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  • The halting problem itself is unequivocally a category error

    From olcott@polcott333@gmail.com to comp.theory,sci.logic,sci.math,comp.ai.philosophy on Sat Dec 13 15:07:25 2025
    From Newsgroup: comp.theory

    All of the textbooks require halt deciders to
    report on the behavior of machine M on input w.

    Since no Turing machine ever takes any Machine
    M as an input this <is> a category error even
    when this make no difference.

    We correct this error by saying that halt
    deciders must report on the basis of the
    behavior specified by their input finite string.
    --
    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>

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  • From Richard Damon@Richard@Damon-Family.org to comp.theory,sci.logic,sci.math,comp.ai.philosophy on Sat Dec 13 16:49:15 2025
    From Newsgroup: comp.theory

    On 12/13/25 4:07 PM, olcott wrote:
    All of the textbooks require halt deciders to
    report on the behavior of machine M on input w.

    Since no Turing machine ever takes any Machine
    M as an input this <is> a category error even
    when this make no difference.

    We correct this error by saying that halt
    deciders must report on the basis of the
    behavior specified by their input finite string.


    And the "behavior specified by their input finite string" *IS* the
    behavior of the machine they describe. So, no problem in asking the
    question as done origninally, when you understand that Turing Machines virtually always deal with a representation of the thing they are to
    decide on, as few real problems are stated in terms of the arbitrary
    symbol set of the Turing Machine.
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