) --- Truth Itself is not Broken. (Just misunderstood)

On 6/15/24 10:44 AM, olcott wrote:

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.
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G, the statement about the non-existance of a Natural Number 'g' that satisfied the specified relationship.
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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*
 

You have it wrong because you don't understand the meaning of your own terms or are just lying.
Yes, there is no PROOF in PA that no number 'g' exists, so no proof in PA of G.
That does not mean there isn't a set of TRUTH-MAKERS that establish that G is true, and that no number 'g exists.
It takes an INFINITE number of steps, that of testing each individual Natural Number to see if it satisfies the relationship, and it turns out that none of them will. This is not a "Proof", as BY DEFINITION, Proofs are a finite sequence of steps, but it DOES establish that G is true, and no such number exists.
So, if your terminology says that isn't a Truth-Maker fof G, your truthmaker terminology is just incorrect.
Note, most statements don't have *A* Truth-maker, but a set of Truth-makers that establish them.