• Re: Very simple first principles showing the halting problem error

    From Mikko@mikko.levanto@iki.fi to comp.theory on Thu Dec 18 13:10:28 2025
    From Newsgroup: comp.theory

    On 18/12/2025 06:29, olcott wrote:
    On 12/17/2025 4:41 AM, Mikko wrote:
    On 15/12/2025 16:31, olcott wrote:
    On 12/15/2025 3:20 AM, Mikko wrote:
    On 15/12/2025 02:15, olcott wrote:
    On 12/14/2025 4:46 AM, Mikko wrote:
    On 11/12/2025 16:38, olcott wrote:
    On 12/11/2025 2:53 AM, Mikko wrote:
    olcott kirjoitti 10.12.2025 klo 18.27:

    DD() executed from main() calls HHH(DD) thus is
    not one-and-the-same-thing as an argument to HHH.

    If the last sentence is true then this is not the counter exmaple >>>>>>>> mentioned in certain proofs of noncomputability of halting and >>>>>>>> therefore not relevant in that context. The halting problem
    reuqires
    that HHH can determine whether the counter example halts. That is, >>>>>>>> you must be able to replace "???" in

       #include <stdio.h> // or your replacement
       int main (void)
       {
         int Halt_Status = HHH(???); // put the correct argument here >>>>>>>>      printf("HHH says: %s\n", Halt_Status ? "halts" : "does not >>>>>>>> halt");
         return Halt_Status;
       }

    with whatever specifies the behaviour of DD to HHH. If you can't >>>>>>>> do this then HHH is not a halt decider nor a partial halt decider. >>>>>>
    When the halting problem requires a halt decider
    to report on the behavior of a Turing machine this
    is always a category error.

    That you don't know what "category error" means does not justify your >>>>>> claim. Apparently you can't apply definitions.

    Turing machines only compute functions from finite
    strings they never compute functions from Turing
    machines.

    True, but irrelevant to questions about category errors.

    A halt decider can at best compute the behavior of
    a Turing machine through the proxy of a finite
    string machine description it never computes it
    directly from another Turing machine.

    Whenever any textbook says that a halt decider
    must compute halting for machine M on input w
    is it wrong.

    Which textbook actually says "must"? It is not wrong to say "must" in
    the sense that any decider that does not compute whether machine M
    halts on input w is not a halt decider. But using "must" is not the
    clearest way to say it because the word "must" other meanings.

    It actually computes halting that this input pair specifies (⟨M⟩, >>>> w).

    There is an unbalanced parenthesis above.

    No halt decider ever computes the halt status
    of a machine except through the proxy of finite
    strings.

    No halt decider computes anything because there are not halt deciders.

    I am trying to state the gist of this and not get so
    bogged down in tedious details that the gist cannot
    possibly ever be understood because we have too much
    detail for the capacity of the human mind.

    If you can't state the gist without causing more confusion than
    clarity you should try something else.

    You still havn't answered the question which textbook says "must".
    --
    Mikko
    --- Synchronet 3.21a-Linux NewsLink 1.2
  • From olcott@polcott333@gmail.com to comp.theory on Thu Dec 18 07:07:49 2025
    From Newsgroup: comp.theory

    On 12/18/2025 5:10 AM, Mikko wrote:
    On 18/12/2025 06:29, olcott wrote:
    On 12/17/2025 4:41 AM, Mikko wrote:
    On 15/12/2025 16:31, olcott wrote:
    On 12/15/2025 3:20 AM, Mikko wrote:
    On 15/12/2025 02:15, olcott wrote:
    On 12/14/2025 4:46 AM, Mikko wrote:
    On 11/12/2025 16:38, olcott wrote:
    On 12/11/2025 2:53 AM, Mikko wrote:
    olcott kirjoitti 10.12.2025 klo 18.27:

    DD() executed from main() calls HHH(DD) thus is
    not one-and-the-same-thing as an argument to HHH.

