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 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. There can not be a number that proves that itself doesn't exist, so there must not be such a number.
The only other alternative is the doomsday assumption that there exists NO consistant logic system that meets the minimum requirements for the proof, when basically means all the math we normally used has to be part of an inconsistant system, and thus, by the principle of explosion, EVERYTHING can be proven true somehow.

 G lacks a truthmaker in PA and has a truthmaker in metamath.
Tarski did the same thing yet started with the actual Liar Paradox.
I am not going to bother to show you his proof it is over your head.
 

No, it has a 'truth-maker' and tha truth-maker is the INFINITE SEQUENCE of testing EVERY Natural Number and seeing that none of the satisfy the relationship. Being an infinite sequence of steps, means that it is not a "proof", which BY DEFINITION, must be a finite series of steps.
The meta-math allows a relationship that allows us to compress that infinite sequence into a finite sequence, so we can prove it in the meta-math