The halting problem is defined as:

In computability theory, the halting problem is the problem of
determining, from a description of an arbitrary computer program and an
input, whether the program will finish running, or continue to run
forever. Alan Turing proved in 1936 that a general algorithm to solve
the halting problem for all possible program-input pairs cannot exist.

The only extant proof that the halting problem is unsolvable is:

For any program f that might determine if programs halt, a
"pathological" program g, called with some input, can pass its own
source and its input to f and then specifically do the opposite of what
f predicts g will do. No f can exist that handles this case.

This proof contains an infinite recursion category error (f and g are
in different categories) which makes the proof invalid (erroneous)
making the halting problem itself not unsolvable (as predicated on
this erroneous proof).

The halting problem *might* be unsolvable but at present there is no
currently extant proof proving this to be the case.

/Flibble

Leigh Johnston, aka Mr Flibble wrote:
> The halting problem is defined as:
>
> In computability theory, the halting problem is the problem of
> determining, from a description of an arbitrary computer program and an
> input, whether the program will finish running, or continue to run
> forever. Alan Turing proved in 1936 that a general algorithm to solve
> the halting problem for all possible program-input pairs cannot exist.
>
> The only extant proof that the halting problem is unsolvable is:
>
> For any program f that might determine if programs halt, a
> "pathological" program g, called with some input, can pass its own
> source and its input to f and then specifically do the opposite of what
> f predicts g will do. No f can exist that handles this case.
>
> This proof contains an infinite recursion category error (f and g are
> in different categories)

You cannot avoid what you call a "category error" in computing Leigh,
i.e. that a program text is also a data. Without that compilers
couldn't even exists.

Neither IT or CS are your thing Leigh, give up.

On Mon, 18 Apr 2022 14:02:11 +0200
Python <python@example.invalid> wrote:

> Leigh Johnston, aka Mr Flibble wrote:
> > The halting problem is defined as:
> >
> > In computability theory, the halting problem is the problem of
> > determining, from a description of an arbitrary computer program
> > and an input, whether the program will finish running, or continue
> > to run forever. Alan Turing proved in 1936 that a general algorithm
> > to solve the halting problem for all possible program-input pairs
> > cannot exist.
> >
> > The only extant proof that the halting problem is unsolvable is:
> >
> > For any program f that might determine if programs halt, a
> > "pathological" program g, called with some input, can pass its own
> > source and its input to f and then specifically do the opposite of
> > what f predicts g will do. No f can exist that handles this case.
> >
> > This proof contains an infinite recursion category error (f and g
> > are in different categories)
>
> You cannot avoid what you call a "category error" in computing Leigh,
> i.e. that a program text is also a data. Without that compilers
> couldn't even exists.

A compiler compiling program text into an executable isn't infinitely
recursive, dear.

>
> Neither IT or CS are your thing Leigh, give up.
My career seems to disagree with your assertion, dear: I was a member of
the team that invented the smartphone. What did you ever achieve, Mr
Anonymous?

/Flibble

Le 18/04/2022 à 14:06, Mr Flibble a écrit :
> On Mon, 18 Apr 2022 14:02:11 +0200
> Python <python@example.invalid> wrote:
>
>> Leigh Johnston, aka Mr Flibble wrote:
>>> The halting problem is defined as:
>>>
>>> In computability theory, the halting problem is the problem of
>>> determining, from a description of an arbitrary computer program
>>> and an input, whether the program will finish running, or continue
>>> to run forever. Alan Turing proved in 1936 that a general algorithm
>>> to solve the halting problem for all possible program-input pairs
>>> cannot exist.
>>>
>>> The only extant proof that the halting problem is unsolvable is:
>>>
>>> For any program f that might determine if programs halt, a
>>> "pathological" program g, called with some input, can pass its own
>>> source and its input to f and then specifically do the opposite of
>>> what f predicts g will do. No f can exist that handles this case.
>>>
>>> This proof contains an infinite recursion category error (f and g
>>> are in different categories)
>>
>> You cannot avoid what you call a "category error" in computing Leigh,
>> i.e. that a program text is also a data. Without that compilers
>> couldn't even exists.
>
> A compiler compiling program text into an executable isn't infinitely
> recursive, dear.

There is nothing infinitely recursive in the Halting Problem. This has
been pointed to you before.

>> Neither IT or CS are your thing Leigh, give up.
>
> My career seems to disagree with your assertion, dear: I was a member of
> the team that invented the smartphone. What did you ever achieve, Mr
> Anonymous?

