• Re: Church-Turing and computable functions --- very excellent reply

    From olcott@[email protected] to sci.math,comp.theory,sci.logic,comp.ai.philosophy,sci.math.symbolic on Fri Oct 2 17:42:56 2026
    From Newsgroup: comp.ai.philosophy

    On 10/2/2026 9:32 AM, Python wrote:
    Le 02/10/2026 à 16:15, olcott a écrit :
    On 10/2/2026 8:58 AM, Python wrote:
    Le 02/10/2026 à 15:56, olcott a écrit :
    On 10/2/2026 8:32 AM, Python wrote:
    Le 02/10/2026 à 15:24, olcott a écrit :
    On 10/2/2026 7:59 AM, Python wrote:
    Le 02/10/2026 à 14:28, olcott a écrit :
    On 10/1/2026 10:05 PM, dart200 wrote:
    On 10/1/26 5:28 PM, Chris M. Thomasson wrote:
    On 10/1/2026 3:54 PM, dart200 wrote:
    [...]

    Are you saying that the halting problem is not solvable? If >>>>>>>>>> so, so what?

    it is solvable for an enumerable set of machines that includes >>>>>>>>> all possible output sequences, it is not solvable for all
    possible machines


    The key mistake of the halting theorem is that
    it requires a halt decider to report on the behavior
    of the direct execution of DD() from main()

    https://github.com/plolcott/x86utm/blob/master/README.md
    This is outside of the Church-Turing scope when this scope
    is understood to only allow finite string transformation
    rules to be applied to finite string inputs to derive any
    any all outputs.

    The only correct finite string transformation rules that
    HHH is allowed to apply to its finite string input DD are
    specified by the operational semantics of the C programming
    language.

    There are no correct finite string transformation rules that
    HHH can possibly apply to its input finite string that derive
    the behavior of DD directly executed in main().

    Peter, this distinction between "the operational semantics of C" >>>>>>> and "the behavior of DD directly executed from main()" does not >>>>>>> exist.


    Counter-factual you just did not pay close enough
    attention and merely leaped to a false conclusion.

    Peter, saying "counter-factual" is not a counterargument.

    It has taken me many thousands of hours very carefully
    compose the few words that I just said. Carefully
    study them for a few hours until you fully understand
    every subtle nuance of every single detail before you
    reply.

    Peter, the number of hours you spent composing a statement has no
    bearing on whether it is true.


    That is true, None-the-less I will no longer
    tolerate people that glance at a couple of
    my words before artificially contriving a
    rebuttal that conclusively proves that they
    did not bother to pay complete attention
    to every detail of what I said.

    Peter, then demonstrate that.


    This was a very excellent reply:

    Quote the specific words of yours that I failed to pay attention to, and explain what they mean that my response failed to address.

    You wrote:

       "The only correct finite string transformation rules that
        HHH is allowed to apply to its finite string input DD are
        specified by the operational semantics of the C programming
        language."

    I explicitly agreed with that premise.

    You then wrote:

       "There are no correct finite string transformation rules that
        HHH can possibly apply to its input finite string that derive
        the behavior of DD directly executed in main()."

    That is the conclusion I challenged.

    My objection is very specific: the behavior of DD when executed from
    main() is itself generated by successive applications of the operational semantics of C.

    So there is no "artificially contrived rebuttal" here.

    If I have misunderstood what you mean by "derive the behavior of DD
    directly executed in main()", define that phrase precisely and show
    where my interpretation differs from yours.

    That would resolve the issue immediately.
    --
    Copyright 2026 Olcott

    My 28 year goal has been to make
    "true on the basis of meaning expressed in language"
    reliably computable for the entire body of general knowledge.
    The complete structure of this system is now defined.

    The entire body of knowledge expressed in language is
    comprised of two types of relations between finite strings:
    (a) *Axioms* Expressions of language that are stipulated to be true.

    My system bridges the analytic/synthetic distinction by
    expressly encoding all empirical "atomic facts" in a formal
    language such as CycL of the Cyc project.

    (b) *Inference Rules* Expressions of language that are semantically
    entailed syntactically from (a) and/or (b).
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