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Re: ChatGPT agrees that the halting problem input can be construed as an incorrect question

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On 6/17/23 10:29 PM, olcott wrote:
> On 6/17/2023 8:31 PM, Richard Damon wrote:
>> On 6/17/23 7:58 PM, olcott wrote:
>>> On 6/17/2023 6:13 PM, Richard Damon wrote:
>>>> On 6/17/23 5:46 PM, olcott wrote:
>>>>> On 6/17/2023 4:09 PM, Ben Bacarisse wrote:
>>>>>> Richard Damon <Richard@Damon-Family.org> writes:
>>>>>>
>>>>>>> Except that the Halting Problem isn't a "Self-Contradictory" 
>>>>>>> Quesiton, so
>>>>>>> the answer doesn't apply.
>>>>>>
>>>>>> That's an interesting point that would often catch students out.  And
>>>>>> the reason /why/ it catches so many out eventually led me to stop 
>>>>>> using
>>>>>> the proof-by-contradiction argument in my classes.
>>>>>>
>>>>>> The thing is, it looks so very much like a self-contradicting 
>>>>>> question
>>>>>> is being asked.  The students think they can see it right there in 
>>>>>> the
>>>>>> constructed code: "if H says I halt, I don't halt!".
>>>>>>
>>>>>> Of course, they are wrong.  The code is /not/ there.  The code 
>>>>>> calls a
>>>>>> function that does not exist, so "it" (the constructed code, the 
>>>>>> whole
>>>>>> program) does not exist either.
>>>>>>
>>>>>> The fact that it's code, and the students are almost all 
>>>>>> programmers and
>>>>>> not mathematicians, makes it worse.  A mathematician seeing "let p be
>>>>>> the largest prime" does not assume that such a p exists.  So when a
>>>>>> prime number p' > p is constructed from p, this is not seen as a
>>>>>> "self-contradictory number" because neither p nor p' exist.  But the
>>>>>> halting theorem is even more deceptive for programmers, because the
>>>>>> desired function, H (or whatever), appears to be so well defined 
>>>>>> -- much
>>>>>> more well-defined than "the largest prime".  We have an exact
>>>>>> specification for it, mapping arguments to returned values.  It's 
>>>>>> just
>>>>>> software engineering to write such things (they erroneously assume).
>>>>>>
>>>>>> These sorts of proof can always be re-worded so as to avoid the 
>>>>>> initial
>>>>>> assumption.  For example, we can start "let p be any prime", and 
>>>>>> from p
>>>>>> we construct a prime p' > p.  And for halting, we can start "let H be
>>>>>> any subroutine of two arguments always returning true or false".  
>>>>>> Now,
>>>>>> all the objects /do/ exist.  In the first case, the construction 
>>>>>> shows
>>>>>> that no prime is the largest, and in the second it shows that no
>>>>>> subroutine computes the halting function.
>>>>>>
>>>>>> This issue led to another change.  In the last couple of years, I 
>>>>>> would
>>>>>> start the course by setting Post's correspondence problem as if it 
>>>>>> were
>>>>>> just a fun programming challenge.  As the days passed (and the course
>>>>>> got into more and more serious material) it would start to become 
>>>>>> clear
>>>>>> that this was no ordinary programming challenge.  Many students 
>>>>>> started
>>>>>> to suspect that, despite the trivial sounding specification, no 
>>>>>> program
>>>>>> could do the job.  I always felt a bit uneasy doing this, as if I was
>>>>>> not being 100% honest, but it was a very useful learning 
>>>>>> experience for
>>>>>> most.
>>>>>>
>>>>>
>>>>> sci.logic Daryl McCullough Jun 25, 2004, 6:30:39 PM
>>>>>     You ask someone (we'll call him "Jack") to give a truthful
>>>>>     yes/no answer to the following question:
>>>>>
>>>>>     Will Jack's answer to this question be no?
>>>>>
>>>>>     Jack can't possibly give a correct yes/no answer to the question.
>>>>>
>>>>> It is an easily verified fact that when Jack's question is posed to 
>>>>> Jack
>>>>> that this question is self-contradictory for Jack or anyone else 
>>>>> having
>>>>> a pathological relationship to the question.
>>>>
>>>> But the problem is "Jack" here is assumed to be a volitional being.
>>>>
>>>> H is not, it is a program, so before we even ask H what will happen, 
>>>> the answer has been fixed by the definition of the codr of H.
>>>>
>>>>>
>>>>> It is also clear that when a question has no yes or no answer because
>>>>> it is self-contradictory that this question is aptly classified as
>>>>> incorrect.
>>>>
>>>> And the actual question DOES have a yes or no answer, in this case, 
>>>> since H(D,D) says 0 (non-Halting) the actual answer to the question 
>>>> does D(D) Halt is YES.
>>>>
>>>> You just confuse yourself by trying to imagine a program that can 
>>>> somehow change itself "at will".
>>>>
>>>>>
>>>>> It is incorrect to say that a question is not self-contradictory on 
>>>>> the
>>>>> basis that it is not self-contradictory in some contexts. If a 
>>>>> question
>>>>> is self-contradictory in some contexts then in these contexts it is an
>>>>> incorrect question.
>>>>
>>>> In what context is "Does the Machine D(D) Halt When run" become 
>>>> self-contradictory?
>>> When this question is posed to machine H.
>>>
>>> Jack could be asked the question:
>>> Will Jack answer "no" to this question?
>>>
>>> For Jack it is self-contradictory for others that are not
>>> Jack it is not self-contradictory. Context changes the semantics.
>>>
>>
>> But you are missing the difference. A Decider is a fixed piece of 
>> code, so its answer has always been fixed to this question since it 
>> has been designed. Thus what it will say isn't a varialbe that can 
>> lead to the self-contradiction cycle, but a fixed result that will 
>> either be correct or incorrect.
>>
> 
> Every input to a Turing machine decider such that both Boolean return
> values are incorrect is an incorrect input.
> 

