• The fundamental nature of computational undecidability

    From olcott@polcott333@gmail.com to comp.theory,sci.math,sci.logic,comp.ai.philosophy on Sat Dec 20 20:33:18 2025
    From Newsgroup: comp.ai.philosophy

    On 12/20/2025 8:16 PM, Tristan Wibberley wrote:
    On 20/12/2025 23:14, Richard Damon wrote:
    On 12/20/25 6:09 PM, Tristan Wibberley wrote:
    On 20/12/2025 13:32, Richard Damon wrote:
    On 12/20/25 8:01 AM, Tristan Wibberley wrote:
    On 19/12/2025 23:01, olcott wrote:
    Deciders: Transform finite strings by finite string
    transformation rules into {Accept, Reject}.

    I continue to Reject your asymmetric and functionally-loaded labels for >>>>> the classes.



    That is just one of the few accurate quotations Olcott makes.

    In ONE of the version of defining Deciders, they are determinators of
    sentences matching a defined language, and they are to ACCEPT strings
    that match that grammar, and REJECT statements that fail to meet the
    grammar.

    It's only valid in an elementary corpus of principle where the
    correspondence is drawn such that the terms ACCEPT and REJECT are
    characterised as references into that model and not just ordinary
    English words. The capitalisation is not really enough; double-quotes
    might barely do the trick but without the computational-linguistics
    context it's really just politics. The politics is of nudging the
    population of poorly educated readers into accepting or rejecting actual >>> programs instead of merely characterising them, whether Olcott is doing
    the politics or is being nudged by search results into effecting another >>> group's politics.

    The only clues that the context is CompLang/AI within Olcott's
    statements of principles themselves is the use of the word "string"
    which is highly ambiguous in the context of computation such that any
    formal meaning in logistic philosophy is almost diluted away.


    The use of the term "Halt Decider" and "Turing Machine" focus the
    context fairly well. Add in his rambling about the Halting Problem, and
    it seems clear.

    Of course, it does also show is limited understanding, as deciders only
    answering Accept or Reject is a somewhat limited space in that field,
    but was the initial field which used the term.

    Do you mean to say that Computation Theory first used "decider" and used
    it to describe a machine that decides whether to accept a formula as a specimen of the set of formulas described by a given grammar or whether
    to reject it as specimen of the set?


    Do you also mean to say that "decider" is elementary without reference
    to grammars and specimens of their matches? Don't you agree that it is ambiguous as an term in an elementary principle due to the ordinary
    meaning of "decider" being to classify a specimen one of two classes (a specimen being as general as even "the current state of the world" and
    the classes being as correspondingly general as its suitability to
    respond with one plan or another)?

    I am concerned that the semantic ambiguity is particularly awkward
    because the untrained reader will take "decider" in the ordinary sense
    and take the principle already stated as a philosophical perspective on
    its nature; the reader will not backtrack to the correct reading soon
    enough to prevent misunderstanding. They will not settle on the intended reading which is instead to /define/ the term-of-art "decider" vis-a-vis
    the grammar-matching sense. That will cause the population of readers to adopt acceptance and rejection as classes for the first sense when such specificity is not /correct/ for that sense.



    It seems to me that in the broadest computational sense
    that a decider is intended to address decision problems.

    In computability theory and computational complexity
    theory, a decision problem is a computational problem
    that can be posed as a yes–no question on a set of input
    values.

    https://en.wikipedia.org/wiki/Decision_problem

    Yet can only do so by
    Transforming finite string inputs by finite
    string transformation rules into Boolean Values.

    In the broadest sense my 28 years of primary
    research has focused on undecidability.
    --
    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 Richard Damon@Richard@Damon-Family.org to comp.theory,sci.math,sci.logic,comp.ai.philosophy on Sat Dec 20 21:57:22 2025
    From Newsgroup: comp.ai.philosophy

    On 12/20/25 9:33 PM, olcott wrote:
    On 12/20/2025 8:16 PM, Tristan Wibberley wrote:
    On 20/12/2025 23:14, Richard Damon wrote:
    On 12/20/25 6:09 PM, Tristan Wibberley wrote:
    On 20/12/2025 13:32, Richard Damon wrote:
    On 12/20/25 8:01 AM, Tristan Wibberley wrote:
    On 19/12/2025 23:01, olcott wrote:
    Deciders: Transform finite strings by finite string
    transformation rules into {Accept, Reject}.

    I continue to Reject your asymmetric and functionally-loaded
    labels for
    the classes.



    That is just one of the few accurate quotations Olcott makes.

    In ONE of the version of defining Deciders, they are determinators of >>>>> sentences matching a defined language, and they are to ACCEPT strings >>>>> that match that grammar, and REJECT statements that fail to meet the >>>>> grammar.

