On 8/29/22 11:52 PM, olcott wrote:
> On 8/29/2022 10:44 PM, Richard Damon wrote:
>>
>> On 8/29/22 11:27 PM, olcott wrote:
>>> On 8/29/2022 10:13 PM, Richard Damon wrote:
>>>> On 8/29/22 10:39 PM, olcott wrote:
>>>>> On 8/29/2022 9:32 PM, Richard Damon wrote:
>>>>>>
>>>>>> On 8/29/22 10:16 PM, olcott wrote:
>>>>>>> On 8/29/2022 8:50 PM, Richard Damon wrote:
>>>>>>>> On 8/29/22 9:05 PM, olcott wrote:
>>>>>>>>> On 8/29/2022 7:50 PM, Richard Damon wrote:
>>>>>>>>>>
>>>>>>>>>> On 8/29/22 7:28 PM, olcott wrote:
>>>>>>>>>>> On 8/29/2022 6:18 PM, Richard Damon wrote:
>>>>>>>>>>>>
>>>>>>>>>>>> On 8/29/22 1:12 PM, olcott wrote:
>>>>>>>>>>>>> On 8/28/2022 10:18 PM, Richard Damon wrote:
>>>>>>>>>>>>>> On 8/28/22 11:15 PM, olcott wrote:
>>>>>>>>>>>>>>> On 8/28/2022 10:01 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>> On 8/28/22 10:47 PM, olcott wrote:
>>>>>>>>>>>>>>>>> On 8/28/2022 8:19 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> On 8/28/22 9:15 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>> On 8/28/2022 7:47 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>> On 8/28/22 8:07 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>> On 8/28/2022 3:44 PM, Skep Dick wrote:
>>>>>>>>>>>>>>>>>>>>>> On Sunday, 28 August 2022 at 22:10:37 UTC+2,
>>>>>>>>>>>>>>>>>>>>>> olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>> On 8/28/2022 3:02 PM, Mr Flibble wrote:
>>>>>>>>>>>>>>>>>>>>>>>> On Sun, 28 Aug 2022 14:47:08 -0500
>>>>>>>>>>>>>>>>>>>>>>>> olcott <No...@NoWhere.com> wrote:
>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>> Since Turing machines are mathematical objects
>>>>>>>>>>>>>>>>>>>>>>>>> that only exist in the
>>>>>>>>>>>>>>>>>>>>>>>>> mind people can have contradictory thus
>>>>>>>>>>>>>>>>>>>>>>>>> incoherent ideas about these
>>>>>>>>>>>>>>>>>>>>>>>>> abstract mathematical objects and never realize
>>>>>>>>>>>>>>>>>>>>>>>>> that their ideas are
>>>>>>>>>>>>>>>>>>>>>>>>> incoherent.
>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>> When we study the theory of computation using
>>>>>>>>>>>>>>>>>>>>>>>>> physically existing
>>>>>>>>>>>>>>>>>>>>>>>>> machines such as the x86 architecture then the
>>>>>>>>>>>>>>>>>>>>>>>>> incoherent abstract
>>>>>>>>>>>>>>>>>>>>>>>>> ideas are shown to be incoherent in that they
>>>>>>>>>>>>>>>>>>>>>>>>> cannot be physically
>>>>>>>>>>>>>>>>>>>>>>>>> implemented.
>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>> void Px(ptr x)
>>>>>>>>>>>>>>>>>>>>>>>>> {
>>>>>>>>>>>>>>>>>>>>>>>>> H(x, x);
>>>>>>>>>>>>>>>>>>>>>>>>> return;
>>>>>>>>>>>>>>>>>>>>>>>>> }
>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>> int main()
>>>>>>>>>>>>>>>>>>>>>>>>> {
>>>>>>>>>>>>>>>>>>>>>>>>> Output("Input_Halts = ", H(Px, Px));
>>>>>>>>>>>>>>>>>>>>>>>>> }
>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>> If a decider must always return a value
>>>>>>>>>>>>>>>>>>>>>>>>> whenever it is called this
>>>>>>>>>>>>>>>>>>>>>>>>> requires H to return a value to Px even though
>>>>>>>>>>>>>>>>>>>>>>>>> H is called in
>>>>>>>>>>>>>>>>>>>>>>>>> infinite recursion.
>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>> This even requires that the function call from
>>>>>>>>>>>>>>>>>>>>>>>>> Px to H(Px,Px) must
>>>>>>>>>>>>>>>>>>>>>>>>> return a value to Px even if this function call
>>>>>>>>>>>>>>>>>>>>>>>>> to H is not even
>>>>>>>>>>>>>>>>>>>>>>>>> executed. In the physical model of computation
>>>>>>>>>>>>>>>>>>>>>>>>> it is an axiom the
>>>>>>>>>>>>>>>>>>>>>>>>> programs that are not executed never return
>>>>>>>>>>>>>>>>>>>>>>>>> values because it is
>>>>>>>>>>>>>>>>>>>>>>>>> physically impossible.
>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>> When simulating halt decider H sees that Px is
>>>>>>>>>>>>>>>>>>>>>>>>> about to call H(Px,Px)
>>>>>>>>>>>>>>>>>>>>>>>>> in infinite recursion H aborts its simulation
>>>>>>>>>>>>>>>>>>>>>>>>> of Px before this call
>>>>>>>>>>>>>>>>>>>>>>>>> is executed.
>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>> *Clearly computer science is incorrect on this
>>>>>>>>>>>>>>>>>>>>>>>>> point*
>>>>>>>>>>>>>>>>>>>>>>>>> Computer science says that H must still return
>>>>>>>>>>>>>>>>>>>>>>>>> a value to Px even
>>>>>>>>>>>>>>>>>>>>>>>>> though the call to H is not even executed
>>>>>>>>>>>>>>>>>>>>>>>>> because all deciders must
>>>>>>>>>>>>>>>>>>>>>>>>> ALWAYS return to their caller.
>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>> Computer science is correct on this point, what
>>>>>>>>>>>>>>>>>>>>>>>> is incorrect is your
>>>>>>>>>>>>>>>>>>>>>>>> implementation of H.
>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>> /Flibble
>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>> So you are saying the a computer program that is
>>>>>>>>>>>>>>>>>>>>>>> never even executed
>>>>>>>>>>>>>>>>>>>>>>> must still return a result?
>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>> The "result" of a program that never returns is None!
>>>>>>>>>>>>>>>>>>>>>> This is equivalent of treating non-termination as
>>>>>>>>>>>>>>>>>>>>>> an effect.
>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>> No problem - is just a definition.
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>> H(Px,Px) returns 0 to main. Some people have said
>>>>>>>>>>>>>>>>>>>>> that the when Px calls H(Px,Px) that H must return
>>>>>>>>>>>>>>>>>>>>> a value to Px even though this function call from
>>>>>>>>>>>>>>>>>>>>> Px to H is never executed.
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>> Except that in the ACTUAL BEHAVIOR of the input, the
>>>>>>>>>>>>>>>>>>>> call IS executed.
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>> You are just confusiong the ACTUAL BEHAVIOR with the
>>>>>>>>>>>>>>>>>>>> behavior that H determines.
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>> You said that H must always return a result to its
>>>>>>>>>>>>>>>>>>> caller even if this call is never actually executed.
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> You don't HAVE a caller unless you execute the call
>>>>>>>>>>>>>>>>>> instruction.
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> DON'T CHANGE THE SUBJECT
>>>>>>>>>>>>>>>>> DON'T CHANGE THE SUBJECT
>>>>>>>>>>>>>>>>> DON'T CHANGE THE SUBJECT
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> I DIDN'T. I don't think you know what a subject is.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> A decider must always return to its caller:
>>>>>>>>>>>>>>>>> *ONLY THOSE TIMES WHERE THE CALL TO THE DECIDER IS
>>>>>>>>>>>>>>>>> ACTUALLY EXECUTED*
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> So, you don't think that Px calls H?
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> The call to H(Px,Px) from P is never executed, thus H
>>>>>>>>>>>>>>> need not return to Px.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> But it is in the complete simulation of the input to
>>>>>>>>>>>>>> H(Px,Px), and that is what matters for the answer that H
>>>>>>>>>>>>>> is supposed to give.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> *This thread had nothing to do with that*
>>>>>>>>>>>>> The question is whether or not H must return a value to Px
>>>>>>>>>>>>> when the call to H(Px,Px) from Px is never invoked.
>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> Which is a meaningless question except in the context of a
>>>>>>>>>>>> complete simulation/execution.
>>>>>>>>>>> Does the fact that the invocation of H(Px,Px) from Px that is
>>>>>>>>>>> never executed prevent H from being a decider?
>>>>>>>>>>
>>>>>>>>>> What do you meen it never "gets executed"?
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> H(Px,Px) cannot return any value to the correctly simulated Px
>>>>>>>>> because the correctly simulated Px is aborted before its call
>>>>>>>>> to H(Px,Px) is executed.
>>>>>>>>
>>>>>>>> Nope. because the actual behavior of Px is to directly call
>>>>>>>> H(Px,Px)
>>>>>>>>
>>>>>>>
>>>>>>> There is no actual behavior of Px such that H can possibly return
>>>>>>> any value to its simulated Px.
>>>>>>>
>>>>>>>
>>>>>> Your being illogical again.
>>>>>>
>>>>>
>>>>> Ah so you admit that you lied when you said that H(Px,Px)
>>>>> eventually returns a value to its simulated input.
>>>>>
>>>>
>>>> No, I didn't say that, I said every call to H(Px,Px) needs to see
>>>> the 0 returned.
>>>>
>>>> I said NOTHING about "to its simulated input" because that is just
>>>> non-sense.
>>>
>>> On 8/28/2022 7:02 PM, Richard Damon wrote:
>>>  > Yes, the COMPLETE simulation of the input will see
>>>  > that call and return, yes. If it saw the Call, it
>>>  > will see the Return.
>>>
>>> This was in the context of a simulated P returning to its simulated H.
>>>
>>
>> And what did I say?
>>
>> The COMPLETE simulation will see the call and return.
>>
>
> The complete simulation of the input to H never stops.