Yes, I've heard of the huge success of neos. Oh, that you invented the
concept of smartphone too :-)

https://github.com/i42output/neos/pulse

On Mon, 18 Apr 2022 14:56:16 +0200
Python <python@example.invalid> wrote:

> Le 18/04/2022 à 14:06, Mr Flibble a écrit :
> > On Mon, 18 Apr 2022 14:02:11 +0200
> > Python <python@example.invalid> wrote:
> >
> >> Leigh Johnston, aka Mr Flibble wrote:
> >>> The halting problem is defined as:
> >>>
> >>> In computability theory, the halting problem is the problem of
> >>> determining, from a description of an arbitrary computer program
> >>> and an input, whether the program will finish running, or continue
> >>> to run forever. Alan Turing proved in 1936 that a general
> >>> algorithm to solve the halting problem for all possible
> >>> program-input pairs cannot exist.
> >>>
> >>> The only extant proof that the halting problem is unsolvable is:
> >>>
> >>> For any program f that might determine if programs halt, a
> >>> "pathological" program g, called with some input, can pass its own
> >>> source and its input to f and then specifically do the opposite of
> >>> what f predicts g will do. No f can exist that handles this case.
> >>>
> >>> This proof contains an infinite recursion category error (f and g
> >>> are in different categories)
> >>
> >> You cannot avoid what you call a "category error" in computing
> >> Leigh, i.e. that a program text is also a data. Without that
> >> compilers couldn't even exists.
> >
> > A compiler compiling program text into an executable isn't
> > infinitely recursive, dear.
>
> There is nothing infinitely recursive in the Halting Problem. This has
> been pointed to you before.

Try reading what I actually wrote: the halting problem proof is
infinitely recursive not the halting problem itself.

>
> >> Neither IT or CS are your thing Leigh, give up.
> >
> > My career seems to disagree with your assertion, dear: I was a
> > member of the team that invented the smartphone. What did you ever
> > achieve, Mr Anonymous?
>
> Yes, I've heard of the huge success of neos. Oh, that you invented the
> concept of smartphone too :-)
>
> https://github.com/i42output/neos/pulse

Again, why are you obsessed with my progress on a particular project? I
am working on MULTIPLE projects at the same time; I will rotate back
around to neos at the appropriate time.

/Flibble

Leigh Johnston, aka Mr Flibble wrote:
> On Mon, 18 Apr 2022 14:56:16 +0200
> Python <python@example.invalid> wrote:
>
>> Le 18/04/2022 à 14:06, Mr Flibble a écrit :
>>> On Mon, 18 Apr 2022 14:02:11 +0200
>>> Python <python@example.invalid> wrote:
>>>
>>>> Leigh Johnston, aka Mr Flibble wrote:
>>>>> The halting problem is defined as:
>>>>>
>>>>> In computability theory, the halting problem is the problem of
>>>>> determining, from a description of an arbitrary computer program
>>>>> and an input, whether the program will finish running, or continue
>>>>> to run forever. Alan Turing proved in 1936 that a general
>>>>> algorithm to solve the halting problem for all possible
>>>>> program-input pairs cannot exist.
>>>>>
>>>>> The only extant proof that the halting problem is unsolvable is:
>>>>>
>>>>> For any program f that might determine if programs halt, a
>>>>> "pathological" program g, called with some input, can pass its own
>>>>> source and its input to f and then specifically do the opposite of
>>>>> what f predicts g will do. No f can exist that handles this case.
>>>>>
>>>>> This proof contains an infinite recursion category error (f and g
>>>>> are in different categories)
>>>>
>>>> You cannot avoid what you call a "category error" in computing
>>>> Leigh, i.e. that a program text is also a data. Without that
>>>> compilers couldn't even exists.
>>>
>>> A compiler compiling program text into an executable isn't
>>> infinitely recursive, dear.
>>
>> There is nothing infinitely recursive in the Halting Problem. This has
>> been pointed to you before.
>
> Try reading what I actually wrote: the halting problem proof is
> infinitely recursive not the halting problem itself.

Neither is the proof infinitely recursive.

>>>> Neither IT or CS are your thing Leigh, give up.
>>>
>>> My career seems to disagree with your assertion, dear: I was a
>>> member of the team that invented the smartphone. What did you ever
>>> achieve, Mr Anonymous?
>>
>> Yes, I've heard of the huge success of neos. Oh, that you invented the
>> concept of smartphone too :-)
>>
>> https://github.com/i42output/neos/pulse
>
> Again, why are you obsessed with my progress on a particular project? I
> am working on MULTIPLE projects at the same time; I will rotate back
> around to neos at the appropriate time.

Because you bragged a lot about it, and would love to look at actual
code.