    It's only valid in an elementary corpus of principle where the
    correspondence is drawn such that the terms ACCEPT and REJECT are
    characterised as references into that model and not just ordinary
    English words. The capitalisation is not really enough; double-quotes
    might barely do the trick but without the computational-linguistics
    context it's really just politics. The politics is of nudging the
    population of poorly educated readers into accepting or rejecting
    actual
    programs instead of merely characterising them, whether Olcott is doing >>>> the politics or is being nudged by search results into effecting
    another
    group's politics.

    The only clues that the context is CompLang/AI within Olcott's
    statements of principles themselves is the use of the word "string"
    which is highly ambiguous in the context of computation such that any
    formal meaning in logistic philosophy is almost diluted away.


    The use of the term "Halt Decider" and "Turing Machine" focus the
    context fairly well. Add in his rambling about the Halting Problem, and
    it seems clear.

    Of course, it does also show is limited understanding, as deciders only
    answering Accept or Reject is a somewhat limited space in that field,
    but was the initial field which used the term.

    Do you mean to say that Computation Theory first used "decider" and used
    it to describe a machine that decides whether to accept a formula as a
    specimen of the set of formulas described by a given grammar or whether
    to reject it as specimen of the set?


    Do you also mean to say that "decider" is elementary without reference
    to grammars and specimens of their matches? Don't you agree that it is
    ambiguous as an term in an elementary principle due to the ordinary
    meaning of "decider" being to classify a specimen one of two classes (a
    specimen being as general as even "the current state of the world" and
    the classes being as correspondingly general as its suitability to
    respond with one plan or another)?

    I am concerned that the semantic ambiguity is particularly awkward
    because the untrained reader will take "decider" in the ordinary sense
    and take the principle already stated as a philosophical perspective on
    its nature; the reader will not backtrack to the correct reading soon
    enough to prevent misunderstanding. They will not settle on the intended
    reading which is instead to /define/ the term-of-art "decider" vis-a-vis
    the grammar-matching sense. That will cause the population of readers to
    adopt acceptance and rejection as classes for the first sense when such
    specificity is not /correct/ for that sense.



    It seems to me that in the broadest computational sense
    that a decider is intended to address decision problems.

    That is one sub-space you can work in.

    The term has also be overloaded as a term-of-art to more general cases,
    where the results can be part of a countable-infinite class.


    In computability theory and computational complexity
    theory, a decision problem is a computational problem
    that can be posed as a yes–no question on a set of input
    values.

    https://en.wikipedia.org/wiki/Decision_problem

    Yes, that is for DECISION problems, but deciders can be used for more
    than decision problems in the more general parts of the theory.


    Yet can only do so by
    Transforming finite string inputs by finite
    string transformation rules into Boolean Values.

    Right, and that transformation needs to match the Function they are
    trying to compute, which might be uncomputable


    In the broadest sense my 28 years of primary
    research has focused on undecidability.

    Which in a broader sense isn't just on decision problems. But, if you
    want to restrict yourself to just "Decison Problems" that is ok.

    Yes, the Halting Problem IS a decision problem, and thus has only a
    binary result.

    A result that can't always be achieved by a finite deterministic
    algrotihm in finite steps, and thus the problem is uncomputable.

    Which doesn't make it invalid, just impossible to make a full Halt
    Decider that always gives the right answer.


    --- Synchronet 3.21a-Linux NewsLink 1.2
  • From olcott@polcott333@gmail.com to comp.theory,sci.math,sci.logic,comp.ai.philosophy on Sun Dec 21 08:57:24 2025
    From Newsgroup: comp.ai.philosophy

    On 12/20/2025 8:57 PM, Richard Damon wrote:
    On 12/20/25 9:33 PM, olcott wrote:
    On 12/20/2025 8:16 PM, Tristan Wibberley wrote:
    On 20/12/2025 23:14, Richard Damon wrote:
    On 12/20/25 6:09 PM, Tristan Wibberley wrote:
    On 20/12/2025 13:32, Richard Damon wrote:
    On 12/20/25 8:01 AM, Tristan Wibberley wrote:
    On 19/12/2025 23:01, olcott wrote:
    Deciders: Transform finite strings by finite string
    transformation rules into {Accept, Reject}.

    I continue to Reject your asymmetric and functionally-loaded
    labels for
    the classes.



    That is just one of the few accurate quotations Olcott makes.

    In ONE of the version of defining Deciders, they are determinators of >>>>>> sentences matching a defined language, and they are to ACCEPT strings >>>>>> that match that grammar, and REJECT statements that fail to meet the >>>>>> grammar.

