• Banno
    25k
    Ok.
    What I am saying is much the same as you received elsewhere:

    As a theoretical computer scientist, I can confirm that nothing in this paper shows anything about Turing's proof to be erroneous. Indeed, it is not a work of mathematics or theoretical computer science at all (due to lack of formality) and judt vaguely discusses some general points about objective and subjective specifications, nothing of which is relevant for the halting problem or the proof of its unsolvability. Also, notice that "This statement is not true" is not a statement that can even be formulated in first-order arithmetic or any standard logical system Turing or Church were concerned with. Indeed, Tarski's theorem on the undefinability of the truth predicate shows that statements of this type cannot even be formulated in these systems, so it is meaningless to discuss their formal validity or "truth" since they do not even exist formally. — Gutsfeld
    ...and so on. I don't think it's just me.
  • PL Olcott
    626
    ..and so on. I don't think it's just me.Banno

    Yes everyone that does not pay complete attention makes sure
    that they never understand what is said. I will sum up the point
    much much more concisely.

    When input D to program H does that opposite of whatever program
    H says that it will do it is logically impossible for program H to correctly
    say what input D will do.

    The inability to do the logically impossible never places any actual
    limits on anyone or anything.


    That no CAD system can possibly correctly draw a square circle places
    no actual limits on computation. Thus the halting problem proof places
    no actual limit on what can be computed.
  • Banno
    25k
    If you would show that a well-accepted and well-understood part of logic is in error, you will need a good deal of strong, formal argument to carry your case.

    But such is absent here.

    Cheers.
  • PL Olcott
    626
    ↪PL Olcott If you would show that a well-accepted and well-understood part of logic is in error, you will need a good deal of strong, formal argument to carry your case.Banno

    Once this is understood to be true
    (1) The inability to do the logically impossible never places any actual limits
    on anyone or anything

    (2) then the logical impossibility of solving the halting problem the way it is
    currently defined places no actual limit on computation.

    Introduction to the Theory of Computation 3rd Edition by Michael Sipser

    When we apply the MIT Professor Michael Sipser approved halt status critieria
    (a) If simulating halt decider H correctly simulates its input D until H correctly determines that its simulated D would never stop running unless aborted then
    (b) H can abort its simulation of D and correctly report that D specifies a non-halting sequence of configurations.

    Then H does correctly determine that halt status of every input that was
    defined to do the opposite of whatever Boolean value that H returns.
    All of the details of this are fully elboarated on the first page of this paper:

    Termination Analyzer H is Not Fooled by Pathological Input D
    https://www.researchgate.net/publication/369971402_Termination_Analyzer_H_is_Not_Fooled_by_Pathological_Input_D
  • Banno
    25k
    I think you have some interesting stuff here, but you haven't demonstrated an error in Gödel or Turing.
  • PL Olcott
    626
    ↪PL Olcott I think you have some interesting stuff here, but you haven't demonstrated an error on Gödel or Turing.Banno

    The key error that I and Professor demonstrated that the inability of solving the halting problem is the same as the inability for a CAD system to correctly draw a square circle both are logically impossible thus place no actual limit on computation what-so-ever.
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