    If the last sentence is true then this is not the counter exmaple >>>>>>>>> mentioned in certain proofs of noncomputability of halting and >>>>>>>>> therefore not relevant in that context. The halting problem >>>>>>>>> reuqires
    that HHH can determine whether the counter example halts. That is, >>>>>>>>> you must be able to replace "???" in

       #include <stdio.h> // or your replacement
       int main (void)
       {
         int Halt_Status = HHH(???); // put the correct argument here >>>>>>>>>      printf("HHH says: %s\n", Halt_Status ? "halts" : "does not >>>>>>>>> halt");
         return Halt_Status;
       }

    with whatever specifies the behaviour of DD to HHH. If you can't >>>>>>>>> do this then HHH is not a halt decider nor a partial halt decider. >>>>>>>
    When the halting problem requires a halt decider
    to report on the behavior of a Turing machine this
    is always a category error.

    That you don't know what "category error" means does not justify >>>>>>> your
    claim. Apparently you can't apply definitions.

    Turing machines only compute functions from finite
    strings they never compute functions from Turing
    machines.

    True, but irrelevant to questions about category errors.

    A halt decider can at best compute the behavior of
    a Turing machine through the proxy of a finite
    string machine description it never computes it
    directly from another Turing machine.

    Whenever any textbook says that a halt decider
    must compute halting for machine M on input w
    is it wrong.

    Which textbook actually says "must"? It is not wrong to say "must" in >>>>> the sense that any decider that does not compute whether machine M
    halts on input w is not a halt decider. But using "must" is not the
    clearest way to say it because the word "must" other meanings.

    It actually computes halting that this input pair specifies
    (⟨M⟩, w).

    There is an unbalanced parenthesis above.

    No halt decider ever computes the halt status
    of a machine except through the proxy of finite
    strings.

    No halt decider computes anything because there are not halt deciders.

    I am trying to state the gist of this and not get so
    bogged down in tedious details that the gist cannot
    possibly ever be understood because we have too much
    detail for the capacity of the human mind.

    If you can't state the gist without causing more confusion than
    clarity you should try something else.



    When people demand too many irrelevant details
    I must so no.

    You still havn't answered the question which textbook says "must".

    --
    Copyright 2025 Olcott<br><br>

    My 28 year goal has been to make <br>
    "true on the basis of meaning expressed in language"<br>
    reliably computable.<br><br>

    This required establishing a new foundation<br>
    --- Synchronet 3.21a-Linux NewsLink 1.2
  • From Mikko@mikko.levanto@iki.fi to comp.theory on Fri Dec 19 12:09:28 2025
    From Newsgroup: comp.theory

    On 18/12/2025 15:07, olcott wrote:
    On 12/18/2025 5:10 AM, Mikko wrote:
    On 18/12/2025 06:29, olcott wrote:
    On 12/17/2025 4:41 AM, Mikko wrote:
    On 15/12/2025 16:31, olcott wrote:
    On 12/15/2025 3:20 AM, Mikko wrote:
    On 15/12/2025 02:15, olcott wrote:
    On 12/14/2025 4:46 AM, Mikko wrote:
    On 11/12/2025 16:38, olcott wrote:
    On 12/11/2025 2:53 AM, Mikko wrote:
    olcott kirjoitti 10.12.2025 klo 18.27:

    DD() executed from main() calls HHH(DD) thus is
    not one-and-the-same-thing as an argument to HHH.

    If the last sentence is true then this is not the counter exmaple >>>>>>>>>> mentioned in certain proofs of noncomputability of halting and >>>>>>>>>> therefore not relevant in that context. The halting problem >>>>>>>>>> reuqires
    that HHH can determine whether the counter example halts. That >>>>>>>>>> is,
    you must be able to replace "???" in

       #include <stdio.h> // or your replacement
       int main (void)
       {
         int Halt_Status = HHH(???); // put the correct argument here
         printf("HHH says: %s\n", Halt_Status ? "halts" : "does >>>>>>>>>> not halt");
         return Halt_Status;
       }

    with whatever specifies the behaviour of DD to HHH. If you can't >>>>>>>>>> do this then HHH is not a halt decider nor a partial halt >>>>>>>>>> decider.

    When the halting problem requires a halt decider
    to report on the behavior of a Turing machine this
    is always a category error.

    That you don't know what "category error" means does not justify >>>>>>>> your
    claim. Apparently you can't apply definitions.

    Turing machines only compute functions from finite
    strings they never compute functions from Turing
    machines.

    True, but irrelevant to questions about category errors.

    A halt decider can at best compute the behavior of
    a Turing machine through the proxy of a finite
    string machine description it never computes it
    directly from another Turing machine.

