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

On 2025-06-06 17:04:46 +0000, olcott said:

On 6/6/2025 2:47 AM, Mikko wrote:

On 2025-06-05 16:12:41 +0000, olcott said:
 

On 6/5/2025 2:58 AM, Mikko wrote:

On 2025-06-05 02:09:19 +0000, olcott said:
 

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.

 Russell's paradox is not complete nonsense. It has a very clear
meaning: a theory where the paradox or some variant of it can
be shown is inconsistent. If a theory is inconsistent then it

 Inconsistent, incoherent, nonsense, all the same thing.

 For practical purposes, yes. In a formal context "inconsistent" is
preferred as a defined formal term. The others are informal.
 

is good to know that it is inconsistent. Conversely, if one
wants to present a new set theory or a new type theory or a new
theory of semantics one should check that the Russell's paradox
is not there nor any simple variant (like Barber's paradox or
the word "heterologous").

 

 int main()
{
    DDD(); // requiring the HHH(DDD) that DDD calls to
}         // report on the behavior of its caller is incorrect.

There is nothing incorrect in the requirement. That HHH answers
either "yes" nor "no" means that HHH accepts the input as a
valid computation in its scope.
--
Mikko