On 8/29/2022 11:09 PM, Richard Damon wrote:
> On 8/29/22 11:52 PM, olcott wrote:
>> On 8/29/2022 10:44 PM, Richard Damon wrote:
>>>
>>> On 8/29/22 11:27 PM, olcott wrote:
>>>> On 8/29/2022 10:13 PM, Richard Damon wrote:
>>>>> On 8/29/22 10:39 PM, olcott wrote:
>>>>>> On 8/29/2022 9:32 PM, Richard Damon wrote:
>>>>>>>
>>>>>>> On 8/29/22 10:16 PM, olcott wrote:
>>>>>>>> On 8/29/2022 8:50 PM, Richard Damon wrote:
>>>>>>>>> On 8/29/22 9:05 PM, olcott wrote:
>>>>>>>>>> On 8/29/2022 7:50 PM, Richard Damon wrote:
>>>>>>>>>>>
>>>>>>>>>>> On 8/29/22 7:28 PM, olcott wrote:
>>>>>>>>>>>> On 8/29/2022 6:18 PM, Richard Damon wrote:
>>>>>>>>>>>>>
>>>>>>>>>>>>> On 8/29/22 1:12 PM, olcott wrote:
>>>>>>>>>>>>>> On 8/28/2022 10:18 PM, Richard Damon wrote:
>>>>>>>>>>>>>>> On 8/28/22 11:15 PM, olcott wrote:
>>>>>>>>>>>>>>>> On 8/28/2022 10:01 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>> On 8/28/22 10:47 PM, olcott wrote:
>>>>>>>>>>>>>>>>>> On 8/28/2022 8:19 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>> On 8/28/22 9:15 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>> On 8/28/2022 7:47 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>> On 8/28/22 8:07 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>> On 8/28/2022 3:44 PM, Skep Dick wrote:
>>>>>>>>>>>>>>>>>>>>>>> On Sunday, 28 August 2022 at 22:10:37 UTC+2,
>>>>>>>>>>>>>>>>>>>>>>> olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>> On 8/28/2022 3:02 PM, Mr Flibble wrote:
>>>>>>>>>>>>>>>>>>>>>>>>> On Sun, 28 Aug 2022 14:47:08 -0500
>>>>>>>>>>>>>>>>>>>>>>>>> olcott <No...@NoWhere.com> wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>> Since Turing machines are mathematical objects
>>>>>>>>>>>>>>>>>>>>>>>>>> that only exist in the
>>>>>>>>>>>>>>>>>>>>>>>>>> mind people can have contradictory thus
>>>>>>>>>>>>>>>>>>>>>>>>>> incoherent ideas about these
>>>>>>>>>>>>>>>>>>>>>>>>>> abstract mathematical objects and never
>>>>>>>>>>>>>>>>>>>>>>>>>> realize that their ideas are
>>>>>>>>>>>>>>>>>>>>>>>>>> incoherent.
>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>> When we study the theory of computation using
>>>>>>>>>>>>>>>>>>>>>>>>>> physically existing
>>>>>>>>>>>>>>>>>>>>>>>>>> machines such as the x86 architecture then the
>>>>>>>>>>>>>>>>>>>>>>>>>> incoherent abstract
>>>>>>>>>>>>>>>>>>>>>>>>>> ideas are shown to be incoherent in that they
>>>>>>>>>>>>>>>>>>>>>>>>>> cannot be physically
>>>>>>>>>>>>>>>>>>>>>>>>>> implemented.
>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>> void Px(ptr x)
>>>>>>>>>>>>>>>>>>>>>>>>>> {
>>>>>>>>>>>>>>>>>>>>>>>>>> H(x, x);
>>>>>>>>>>>>>>>>>>>>>>>>>> return;
>>>>>>>>>>>>>>>>>>>>>>>>>> }
>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>> int main()
>>>>>>>>>>>>>>>>>>>>>>>>>> {
>>>>>>>>>>>>>>>>>>>>>>>>>> Output("Input_Halts = ", H(Px, Px));
>>>>>>>>>>>>>>>>>>>>>>>>>> }
>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>> If a decider must always return a value
>>>>>>>>>>>>>>>>>>>>>>>>>> whenever it is called this
>>>>>>>>>>>>>>>>>>>>>>>>>> requires H to return a value to Px even though
>>>>>>>>>>>>>>>>>>>>>>>>>> H is called in
>>>>>>>>>>>>>>>>>>>>>>>>>> infinite recursion.
>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>> This even requires that the function call from
>>>>>>>>>>>>>>>>>>>>>>>>>> Px to H(Px,Px) must
>>>>>>>>>>>>>>>>>>>>>>>>>> return a value to Px even if this function
>>>>>>>>>>>>>>>>>>>>>>>>>> call to H is not even
>>>>>>>>>>>>>>>>>>>>>>>>>> executed. In the physical model of computation
>>>>>>>>>>>>>>>>>>>>>>>>>> it is an axiom the
>>>>>>>>>>>>>>>>>>>>>>>>>> programs that are not executed never return
>>>>>>>>>>>>>>>>>>>>>>>>>> values because it is
>>>>>>>>>>>>>>>>>>>>>>>>>> physically impossible.
>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>> When simulating halt decider H sees that Px is
>>>>>>>>>>>>>>>>>>>>>>>>>> about to call H(Px,Px)
>>>>>>>>>>>>>>>>>>>>>>>>>> in infinite recursion H aborts its simulation
>>>>>>>>>>>>>>>>>>>>>>>>>> of Px before this call
>>>>>>>>>>>>>>>>>>>>>>>>>> is executed.
>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>> *Clearly computer science is incorrect on this
>>>>>>>>>>>>>>>>>>>>>>>>>> point*
>>>>>>>>>>>>>>>>>>>>>>>>>> Computer science says that H must still return
>>>>>>>>>>>>>>>>>>>>>>>>>> a value to Px even
>>>>>>>>>>>>>>>>>>>>>>>>>> though the call to H is not even executed
>>>>>>>>>>>>>>>>>>>>>>>>>> because all deciders must
>>>>>>>>>>>>>>>>>>>>>>>>>> ALWAYS return to their caller.
>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>> Computer science is correct on this point, what
>>>>>>>>>>>>>>>>>>>>>>>>> is incorrect is your
>>>>>>>>>>>>>>>>>>>>>>>>> implementation of H.
>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>> /Flibble
>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>> So you are saying the a computer program that is
>>>>>>>>>>>>>>>>>>>>>>>> never even executed
>>>>>>>>>>>>>>>>>>>>>>>> must still return a result?
>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>> The "result" of a program that never returns is
>>>>>>>>>>>>>>>>>>>>>>> None!
>>>>>>>>>>>>>>>>>>>>>>> This is equivalent of treating non-termination as
>>>>>>>>>>>>>>>>>>>>>>> an effect.
>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>> No problem - is just a definition.
>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>> H(Px,Px) returns 0 to main. Some people have said
>>>>>>>>>>>>>>>>>>>>>> that the when Px calls H(Px,Px) that H must return
>>>>>>>>>>>>>>>>>>>>>> a value to Px even though this function call from
>>>>>>>>>>>>>>>>>>>>>> Px to H is never executed.
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>> Except that in the ACTUAL BEHAVIOR of the input,
>>>>>>>>>>>>>>>>>>>>> the call IS executed.
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>> You are just confusiong the ACTUAL BEHAVIOR with
>>>>>>>>>>>>>>>>>>>>> the behavior that H determines.
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>> You said that H must always return a result to its
>>>>>>>>>>>>>>>>>>>> caller even if this call is never actually executed.
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>> You don't HAVE a caller unless you execute the call
>>>>>>>>>>>>>>>>>>> instruction.
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> DON'T CHANGE THE SUBJECT
>>>>>>>>>>>>>>>>>> DON'T CHANGE THE SUBJECT
>>>>>>>>>>>>>>>>>> DON'T CHANGE THE SUBJECT
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> I DIDN'T. I don't think you know what a subject is.
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> A decider must always return to its caller:
>>>>>>>>>>>>>>>>>> *ONLY THOSE TIMES WHERE THE CALL TO THE DECIDER IS
>>>>>>>>>>>>>>>>>> ACTUALLY EXECUTED*
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> So, you don't think that Px calls H?
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> The call to H(Px,Px) from P is never executed, thus H
>>>>>>>>>>>>>>>> need not return to Px.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> But it is in the complete simulation of the input to
>>>>>>>>>>>>>>> H(Px,Px), and that is what matters for the answer that H
>>>>>>>>>>>>>>> is supposed to give.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> *This thread had nothing to do with that*
>>>>>>>>>>>>>> The question is whether or not H must return a value to Px
>>>>>>>>>>>>>> when the call to H(Px,Px) from Px is never invoked.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> Which is a meaningless question except in the context of a
>>>>>>>>>>>>> complete simulation/execution.
>>>>>>>>>>>> Does the fact that the invocation of H(Px,Px) from Px that
>>>>>>>>>>>> is never executed prevent H from being a decider?
>>>>>>>>>>>
>>>>>>>>>>> What do you meen it never "gets executed"?
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> H(Px,Px) cannot return any value to the correctly simulated Px
>>>>>>>>>> because the correctly simulated Px is aborted before its call
>>>>>>>>>> to H(Px,Px) is executed.
>>>>>>>>>
>>>>>>>>> Nope. because the actual behavior of Px is to directly call
>>>>>>>>> H(Px,Px)
>>>>>>>>>
>>>>>>>>
>>>>>>>> There is no actual behavior of Px such that H can possibly
>>>>>>>> return any value to its simulated Px.
>>>>>>>>
>>>>>>>>
>>>>>>> Your being illogical again.
>>>>>>>
>>>>>>
>>>>>> Ah so you admit that you lied when you said that H(Px,Px)
>>>>>> eventually returns a value to its simulated input.
>>>>>>
>>>>>
>>>>> No, I didn't say that, I said every call to H(Px,Px) needs to see
>>>>> the 0 returned.
>>>>>
>>>>> I said NOTHING about "to its simulated input" because that is just
>>>>> non-sense.
>>>>
>>>> On 8/28/2022 7:02 PM, Richard Damon wrote:
>>>>  > Yes, the COMPLETE simulation of the input will see
>>>>  > that call and return, yes. If it saw the Call, it
>>>>  > will see the Return.
>>>>
>>>> This was in the context of a simulated P returning to its simulated H.
>>>>
>>>
>>> And what did I say?
>>>
>>> The COMPLETE simulation will see the call and return.
>>>
>>
>> The complete simulation of the input to H never stops.
>
> That isn't the input we were giving to H, so you are just lying because
> you are caught in the trap you made for yourself.
>