    Whenever any textbook says that a halt decider
    must compute halting for machine M on input w
    is it wrong.

    Which textbook actually says "must"? It is not wrong to say "must" in >>>>>> the sense that any decider that does not compute whether machine M >>>>>> halts on input w is not a halt decider. But using "must" is not the >>>>>> clearest way to say it because the word "must" other meanings.

    It actually computes halting that this input pair specifies
    (⟨M⟩, w).

    There is an unbalanced parenthesis above.

    No halt decider ever computes the halt status
    of a machine except through the proxy of finite
    strings.

    No halt decider computes anything because there are not halt deciders.

    I am trying to state the gist of this and not get so
    bogged down in tedious details that the gist cannot
    possibly ever be understood because we have too much
    detail for the capacity of the human mind.

    If you can't state the gist without causing more confusion than
    clarity you should try something else.

    When people demand too many irrelevant details
    I must so no.

    You should put the whole story to GitHub. Then you can add any detail
    aomeone asks. If the same quiestion is asked again you only need to
    give a pointer as the answer.

    You still havn't answered the question which textbook says "must".
    --
    Mikko
    --- Synchronet 3.21a-Linux NewsLink 1.2
  • From olcott@polcott333@gmail.com to comp.theory,sci.logic,sci.math on Fri Dec 19 08:52:47 2025
    From Newsgroup: comp.theory

    On 12/19/2025 4:09 AM, Mikko wrote:
    On 18/12/2025 15:07, olcott wrote:
    On 12/18/2025 5:10 AM, Mikko wrote:
    On 18/12/2025 06:29, olcott wrote:
    On 12/17/2025 4:41 AM, Mikko wrote:
    On 15/12/2025 16:31, olcott wrote:
    On 12/15/2025 3:20 AM, Mikko wrote:
    On 15/12/2025 02:15, olcott wrote:
    On 12/14/2025 4:46 AM, Mikko wrote:
    On 11/12/2025 16:38, olcott wrote:
    On 12/11/2025 2:53 AM, Mikko wrote:
    olcott kirjoitti 10.12.2025 klo 18.27:

    DD() executed from main() calls HHH(DD) thus is
    not one-and-the-same-thing as an argument to HHH.

    If the last sentence is true then this is not the counter >>>>>>>>>>> exmaple
    mentioned in certain proofs of noncomputability of halting and >>>>>>>>>>> therefore not relevant in that context. The halting problem >>>>>>>>>>> reuqires
    that HHH can determine whether the counter example halts. >>>>>>>>>>> That is,
    you must be able to replace "???" in

       #include <stdio.h> // or your replacement
       int main (void)
       {
         int Halt_Status = HHH(???); // put the correct argument >>>>>>>>>>> here
         printf("HHH says: %s\n", Halt_Status ? "halts" : "does >>>>>>>>>>> not halt");
         return Halt_Status;
       }

    with whatever specifies the behaviour of DD to HHH. If you can't >>>>>>>>>>> do this then HHH is not a halt decider nor a partial halt >>>>>>>>>>> decider.

    When the halting problem requires a halt decider
    to report on the behavior of a Turing machine this
    is always a category error.

    That you don't know what "category error" means does not
    justify your
    claim. Apparently you can't apply definitions.

    Turing machines only compute functions from finite
    strings they never compute functions from Turing
    machines.

    True, but irrelevant to questions about category errors.

    A halt decider can at best compute the behavior of
    a Turing machine through the proxy of a finite
    string machine description it never computes it
    directly from another Turing machine.

    Whenever any textbook says that a halt decider
    must compute halting for machine M on input w
    is it wrong.

    Which textbook actually says "must"? It is not wrong to say
    "must" in
    the sense that any decider that does not compute whether machine M >>>>>>> halts on input w is not a halt decider. But using "must" is not the >>>>>>> clearest way to say it because the word "must" other meanings.

    It actually computes halting that this input pair specifies >>>>>>> (⟨M⟩, w).

    There is an unbalanced parenthesis above.

    No halt decider ever computes the halt status
    of a machine except through the proxy of finite
    strings.

    No halt decider computes anything because there are not halt deciders. >>>>
    I am trying to state the gist of this and not get so
    bogged down in tedious details that the gist cannot
    possibly ever be understood because we have too much
    detail for the capacity of the human mind.