Except it isn't. The problem is you are looking at two different 
machines and two different inputs.

If you define your H0 to return 0 when given the input <D0> <D0> for the 
D0 built on D0, then since D0 applied to <D0> will halt so the correct 
answer is 1. If H0 returned that answer, it would have been correct, but 
since H0 was defined with code that answered 0, that is the only thing 
that it can answer.

On the other hand, if you instead defined a DIFFERENT machine H1, that 
uses similar logic, but instead of returning Non-Halting, returned 
Halting, the H1 applied to <D0> <D0> would abort its simulation and 
return 1, and it would have been correct. The problem here is that since 
H1 is a different machine, its "pathological" program is different, 
(since it will be built on H1, not H0) and H1 applied to <D1> <D1> will 
abort its simulation and return 1, but D1 applied to <D1> will go into 
an infinite loop, so the correct answer should have been 0.

So, the problem is that the two cases you are looking at are DIFF#RENT 
inputs, because they are built on DIFFERENT machines. You don't seem to 
understand that a machine WILL generate the results that machine is 
programmed for, so "hypothetical" about it doing somethng different are 
just looking at impossible actions.

So, it isn't the case that both answers are wrong for the same question, 
it is that the question changes when you alter your decider and whatever 
answer you make you decider give, will be wrong, and the other one right.

Other deciders can get the correct answer for THAT input, but there will 
be a different input, based on them, that they will get wrong.

You just seem to have a blind spot about what needs to stay the same, 
and what changes when you play your mind games.

You dig your gas-lit hole because you seem to naturally do the deceptive 
thing of not giving new names to things when you change them, but try to 
hide the fact that you changed things by reusing names. This is a sign 
of potentially intentional deception.

