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

On 2025-06-05 16:15:20 +0000, olcott said:

On 6/5/2025 3:02 AM, Mikko wrote:

On 2025-06-05 02:13:32 +0000, dbush said:
 

On 6/4/2025 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.

 But unlike Russel's Paradox, which showed a contradiction in the axioms of naive set theory, there is no contradiction in the axioms of computation theory.

 That is easy to fix. Just add the axiom that HHH correctly computes
whether DDD halts.

 Incoherent axioms cannot be added.

There is nothing to prevent incoherent axioms. For example, the axiom of
comprehension of the Naive Set Theory is incoherent.
--
Mikko