    It's only valid in an elementary corpus of principle where the
    correspondence is drawn such that the terms ACCEPT and REJECT are
    characterised as references into that model and not just ordinary
    English words. The capitalisation is not really enough; double-quotes >>>>> might barely do the trick but without the computational-linguistics
    context it's really just politics. The politics is of nudging the
    population of poorly educated readers into accepting or rejecting
    actual
    programs instead of merely characterising them, whether Olcott is
    doing
    the politics or is being nudged by search results into effecting
    another
    group's politics.

    The only clues that the context is CompLang/AI within Olcott's
    statements of principles themselves is the use of the word "string"
    which is highly ambiguous in the context of computation such that any >>>>> formal meaning in logistic philosophy is almost diluted away.


    The use of the term "Halt Decider" and "Turing Machine" focus the
    context fairly well. Add in his rambling about the Halting Problem, and >>>> it seems clear.

    Of course, it does also show is limited understanding, as deciders only >>>> answering Accept or Reject is a somewhat limited space in that field,
    but was the initial field which used the term.

    Do you mean to say that Computation Theory first used "decider" and used >>> it to describe a machine that decides whether to accept a formula as a
    specimen of the set of formulas described by a given grammar or whether
    to reject it as specimen of the set?


    Do you also mean to say that "decider" is elementary without reference
    to grammars and specimens of their matches? Don't you agree that it is
    ambiguous as an term in an elementary principle due to the ordinary
    meaning of "decider" being to classify a specimen one of two classes (a
    specimen being as general as even "the current state of the world" and
    the classes being as correspondingly general as its suitability to
    respond with one plan or another)?

    I am concerned that the semantic ambiguity is particularly awkward
    because the untrained reader will take "decider" in the ordinary sense
    and take the principle already stated as a philosophical perspective on
    its nature; the reader will not backtrack to the correct reading soon
    enough to prevent misunderstanding. They will not settle on the intended >>> reading which is instead to /define/ the term-of-art "decider" vis-a-vis >>> the grammar-matching sense. That will cause the population of readers to >>> adopt acceptance and rejection as classes for the first sense when such
    specificity is not /correct/ for that sense.



    It seems to me that in the broadest computational sense
    that a decider is intended to address decision problems.

    That is one sub-space you can work in.

    The term has also be overloaded as a term-of-art to more general cases, where the results can be part of a countable-infinite class.


    That would be a machine that never halts, thus out of scope.


    In computability theory and computational complexity
    theory, a decision problem is a computational problem
    that can be posed as a yes–no question on a set of input
    values.

    https://en.wikipedia.org/wiki/Decision_problem

    Yes, that is for DECISION problems, but deciders can be used for more
    than decision problems in the more general parts of the theory.


    Does this finite string contain: 111?
    accept or yes for true reject or no for false.


    Yet can only do so by
    Transforming finite string inputs by finite
    string transformation rules into Boolean Values.

    Right, and that transformation needs to match the Function they are
    trying to compute, which might be uncomputable


    If the function cannot be computed from the input
    then the input does not contain the value to be computed.

    There is no magical way to compute the behavior
    of DD simulated by HHH1 from DD simulated by HHH.


    In the broadest sense my 28 years of primary
    research has focused on undecidability.

    Which in a broader sense isn't just on decision problems. But, if you
    want to restrict yourself to just "Decison Problems" that is ok.

    Yes, the Halting Problem IS a decision problem, and thus has only a
    binary result.

    A result that can't always be achieved by a finite deterministic
    algrotihm in finite steps, and thus the problem is uncomputable.

    Which doesn't make it invalid, just impossible to make a full Halt
    Decider that always gives the right answer.


    --
    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 Richard Damon@Richard@Damon-Family.org to comp.theory,sci.math,sci.logic,comp.ai.philosophy on Sun Dec 21 12:38:38 2025
    From Newsgroup: comp.ai.philosophy

    On 12/21/25 9:57 AM, olcott wrote:
    On 12/20/2025 8:57 PM, Richard Damon wrote:
    On 12/20/25 9:33 PM, olcott wrote:
    On 12/20/2025 8:16 PM, Tristan Wibberley wrote:
    On 20/12/2025 23:14, Richard Damon wrote:
    On 12/20/25 6:09 PM, Tristan Wibberley wrote:
    On 20/12/2025 13:32, Richard Damon wrote:
    On 12/20/25 8:01 AM, Tristan Wibberley wrote:
    On 19/12/2025 23:01, olcott wrote:
    Deciders: Transform finite strings by finite string
    transformation rules into {Accept, Reject}.

    I continue to Reject your asymmetric and functionally-loaded
    labels for
    the classes.



    That is just one of the few accurate quotations Olcott makes.

    In ONE of the version of defining Deciders, they are
    determinators of
    sentences matching a defined language, and they are to ACCEPT
    strings
    that match that grammar, and REJECT statements that fail to meet the >>>>>>> grammar.