On 4/18/2022 6:42 AM, Mr Flibble wrote:
> The halting problem is defined as:
>
> In computability theory, the halting problem is the problem of
> determining, from a description of an arbitrary computer program and an
> input, whether the program will finish running, or continue to run
> forever. Alan Turing proved in 1936 that a general algorithm to solve
> the halting problem for all possible program-input pairs cannot exist.
>
> The only extant proof that the halting problem is unsolvable is:
>
> For any program f that might determine if programs halt, a
> "pathological" program g, called with some input, can pass its own
> source and its input to f and then specifically do the opposite of what
> f predicts g will do. No f can exist that handles this case.
>

void P(u32 x)
{ if (H(x, x))
HERE: goto HERE;
}

int main()
{ Output("Input_Halts = ", H((u32)P, (u32)P));
}

_P()
[000009d6](01) 55 push ebp
[000009d7](02) 8bec mov ebp,esp
[000009d9](03) 8b4508 mov eax,[ebp+08]
[000009dc](01) 50 push eax // push P
[000009dd](03) 8b4d08 mov ecx,[ebp+08]
[000009e0](01) 51 push ecx // push P
[000009e1](05) e840feffff call 00000826 // call H
[000009e6](03) 83c408 add esp,+08
[000009e9](02) 85c0 test eax,eax
[000009eb](02) 7402 jz 000009ef
[000009ed](02) ebfe jmp 000009ed
[000009ef](01) 5d pop ebp
[000009f0](01) c3 ret // Final state
Size in bytes:(0027) [000009f0]

The simulated input to H(P,P) cannot possibly reach its own final state
of [000009f0] it keeps repeating [000009d6] to [000009e1] until aborted.

Begin Local Halt Decider Simulation
....[000009d6][00211368][0021136c] 55 push ebp // enter P
....[000009d7][00211368][0021136c] 8bec mov ebp,esp
....[000009d9][00211368][0021136c] 8b4508 mov eax,[ebp+08]
....[000009dc][00211364][000009d6] 50 push eax // Push P
....[000009dd][00211364][000009d6] 8b4d08 mov ecx,[ebp+08]
....[000009e0][00211360][000009d6] 51 push ecx // Push P
....[000009e1][0021135c][000009e6] e840feffff call 00000826 // Call H
....[000009d6][0025bd90][0025bd94] 55 push ebp // enter P
....[000009d7][0025bd90][0025bd94] 8bec mov ebp,esp
....[000009d9][0025bd90][0025bd94] 8b4508 mov eax,[ebp+08]
....[000009dc][0025bd8c][000009d6] 50 push eax // Push P
....[000009dd][0025bd8c][000009d6] 8b4d08 mov ecx,[ebp+08]
....[000009e0][0025bd88][000009d6] 51 push ecx // Push P
....[000009e1][0025bd84][000009e6] e840feffff call 00000826 // Call H
Local Halt Decider: Infinite Recursion Detected Simulation Stopped

> This proof contains an infinite recursion category error (f and g are
> in different categories) which makes the proof invalid (erroneous)
> making the halting problem itself not unsolvable (as predicated on
> this erroneous proof).
>
> The halting problem *might* be unsolvable but at present there is no
> currently extant proof proving this to be the case.
>
> /Flibble
>

--
Copyright 2022 Pete Olcott

"Talent hits a target no one else can hit;
Genius hits a target no one else can see."
Arthur Schopenhauer

On 4/18/2022 7:56 AM, Python wrote:
> Le 18/04/2022 à 14:06, Mr Flibble a écrit :
>> On Mon, 18 Apr 2022 14:02:11 +0200
>> Python <python@example.invalid> wrote:
>>
>>> Leigh Johnston, aka Mr Flibble wrote:
>>>> The halting problem is defined as:
>>>>
>>>> In computability theory, the halting problem is the problem of
>>>> determining, from a description of an arbitrary computer program
>>>> and an input, whether the program will finish running, or continue
>>>> to run forever. Alan Turing proved in 1936 that a general algorithm
>>>> to solve the halting problem for all possible program-input pairs
>>>> cannot exist.
>>>>
>>>> The only extant proof that the halting problem is unsolvable is:
>>>>
>>>> For any program f that might determine if programs halt, a
>>>> "pathological" program g, called with some input, can pass its own
>>>> source and its input to f and then specifically do the opposite of
>>>> what f predicts g will do. No f can exist that handles this case.
>>>>
>>>> This proof contains an infinite recursion category error (f and g
>>>> are in different categories)
>>>
>>> You cannot avoid what you call a "category error" in computing Leigh,
>>> i.e. that a program text is also a data. Without that compilers
>>> couldn't even exists.
>>
>> A compiler compiling program text into an executable isn't infinitely
>> recursive, dear.
>
> There is nothing infinitely recursive in the Halting Problem. This has
> been pointed to you before.
>

I just proved there is. In the case that I just showed H recognizes the
infinite recursion, aborts the simulation of its input and rejects this
input, on the basis that it is infinitely recursive. Computations can do
this because they have intelligence.

In the case of the 1931 Incompleteness theorem Gödel's logic sentence
just sits there on the page unable to be evaluated because of its
infinite recursion.

