Re: My reviewers think that halt deciders must report on the behavior of their caller

On 6/4/25 10:09 PM, olcott wrote:

On 6/4/2025 8:43 PM, Richard Damon wrote:

On 6/4/25 11:50 AM, olcott wrote:

On 6/4/2025 2:04 AM, Mikko wrote:

On 2025-06-03 21:39:46 +0000, olcott said:
>

They all say that HHH must report on the behavior of
direct execution of DDD()

>
No, they don't say that. A halting decider (and a partial halting
decider when it reports) must report whether the direct execution
of the computation asked about terminates. Unless that computation
happens to be DDD() it must report about another behaviour instead
of DDD().
>

yet never bother to notice that the directly executed DDD() is
the caller of HHH(DDD).

>
To say that nobody has noticed that is a lie. Perhaps they have not
mentioned what is irrelevant to whatever they said. In particular,
whether DDD() calls HHH(DDD) is irrelevant to the requirement that
a halting decider must report about a direct exection of the
computation the input specifies.
>

>
*People have ignored this for 90 years*
*People have ignored this for 90 years*
*People have ignored this for 90 years*
>
The only possible way that HHH can report on the
direct execution of DDD() is for HHH to report on
the behavior of its caller:

>
So?
>
It *IS* a fact that to be correct, it needs to answer about the direct executiom of the program that input represents.
>
That is DEFINITION.
>

 Likewise with the definition of Russell's Paradox
until ZFC showed that this definition is complete
nonsense.
 

No, Russell's Paradox showed a fundamental error in "Naive" Set Theory. ZFC did nothing with Russell's Paradox, except to define a system that can't support it, but still was able to handle a large portion of the problems that the original theory was trying to be used on.
Until you can show a similar problem with the definitions from computation theory, you don't have something to stand on.
The fact that some things turn out to be not-computable is not such a problem, in fact after it was discovered that this problem was non-computable, mathematics figured out that there had to be uncomputable problems by a simple counting argument.
If you think non-computable functions ARE a problem, and you want to define some alternate theory of computations, go ahead. You then have teh second half of what ZFC did, show that your system solves the problems that the original theory was being used on.
Since, it is clear you don't understand the purpose that Computation Theory was developed for (Hint, it isn't about programs on modern digital computers, as it predates their existance), this will be hard for you.