On Tuesday, 30 August 2022 at 00:43:34 UTC+2, Ben Bacarisse wrote:
> Skep Dick <skepd...@gmail.com> writes:
>
> > On Monday, 29 August 2022 at 20:29:32 UTC+2, Ben Bacarisse wrote:
> >> Skep Dick <skepd...@gmail.com> writes:
> <cut>
> >> > He hasn't persuaded me.
> >> Great. Is there some point of disagreement between us on PO's non-result?
> >
> > Absolutely there is! I am neither agreeing nor disagreeing with PO
> > (beyond wearing different hats/perspectives) - It's his model/topos,
> > he can interpret it however he likes; and do within it as he pleases.
> Ah then we agree. He can say any old junk he likes. The trouble is
> that PO thinks someone might be interested in his model and his
> interpretation of it (as you put it).
When have mathematicians ever been bothered with other people’s interests?

Apparently the best Mathematics is useless.

> But I'm going to guess that you are neither interested nor are you not
> interested in it (since I doubt you've ever seen a fence you didn't want
> to sit on) so we disagree about that?
My “fence” is just undecidability. Surely you understand that Mathematics looks very different with and without the axiom of choice?

> > On the other hand you do seem to be disagreeing. Quite strongly at
> > that.
> No, you are quite right. He can make up any old model and interpret it
> in any way he pleases. But /PO/ disagrees because he wants to be
> talking about the conventional model and the conventional results.
Yeah but the “conventional” model is open to interpretation, no?

And let’s not get bogged down on decision procedures for “right” vs “wrong” interpretations.

>He's never been interested in being right about some junk model and some
> silly interpretation of it.
I think he just wants to formalize/express his intuitions.

> > Why is it "dishonest"?
> Oh dear. You don't even know when you are being dishonest (or so you
> claim). Well, I think others can decide for themselves.
Let them decide. And then they can tell me in which model they have made the decision…

> "What's the 0th integer greater than 4? It's 4!" (Skep Dick, Aug 2022)
> Message-ID: <a3d63c9e-a151-4fc6...@googlegroups.com>
Yes, you seem to have found the message ID and left out the context.

Wonder if that is a form of dishonesty.

On Tuesday, 30 August 2022 at 03:09:11 UTC+2, richar...@gmail.com wrote:
> On 8/29/22 3:53 PM, Skep Dick wrote:
> > On Monday, 29 August 2022 at 21:43:48 UTC+2, olcott wrote:
> >> That you do not understand that when the simulator derives a
> >> line-by-line execution trace that exactly matches the line-by-line x86
> >> source-code of P conclusively proves that the simulation is correct is
> >> again NO REBUTTAL AT ALL.
> > Neither they get it.
> > Nor you get it.
> >
> > The result of the sumulation is precisely what the result of the simulattion is. Neither more. Nor less.
> > The function returns precisely the answer that it returns which signals precisely whatever H is configured to detect.
> >
> > That doesn't make H "correct" or "incorrect". It makes H map some peculiarity about the execution of P to a Boolean.
> >
> > YOU (the human/oracle) are DEFINING that result as "correct". You are injecting your own meaning into the system.
> >
> >
> No, the AUTHOR of the program made a claim that it answers a particular
> question.
Yes. And the particular question is a yes/no question. So if one answer is “wrong” then the inverse of that answer must is right. This is not a claim I am making. This is a direct consequence of your claimed foundations.

You acclaiming to be in a classical setting. Axiom of choice, law of excluded middle etc..

Either Halt(P) is true, or Halt(P) is false.
If one is wrong the other is right.

> The answer it gives does not match the correct answer to that question,
> so it is just wrong in answering that question.
What determines the “correct answer” in the theory?
If the procedure returns False instead of true, or true instead of false - is it now correct?

> It may be answering some other question correctly, but the question it
> was said to answer, it did not.
I don’t know why you are saying SOME OTHER question.

It is off-by-one negation. Just return the opposite value then?

Or are you now going to move the goalposts and tell me that the only other possible value of a Boolean is not the right answer either?