Read the Clocksin Mellish Prolog textbook on page 3, it shows the
infinite recursion the the Incompleteness Theorem:

https://www.researchgate.net/publication/350789898_Prolog_detects_and_rejects_pathological_self_reference_in_the_Godel_sentence

>>> Neither IT or CS are your thing Leigh, give up.
>> My career seems to disagree with your assertion, dear: I was a member of
>> the team that invented the smartphone. What did you ever achieve, Mr
>> Anonymous?
>
> Yes, I've heard of the huge success of neos. Oh, that you invented the
> concept of smartphone too :-)
>
> https://github.com/i42output/neos/pulse

--
Copyright 2022 Pete Olcott

"Talent hits a target no one else can hit;
Genius hits a target no one else can see."
Arthur Schopenhauer

Mr Flibble <flibble@reddwarf.jmc.corp> writes:

> The halting problem is defined as:
>
> In computability theory, the halting problem is the problem of
> determining, from a description of an arbitrary computer program and an
> input, whether the program will finish running, or continue to run
> forever. Alan Turing proved in 1936 that a general algorithm to solve
> the halting problem for all possible program-input pairs cannot exist.

Actually he didn't. That's a common misconception. The halting theorem
follow as a simple corollary from his 1936 proof, but Turing never
published an explicit proof of the theorem.

> The only extant proof that the halting problem is unsolvable is:

There are others.

> For any program f that might determine if programs halt, a
> "pathological" program g, called with some input, can pass its own
> source and its input to f and then specifically do the opposite of what
> f predicts g will do. No f can exist that handles this case.
>
> This proof contains an infinite recursion category error (f and g are
> in different categories) which makes the proof invalid (erroneous)
> making the halting problem itself not unsolvable (as predicated on
> this erroneous proof).
>
> The halting problem *might* be unsolvable but at present there is no
> currently extant proof proving this to be the case.

There are many. You outline one in this post. Interested readers
should consult a proper textbook.

--
Ben.

On Mon, 18 Apr 2022 17:00:59 +0100
Ben <ben.usenet@bsb.me.uk> wrote:

> Mr Flibble <flibble@reddwarf.jmc.corp> writes:
>
> > The halting problem is defined as:
> >
> > In computability theory, the halting problem is the problem of
> > determining, from a description of an arbitrary computer program
> > and an input, whether the program will finish running, or continue
> > to run forever. Alan Turing proved in 1936 that a general algorithm
> > to solve the halting problem for all possible program-input pairs
> > cannot exist.
>
> Actually he didn't. That's a common misconception. The halting
> theorem follow as a simple corollary from his 1936 proof, but Turing
> never published an explicit proof of the theorem.

If what you said is true then you should correct the Halting
Problem Wikipedia article; until then I will assume the Wikipedia
article is correct and random Usenet guy is incorrect.

>
> > The only extant proof that the halting problem is unsolvable is:
>
> There are others.
>
> > For any program f that might determine if programs halt, a
> > "pathological" program g, called with some input, can pass its own
> > source and its input to f and then specifically do the opposite of
> > what f predicts g will do. No f can exist that handles this case.
> >
> > This proof contains an infinite recursion category error (f and g
> > are in different categories) which makes the proof invalid
> > (erroneous) making the halting problem itself not unsolvable (as
> > predicated on this erroneous proof).
> >
> > The halting problem *might* be unsolvable but at present there is no
> > currently extant proof proving this to be the case.
>
> There are many. You outline one in this post. Interested readers
> should consult a proper textbook.
If what you said is true then you should correct the Halting
Problem Wikipedia article; until then I will assume the Wikipedia
article is correct and random Usenet guy is incorrect.

/Flibble

On 4/18/2022 11:23 AM, Mr Flibble wrote:
> On Mon, 18 Apr 2022 17:00:59 +0100
> Ben <ben.usenet@bsb.me.uk> wrote:
>
>> Mr Flibble <flibble@reddwarf.jmc.corp> writes:
>>
>>> The halting problem is defined as:
>>>
>>> In computability theory, the halting problem is the problem of
>>> determining, from a description of an arbitrary computer program
>>> and an input, whether the program will finish running, or continue
>>> to run forever. Alan Turing proved in 1936 that a general algorithm
>>> to solve the halting problem for all possible program-input pairs
>>> cannot exist.
>>
>> Actually he didn't. That's a common misconception. The halting
>> theorem follow as a simple corollary from his 1936 proof, but Turing
>> never published an explicit proof of the theorem.
>
> If what you said is true then you should correct the Halting
> Problem Wikipedia article; until then I will assume the Wikipedia
> article is correct and random Usenet guy is incorrect.
>
>>
>>> The only extant proof that the halting problem is unsolvable is:
>>
>> There are others.
>>
>>> For any program f that might determine if programs halt, a
>>> "pathological" program g, called with some input, can pass its own
>>> source and its input to f and then specifically do the opposite of
>>> what f predicts g will do. No f can exist that handles this case.
>>>
>>> This proof contains an infinite recursion category error (f and g
>>> are in different categories) which makes the proof invalid
>>> (erroneous) making the halting problem itself not unsolvable (as
>>> predicated on this erroneous proof).
>>>
>>> The halting problem *might* be unsolvable but at present there is no
>>> currently extant proof proving this to be the case.
>>
>> There are many. You outline one in this post. Interested readers
>> should consult a proper textbook.
>
> If what you said is true then you should correct the Halting
> Problem Wikipedia article; until then I will assume the Wikipedia
> article is correct and random Usenet guy is incorrect.
>
> /Flibble
>

I think that all of these alternative proofs can be reduced to an
instance of the conventional HP counter-example thus are refuted by the
correct refutation of the conventional HP counter-example.