    If you can't state the gist without causing more confusion than
    clarity you should try something else.

    When people demand too many irrelevant details
    I must so no.

    You should put the whole story to GitHub. Then you can add any detail
    aomeone asks. If the same quiestion is asked again you only need to
    give a pointer as the answer.


    I am making one single point. A bunch of irrelevant
    questions distract away from this one point.

    I have gone over these things thousands of times
    and what seem obvious to me cannot possibly be
    understood by anyone besides LLM systems.

    These are the correct first principles of all
    computation.

    Computations: Transform finite strings by finite
    string transformation rules into values or non-termination.

    Deciders: Transform finite strings by finite string
    transformation rules into {Accept, Reject}.

    You still havn't answered the question which textbook says "must".
    --
    Copyright 2025 Olcott<br><br>

    My 28 year goal has been to make <br>
    "true on the basis of meaning expressed in language"<br>
    reliably computable.<br><br>

    This required establishing a new foundation<br>
    --- Synchronet 3.21a-Linux NewsLink 1.2
  • From Mikko@mikko.levanto@iki.fi to comp.theory,sci.logic,sci.math on Sat Dec 20 12:22:00 2025
    From Newsgroup: comp.theory

    On 19/12/2025 16:52, olcott wrote:
    On 12/19/2025 4:09 AM, Mikko wrote:
    On 18/12/2025 15:07, olcott wrote:
    On 12/18/2025 5:10 AM, Mikko wrote:
    On 18/12/2025 06:29, olcott wrote:
    On 12/17/2025 4:41 AM, Mikko wrote:
    On 15/12/2025 16:31, olcott wrote:
    On 12/15/2025 3:20 AM, Mikko wrote:
    On 15/12/2025 02:15, olcott wrote:
    On 12/14/2025 4:46 AM, Mikko wrote:
    On 11/12/2025 16:38, olcott wrote:
    On 12/11/2025 2:53 AM, Mikko wrote:
    olcott kirjoitti 10.12.2025 klo 18.27:

    DD() executed from main() calls HHH(DD) thus is
    not one-and-the-same-thing as an argument to HHH.

    If the last sentence is true then this is not the counter >>>>>>>>>>>> exmaple
    mentioned in certain proofs of noncomputability of halting and >>>>>>>>>>>> therefore not relevant in that context. The halting problem >>>>>>>>>>>> reuqires
    that HHH can determine whether the counter example halts. >>>>>>>>>>>> That is,
    you must be able to replace "???" in

       #include <stdio.h> // or your replacement
       int main (void)
       {
         int Halt_Status = HHH(???); // put the correct argument >>>>>>>>>>>> here
         printf("HHH says: %s\n", Halt_Status ? "halts" : "does >>>>>>>>>>>> not halt");
         return Halt_Status;
       }

    with whatever specifies the behaviour of DD to HHH. If you >>>>>>>>>>>> can't
    do this then HHH is not a halt decider nor a partial halt >>>>>>>>>>>> decider.

    When the halting problem requires a halt decider
    to report on the behavior of a Turing machine this
    is always a category error.

    That you don't know what "category error" means does not
    justify your
    claim. Apparently you can't apply definitions.

    Turing machines only compute functions from finite
    strings they never compute functions from Turing
    machines.

    True, but irrelevant to questions about category errors.

    A halt decider can at best compute the behavior of
    a Turing machine through the proxy of a finite
    string machine description it never computes it
    directly from another Turing machine.

    Whenever any textbook says that a halt decider
    must compute halting for machine M on input w
    is it wrong.

    Which textbook actually says "must"? It is not wrong to say
    "must" in
    the sense that any decider that does not compute whether machine M >>>>>>>> halts on input w is not a halt decider. But using "must" is not the >>>>>>>> clearest way to say it because the word "must" other meanings. >>>>>>>>
    It actually computes halting that this input pair specifies >>>>>>>> (⟨M⟩, w).

    There is an unbalanced parenthesis above.

    No halt decider ever computes the halt status
    of a machine except through the proxy of finite
    strings.

    No halt decider computes anything because there are not halt
    deciders.

    I am trying to state the gist of this and not get so
    bogged down in tedious details that the gist cannot
    possibly ever be understood because we have too much
    detail for the capacity of the human mind.