On 8/30/22 12:38 AM, olcott wrote:
> On 8/29/2022 11:09 PM, Richard Damon wrote:
>> On 8/29/22 11:52 PM, olcott wrote:
>>> On 8/29/2022 10:44 PM, Richard Damon wrote:
>>>>
>>>> On 8/29/22 11:27 PM, olcott wrote:
>>>>> On 8/29/2022 10:13 PM, Richard Damon wrote:
>>>>>> On 8/29/22 10:39 PM, olcott wrote:
>>>>>>> On 8/29/2022 9:32 PM, Richard Damon wrote:
>>>>>>>>
>>>>>>>> On 8/29/22 10:16 PM, olcott wrote:
>>>>>>>>> On 8/29/2022 8:50 PM, Richard Damon wrote:
>>>>>>>>>> On 8/29/22 9:05 PM, olcott wrote:
>>>>>>>>>>> On 8/29/2022 7:50 PM, Richard Damon wrote:
>>>>>>>>>>>>
>>>>>>>>>>>> On 8/29/22 7:28 PM, olcott wrote:
>>>>>>>>>>>>> On 8/29/2022 6:18 PM, Richard Damon wrote:
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> On 8/29/22 1:12 PM, olcott wrote:
>>>>>>>>>>>>>>> On 8/28/2022 10:18 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>> On 8/28/22 11:15 PM, olcott wrote:
>>>>>>>>>>>>>>>>> On 8/28/2022 10:01 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>> On 8/28/22 10:47 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>> On 8/28/2022 8:19 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>> On 8/28/22 9:15 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>> On 8/28/2022 7:47 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>>> On 8/28/22 8:07 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>> On 8/28/2022 3:44 PM, Skep Dick wrote:
>>>>>>>>>>>>>>>>>>>>>>>> On Sunday, 28 August 2022 at 22:10:37 UTC+2,
>>>>>>>>>>>>>>>>>>>>>>>> olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>> On 8/28/2022 3:02 PM, Mr Flibble wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>> On Sun, 28 Aug 2022 14:47:08 -0500
>>>>>>>>>>>>>>>>>>>>>>>>>> olcott <No...@NoWhere.com> wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>> Since Turing machines are mathematical
>>>>>>>>>>>>>>>>>>>>>>>>>>> objects that only exist in the
>>>>>>>>>>>>>>>>>>>>>>>>>>> mind people can have contradictory thus
>>>>>>>>>>>>>>>>>>>>>>>>>>> incoherent ideas about these
>>>>>>>>>>>>>>>>>>>>>>>>>>> abstract mathematical objects and never
>>>>>>>>>>>>>>>>>>>>>>>>>>> realize that their ideas are
>>>>>>>>>>>>>>>>>>>>>>>>>>> incoherent.
>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>> When we study the theory of computation using
>>>>>>>>>>>>>>>>>>>>>>>>>>> physically existing
>>>>>>>>>>>>>>>>>>>>>>>>>>> machines such as the x86 architecture then
>>>>>>>>>>>>>>>>>>>>>>>>>>> the incoherent abstract
>>>>>>>>>>>>>>>>>>>>>>>>>>> ideas are shown to be incoherent in that they
>>>>>>>>>>>>>>>>>>>>>>>>>>> cannot be physically
>>>>>>>>>>>>>>>>>>>>>>>>>>> implemented.
>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>> void Px(ptr x)
>>>>>>>>>>>>>>>>>>>>>>>>>>> {
>>>>>>>>>>>>>>>>>>>>>>>>>>> H(x, x);
>>>>>>>>>>>>>>>>>>>>>>>>>>> return;
>>>>>>>>>>>>>>>>>>>>>>>>>>> }
>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>> int main()
>>>>>>>>>>>>>>>>>>>>>>>>>>> {
>>>>>>>>>>>>>>>>>>>>>>>>>>> Output("Input_Halts = ", H(Px, Px));
>>>>>>>>>>>>>>>>>>>>>>>>>>> }
>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>> If a decider must always return a value
>>>>>>>>>>>>>>>>>>>>>>>>>>> whenever it is called this
>>>>>>>>>>>>>>>>>>>>>>>>>>> requires H to return a value to Px even
>>>>>>>>>>>>>>>>>>>>>>>>>>> though H is called in
>>>>>>>>>>>>>>>>>>>>>>>>>>> infinite recursion.
>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>> This even requires that the function call
>>>>>>>>>>>>>>>>>>>>>>>>>>> from Px to H(Px,Px) must
>>>>>>>>>>>>>>>>>>>>>>>>>>> return a value to Px even if this function
>>>>>>>>>>>>>>>>>>>>>>>>>>> call to H is not even
>>>>>>>>>>>>>>>>>>>>>>>>>>> executed. In the physical model of
>>>>>>>>>>>>>>>>>>>>>>>>>>> computation it is an axiom the
>>>>>>>>>>>>>>>>>>>>>>>>>>> programs that are not executed never return
>>>>>>>>>>>>>>>>>>>>>>>>>>> values because it is
>>>>>>>>>>>>>>>>>>>>>>>>>>> physically impossible.
>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>> When simulating halt decider H sees that Px
>>>>>>>>>>>>>>>>>>>>>>>>>>> is about to call H(Px,Px)
>>>>>>>>>>>>>>>>>>>>>>>>>>> in infinite recursion H aborts its simulation
>>>>>>>>>>>>>>>>>>>>>>>>>>> of Px before this call
>>>>>>>>>>>>>>>>>>>>>>>>>>> is executed.
>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>> *Clearly computer science is incorrect on
>>>>>>>>>>>>>>>>>>>>>>>>>>> this point*
>>>>>>>>>>>>>>>>>>>>>>>>>>> Computer science says that H must still
>>>>>>>>>>>>>>>>>>>>>>>>>>> return a value to Px even
>>>>>>>>>>>>>>>>>>>>>>>>>>> though the call to H is not even executed
>>>>>>>>>>>>>>>>>>>>>>>>>>> because all deciders must
>>>>>>>>>>>>>>>>>>>>>>>>>>> ALWAYS return to their caller.
>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>> Computer science is correct on this point,
>>>>>>>>>>>>>>>>>>>>>>>>>> what is incorrect is your
>>>>>>>>>>>>>>>>>>>>>>>>>> implementation of H.