--
Copyright 2022 Pete Olcott

"Talent hits a target no one else can hit;
Genius hits a target no one else can see."
Arthur Schopenhauer

Mr Flibble <flibble@reddwarf.jmc.corp> writes:

> On Mon, 18 Apr 2022 17:00:59 +0100
> Ben <ben.usenet@bsb.me.uk> wrote:
>
>> Mr Flibble <flibble@reddwarf.jmc.corp> writes:
>>
>> > The halting problem is defined as:
>> >
>> > In computability theory, the halting problem is the problem of
>> > determining, from a description of an arbitrary computer program
>> > and an input, whether the program will finish running, or continue
>> > to run forever. Alan Turing proved in 1936 that a general algorithm
>> > to solve the halting problem for all possible program-input pairs
>> > cannot exist.
>>
>> Actually he didn't. That's a common misconception. The halting
>> theorem follow as a simple corollary from his 1936 proof, but Turing
>> never published an explicit proof of the theorem.
>
> If what you said is true then you should correct the Halting
> Problem Wikipedia article; until then I will assume the Wikipedia
> article is correct and random Usenet guy is incorrect.

Who you believe is up to you. But we are not unknown quantities. Other
readers can see my posting history a form a judgement as whether it seems
likely that I know what I am talking about.

The article does say

"It is often said that Turing stated and proved the halting theorem in
'On Comuutable Numbers', but strictly this is not true"

so that detail is covered. Didn't you read the article?

>> > The only extant proof that the halting problem is unsolvable is:
>>
>> There are others.
>>
>> > For any program f that might determine if programs halt, a
>> > "pathological" program g, called with some input, can pass its own
>> > source and its input to f and then specifically do the opposite of
>> > what f predicts g will do. No f can exist that handles this case.
>> >
>> > This proof contains an infinite recursion category error (f and g
>> > are in different categories) which makes the proof invalid
>> > (erroneous) making the halting problem itself not unsolvable (as
>> > predicated on this erroneous proof).
>> >
>> > The halting problem *might* be unsolvable but at present there is no
>> > currently extant proof proving this to be the case.
>>
>> There are many. You outline one in this post. Interested readers
>> should consult a proper textbook.
>
> If what you said is true then you should correct the Halting
> Problem Wikipedia article; until then I will assume the Wikipedia
> article is correct and random Usenet guy is incorrect.

It must the "there are many" you think is missing from the article.
It's not really crucial since one proof is enough, but the article
certainly says that there various proofs, even if it's less than 100%
explicit. Even so, the article includes outlines of two proofs and
references Davis's as probably the first one published.

The proofs via Turing, Church, Rice and Chaitin are only implied, but I
don't think the article would be significantly improved by making that
explicit. After all, the article is not aimed a math deniers.

--
Ben.

olcott <NoOne@NoWhere.com> writes:

> I think that all of these alternative proofs can be reduced to an
> instance of the conventional HP counter-example thus are refuted by
> the correct refutation of the conventional HP counter-example.

Readers should know, before deciding if you opinion on the matter is to
be taken seriously, that you have not even read the proper proof of the
theorem in the book you claim to have been studying for years, much less
any of the others that use a different strategy.

Oh, and readers should also know that you don't know what a proof is
since you still claim that if A,B,C ⊦ X then A,B,C,~A ⊬ X.

--
Ben.
"le génie humain a des limites, quand la bêtise humaine n’en a pas"
Alexandre Dumas (fils)

On 4/18/2022 3:13 PM, Ben wrote:
> olcott <NoOne@NoWhere.com> writes:
>
>> I think that all of these alternative proofs can be reduced to an
>> instance of the conventional HP counter-example thus are refuted by
>> the correct refutation of the conventional HP counter-example.
>
> Readers should know, before deciding if you opinion on the matter is to
> be taken seriously, that you have not even read the proper proof of the
> theorem in the book you claim to have been studying for years, much less
> any of the others that use a different strategy.
>
> Oh, and readers should also know that you don't know what a proof is
> since you still claim that if A,B,C ⊦ X then A,B,C,~A ⊬ X.
>

So bottom line you neither affirm nor deny my assertion which for you is
an indication of affirmation because you always deny everything that you
can and you never affirm anything.