    If you can't state the gist without causing more confusion than
    clarity you should try something else.

    When people demand too many irrelevant details
    I must so no.

    You should put the whole story to GitHub. Then you can add any detail
    aomeone asks. If the same quiestion is asked again you only need to
    give a pointer as the answer.


    I am making one single point.

    WHich one?

    A bunch of irrelevant
    questions distract away from this one point.

    A sufficient answer to an irelevant question is "doesn't matter".
    If a quetion is irrelevant it is sufficient to say "doesn't matter".

    I have gone over these things thousands of times
    and what seem obvious to me cannot possibly be
    understood by anyone besides LLM systems.

    These are the correct first principles of all
    computation.

    Computations: Transform finite strings by finite
    string transformation rules into values or non-termination.

    Deciders: Transform finite strings by finite string
    transformation rules into {Accept, Reject}.

    The terms "computation" and "decider" are not parallel. The suffix
    of "decider" means that it is an agent. The word "computation" has
    a diferent suffix bedause it is an action. A decider performs a
    computation but it isn't one. But you can say that a decider is a
    computer although more ofthen the term "automaton" is used.

    One should also note that definitions are not principles.
    --
    Mikko
    --- Synchronet 3.21a-Linux NewsLink 1.2
  • From olcott@polcott333@gmail.com to comp.theory,sci.logic,sci.math on Sat Dec 20 05:54:51 2025
    From Newsgroup: comp.theory

    On 12/20/2025 4:22 AM, Mikko wrote:
    On 19/12/2025 16:52, olcott wrote:
    On 12/19/2025 4:09 AM, Mikko wrote:
    On 18/12/2025 15:07, olcott wrote:
    On 12/18/2025 5:10 AM, Mikko wrote:
    On 18/12/2025 06:29, olcott wrote:
    On 12/17/2025 4:41 AM, Mikko wrote:
    On 15/12/2025 16:31, olcott wrote:
    On 12/15/2025 3:20 AM, Mikko wrote:
    On 15/12/2025 02:15, olcott wrote:
    On 12/14/2025 4:46 AM, Mikko wrote:
    On 11/12/2025 16:38, olcott wrote:
    On 12/11/2025 2:53 AM, Mikko wrote:
    olcott kirjoitti 10.12.2025 klo 18.27:

    DD() executed from main() calls HHH(DD) thus is
    not one-and-the-same-thing as an argument to HHH.

    If the last sentence is true then this is not the counter >>>>>>>>>>>>> exmaple
    mentioned in certain proofs of noncomputability of halting and >>>>>>>>>>>>> therefore not relevant in that context. The halting problem >>>>>>>>>>>>> reuqires
    that HHH can determine whether the counter example halts. >>>>>>>>>>>>> That is,
    you must be able to replace "???" in

       #include <stdio.h> // or your replacement
       int main (void)
       {
         int Halt_Status = HHH(???); // put the correct >>>>>>>>>>>>> argument here
         printf("HHH says: %s\n", Halt_Status ? "halts" : "does >>>>>>>>>>>>> not halt");
         return Halt_Status;
       }

    with whatever specifies the behaviour of DD to HHH. If you >>>>>>>>>>>>> can't
    do this then HHH is not a halt decider nor a partial halt >>>>>>>>>>>>> decider.

    When the halting problem requires a halt decider
    to report on the behavior of a Turing machine this
    is always a category error.

    That you don't know what "category error" means does not >>>>>>>>>>> justify your
    claim. Apparently you can't apply definitions.

    Turing machines only compute functions from finite
    strings they never compute functions from Turing
    machines.

    True, but irrelevant to questions about category errors.

    A halt decider can at best compute the behavior of
    a Turing machine through the proxy of a finite
    string machine description it never computes it
    directly from another Turing machine.

    Whenever any textbook says that a halt decider
    must compute halting for machine M on input w
    is it wrong.

    Which textbook actually says "must"? It is not wrong to say >>>>>>>>> "must" in
    the sense that any decider that does not compute whether machine M >>>>>>>>> halts on input w is not a halt decider. But using "must" is not >>>>>>>>> the
    clearest way to say it because the word "must" other meanings. >>>>>>>>>
    It actually computes halting that this input pair specifies >>>>>>>>> (⟨M⟩, w).

    There is an unbalanced parenthesis above.