>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>> /Flibble
>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>> So you are saying the a computer program that
>>>>>>>>>>>>>>>>>>>>>>>>> is never even executed
>>>>>>>>>>>>>>>>>>>>>>>>> must still return a result?
>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>> The "result" of a program that never returns is
>>>>>>>>>>>>>>>>>>>>>>>> None!
>>>>>>>>>>>>>>>>>>>>>>>> This is equivalent of treating non-termination
>>>>>>>>>>>>>>>>>>>>>>>> as an effect.
>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>> No problem - is just a definition.
>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>> H(Px,Px) returns 0 to main. Some people have said
>>>>>>>>>>>>>>>>>>>>>>> that the when Px calls H(Px,Px) that H must
>>>>>>>>>>>>>>>>>>>>>>> return a value to Px even though this function
>>>>>>>>>>>>>>>>>>>>>>> call from Px to H is never executed.
>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>> Except that in the ACTUAL BEHAVIOR of the input,
>>>>>>>>>>>>>>>>>>>>>> the call IS executed.
>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>> You are just confusiong the ACTUAL BEHAVIOR with
>>>>>>>>>>>>>>>>>>>>>> the behavior that H determines.
>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>> You said that H must always return a result to its
>>>>>>>>>>>>>>>>>>>>> caller even if this call is never actually executed.
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>> You don't HAVE a caller unless you execute the call
>>>>>>>>>>>>>>>>>>>> instruction.
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>> DON'T CHANGE THE SUBJECT
>>>>>>>>>>>>>>>>>>> DON'T CHANGE THE SUBJECT
>>>>>>>>>>>>>>>>>>> DON'T CHANGE THE SUBJECT
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> I DIDN'T. I don't think you know what a subject is.
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>> A decider must always return to its caller:
>>>>>>>>>>>>>>>>>>> *ONLY THOSE TIMES WHERE THE CALL TO THE DECIDER IS
>>>>>>>>>>>>>>>>>>> ACTUALLY EXECUTED*
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> So, you don't think that Px calls H?
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> The call to H(Px,Px) from P is never executed, thus H
>>>>>>>>>>>>>>>>> need not return to Px.
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> But it is in the complete simulation of the input to
>>>>>>>>>>>>>>>> H(Px,Px), and that is what matters for the answer that H
>>>>>>>>>>>>>>>> is supposed to give.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> *This thread had nothing to do with that*
>>>>>>>>>>>>>>> The question is whether or not H must return a value to
>>>>>>>>>>>>>>> Px when the call to H(Px,Px) from Px is never invoked.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Which is a meaningless question except in the context of a
>>>>>>>>>>>>>> complete simulation/execution.
>>>>>>>>>>>>> Does the fact that the invocation of H(Px,Px) from Px that
>>>>>>>>>>>>> is never executed prevent H from being a decider?
>>>>>>>>>>>>
>>>>>>>>>>>> What do you meen it never "gets executed"?
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> H(Px,Px) cannot return any value to the correctly simulated
>>>>>>>>>>> Px because the correctly simulated Px is aborted before its
>>>>>>>>>>> call to H(Px,Px) is executed.
>>>>>>>>>>
>>>>>>>>>> Nope. because the actual behavior of Px is to directly call
>>>>>>>>>> H(Px,Px)
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> There is no actual behavior of Px such that H can possibly
>>>>>>>>> return any value to its simulated Px.
>>>>>>>>>
>>>>>>>>>
>>>>>>>> Your being illogical again.
>>>>>>>>
>>>>>>>
>>>>>>> Ah so you admit that you lied when you said that H(Px,Px)
>>>>>>> eventually returns a value to its simulated input.
>>>>>>>
>>>>>>
>>>>>> No, I didn't say that, I said every call to H(Px,Px) needs to see
>>>>>> the 0 returned.
>>>>>>
>>>>>> I said NOTHING about "to its simulated input" because that is just
>>>>>> non-sense.
>>>>>
>>>>> On 8/28/2022 7:02 PM, Richard Damon wrote:
>>>>>  > Yes, the COMPLETE simulation of the input will see
>>>>>  > that call and return, yes. If it saw the Call, it
>>>>>  > will see the Return.
>>>>>
>>>>> This was in the context of a simulated P returning to its simulated H.
>>>>>
>>>>
>>>> And what did I say?
>>>>
>>>> The COMPLETE simulation will see the call and return.
>>>>
>>>
>>> The complete simulation of the input to H never stops.
>>
>> That isn't the input we were giving to H, so you are just lying
>> because you are caught in the trap you made for yourself.
>>
>
> The input is ALWAYS these machine code bytes:
> 558bec518b4508508b4d0851e82ffdffff83c4088945fc837dfc007402ebfe8be55dc3
>
>
>

Skep Dick <skepdick22@gmail.com> writes:

> Either Halt(P) is true, or Halt(P) is false.
> If one is wrong the other is right.