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ChatGPT agrees that the halting problem input can be construed as an incorrect question olcott <polcott2@gmail.com> - 2023-06-17 00:54 -0500
  Re: ChatGPT agrees that the halting problem input can be construed as an incorrect question Richard Damon <Richard@Damon-Family.org> - 2023-06-17 08:09 -0400
    Re: ChatGPT agrees that the halting problem input can be construed as an incorrect question olcott <polcott2@gmail.com> - 2023-06-17 11:59 -0500
      Re: ChatGPT agrees that the halting problem input can be construed as an incorrect question Richard Damon <Richard@Damon-Family.org> - 2023-06-17 13:43 -0400
        Re: ChatGPT agrees that the halting problem input can be construed as an incorrect question olcott <polcott2@gmail.com> - 2023-06-17 13:23 -0500
          Re: ChatGPT agrees that the halting problem input can be construed as an incorrect question Richard Damon <Richard@Damon-Family.org> - 2023-06-17 16:27 -0400
    Re: ChatGPT agrees that the halting problem input can be construed as an incorrect question Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-17 22:09 +0100
      Re: ChatGPT agrees that the halting problem input can be construed as an incorrect question olcott <polcott2@gmail.com> - 2023-06-17 16:46 -0500
        Re: ChatGPT agrees that the halting problem input can be construed as an incorrect question Jeff Barnett <jbb@notatt.com> - 2023-06-17 16:03 -0600
          Re: ChatGPT agrees that the halting problem input can be construed as an incorrect question Richard Damon <Richard@Damon-Family.org> - 2023-06-17 19:18 -0400
            Re: ChatGPT agrees that the halting problem input can be construed as an incorrect question olcott <polcott2@gmail.com> - 2023-06-17 18:44 -0500
              Re: ChatGPT agrees that the halting problem input can be construed as an incorrect question Richard Damon <Richard@Damon-Family.org> - 2023-06-17 21:46 -0400
                Re: ChatGPT agrees that the halting problem input can be construed as an incorrect question olcott <polcott2@gmail.com> - 2023-06-17 21:35 -0500
                Re: ChatGPT agrees that the halting problem input can be construed as an incorrect question Richard Damon <Richard@Damon-Family.org> - 2023-06-17 23:03 -0400
        Re: ChatGPT agrees that the halting problem input can be construed as an incorrect question Richard Damon <Richard@Damon-Family.org> - 2023-06-17 19:13 -0400
          Re: ChatGPT agrees that the halting problem input can be construed as an incorrect question olcott <polcott2@gmail.com> - 2023-06-17 18:58 -0500
            Re: ChatGPT agrees that the halting problem input can be construed as an incorrect question Richard Damon <Richard@Damon-Family.org> - 2023-06-17 21:31 -0400
              Re: ChatGPT agrees that the halting problem input can be construed as an incorrect question olcott <polcott2@gmail.com> - 2023-06-17 21:29 -0500
                Re: ChatGPT agrees that the halting problem input can be construed as an incorrect question Richard Damon <Richard@Damon-Family.org> - 2023-06-17 22:57 -0400
                Re: ChatGPT agrees that the halting problem input can be construed as an incorrect question olcott <polcott2@gmail.com> - 2023-06-17 22:10 -0500
                Re: ChatGPT agrees that the halting problem input can be construed as an incorrect question Richard Damon <Richard@Damon-Family.org> - 2023-06-18 08:02 -0400
                Re: ChatGPT agrees that the halting problem input can be construed as an incorrect question olcott <polcott2@gmail.com> - 2023-06-18 09:32 -0500
                Re: ChatGPT agrees that the halting problem input can be construed as an incorrect question Richard Damon <Richard@Damon-Family.org> - 2023-06-18 12:31 -0400
                Re: ChatGPT agrees that the halting problem input can be construed as an incorrect question olcott <polcott2@gmail.com> - 2023-06-18 11:41 -0500
                Re: ChatGPT agrees that the halting problem input can be construed as an incorrect question Richard Damon <Richard@Damon-Family.org> - 2023-06-18 12:54 -0400
                Re: ChatGPT agrees that the halting problem input can be construed as an incorrect question olcott <polcott2@gmail.com> - 2023-06-18 12:09 -0500
                Re: ChatGPT agrees that the halting problem input can be construed as an incorrect question Richard Damon <Richard@Damon-Family.org> - 2023-06-18 13:46 -0400
