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From: Richard Damon <richard@damon-family.org>
Newsgroups: comp.theory
Subject: Re: Incorrect requirements --- Computing the mapping from the input
 to HHH(DD)
Date: Sun, 11 May 2025 17:02:38 -0400
Organization: i2pn2 (i2pn.org)
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On 5/11/25 12:44 PM, olcott wrote:
> On 5/11/2025 6:13 AM, joes wrote:
>> Am Sat, 10 May 2025 15:42:13 -0500 schrieb olcott:
>>> On 5/10/2025 3:22 PM, Alan Mackenzie wrote:
>>
>>>> OK, then, give the page and line numbers from Turing's 1936 paper where
>>>> this alleged mistake was made.  I would be surprised indeed if you'd
>>>> even looked at Turing's paper, far less understood it.  Yet you're
>>>> ready to denigrate his work.
>>>> Perhaps it is time for you to withdraw these uncalled for insinuations.
>>>>
>>> It is the whole gist of the entire idea of the halting problem proof
>>> that is wrongheaded.
>>> (1) It is anchored in the false assumption that an input to a
>>> termination analyzer can actually do this opposite of whatever value
>>> that this analyzer returns. No one ever notices that this "do the
>>> opposite" code is unreachable.
> 
>> The simulated DDD doesn't matter. HHH returns to DDD, and DDD then does
>> the opposite.
>>
> 
> HHH is only allowed to report on the behavior that
> its actual input actually specifies.


Which is DEFINED to be the bahavior of the program that the input 
represents when run.
> 
> int sum(int x, int y) { return x + y; }
> sum(3,2) is not allowed to report on the sum of 5 + 7
> because that is not what its input specifies.

and your HHH is doing the equivalent of doing:

int *p = 0;
sum(5,*p)

as it doesn't have all the needed information, and thus accesses data it 
isn't supposed to.

If you fix the defintion of DD to inlude its HHH then you sample is that


sum(3,2) returning the results of 5 + 2, as it doesn't actually use the 
actual HHH that DD calls, but a mistaken assumption of what that code is.

Remember, this HHH aborts and returns, but it assumes that HHH (which is 
the same) never aborts.

Sorry, it incorrect emulates the input by any reasonable definition that 
isn't based on allowing lying.

> 
>>> (2) It expects a self-contradictory (thus incorrect)
>>> question to have a correct answer.
>> Whether a program halts is not contradictory.
>>
> 
> Asking sum(3,2) about the sum of 5 + 7
> is the same as asking HHH(DDD) about the
> direct execution of DDD().

Nope, it is like HHH not looking at the HHH that its DDD calls, but even 
though it actually is the aborting and returning 0 HHH, it assumes it is 
the never aborting and never returning HHH, which doesn't actualy exist.

> 
>>> Can Carol correctly answer “no” to this (yes/no) question?
>>> When the context of who is asked is understood to be an aspect of the
>>> full meaning of the question then the question posed to Carol is
>>> incorrect because both yes and no are the wrong answer.
>> Yes, HHH cannot answer correctly.
>>
> 
> Any yes/no question where both yes and no are the
> wrong answer is an incorrect polar question.
> Copyright PL Olcott 2025.
> 

But for that actual question that isn't the case.

The question is: Does the program represented by the input halt when run?

TO even ask that question, we need the full definition of that program, 
and for DD or DDD that requires us to have a full definition of the HHH 
that they call (or we don't even have a program) and thus there *IS* a 
definite answer based on that definiton.

Since your HHH(DD) or HHH(DDD) returns 0 becuase it does abort its 
emulation, that means that the actual execution of either DD or DDD will 
call that HHH and it will return the 0 result and thus DD / DDD will 
halt, and thus Halting was the correct answer, just not the answer that 
that HHH gave.

The problem is your strawman question, "What can HHH return for DDD to 
be correct?" is an invalid question, as a given HHH can only return one 
answer, and that is fixed by its definition, so the question itself is 
malformed based on a false assumption of ability to choose.

Your question is like asking what is the length of a side of a square 
circle? It presumes something that is impossible.