• Re: Scientific reasoning [ if H is correct then it is not incorrect ]

    From olcott@21:1/5 to Ben Bacarisse on Tue Oct 26 09:47:28 2021
    XPost: comp.theory, sci.logic, alt.philosophy

    On 10/26/2021 9:28 AM, Ben Bacarisse wrote:
    olcott <NoOne@NoWhere.com> writes:

    Linz's "proof" that no universal halt decider exists is entirely based
    on his belief that H cannot decide ⟨Ĥ⟩ ⟨Ĥ⟩ correctly.

    It's a proof, not a "proof". It only becomes a "proof" when someone
    finds a mistake in it. And it does not rely on his beliefs. That's not
    the word to use when talking about simple logic like this:


    Because this is necessarily true (only a fool would disagree)

    Simulating Halt Decider Theorem (Olcott 2021):
    Whenever simulating halt decider H correctly determines that input P
    never reaches its final state (whether or not its simulation of P is
    aborted) then H correctly decides that P never halts.

    As soon as I show that Ĥq0 <Ĥ> <Ĥ> meets the above theorem then Linz has been refuted. Only a fool would disagree.


    If a TM, H, existed such that

    Hq0 <M> s ⊦* Hqy if M applied to s halts, and
    Hq0 <M> s ⊦* Hqn if M applied to s does not halt,

    we could construct from it an H' such that

    H'q0 <M> s ⊦* oo if M applied to s halts, and
    H'q0 <M> s ⊦* H'qn if M applied to s does not halt.

    And from that we could construct an Ĥ such that

    Ĥq0 <M> ⊦* Ĥqx <M> <M> ⊦* oo if M applied to <M> halts, and
    Ĥq0 <M> ⊦* Ĥqx <M> <M> ⊦* Ĥqn if M applied to <M> does not halt.

    Setting M to Ĥ, so <M> becomes <Ĥ>, we see that the existence of H (as
    Linz defines it) logically entails that a TM Ĥ that does this

    Ĥq0 <Ĥ> ⊦* Ĥqx <Ĥ> <Ĥ> ⊦* oo if Ĥ applied to <Ĥ> halts, and
    Ĥq0 <Ĥ> ⊦* Ĥqx <Ĥ> <Ĥ> ⊦* Ĥqn if Ĥ applied to <Ĥ> does not halt.

    would also have to exist. But, as Linz says, "this is clearly
    nonsense".

    To call such trivial sequence of deductions a belief is just rhetorical
    spin.



    --
    Copyright 2021 Pete Olcott

    "Great spirits have always encountered violent opposition from mediocre
    minds." Einstein

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  • From olcott@21:1/5 to Malcolm McLean on Tue Oct 26 12:13:28 2021
    XPost: comp.theory, sci.logic, alt.philosophy

    On 10/26/2021 10:58 AM, Malcolm McLean wrote:
    On Tuesday, 26 October 2021 at 15:47:36 UTC+1, olcott wrote:
    On 10/26/2021 9:28 AM, Ben Bacarisse wrote:
    olcott <No...@NoWhere.com> writes:

    Linz's "proof" that no universal halt decider exists is entirely based >>>> on his belief that H cannot decide ⟨Ĥ⟩ ⟨Ĥ⟩ correctly.

    It's a proof, not a "proof". It only becomes a "proof" when someone
    finds a mistake in it. And it does not rely on his beliefs. That's not
    the word to use when talking about simple logic like this:

    Because this is necessarily true (only a fool would disagree)

    Simulating Halt Decider Theorem (Olcott 2021):
    Whenever simulating halt decider H correctly determines that input P
    never reaches its final state (whether or not its simulation of P is
    aborted) then H correctly decides that P never halts.

    Well that hasn't been thought through. Assuming simulating halt decider H
    to be a Turing machine, if H's simulation of P is not halted, H never terminates,
    so, using Turing's model, you never see the result of the decision.

    Simulating Halt Decider Theorem (Olcott 2021):
    Whenever simulating halt decider H correctly determines that input P
    WOULD
    never
    REACH
    its final state (whether or not its simulation of P is
    aborted) then H correctly decides that P never halts.

    (In Turing's model, intermediate states of the tape whilst the machine is running can't be treated as results. What looks like a result might be scratch
    space. You have to wait until the machine has halted to read the result).



    void Infinite_Loop()
    {
    HERE: goto HERE;
    }

    _Infinite_Loop()
    [00000ab0](01) 55 push ebp
    [00000ab1](02) 8bec mov ebp,esp
    [00000ab3](02) ebfe jmp 00000ab3
    [00000ab5](01) 5d pop ebp
    [00000ab6](01) c3 ret
    Size in bytes:(0007) [00000ab6]

    I provide this as a simplest example.
    It doesn't take a PhD to understand that the simulation of
    _Infinite_Loop() never reaches machine address 0xab6.

    // Simplified Linz Ĥ (Linz:1990:319)
    // Strachey(1965) CPL translated to C
    01 void P(u32 x)
    02 {
    03 if (H(x, x))
    04 HERE: goto HERE;
    05 }

    The above code can be analyzed using a similar axiomatic basis to
    determine that no simulation of the input to H(P,P) ever gets past line 03.