    No halt decider ever computes the halt status
    of a machine except through the proxy of finite
    strings.

    No halt decider computes anything because there are not halt
    deciders.

    I am trying to state the gist of this and not get so
    bogged down in tedious details that the gist cannot
    possibly ever be understood because we have too much
    detail for the capacity of the human mind.

    If you can't state the gist without causing more confusion than
    clarity you should try something else.

    When people demand too many irrelevant details
    I must so no.

    You should put the whole story to GitHub. Then you can add any detail
    aomeone asks. If the same quiestion is asked again you only need to
    give a pointer as the answer.


    I am making one single point.

    WHich one?

    A bunch of irrelevant
    questions distract away from this one point.

    A sufficient answer to an irelevant question is "doesn't matter".
    If a quetion is irrelevant it is sufficient to say "doesn't matter".

    I have gone over these things thousands of times
    and what seem obvious to me cannot possibly be
    understood by anyone besides LLM systems.

    These are the correct first principles of all
    computation.

    Computations: Transform finite strings by finite
    string transformation rules into values or non-termination.

    Deciders: Transform finite strings by finite string
    transformation rules into {Accept, Reject}.

    The terms "computation" and "decider" are not parallel. The suffix

    One is a subset of the other.

    of "decider" means that it is an agent. The word "computation" has
    a diferent suffix bedause it is an action. A decider performs a
    computation but it isn't one. But you can say that a decider is a
    computer although more ofthen the term "automaton" is used.

    One should also note that definitions are not principles.


    A definition of computation does specify the principles
    of computation.
    --
    Copyright 2025 Olcott<br><br>

    My 28 year goal has been to make <br>
    "true on the basis of meaning expressed in language"<br>
    reliably computable.<br><br>

    This required establishing a new foundation<br>
    --- Synchronet 3.21a-Linux NewsLink 1.2
  • From Mikko@mikko.levanto@iki.fi to comp.theory,sci.logic,sci.math on Sun Dec 21 13:11:05 2025
    From Newsgroup: comp.theory

    On 20/12/2025 13:54, olcott wrote:
    On 12/20/2025 4:22 AM, Mikko wrote:
    On 19/12/2025 16:52, olcott wrote:
    On 12/19/2025 4:09 AM, Mikko wrote:
    On 18/12/2025 15:07, olcott wrote:
    On 12/18/2025 5:10 AM, Mikko wrote:
    On 18/12/2025 06:29, olcott wrote:
    On 12/17/2025 4:41 AM, Mikko wrote:
    On 15/12/2025 16:31, olcott wrote:
    On 12/15/2025 3:20 AM, Mikko wrote:
    On 15/12/2025 02:15, olcott wrote:
    On 12/14/2025 4:46 AM, Mikko wrote:
    On 11/12/2025 16:38, olcott wrote:
    On 12/11/2025 2:53 AM, Mikko wrote:
    olcott kirjoitti 10.12.2025 klo 18.27:

    DD() executed from main() calls HHH(DD) thus is
    not one-and-the-same-thing as an argument to HHH. >>>>>>>>>>>>>>
    If the last sentence is true then this is not the counter >>>>>>>>>>>>>> exmaple
    mentioned in certain proofs of noncomputability of halting >>>>>>>>>>>>>> and
    therefore not relevant in that context. The halting >>>>>>>>>>>>>> problem reuqires
    that HHH can determine whether the counter example halts. >>>>>>>>>>>>>> That is,
    you must be able to replace "???" in

       #include <stdio.h> // or your replacement
       int main (void)
       {
         int Halt_Status = HHH(???); // put the correct >>>>>>>>>>>>>> argument here
         printf("HHH says: %s\n", Halt_Status ? "halts" : >>>>>>>>>>>>>> "does not halt");
         return Halt_Status;
       }

    with whatever specifies the behaviour of DD to HHH. If you >>>>>>>>>>>>>> can't
    do this then HHH is not a halt decider nor a partial halt >>>>>>>>>>>>>> decider.

    When the halting problem requires a halt decider
    to report on the behavior of a Turing machine this
    is always a category error.

    That you don't know what "category error" means does not >>>>>>>>>>>> justify your
    claim. Apparently you can't apply definitions.

    Turing machines only compute functions from finite
    strings they never compute functions from Turing
    machines.

