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From: Richard Damon <richard@damon-family.org>
Newsgroups: comp.theory
Subject: Re: key error in all the proofs --- Correction of Fred
Date: Fri, 16 Aug 2024 12:00:15 -0400
Organization: i2pn2 (i2pn.org)
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On 8/16/24 11:45 AM, olcott wrote:
> On 8/16/2024 10:39 AM, Richard Damon wrote:
>> On 8/16/24 11:05 AM, olcott wrote:
>>> On 8/16/2024 9:56 AM, Richard Damon wrote:
>>>> On 8/16/24 10:42 AM, olcott wrote:
>>>>> On 8/16/2024 9:28 AM, Richard Damon wrote:
>>>>>> On 8/16/24 10:09 AM, olcott wrote:
>>>>>>> On 8/16/2024 8:34 AM, Mikko wrote:
>>>>>>>> On 2024-08-16 12:02:00 +0000, olcott said:
>>>>>>>>
>>>>>>>>>
>>>>>>>>> I must go one step at a time.
>>>>>>>>
>>>>>>>> That's reasonable in a discussion. The one thing you were 
>>>>>>>> discussing
>>>>>>>> above is what is the meaning of the output of HHH. Its OK to stay
>>>>>>>> at that step until we are sure it is understood.
>>>>>>>>
>>>>>>>
>>>>>>> void DDD()
>>>>>>> {
>>>>>>>    HHH(DDD);
>>>>>>>    return;
>>>>>>> }
>>>>>>>
>>>>>>> Unless an unlimited emulation of DDD by HHH
>>>>>>> can reach the "return" instruction of DDD it is
>>>>>>> construed that this instance of DDD never halts.
>>>>>>
>>>>>> But that also construes that HHH is a program that DOES an 
>>>>>> unlimited emulation of DDD, and thus isn't a decider
>>>>>>
>>>>>
>>>>> Not at all. never has.
>>>>> HHH must predict what the behavior of an unlimited
>>>>> simulation would be.
>>>>>
>>>>
>>>> Right, unlimited emulation of the EXACT input that HHH got, that is 
>>>> the DDD that calls the HHH that is the decider
>>>>
>>>
>>> PREDICT WHAT THE BEHAVIOR WOULD BE
>>> PREDICT WHAT THE BEHAVIOR WOULD BE
>>> PREDICT WHAT THE BEHAVIOR WOULD BE
>>> PREDICT WHAT THE BEHAVIOR WOULD BE
>>>
>>> IF IT WAS AN UNLIMITED EMULATION
>>> IF IT WAS AN UNLIMITED EMULATION
>>> IF IT WAS AN UNLIMITED EMULATION
>>> IF IT WAS AN UNLIMITED EMULATION
>>>
>>
>> So, I guess you aren't working on the Halting Problem, 
> 
> Halt deciders have always been required to predict what the
> behavior of their input would be.
> 

Right, and the input to the Halt Decider HHH is the DDD that calls the 
Halt Decider HHH, not the DDD that calls the unlimited emulator HHH.

If we have an unlimited Emulator U, then U(DDD) will have U emulate DDD 
calling HHH, which will then emulated DDD calling HHH, and HHH deciding 
(incorrectly) that it won't halt, and then HHH returns to DDD which then 
Halts.

Thus, the CORRECT answer that HHH should have gotten, if it was a 
correct Halt Decider is that its input Halts.

You problem is you seem to have a funny-mental block on the concept of a 
program, and don't understand that as a program, the thing that a Halt 
Decider needs as its input, includes all the code of the program, which 
is the HHH that DDD calls.

This causes you to use just lying logic claiming that all version of DDD 
that call different HHHs are "the same", when they are not.

The confusion of things that are different as being the same is one form 
of insnaity, showing what you mental state actually is.