Yes. Make sure you remind Mr Flibble of this since he does not accept
it.

>> The answer it gives does not match the correct answer to that question,
>> so it is just wrong in answering that question.
>
> What determines the “correct answer” in the theory?

Why the scare quotes? There's nothing weird or peculiar about there
being a correct answer but, as usual, you are asking other people to
answer a question you should know the answer to.

Every model of computation that has a halting problem, has a
well-defined notion of what halting means. Unsurprisingly, that's what
determines what the oh-so-mysterious "correct answer" is. For a Turing
machine, it is whether the sequence of configurations generated by the
state transition function is finite or not. For PO's daft C model it
should be whether a top-level function call returns. (I say should be
because PO has let it slip that he has "extended" the definition of
non-halting.)

> If the procedure returns False instead of true, or true instead of
> false - is it now correct?

Of course. For every case that some putative decider gets wrong, there
is another procedure that returns the opposite result that gets it
right. The halting theorem (where such a thing exists for a given
model) simply states that no one procedure gives the right answer for
all instances of the problem.

--
Ben.

On Tuesday, 30 August 2022 at 14:39:16 UTC+2, Ben Bacarisse wrote:
> Skep Dick <skepd...@gmail.com> writes:
>
> > Either Halt(P) is true, or Halt(P) is false.
> > If one is wrong the other is right.
> Yes. Make sure you remind Mr Flibble of this since he does not accept
> it.
Couldn’t care what Mr Fibble thinks.

But if you claim to be operating in a system of classical logic… your axioms force you to accept it.

> > What determines the “correct answer” in the theory?
> Why the scare quotes? There's nothing weird or peculiar about there
> being a correct answer but, as usual, you are asking other people to
> answer a question you should know the answer to.
I am not in the business of pretending to be an oracle to my computational models.

Which function in the model produces the correct answer?

> Every model of computation that has a halting problem, has a
> well-defined notion of what halting means.
> determines what the oh-so-mysterious "correct answer" is. For a Turing
> machine, it is whether the sequence of configurations generated by the
> state transition function is finite or not.
That makes absolutely no sense to me.

At what point in the execution of a TM do you arrive at the conclusion that the state transition function is NOT finite?

On Tuesday, 30 August 2022 at 14:39:16 UTC+2, Ben Bacarisse wrote:
> > If the procedure returns False instead of true, or true instead of
> > false - is it now correct?
> Of course. For every case that some putative decider gets wrong, there
> is another procedure that returns the opposite result that gets it
> right. The halting theorem (where such a thing exists for a given
> model) simply states that no one procedure gives the right answer for
> all instances of the problem.

See! That is why Maths is so easy!

There is a decider which gets it right that the transition function is NOT finite,
And a decider that gets it wrong that the transition function is NOT finite.

Skep Dick <skepdick22@gmail.com> writes:

> On Tuesday, 30 August 2022 at 00:43:34 UTC+2, Ben Bacarisse wrote:
>> Skep Dick <skepd...@gmail.com> writes:
>>
>> > On Monday, 29 August 2022 at 20:29:32 UTC+2, Ben Bacarisse wrote:
>> >> Skep Dick <skepd...@gmail.com> writes:
>> <cut>
>> >> > He hasn't persuaded me.
>> >> Great. Is there some point of disagreement between us on PO's non-result?
>> >
>> > Absolutely there is! I am neither agreeing nor disagreeing with PO
>> > (beyond wearing different hats/perspectives) - It's his model/topos,
>> > he can interpret it however he likes; and do within it as he pleases.
>> Ah then we agree. He can say any old junk he likes. The trouble is
>> that PO thinks someone might be interested in his model and his
>> interpretation of it (as you put it).
>
> When have mathematicians ever been bothered with other people’s
> interests?

So you agree that no one is interested in PO's claims?

> Apparently the best Mathematics is useless.

An odd opinion, but I'm sure you consider it true by definition so
there's no reasonable way to discuss it.

>> But I'm going to guess that you are neither interested nor are you not
>> interested in it (since I doubt you've ever seen a fence you didn't want
>> to sit on) so we disagree about that?
>
> My “fence” is just undecidability. Surely you understand that
> Mathematics looks very different with and without the axiom of choice?

And have you ever read a technical term you want to drop?

>> > On the other hand you do seem to be disagreeing. Quite strongly at
>> > that.
>> No, you are quite right. He can make up any old model and interpret it
>> in any way he pleases. But /PO/ disagrees because he wants to be
>> talking about the conventional model and the conventional results.
>
> Yeah but the “conventional” model is open to interpretation, no?

Not according PO. He insists that his result is about conventional
programs in C and about conventional Turing machines "exactly and
precisely as in Linz". (And that is a quote.)

>> > Why is it "dishonest"?
>> Oh dear. You don't even know when you are being dishonest (or so you
>> claim). Well, I think others can decide for themselves.
>
> Let them decide.

That would be easier if you left the dishonest non-quote for people to
see, but you cut it just to make that harder for them. Good choice.

>> "What's the 0th integer greater than 4? It's 4!" (Skep Dick, Aug 2022)
>> Message-ID: <a3d63c9e-a151-4fc6...@googlegroups.com>
>
> Yes, you seem to have found the message ID and left out the context.

The context is easily found from the message ID. But let me put it in
context so it's all clear. You posted that right after posting a
question:

"Question: What’s the biggest integer you can precisely defined in n
characters?"

No hint there of secret meanings for "biggest" or "integer" or anything.
But /now/ you claim you have secret axioms that make

"What's the 0th integer greater than 4? It's 4!"

a valid thing to say? When did you first decide you were using your
own, as yet unseen, axioms?

--
Ben.

Skep Dick <skepdick22@gmail.com> writes:

> On Tuesday, 30 August 2022 at 14:39:16 UTC+2, Ben Bacarisse wrote:
>> > If the procedure returns False instead of true, or true instead of
>> > false - is it now correct?
>
>> Of course. For every case that some putative decider gets wrong, there
>> is another procedure that returns the opposite result that gets it
>> right. The halting theorem (where such a thing exists for a given
>> model) simply states that no one procedure gives the right answer for
>> all instances of the problem.
>
> See! That is why Maths is so easy!