                Re: ChatGPT agrees that the halting problem input can be construed as an incorrect question olcott <polcott2@gmail.com> - 2023-06-18 13:05 -0500
                Re: ChatGPT agrees that the halting problem input can be construed as an incorrect question Richard Damon <Richard@Damon-Family.org> - 2023-06-18 14:20 -0400
                Re: ChatGPT agrees that the halting problem input can be construed as an incorrect question olcott <polcott2@gmail.com> - 2023-06-18 13:30 -0500
                Re: ChatGPT agrees that the halting problem input can be construed as an incorrect question Richard Damon <Richard@Damon-Family.org> - 2023-06-18 14:43 -0400
                Re: ChatGPT agrees that the halting problem input can be construed as an incorrect question olcott <polcott2@gmail.com> - 2023-06-18 13:47 -0500
                Re: ChatGPT agrees that the halting problem input can be construed as an incorrect question Richard Damon <Richard@Damon-Family.org> - 2023-06-18 15:19 -0400
                Re: ChatGPT agrees that the halting problem input can be construed as an incorrect question olcott <polcott2@gmail.com> - 2023-06-18 14:26 -0500
                Re: ChatGPT agrees that the halting problem input can be construed as an incorrect question Richard Damon <Richard@Damon-Family.org> - 2023-06-18 16:10 -0400
                Re: ChatGPT agrees that the halting problem input can be construed as an incorrect question olcott <polcott2@gmail.com> - 2023-06-18 18:43 -0500
                Re: ChatGPT agrees that the halting problem input can be construed as an incorrect question Richard Damon <Richard@Damon-Family.org> - 2023-06-18 19:59 -0400
                Re: ChatGPT agrees that the halting problem input can be construed as an incorrect question olcott <polcott2@gmail.com> - 2023-06-18 18:41 -0500
                Re: ChatGPT agrees that the halting problem input can be construed as an incorrect question Richard Damon <Richard@Damon-Family.org> - 2023-06-18 20:01 -0400
                Re: ChatGPT agrees that the halting problem input can be construed as an incorrect question olcott <polcott2@gmail.com> - 2023-06-18 19:59 -0500
                Re: ChatGPT agrees that the halting problem input can be construed as an incorrect question Richard Damon <Richard@Damon-Family.org> - 2023-06-18 21:29 -0400
                Re: ChatGPT agrees that the halting problem input can be construed as an incorrect question olcott <polcott2@gmail.com> - 2023-06-18 20:43 -0500
                Re: ChatGPT agrees that the halting problem input can be construed as an incorrect question Richard Damon <Richard@Damon-Family.org> - 2023-06-18 22:38 -0400
                Does input D have semantic property S or is input D [BAD INPUT]? olcott <polcott2@gmail.com> - 2023-06-18 22:31 -0500
                Re: Does input D have semantic property S or is input D [BAD INPUT]? Richard Damon <Richard@Damon-Family.org> - 2023-06-19 07:38 -0400
                Re: Does input D have semantic property S or is input D [BAD INPUT]? olcott <polcott2@gmail.com> - 2023-06-19 09:30 -0500
                Re: Does input D have semantic property S or is input D [BAD INPUT]? Richard Damon <Richard@Damon-Family.org> - 2023-06-19 20:45 -0400
                Re: Does input D have semantic property S or is input D [BAD INPUT]? olcott <polcott2@gmail.com> - 2023-06-19 22:57 -0500
                Re: Does input D have semantic property S or is input D [BAD INPUT]? Richard Damon <Richard@Damon-Family.org> - 2023-06-20 07:19 -0400
                Re: Does input D have semantic property S or is input D [BAD INPUT]? olcott <polcott2@gmail.com> - 2023-06-20 10:09 -0500
                Re: Does input D have semantic property S or is input D [BAD INPUT]? Richard Damon <Richard@Damon-Family.org> - 2023-06-20 11:48 -0400
                Termination Analyzer H determines the semantic property of .. olcott <polcott2@gmail.com> - 2023-06-18 23:58 -0500
                Re: Termination Analyzer H determines the semantic property of .. Richard Damon <Richard@Damon-Family.org> - 2023-06-19 07:38 -0400
                Re: ChatGPT agrees that the halting problem input can be construed as an incorrect question olcott <polcott2@gmail.com> - 2023-06-18 20:27 -0500