    True, but irrelevant to questions about category errors.

    A halt decider can at best compute the behavior of
    a Turing machine through the proxy of a finite
    string machine description it never computes it
    directly from another Turing machine.

    Whenever any textbook says that a halt decider
    must compute halting for machine M on input w
    is it wrong.

    Which textbook actually says "must"? It is not wrong to say >>>>>>>>>> "must" in
    the sense that any decider that does not compute whether
    machine M
    halts on input w is not a halt decider. But using "must" is >>>>>>>>>> not the
    clearest way to say it because the word "must" other meanings. >>>>>>>>>>
    It actually computes halting that this input pair specifies >>>>>>>>>> (⟨M⟩, w).

    There is an unbalanced parenthesis above.

    No halt decider ever computes the halt status
    of a machine except through the proxy of finite
    strings.

    No halt decider computes anything because there are not halt
    deciders.

    I am trying to state the gist of this and not get so
    bogged down in tedious details that the gist cannot
    possibly ever be understood because we have too much
    detail for the capacity of the human mind.

    If you can't state the gist without causing more confusion than
    clarity you should try something else.

    When people demand too many irrelevant details
    I must so no.

    You should put the whole story to GitHub. Then you can add any detail
    aomeone asks. If the same quiestion is asked again you only need to
    give a pointer as the answer.


    I am making one single point.

    WHich one?

    A bunch of irrelevant
    questions distract away from this one point.

    A sufficient answer to an irelevant question is "doesn't matter".
    If a quetion is irrelevant it is sufficient to say "doesn't matter".

    I have gone over these things thousands of times
    and what seem obvious to me cannot possibly be
    understood by anyone besides LLM systems.

    These are the correct first principles of all
    computation.

    Computations: Transform finite strings by finite
    string transformation rules into values or non-termination.

    Deciders: Transform finite strings by finite string
    transformation rules into {Accept, Reject}.

    The terms "computation" and "decider" are not parallel. The suffix

    One is a subset of the other.

    No, they are not. Being a subset means they share common elements. But,
    as pointed out below, a decider is an agent and a computation is a non-
    agent. Therefore one being a subset of another requires either tant one
    of the sets is empty or that there are agents that are non-agents.

    of "decider" means that it is an agent. The word "computation" has
    a diferent suffix bedause it is an action. A decider performs a
    computation but it isn't one. But you can say that a decider is a
    computer although more ofthen the term "automaton" is used.

    Note that no counter argument is presented.

    One should also note that definitions are not principles.

    A definition of computation does specify the principles
    of computation.

    A definition may refer to a principle but a definition is not a
    principle.
    --
    Mikko
    --- Synchronet 3.21a-Linux NewsLink 1.2
  • From olcott@polcott333@gmail.com to sci.logic,comp.theory on Sun Dec 21 08:12:14 2025
    From Newsgroup: comp.theory

    On 12/21/2025 5:11 AM, Mikko wrote:
    On 20/12/2025 13:54, olcott wrote:
    On 12/20/2025 4:22 AM, Mikko wrote:
    On 19/12/2025 16:52, olcott wrote:
    On 12/19/2025 4:09 AM, Mikko wrote:
    On 18/12/2025 15:07, olcott wrote:
    On 12/18/2025 5:10 AM, Mikko wrote:
    On 18/12/2025 06:29, olcott wrote:
    On 12/17/2025 4:41 AM, Mikko wrote:
    On 15/12/2025 16:31, olcott wrote:
    On 12/15/2025 3:20 AM, Mikko wrote:
    On 15/12/2025 02:15, olcott wrote:
    On 12/14/2025 4:46 AM, Mikko wrote:
    On 11/12/2025 16:38, olcott wrote:
    On 12/11/2025 2:53 AM, Mikko wrote:
    olcott kirjoitti 10.12.2025 klo 18.27:

    DD() executed from main() calls HHH(DD) thus is >>>>>>>>>>>>>>>> not one-and-the-same-thing as an argument to HHH. >>>>>>>>>>>>>>>
    If the last sentence is true then this is not the counter >>>>>>>>>>>>>>> exmaple
    mentioned in certain proofs of noncomputability of >>>>>>>>>>>>>>> halting and
    therefore not relevant in that context. The halting >>>>>>>>>>>>>>> problem reuqires
    that HHH can determine whether the counter example halts. >>>>>>>>>>>>>>> That is,
    you must be able to replace "???" in