--
Copyright 2022 Pete Olcott

"Talent hits a target no one else can hit;
Genius hits a target no one else can see."
Arthur Schopenhauer

On 4/18/2022 3:57 PM, olcott wrote:
> On 4/18/2022 3:13 PM, Ben wrote:
>> olcott <NoOne@NoWhere.com> writes:
>>
>>> I think that all of these alternative proofs can be reduced to an
>>> instance of the conventional HP counter-example thus are refuted by
>>> the correct refutation of the conventional HP counter-example.
>>
>> Readers should know, before deciding if you opinion on the matter is to
>> be taken seriously, that you have not even read the proper proof of the
>> theorem in the book you claim to have been studying for years, much less
>> any of the others that use a different strategy.
>>
>> Oh, and readers should also know that you don't know what a proof is
>> since you still claim that if A,B,C ⊦ X then A,B,C,~A ⊬ X.
>>
>
> So bottom line you neither affirm nor deny my assertion which for you is
> an indication of affirmation because you always deny everything that you
> can and you never affirm anything.
>

We show a problem decidable/undecidable by reducing it to another
problem. One type of reduction: mapping reduction.
http://cobweb.cs.uga.edu/~potter/theory/6_reducibility.pdf

--
Copyright 2022 Pete Olcott

"Talent hits a target no one else can hit;
Genius hits a target no one else can see."
Arthur Schopenhauer

olcott <NoOne@NoWhere.com> writes:

> On 4/18/2022 3:57 PM, olcott wrote:
>> On 4/18/2022 3:13 PM, Ben wrote:
>>> olcott <NoOne@NoWhere.com> writes:
>>>
>>>> I think that all of these alternative proofs can be reduced to an
>>>> instance of the conventional HP counter-example thus are refuted by
>>>> the correct refutation of the conventional HP counter-example.
>>>
>>> Readers should know, before deciding if you opinion on the matter is to
>>> be taken seriously, that you have not even read the proper proof of the
>>> theorem in the book you claim to have been studying for years, much less
>>> any of the others that use a different strategy.
>>>
>>> Oh, and readers should also know that you don't know what a proof is
>>> since you still claim that if A,B,C ⊦ X then A,B,C,~A ⊬ X.
>>>
>> So bottom line you neither affirm nor deny my assertion which for you
>> is an indication of affirmation because you always deny everything
>> that you can and you never affirm anything.

You are paraphrasing again. Remember what I said about you trying to do
that?

> We show a problem decidable/undecidable by reducing it to another
> problem. One type of reduction: mapping reduction.
> http://cobweb.cs.uga.edu/~potter/theory/6_reducibility.pdf

You are funny! This is about problems not proofs. Of course, since all
the proofs are proofs of a valid theorem, they are in some sense
interconnected. But if any one is, in fact, flawed it falls out of that
web of interconnected proofs by virtue of not being a proof anymore!

--
Ben.
"le génie humain a des limites, quand la bêtise humaine n’en a pas"
Alexandre Dumas (fils)

On 4/18/2022 4:53 PM, Ben wrote:
> olcott <NoOne@NoWhere.com> writes:
>
>> On 4/18/2022 3:57 PM, olcott wrote:
>>> On 4/18/2022 3:13 PM, Ben wrote:
>>>> olcott <NoOne@NoWhere.com> writes:
>>>>
>>>>> I think that all of these alternative proofs can be reduced to an
>>>>> instance of the conventional HP counter-example thus are refuted by
>>>>> the correct refutation of the conventional HP counter-example.
>>>>
>>>> Readers should know, before deciding if you opinion on the matter is to
>>>> be taken seriously, that you have not even read the proper proof of the
>>>> theorem in the book you claim to have been studying for years, much less
>>>> any of the others that use a different strategy.
>>>>
>>>> Oh, and readers should also know that you don't know what a proof is
>>>> since you still claim that if A,B,C ⊦ X then A,B,C,~A ⊬ X.
>>>>
>>> So bottom line you neither affirm nor deny my assertion which for you
>>> is an indication of affirmation because you always deny everything
>>> that you can and you never affirm anything.
>
> You are paraphrasing again. Remember what I said about you trying to do
> that?
>
>> We show a problem decidable/undecidable by reducing it to another
>> problem. One type of reduction: mapping reduction.
>> http://cobweb.cs.uga.edu/~potter/theory/6_reducibility.pdf
>
> You are funny! This is about problems not proofs. Of course, since all
> the proofs are proofs of a valid theorem, they are in some sense
> interconnected. But if any one is, in fact, flawed it falls out of that
> web of interconnected proofs by virtue of not being a proof anymore!
>

You are not going to have an honest dialogue on this so no sense for me
to expend the effort.

