Re: The error of the halting problem --- G is untrue in PA

On 6/4/24 1:45 PM, olcott wrote:

On 6/4/2024 3:29 AM, joes wrote:

Am Mon, 03 Jun 2024 21:58:06 -0500 schrieb olcott:

On 6/3/2024 9:47 PM, Richard Damon wrote:

On 6/3/24 10:32 PM, olcott wrote:

On 6/3/2024 9:26 PM, Richard Damon wrote:

On 6/3/24 10:14 PM, olcott wrote:

On 6/3/2024 8:58 PM, Richard Damon wrote:

On 6/3/24 9:51 PM, olcott wrote:

>
When H is asked a yes/no question where both answers are
contradicted by its input *IT IS A FREAKING RIGGED GAME*

>
But both answers aren't wrong. Remember, the question is built to
make a SPECIFIC decider wrong, and by its algorithm, it will give a
SPECIFIC answer to each SPECIFIC question.
>

You can't get away with that head game by pretending to not
understand what infinite an set of H/D pairs is.

>
But it doesn't matter.
>

It matters enormously. Once we fully understand that the limits of
computation were always a ruse then we can give computation the
priority that it truly deserves. It might be the life on earth is
killed off because we did not build a semantic lie detector quickly
enough.

>
But you are working on it wrong, because you just don't understand the
actual nature of truth.

>
Every expression X that is true on the basis of its meaning can be
proven untrue by a lack of a connection to the meaning that makes it
true. *You have understood this better than anyone else*

No. "true expressions can be proven untrue"? There are true but unprovable
sentences (see Gödel).
>

 G cannot be linked by truth preserving operations to expressions of language in PA that show that G is true in PA.

But it CAN.
Each natural number can be checked in a finite time against the primative recursive relationship, to see that it does not satisfy that relationship.
We can check EVERY SINGLE NUMBER, in a countable infinite number of steps, and thus establish that G, the statement that no natural number satisfies that relationship, is in fact true.
Your problem is you just don't understand what the statement G in PA actually is, because the math is just beyond you, so you replace it with something that isn't the same thing but can be shown to express things about the nature and implications of G.
So, your arguement is just proved to be a LIE, as most of your assertions.

 G can be linked by truth preserving operations to expressions of language in meta-math that show that G is true in meta-math.

Yes, and in the meta-math, we have a short cut, that actually allows us to PROVE the statement, not just have it established by an infinite number of steps.

 

When D is defined to contradict both values that H returns then D is not
a truth bearer in H in the same way that the Liar Paradox "This sentence
is not true" is not a truth bearer in English.

>