       #include <stdio.h> // or your replacement
       int main (void)
       {
         int Halt_Status = HHH(???); // put the correct >>>>>>>>>>>>>>> argument here
         printf("HHH says: %s\n", Halt_Status ? "halts" : >>>>>>>>>>>>>>> "does not halt");
         return Halt_Status;
       }

    with whatever specifies the behaviour of DD to HHH. If >>>>>>>>>>>>>>> you can't
    do this then HHH is not a halt decider nor a partial halt >>>>>>>>>>>>>>> decider.

    When the halting problem requires a halt decider
    to report on the behavior of a Turing machine this >>>>>>>>>>>>>> is always a category error.

    That you don't know what "category error" means does not >>>>>>>>>>>>> justify your
    claim. Apparently you can't apply definitions.

    Turing machines only compute functions from finite
    strings they never compute functions from Turing
    machines.

    True, but irrelevant to questions about category errors. >>>>>>>>>>>
    A halt decider can at best compute the behavior of
    a Turing machine through the proxy of a finite
    string machine description it never computes it
    directly from another Turing machine.

    Whenever any textbook says that a halt decider
    must compute halting for machine M on input w
    is it wrong.

    Which textbook actually says "must"? It is not wrong to say >>>>>>>>>>> "must" in
    the sense that any decider that does not compute whether >>>>>>>>>>> machine M
    halts on input w is not a halt decider. But using "must" is >>>>>>>>>>> not the
    clearest way to say it because the word "must" other meanings. >>>>>>>>>>>
    It actually computes halting that this input pair
    specifies (⟨M⟩, w).

    There is an unbalanced parenthesis above.

    No halt decider ever computes the halt status
    of a machine except through the proxy of finite
    strings.

    No halt decider computes anything because there are not halt >>>>>>>>> deciders.

    I am trying to state the gist of this and not get so
    bogged down in tedious details that the gist cannot
    possibly ever be understood because we have too much
    detail for the capacity of the human mind.

    If you can't state the gist without causing more confusion than
    clarity you should try something else.

    When people demand too many irrelevant details
    I must so no.

    You should put the whole story to GitHub. Then you can add any detail >>>>> aomeone asks. If the same quiestion is asked again you only need to
    give a pointer as the answer.


    I am making one single point.

    WHich one?

    A bunch of irrelevant
    questions distract away from this one point.

    A sufficient answer to an irelevant question is "doesn't matter".
    If a quetion is irrelevant it is sufficient to say "doesn't matter".

    I have gone over these things thousands of times
    and what seem obvious to me cannot possibly be
    understood by anyone besides LLM systems.

    These are the correct first principles of all
    computation.

    Computations: Transform finite strings by finite
    string transformation rules into values or non-termination.

    Deciders: Transform finite strings by finite string
    transformation rules into {Accept, Reject}.

    The terms "computation" and "decider" are not parallel. The suffix

    One is a subset of the other.

    No, they are not. Being a subset means they share common elements. But,
    as pointed out below, a decider is an agent and a computation is a non- agent. Therefore one being a subset of another requires either tant one
    of  the sets is empty or that there are agents that are non-agents.

    of "decider" means that it is an agent. The word "computation" has
    a diferent suffix bedause it is an action. A decider performs a
    computation but it isn't one. But you can say that a decider is a
    computer although more ofthen the term "automaton" is used.

    Note that no counter argument is presented.

    One should also note that definitions are not principles.

    A definition of computation does specify the principles
    of computation.

    A definition may refer to a principle but a definition is not a
    principle.


    Computations: Transform finite string inputs by finite
    string transformation rules into values or nontermination.

    Deciders: Transform finite string inputs by finite
    string transformation rules into {Accept, Reject}.

    Deciders are the subset of computations that always halt

    both Deciders and Computations Transform finite string
    inputs by finite string transformation rules into values.

    With deciders the value is one of Accept or Reject
    --
    Copyright 2025 Olcott<br><br>

    My 28 year goal has been to make <br>
    "true on the basis of meaning expressed in language"<br>
    reliably computable.<br><br>

    This required establishing a new foundation<br>
    --- Synchronet 3.21a-Linux NewsLink 1.2