--
Copyright 2022 Pete Olcott

"Talent hits a target no one else can hit;
Genius hits a target no one else can see."
Arthur Schopenhauer

On 4/18/22 9:28 AM, olcott wrote:
> On 4/18/2022 7:56 AM, Python wrote:
>> Le 18/04/2022 à 14:06, Mr Flibble a écrit :
>>> On Mon, 18 Apr 2022 14:02:11 +0200
>>> Python <python@example.invalid> wrote:
>>>
>>>> Leigh Johnston, aka Mr Flibble wrote:
>>>>> The halting problem is defined as:
>>>>>
>>>>> In computability theory, the halting problem is the problem of
>>>>> determining, from a description of an arbitrary computer program
>>>>> and an input, whether the program will finish running, or continue
>>>>> to run forever. Alan Turing proved in 1936 that a general algorithm
>>>>> to solve the halting problem for all possible program-input pairs
>>>>> cannot exist.
>>>>>
>>>>> The only extant proof that the halting problem is unsolvable is:
>>>>>
>>>>> For any program f that might determine if programs halt, a
>>>>> "pathological" program g, called with some input, can pass its own
>>>>> source and its input to f and then specifically do the opposite of
>>>>> what f predicts g will do. No f can exist that handles this case.
>>>>>
>>>>> This proof contains an infinite recursion category error (f and g
>>>>> are in different categories)
>>>>
>>>> You cannot avoid what you call a "category error" in computing Leigh,
>>>> i.e. that a program text is also a data. Without that compilers
>>>> couldn't even exists.
>>>
>>> A compiler compiling program text into an executable isn't infinitely
>>> recursive, dear.
>>
>> There is nothing infinitely recursive in the Halting Problem. This has
>> been pointed to you before.
>>
>
> I just proved there is. In the case that I just showed H recognizes the
> infinite recursion, aborts the simulation of its input and rejects this
> input, on the basis that it is infinitely recursive. Computations can do
> this because they have intelligence.

Nope, you CLAIM you did, but H does NOT recognize infinite recursion,
because the act of it thinking there was infinite recursion means that
there actual never was.

If there actually is infinite recursion, H never actually reports it.

>
>
> In the case of the 1931 Incompleteness theorem Gödel's logic sentence
> just sits there on the page unable to be evaluated because of its
> infinite recursion.

Nope, problem is Prolog only handles first order grammers, and Godel's
logic requires higher order logic.

You claim just shows you don't understand this difference.

>
> Read the Clocksin Mellish Prolog textbook on page 3, it shows the
> infinite recursion the the Incompleteness Theorem:
>
> https://www.researchgate.net/publication/350789898_Prolog_detects_and_rejects_pathological_self_reference_in_the_Godel_sentence
>
>
>
>>>> Neither IT or CS are your thing Leigh, give up.
>>> My career seems to disagree with your assertion, dear: I was a member of
>>> the team that invented the smartphone. What did you ever achieve, Mr
>>> Anonymous?
>>
>> Yes, I've heard of the huge success of neos. Oh, that you invented the
>> concept of smartphone too :-)
>>
>> https://github.com/i42output/neos/pulse
>
>

On 4/18/22 9:19 AM, olcott wrote:
> On 4/18/2022 6:42 AM, Mr Flibble wrote:
>> The halting problem is defined as:
>>
>> In computability theory, the halting problem is the problem of
>> determining, from a description of an arbitrary computer program and an
>> input, whether the program will finish running, or continue to run
>> forever. Alan Turing proved in 1936 that a general algorithm to solve
>> the halting problem for all possible program-input pairs cannot exist.
>>
>> The only extant proof that the halting problem is unsolvable is:
>>
>> For any program f that might determine if programs halt, a
>> "pathological" program g, called with some input, can pass its own
>> source and its input to f and then specifically do the opposite of what
>> f predicts g will do. No f can exist that handles this case.
>>
>
> void P(u32 x)
> {
>   if (H(x, x))
>     HERE: goto HERE;
> }
>
> int main()
> {
>   Output("Input_Halts = ", H((u32)P, (u32)P));
> }
>
> _P()
> [000009d6](01) 55         push ebp
> [000009d7](02) 8bec       mov ebp,esp
> [000009d9](03) 8b4508     mov eax,[ebp+08]
> [000009dc](01) 50         push eax         // push P
> [000009dd](03) 8b4d08     mov ecx,[ebp+08]
> [000009e0](01) 51         push ecx         // push P
> [000009e1](05) e840feffff call 00000826    // call H
> [000009e6](03) 83c408     add esp,+08
> [000009e9](02) 85c0       test eax,eax
> [000009eb](02) 7402       jz 000009ef
> [000009ed](02) ebfe       jmp 000009ed
> [000009ef](01) 5d         pop ebp
> [000009f0](01) c3         ret              // Final state
> Size in bytes:(0027) [000009f0]
>
> The simulated input to H(P,P) cannot possibly reach its own final state
> of [000009f0] it keeps repeating [000009d6] to [000009e1] until aborted.
>
> Begin Local Halt Decider Simulation
> ...[000009d6][00211368][0021136c] 55         push ebp         // enter P
> ...[000009d7][00211368][0021136c] 8bec       mov ebp,esp
> ...[000009d9][00211368][0021136c] 8b4508     mov eax,[ebp+08]
> ...[000009dc][00211364][000009d6] 50         push eax         // Push P
> ...[000009dd][00211364][000009d6] 8b4d08     mov ecx,[ebp+08]
> ...[000009e0][00211360][000009d6] 51         push ecx         // Push P
> ...[000009e1][0021135c][000009e6] e840feffff call 00000826    // Call H
> ...[000009d6][0025bd90][0025bd94] 55         push ebp         // enter P
> ...[000009d7][0025bd90][0025bd94] 8bec       mov ebp,esp
> ...[000009d9][0025bd90][0025bd94] 8b4508     mov eax,[ebp+08]
> ...[000009dc][0025bd8c][000009d6] 50         push eax         // Push P
> ...[000009dd][0025bd8c][000009d6] 8b4d08     mov ecx,[ebp+08]
> ...[000009e0][0025bd88][000009d6] 51         push ecx         // Push P
> ...[000009e1][0025bd84][000009e6] e840feffff call 00000826    // Call H
> Local Halt Decider: Infinite Recursion Detected Simulation Stopped
>
>

