• Best First Principle of Turing Machine computation

    From olcott@polcott333@gmail.com to sci.logic,comp.theory,comp.ai.philosophy,sci.math on Sat Dec 13 09:50:39 2025
    From Newsgroup: comp.ai.philosophy

    On 12/13/2025 4:58 AM, Mikko wrote:
    olcott kirjoitti 11.12.2025 klo 16.38:
    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.

    No, it is not. There is nothing in the halting problem that satisfies
    the criteria for "category error": things belonging to a particular
    category are presented as if they belong to a different category, or, alternatively, a property is ascribed to a thing that could not possibly
    have that property. You can't identify either criterion being violated
    in the halting problem.


    Best First Principle
    All Turing machines only compute the mapping
    from an input finite string to some value.

    It is very difficult to see that the halting
    problem definition breaks that rule.

    I will work on making this more clear now that
    I have the best first principle.
    --
    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 Tristan Wibberley@tristan.wibberley+netnews2@alumni.manchester.ac.uk to sci.logic,comp.theory,comp.ai.philosophy,sci.math on Sat Dec 13 16:35:29 2025
    From Newsgroup: comp.ai.philosophy

    On 13/12/2025 15:50, olcott wrote:

    Best First Principle
    All Turing machines only compute the mapping
    ^^^^^^^^^^^^
    compute only
    --
    Tristan Wibberley

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  • From olcott@polcott333@gmail.com to sci.logic,comp.theory,comp.ai.philosophy,sci.math on Sat Dec 13 10:49:42 2025
    From Newsgroup: comp.ai.philosophy

    On 12/13/2025 10:35 AM, Tristan Wibberley wrote:
    On 13/12/2025 15:50, olcott wrote:

    Best First Principle
    All Turing machines only compute the mapping
    ^^^^^^^^^^^^
    compute only


    Semantically equivalent.
    I am going to the store.
    To the store I am going.
    --
    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