                Re: ChatGPT agrees that the halting problem input can be construed as an incorrect question Richard Damon <Richard@Damon-Family.org> - 2023-06-18 21:34 -0400
  Ben Bacarisse specifically targets my posts to discourage honest dialogue olcott <polcott2@gmail.com> - 2023-06-20 10:06 -0500
    Re: Ben Bacarisse specifically targets my posts to discourage honest dialogue Richard Damon <Richard@Damon-Family.org> - 2023-06-20 11:48 -0400
      Re: dishonest subject lines Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-20 17:02 +0100
        Ben Bacarisse specifically targets my posts to discourage honest dialogue olcott <polcott2@gmail.com> - 2023-06-20 12:25 -0500
  Refutation of the Ben Bacarisse Rebuttal [Ben targets my posts to discourage honest dialogue] olcott <polcott2@gmail.com> - 2023-06-20 14:57 -0500
    Re: Refutation of the Ben Bacarisse Rebuttal [Ben targets my posts to discourage honest dialogue] Richard Damon <Richard@Damon-Family.org> - 2023-06-20 16:34 -0400
      Re: Refutation of the Ben Bacarisse Rebuttal [Ben targets my posts to discourage honest dialogue] olcott <polcott2@gmail.com> - 2023-06-20 15:42 -0500
        Re: Refutation of the Ben Bacarisse Rebuttal [Ben targets my posts to discourage honest dialogue] Richard Damon <Richard@Damon-Family.org> - 2023-06-20 16:52 -0400
          Re: Refutation of the Ben Bacarisse Rebuttal [Ben targets my posts to discourage honest dialogue] olcott <polcott2@gmail.com> - 2023-06-20 16:39 -0500
            Re: Refutation of the Ben Bacarisse Rebuttal [Ben targets my posts to discourage honest dialogue] Richard Damon <Richard@Damon-Family.org> - 2023-06-20 17:53 -0400
              Re: Refutation of the Ben Bacarisse Rebuttal [Ben targets my posts to discourage honest dialogue] olcott <polcott2@gmail.com> - 2023-06-20 17:07 -0500
                Re: Refutation of the Ben Bacarisse Rebuttal [Ben targets my posts to discourage honest dialogue] Richard Damon <Richard@Damon-Family.org> - 2023-06-20 18:52 -0400
  Refutation of the Ben Bacarisse Rebuttal [Ben targets my posts] olcott <polcott2@gmail.com> - 2023-06-20 14:59 -0500
  Refutation of the Ben Bacarisse Rebuttal [Ben targets my posts] olcott <polcott2@gmail.com> - 2023-06-20 15:00 -0500
  ChatGPT and stack limits (was: Re: ChatGPT agrees that the halting problem input can be construed as an incorrect question vallor <vallor@cultnix.org> - 2023-06-21 19:10 +0000
    Re: ChatGPT and stack limits (was: Re: ChatGPT agrees that the halting problem input can be construed as an incorrect question vallor <vallor@vallor.earth> - 2023-06-21 19:23 +0000
    Re: ChatGPT and stack limits (was: Re: ChatGPT agrees that the halting problem input can be construed as an incorrect question olcott <polcott2@gmail.com> - 2023-06-21 14:59 -0500
      Re: ChatGPT and stack limits (was: Re: ChatGPT agrees that the halting problem input can be construed as an incorrect question Richard Damon <Richard@Damon-Family.org> - 2023-06-21 19:01 -0400
        Re: ChatGPT and stack limits (was: Re: ChatGPT agrees that the halting problem input can be construed as an incorrect question olcott <polcott2@gmail.com> - 2023-06-21 19:40 -0500
          Re: ChatGPT and stack limits (was: Re: ChatGPT agrees that the halting problem input can be construed as an incorrect question Richard Damon <Richard@Damon-Family.org> - 2023-06-21 22:47 -0400
            Re: ChatGPT and stack limits (was: Re: ChatGPT agrees that the halting problem input can be construed as an incorrect question olcott <polcott2@gmail.com> - 2023-06-21 21:58 -0500
              Re: ChatGPT and stack limits (was: Re: ChatGPT agrees that the halting problem input can be construed as an incorrect question Richard Damon <Richard@Damon-Family.org> - 2023-06-22 07:26 -0400
                Re: ChatGPT and stack limits (was: Re: ChatGPT agrees that the halting problem input can be construed as an incorrect question olcott <polcott2@gmail.com> - 2023-06-22 09:18 -0500
                Re: ChatGPT and stack limits (was: Re: ChatGPT agrees that the halting problem input can be construed as an incorrect question Richard Damon <Richard@Damon-Family.org> - 2023-06-22 21:06 -0400
  Re: ChatGPT agrees that the halting problem input can be construed as an incorrect question olcott <polcott2@gmail.com> - 2023-06-22 23:12 -0500

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