If only 0.999... = 1 were so easy. Do you still not know what I (and,
for example, Terrence Toa) means by that? Wij posted a link to a book
that includes a detailed explanation of exactly this.

> There is a decider which gets it right that the transition function is
> NOT finite, And a decider that gets it wrong that the transition
> function is NOT finite.

Yes, the halting problem is an utterly trivial bit of mathematics. I
don't know why it bothers so many people.

I think there may be a religious motivation in some cases. PO did once
say that if God can't solve the halting problem then there must be
something wrong with it. Note also that PO has claimed to be God /in a
course of law/, so maybe that's the issue he has with it.

--
Ben.
"What's the 0th integer greater than 4? It's 4!" (Skep Dick, Aug 2022)

On Wednesday, 31 August 2022 at 17:57:26 UTC+2, Ben Bacarisse wrote:
> Yes, the halting problem is an utterly trivial bit of mathematics. I
> don't know why it bothers so many people.
Ah well, the "triviality" of the halting problem depends very much on your sacred cows.
The axioms which you've accepted that I am not "allowed" to slaughter.

I mean - take away the axiom of choice and.... *poof* it ain't so trivial anymore.

Why can't you give me a Turing machine which correctly decides whether the transition function of another TM is "finite"; or "infinite"?

> I think there may be a religious motivation in some cases. PO did once
> say that if God can't solve the halting problem then there must be
> something wrong with it. Note also that PO has claimed to be God /in a
> course of law/, so maybe that's the issue he has with it.
Oh, I don't know. I suspect it has something to do with choice.

Can I choose to reject the axiom of choice, or do I have no choice in accepting it?

Skep Dick <skepdick22@gmail.com> writes:

> On Tuesday, 30 August 2022 at 14:39:16 UTC+2, Ben Bacarisse wrote:
>> Skep Dick <skepd...@gmail.com> writes:
>>
>> > Either Halt(P) is true, or Halt(P) is false.
>> > If one is wrong the other is right.
>> Yes. Make sure you remind Mr Flibble of this since he does not accept
>> it.
>
> Couldn’t care what Mr Fibble thinks.

A great choice.

> But if you claim to be operating in a system of classical logic… your
> axioms force you to accept it.

I hope you are not someone who has trouble being agreed with!

>> > What determines the “correct answer” in the theory?
>> Why the scare quotes? There's nothing weird or peculiar about there
>> being a correct answer but, as usual, you are asking other people to
>> answer a question you should know the answer to.
>
> I am not in the business of pretending to be an oracle to my
> computational models.

And I'm not interested in anything you might call "yours". I now know
that everything, even greater than (or maybe even what the integer 4 is)
is up for grabs when it's "your" this or that. It's simply pointless to
comment on any claim of yours without all the secret axioms that we'll
hear about down the line!

> Which function in the model produces the correct answer?

The function is not in the model -- how could it be? The model is a
model of computation. The halting function is (if you insist on going
all the way back) a set from set theory.

>> Every model of computation that has a halting problem, has a
>> well-defined notion of what halting means.
>> determines what the oh-so-mysterious "correct answer" is. For a Turing
>> machine, it is whether the sequence of configurations generated by the
>> state transition function is finite or not.
>
> That makes absolutely no sense to me.

The makes me wonder why you keep asking me to answer questions you
should know (or know where to find) the answers to. My explanations are
unlikely to help, are they?

> At what point in the execution of a TM do you arrive at the conclusion
> that the state transition function is NOT finite?

The state transition function is always finite, by definition. I won't
elaborate on this explanation further since my previous attempt made no
sense to you. You could try a book, but maybe you have the same problem
with CS books as you do with maths books. If that's the case, you might
consider not posting about theoretical computer science.

--
Ben.
"What's the 0th integer greater than 4? It's 4!"
"It is a matter of whether the theorem holds given some axioms (of my
arbitrary choosing)" (Skep Dick, five days later)

On Wednesday, 31 August 2022 at 18:31:35 UTC+2, Ben Bacarisse wrote:
> > But if you claim to be operating in a system of classical logic… your
> > axioms force you to accept it.
> I hope you are not someone who has trouble being agreed with!
Oh, it could just be my upbringing, I guess? I am the distributed consensus kind of guy...

Two-person leader election (consensus) is undecidable.

> > I am not in the business of pretending to be an oracle to my
> > computational models.
> And I'm not interested in anything you might call "yours". I now know
> that everything, even greater than (or maybe even what the integer 4 is)
> is up for grabs when it's "your" this or that. It's simply pointless to
> comment on any claim of yours without all the secret axioms that we'll
> hear about down the line!
And yet you are commenting!

Probably because you read the English words and you brought your Mathematical baggage (full of "usual" definitions) to the table.

Not even bothering to check what the person's even asking.

> > Which function in the model produces the correct answer?
> The function is not in the model -- how could it be? The model is a
> model of computation. The halting function is (if you insist on going
> all the way back) a set from set theory.
And who said we have set theory in our universe of discourse?!?

> > That makes absolutely no sense to me.
> The makes me wonder why you keep asking me to answer questions you
> should know (or know where to find) the answers to. My explanations are
> unlikely to help, are they?
Not for as long as you keep assigning Mathematical meaning to my English questions...

> > At what point in the execution of a TM do you arrive at the conclusion
> > that the state transition function is NOT finite?
> The state transition function is always finite, by definition.
Ahhh, the "by definition" cop-out.

I really dont' know how to explain the difference between propositional and judgmental equality any better than I already have?

>I won't
> elaborate on this explanation further since my previous attempt made no
> sense to you.
Yes. Because your "by definition" presupposes that you have a way for differentiating finite from infinite objects.

> "What's the 0th integer greater than 4? It's 4!"
> "It is a matter of whether the theorem holds given some axioms (of my
> arbitrary choosing)" (Skep Dick, five days later)
The purpose of your quotes remains a mystery...

But hey... let me quote some stuff you said...

"5 > 4." (Ben Whatever his name is)

On Wednesday, 31 August 2022 at 17:44:42 UTC+2, Ben Bacarisse wrote:
> > When have mathematicians ever been bothered with other people’s
> > interests?
> So you agree that no one is interested in PO's claims?
Only if you also agree that nobody is interested in anything you have to say.

> > Apparently the best Mathematics is useless.
> An odd opinion, but I'm sure you consider it true by definition so
> there's no reasonable way to discuss it.
Hardly my own even... It's G.H.Hardy's sentiment.

> > My “fence” is just undecidability. Surely you understand that
> > Mathematics looks very different with and without the axiom of choice?
> And have you ever read a technical term you want to drop?
Yes, I absolutely want to drop of the "law" of excluded middle, it's just that the axiom of choice implies excluded middle also - so I have to drop both.

https://en.wikipedia.org/wiki/Diaconescu%27s_theorem

I hope that's not too "technical" for you?

> > Yeah but the “conventional” model is open to interpretation, no?
> Not according PO. He insists that his result is about conventional
> programs in C and about conventional Turing machines "exactly and
> precisely as in Linz". (And that is a quote.)
OK but he could be absolutely right about that. In his model of all concerning theories.