    --
    Copyright 2021 Pete Olcott

    "Great spirits have always encountered violent opposition from mediocre
    minds." Einstein

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  • From olcott@21:1/5 to Ben Bacarisse on Tue Oct 26 19:05:04 2021
    XPost: comp.theory, sci.logic, alt.philosophy

    On 10/26/2021 6:19 PM, Ben Bacarisse wrote:
    olcott <NoOne@NoWhere.com> writes:

    On 10/26/2021 9:28 AM, Ben Bacarisse wrote:
    olcott <NoOne@NoWhere.com> writes:

    Linz's "proof" that no universal halt decider exists is entirely based >>>> on his belief that H cannot decide ⟨Ĥ⟩ ⟨Ĥ⟩ correctly.
    It's a proof, not a "proof". It only becomes a "proof" when someone
    finds a mistake in it. And it does not rely on his beliefs. That's not >>> the word to use when talking about simple logic like this:

    Because this is necessarily true (only a fool would disagree)

    Simulating Halt Decider Theorem (Olcott 2021):
    Whenever simulating halt decider H correctly determines that input P
    never reaches its final state (whether or not its simulation of P is
    aborted) then H correctly decides that P never halts.

    What is H?
    a simulating halt decider

    What is P?
    input to Simulating Halt Decider

    What is a correct decision?

    Reports whether or not simulated input reaches its final state

    What does it mean
    to say an input does or does not halt?

    the simulation of the input never reaches its final state
    (whether or not its simulation of P is aborted)

    Linz's proof does not leave any
    of these things unspecified. He defines what H should do in all cases.
    He does not introduce new symbols like P without definition. (The last
    time you used P it as a scrap of C code, not an input string to a
    Turning machine.)

    As soon as I show that Ĥq0 <Ĥ> <Ĥ> meets the above theorem then Linz
    has been refuted. Only a fool would disagree.

    No. You need to point out where Linz goes wrong, not pontificate about
    an ill-defined "theorem".

    Linz is wrong is his final conclusion at the top of page 320. https://www.liarparadox.org/Peter_Linz_HP(Pages_315-320).pdf

    q0 ⟨Ĥ⟩ ⊢* Ĥq0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥqn

    The input to Ĥq0 ⟨Ĥ⟩ ⟨Ĥ⟩ specifies infinitely nested simulation thus Ĥq0
    correctly transitions to Ĥqn.

    The mistake that Linz makes is that he is wrongly assuming that Ĥq0 is deciding whether or not itself halts.

    Ĥq0 is NOT deciding whether or not itself halts.
    Ĥq0 is deciding whether or its input: ⟨Ĥ⟩ ⟨Ĥ⟩ halts.

    He confused himself by not provided the full specification for Ĥ.
    He abbreviated it to be concise.



    --
    Copyright 2021 Pete Olcott

    "Great spirits have always encountered violent opposition from mediocre
    minds." Einstein

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  • From olcott@21:1/5 to Richard Damon on Thu Oct 28 10:11:16 2021
    XPost: comp.theory, sci.logic, sci.math

    On 10/27/2021 6:34 PM, Richard Damon wrote:
    On 10/27/21 9:51 AM, olcott wrote:
    On 10/27/2021 8:12 AM, Ben Bacarisse wrote:
    olcott <NoOne@NoWhere.com> writes:

    On 10/26/2021 6:47 PM, Ben Bacarisse wrote:
    olcott <NoOne@NoWhere.com> writes:

    All you do is assert that H decides ⟨Ĥ⟩ ⟨Ĥ⟩ correctly.

    Are you willing to admit that if it is shown that H correctly decides >>>>>> the halt status of ⟨Ĥ⟩ ⟨Ĥ⟩ that Linz has been refuted or are you
    going
    to dishonestly dodge this key point?

    I keep trying not to dodge it but you keep ignoring my answer.  No
    proof
    is invalided by other truths.  You might render all of mathematics
    inconsistent, but previously valid chains of reasoning remains valid. >>>>>
    You made it plain that don't accept what a proof is when you stated
    that
    if A,B,C ⊦ X, then ~A,A,B,C ⊬ X.  As far as I know you have never >>>>> retracted this incorrect statement.

    As it happens, you can't show that Linz's H is correct about the input >>>>> ⟨Ĥ⟩ ⟨Ĥ⟩, so the point is moot, but I have been trying to get you to
    note
    my answer to this hypothetical question for years, but you keep
    pretending not to notice.

    I ask you a YES / NO question and you dodge.

    How could you miss the answer yet again?  Clearly it's no: I don't
    accept that if it is shown that H correctly decides the halt status of
    ⟨Ĥ⟩ ⟨Ĥ⟩ that Linz has been refuted.

    So you reject the idea of a semantic tautology.
    If X says Y is true and I prove that Y is false then X could still be
    correct. No wonder we are having trouble communicating, you are simply
    irrational.


    Perhaps in smaller words so you can understand.

    IF we have one proof that says X.

    And we then come up with another proof that says Not X.

    That second proof does NOT 'disprove' the first proof.

    These are the simple words that Ben cannot understand:
    If Linz says that H cannot correctly decide the halt
    status of ⟨Ĥ⟩ ⟨Ĥ⟩ and I show exactly how H correctly decides
    the halt status of ⟨Ĥ⟩ ⟨Ĥ⟩ then I have proved Linz wrong.

    https://www.liarparadox.org/Peter_Linz_HP(Pages_315-320).pdf
    Since that time I did find the exact mistake that Linz made on the top
    of page 320.

    Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
    Linz incorrectly believes that Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ is deciding the halt status
    of itself rather than the halt status of its input.

    The thing that leads to his confusion is that on line 7 of the top of
    page 320 he simply deletes most of the details of Ĥ: q0ŵ ⊢* Ĥqn, he
    skips the point in Ĥ that actually determines the halt decider of its
    input.


    --
    Copyright 2021 Pete Olcott

    "Great spirits have always encountered violent opposition from mediocre
    minds." Einstein

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