    It's only valid in an elementary corpus of principle where the
    correspondence is drawn such that the terms ACCEPT and REJECT are
    characterised as references into that model and not just ordinary
    English words. The capitalisation is not really enough; double-quotes >>>>>> might barely do the trick but without the computational-linguistics >>>>>> context it's really just politics. The politics is of nudging the
    population of poorly educated readers into accepting or rejecting >>>>>> actual
    programs instead of merely characterising them, whether Olcott is >>>>>> doing
    the politics or is being nudged by search results into effecting
    another
    group's politics.

    The only clues that the context is CompLang/AI within Olcott's
    statements of principles themselves is the use of the word "string" >>>>>> which is highly ambiguous in the context of computation such that any >>>>>> formal meaning in logistic philosophy is almost diluted away.


    The use of the term "Halt Decider" and "Turing Machine" focus the
    context fairly well. Add in his rambling about the Halting Problem, >>>>> and
    it seems clear.

    Of course, it does also show is limited understanding, as deciders
    only
    answering Accept or Reject is a somewhat limited space in that field, >>>>> but was the initial field which used the term.

    Do you mean to say that Computation Theory first used "decider" and
    used
    it to describe a machine that decides whether to accept a formula as a >>>> specimen of the set of formulas described by a given grammar or whether >>>> to reject it as specimen of the set?


    Do you also mean to say that "decider" is elementary without reference >>>> to grammars and specimens of their matches? Don't you agree that it is >>>> ambiguous as an term in an elementary principle due to the ordinary
    meaning of "decider" being to classify a specimen one of two classes (a >>>> specimen being as general as even "the current state of the world" and >>>> the classes being as correspondingly general as its suitability to
    respond with one plan or another)?

    I am concerned that the semantic ambiguity is particularly awkward
    because the untrained reader will take "decider" in the ordinary sense >>>> and take the principle already stated as a philosophical perspective on >>>> its nature; the reader will not backtrack to the correct reading soon
    enough to prevent misunderstanding. They will not settle on the
    intended
    reading which is instead to /define/ the term-of-art "decider" vis-
    a-vis
    the grammar-matching sense. That will cause the population of
    readers to
    adopt acceptance and rejection as classes for the first sense when such >>>> specificity is not /correct/ for that sense.



    It seems to me that in the broadest computational sense
    that a decider is intended to address decision problems.

    That is one sub-space you can work in.

    The term has also be overloaded as a term-of-art to more general
    cases, where the results can be part of a countable-infinite class.


    That would be a machine that never halts, thus out of scope.

    Nope, just shows you don't know what the words mean.

    one good example of a countable-infinite class is the class of all
    finite strings.

    So, any machine that takes in a finite-string and always halts to
    produce a finite-string can be called a "decider" in the more general term-of-art.



    In computability theory and computational complexity
    theory, a decision problem is a computational problem
    that can be posed as a yes–no question on a set of input
    values.

    https://en.wikipedia.org/wiki/Decision_problem

    Yes, that is for DECISION problems, but deciders can be used for more
    than decision problems in the more general parts of the theory.


    Does this finite string contain: 111?
    accept or yes for true reject or no for false.

    ????

    Trying to disprove a definition by giving an example just is stupid.

    Since one definition of "Decider" is a machine that always halts, a
    machine that adds two numbers given by a finite string representation
    also meets that meaning of decider.

    Your problem is you brain just can't even handle the normal complexity
    of language.



    Yet can only do so by
    Transforming finite string inputs by finite
    string transformation rules into Boolean Values.

    Right, and that transformation needs to match the Function they are
    trying to compute, which might be uncomputable


    If the function cannot be computed from the input
    then the input does not contain the value to be computed.

    In other words, your idea of problem solving is people need to tell you
    the answer to ask you the questionl


    There is no magical way to compute the behavior
    of DD simulated by HHH1 from DD simulated by HHH.

    Which is just you spouting nonsense showing you don't know what you are talking about.

    As I said, your logic says that whatever HHH says, it is correct, as
    that is what HHH shows its input means.

    That, or you world doesn't understand that HHH is a SPECIFIC machine,
    but everything is everything and thus nothing is anything in particular.

    Sorry, your "reality" is just insanity.



    In the broadest sense my 28 years of primary
    research has focused on undecidability.

    Which in a broader sense isn't just on decision problems. But, if you
    want to restrict yourself to just "Decison Problems" that is ok.

    Yes, the Halting Problem IS a decision problem, and thus has only a
    binary result.

    A result that can't always be achieved by a finite deterministic
    algrotihm in finite steps, and thus the problem is uncomputable.

    Which doesn't make it invalid, just impossible to make a full Halt
    Decider that always gives the right answer.





    --- Synchronet 3.21a-Linux NewsLink 1.2