> > Let them decide.
> That would be easier if you left the dishonest non-quote for people to
They have the post ID...

> "Question: What’s the biggest integer you can precisely defined in n
> characters?"
>
> No hint there of secret meanings for "biggest" or "integer" or anything.
Secret meaning? It really doesn't matter what the Mathematical meaning of those phrases is!

If you accept the axiom of choice/excluded middle - whatever the Mathematical meaning of the English question then the English answer is Mathematically correct also.
If the maximal element of (-inf, x] is describable in 240 characters, then minimal element of the contrapositive is [x+1, inf) also describable in 240 characters.

I think x + 1 > x ? Of course, it could just be my axioms.

> But /now/ you claim you have secret axioms that make
> "What's the 0th integer greater than 4? It's 4!"
> a valid thing to say? When did you first decide you were using your
> own, as yet unseen, axioms?
I am never really decided on any axioms. I always start with the theorems.

Skep Dick <skepdick22@gmail.com> writes:

> On Wednesday, 31 August 2022 at 17:44:42 UTC+2, Ben Bacarisse wrote:
<lost attribution>
>> > Yeah but the “conventional” model is open to interpretation, no?
>> Not according PO. He insists that his result is about conventional
>> programs in C and about conventional Turing machines "exactly and
>> precisely as in Linz". (And that is a quote.).
>
> OK but he could be absolutely right about that. In his model of all
> concerning theories.

You don't understand PO at all. Like most cranks he's not interested in
being right "in his model" unless "his model" is exactly equivalent to
the usual one. He's convinced he's found out that everyone else is
wrong, not that there's an alternative way to be right.

Your cop-out, that you pick the axioms after the theorems, (see below)
is not something most cranks would do. Their delusion is the they are
right where everyone was wrong. No Usenet crank would ever come up with
non Euclidean geometry. They'd claim that a triangle's angles don't sum
to pi in the Euclidean plane.

>> "Question: What’s the biggest integer you can precisely defined in n
>> characters?"
>>
>> No hint there of secret meanings for "biggest" or "integer" or anything.
>
> Secret meaning? It really doesn't matter what the Mathematical meaning
> of those phrases is!

The secret meanings came later. I was perfectly prepared to take your
question as having been posted in good faith (indeed I did, at first),
but your next post in the thread said

"What's the 0th integer greater than 4? It's 4!"

and you justified it by saying (five days later):

"It is a matter of whether the theorem holds given some axioms (of my
arbitrary choosing)."

>> ... When did you first decide you were using your
>> own, as yet unseen, axioms?
>
> I am never really decided on any axioms. I always start with the
> theorems.

And since there are axioms that make anything a theorem, it's all good!
The only problem is knowing when you are saying things in good faith and
when you might be about the pull the everything's a theorem with the
right axioms defence. I think it's best to be cautions and try to spot
when you are using "your" words, even when you seem to be replying about
mine.

--
Ben.

Skep Dick <skepdick22@gmail.com> writes:

> On Wednesday, 31 August 2022 at 18:31:35 UTC+2, Ben Bacarisse wrote:
<missing attribution: it's Skep Dick <skepdick22@gmail.com>>
>> > I am not in the business of pretending to be an oracle to my
>> > computational models.
>> And I'm not interested in anything you might call "yours". I now know
>> that everything, even greater than (or maybe even what the integer 4 is)
>> is up for grabs when it's "your" this or that. It's simply pointless to
>> comment on any claim of yours without all the secret axioms that we'll
>> hear about down the line!
>
> And yet you are commenting!

Eh? I'm not talking about "your" anything. If I am, point it out so I
can stop. I am very likely to make mistakes, of course, because your
private meanings are not always visible.

>> > Which function in the model produces the correct answer?
>> The function is not in the model -- how could it be? The model is a
>> model of computation. The halting function is (if you insist on going
>> all the way back) a set from set theory.
> And who said we have set theory in our universe of discourse?!?

No one. You, not doubt, have been talking all along about "your"
halting problems, but I can't say anything about those. You asked me to
explain about "correct answers" so I answer /about what I mean/.

But why comment at all when all the axioms, all the definitions, all the
universe of discourse (you love jargon, don't you) is to be decided
afterwards so everything you say had to be re-interpreted?

>> > At what point in the execution of a TM do you arrive at the conclusion
>> > that the state transition function is NOT finite?
>> The state transition function is always finite, by definition.
>
> Ahhh, the "by definition" cop-out.

An odd point of view. You don't define anything so you can't be wrong.
By defining things, mathematicians are constrained to investigate the
consequences. The crank cop-out (and it really is a cop-out) is to
/not/ define anything.

Anyway, true to your "I'm just chatting" style, I see you don't want to
find a way to ask the question in a way that it could be understood. A
side chat about definitions and cop-outs will do just as well.

>>I won't
>> elaborate on this explanation further since my previous attempt made no
>> sense to you.
>
> Yes. Because your "by definition" presupposes that you have a way for
> differentiating finite from infinite objects.

Of course. Can I assume that you are not able to use the words finite
and infinite because you don't? Or at least that you don't today.

>> "What's the 0th integer greater than 4? It's 4!"
>> "It is a matter of whether the theorem holds given some axioms (of my
>> arbitrary choosing)" (Skep Dick, five days later)
>
> The purpose of your quotes remains a mystery...

I think people should know that whatever you say, not matter how daft,
the 'I pick the axioms later' defence will pop up.

> But hey... let me quote some stuff you said...
>
> "5 > 4." (Ben Whatever his name is)

Bacarisse. (I though you'd used it already.) What's yours? Oh don't
bother; you'll just ask what I mean by a name, and what it means for a
name to be possessed, and how can we know anything at all anyway...

--
Ben.

Skep Dick <skepdick22@gmail.com> writes:

> On Wednesday, 31 August 2022 at 17:57:26 UTC+2, Ben Bacarisse wrote:
>> Yes, the halting problem is an utterly trivial bit of mathematics. I
>> don't know why it bothers so many people.

> Ah well, the "triviality" of the halting problem depends very much on
> your sacred cows. The axioms which you've accepted that I am not
> "allowed" to slaughter.

Nonsense. You get to choose any axioms you like. My objection to
cranks is that they won't put the work in. We /never/ get anything
remotely resembling axioms or even a proof. Just bald assertion,
usually hand-in-hand with a steadfast refusal to know the topic before
commenting.

> I mean - take away the axiom of choice and.... *poof* it ain't so
> trivial anymore.

Citation, please? I ask for a citation because I can't believe you
could ever prove such a thing, so I'm assuming you've got it from
somewhere.

> Why can't you give me a Turing machine which correctly decides whether
> the transition function of another TM is "finite"; or "infinite"?

TM transition functions are always finite. I assume you did not intend
to write what you did, but I really can't work what you wanted to say.

--
Ben.
"What's the 0th integer greater than 4? It's 4!"
"It is a matter of whether the theorem holds given some axioms (of my
arbitrary choosing)." (Skep Dick, five days later)