Thus proving this is NOT a CORRECT simulation since that would imply
that the machine disappeared.

This appears to be a simululation by H, which shows that H will return
false, and thus the CORRECT simulation would also see that return from
H, with a zero and then proceeding to the ret instruction and the
program P halting.

You use the wrong defintion of the correct behavior of the input,
proving that you don't actually understand the problem or are just
intentionally lying about it.

Remember, the DEFINITION of a Halt Decider is that H(<M>, w) needs to
return the answer about whether on not M(w) will halt. DEFINITION.

The fact that you claim this CAN'T be the definition just shows your
ignorance, because it IS. PERIOD.

Yes, you are right, the H can't actually compute that value, but it
needs to in order to meet the definition, which is why universally
correct halt deciders are impossible.

FAIL.

>
>> This proof contains an infinite recursion category error (f and g are
>> in different categories) which makes the proof invalid (erroneous)
>> making the halting problem itself not unsolvable (as predicated on
>> this erroneous proof).
>>
>> The halting problem *might* be unsolvable but at present there is no
>> currently extant proof proving this to be the case.
>>
>> /Flibble
>>
>
>

On 2022-04-18 07:28, olcott wrote:
> On 4/18/2022 7:56 AM, Python wrote:
>> Le 18/04/2022 à 14:06, Mr Flibble a écrit :
>>> On Mon, 18 Apr 2022 14:02:11 +0200
>>> Python <python@example.invalid> wrote:
>>>
>>>> Leigh Johnston, aka Mr Flibble wrote:
>>>>> The halting problem is defined as:
>>>>>
>>>>> In computability theory, the halting problem is the problem of
>>>>> determining, from a description of an arbitrary computer program
>>>>> and an input, whether the program will finish running, or continue
>>>>> to run forever. Alan Turing proved in 1936 that a general algorithm
>>>>> to solve the halting problem for all possible program-input pairs
>>>>> cannot exist.
>>>>>
>>>>> The only extant proof that the halting problem is unsolvable is:
>>>>>
>>>>> For any program f that might determine if programs halt, a
>>>>> "pathological" program g, called with some input, can pass its own
>>>>> source and its input to f and then specifically do the opposite of
>>>>> what f predicts g will do. No f can exist that handles this case.
>>>>>
>>>>> This proof contains an infinite recursion category error (f and g
>>>>> are in different categories)
>>>>
>>>> You cannot avoid what you call a "category error" in computing Leigh,
>>>> i.e. that a program text is also a data. Without that compilers
>>>> couldn't even exists.
>>>
>>> A compiler compiling program text into an executable isn't infinitely
>>> recursive, dear.
>>
>> There is nothing infinitely recursive in the Halting Problem. This has
>> been pointed to you before.
>>
>
> I just proved there is. In the case that I just showed H recognizes the
> infinite recursion, aborts the simulation of its input and rejects this
> input, on the basis that it is infinitely recursive. Computations can do
> this because they have intelligence.

This is an extremely peculiar thing to say, even for you.

Computations involve algorithms, and the entire point of an algorithm is
that it does *not* have intelligence. At all. An algorithm simply
involves blindly manipulating some symbols according to a specific set
of purely mechanical rules. An algorithm doesn't even understand what
the symbols it is manipulating represent.

>
> In the case of the 1931 Incompleteness theorem Gödel's logic sentence
> just sits there on the page unable to be evaluated because of its
> infinite recursion.
>
> Read the Clocksin Mellish Prolog textbook on page 3, it shows the
> infinite recursion the the Incompleteness Theorem:
>
> https://www.researchgate.net/publication/350789898_Prolog_detects_and_rejects_pathological_self_reference_in_the_Godel_sentence

Prolog is irrelevant to Gödel's theorem. Prolog implements a very
narrowly defined subset of first-order logic. Gödel's theorem is about
theories of arithmetic which involve higher-order logic.

André

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