* The halting problem is trivially "disproven" by recognizing the
infinite recursion in its definition: a category error.
* Ergo, the halting problem as defined is erroneous.
* Ergo, the halting problem as defined is "solved". QED.

/Flibble

On 4/14/2022 1:34 PM, Mr Flibble wrote:
> * The halting problem is trivially "disproven" by recognizing the
> infinite recursion in its definition: a category error.
> * Ergo, the halting problem as defined is erroneous.
> * Ergo, the halting problem as defined is "solved". QED.
>
> /Flibble
>

I used to say it that way too. It is not that the halting problem is
solved. It is that the proofs that it cannot be solved are refuted.

My halt decider recognizes this infinite recursion and correctly reports
non-halting.

https://www.researchgate.net/publication/356105750_Halting_problem_undecidability_and_infinitely_nested_simulation_V2

--
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 Thu, 14 Apr 2022 13:41:50 -0500
olcott <NoOne@NoWhere.com> wrote:

> On 4/14/2022 1:34 PM, Mr Flibble wrote:
> > * The halting problem is trivially "disproven" by recognizing the
> > infinite recursion in its definition: a category error.
> > * Ergo, the halting problem as defined is erroneous.
> > * Ergo, the halting problem as defined is "solved". QED.
> >
> > /Flibble
> >
>
> I used to say it that way too. It is not that the halting problem is
> solved. It is that the proofs that it cannot be solved are refuted.
>
> My halt decider recognizes this infinite recursion and correctly
> reports non-halting.

Unfortunately (and this is also a reason why your argument with others
in this forum will never end) you have also created another
completely different category error: my use of the word "recognizing"
refers to someone analyzing the halting problem itself and seeing the
infinite recursion (category 1) and not a halt decider deciding some
input (category 2).

/Flibble

On 4/14/2022 1:52 PM, Mr Flibble wrote:
> On Thu, 14 Apr 2022 13:41:50 -0500
> olcott <NoOne@NoWhere.com> wrote:
>
>> On 4/14/2022 1:34 PM, Mr Flibble wrote:
>>> * The halting problem is trivially "disproven" by recognizing the
>>> infinite recursion in its definition: a category error.
>>> * Ergo, the halting problem as defined is erroneous.
>>> * Ergo, the halting problem as defined is "solved". QED.
>>>
>>> /Flibble
>>>
>>
>> I used to say it that way too. It is not that the halting problem is
>> solved. It is that the proofs that it cannot be solved are refuted.
>>
>> My halt decider recognizes this infinite recursion and correctly
>> reports non-halting.
>
> Unfortunately (and this is also a reason why your argument with others
> in this forum will never end) you have also created another
> completely different category error: my use of the word "recognizing"
> refers to someone analyzing the halting problem itself and seeing the
> infinite recursion (category 1) and not a halt decider deciding some
> input (category 2).
>
> /Flibble
>

You are saying that the halting problem counter-example is like the liar
paradox and has no correct Boolean value. I used to think this way for
many years. The actual truth is H(P,P) == false.

The simulated input to H(P,P) cannot possibly reach its own final state
it keeps repeating [00000956] to [00000961] until aborted.

_P()
[00000956](01) 55 push ebp
[00000957](02) 8bec mov ebp,esp
[00000959](03) 8b4508 mov eax,[ebp+08]
[0000095c](01) 50 push eax // push P
[0000095d](03) 8b4d08 mov ecx,[ebp+08]
[00000960](01) 51 push ecx // push P
[00000961](05) e8c0feffff call 00000826 // call H(P,P)
The above keeps repeating until aborted

[00000966](03) 83c408 add esp,+08
[00000969](02) 85c0 test eax,eax
[0000096b](02) 7402 jz 0000096f
[0000096d](02) ebfe jmp 0000096d
[0000096f](01) 5d pop ebp
[00000970](01) c3 ret // final state.
Size in bytes:(0027) [00000970]

--
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 4/14/22 2:41 PM, olcott wrote:
> On 4/14/2022 1:34 PM, Mr Flibble wrote:
>> * The halting problem is trivially "disproven" by recognizing the
>> infinite recursion in its definition: a category error.
>> * Ergo, the halting problem as defined is erroneous.
>> * Ergo, the halting problem as defined is "solved". QED.
>>
>> /Flibble
>>
>
> I used to say it that way too. It is not that the halting problem is
> solved. It is that the proofs that it cannot be solved are refuted.
>
> My halt decider recognizes this infinite recursion and correctly reports
> non-halting.
>
> https://www.researchgate.net/publication/356105750_Halting_problem_undecidability_and_infinitely_nested_simulation_V2
>
>

Except that this logic is flawed, because the definition is NOT
recursive. Yes, the particular problem creates a form of recurrsion, but
if you want ot say that isn't allowed, you need to say that Mathematics
itself is a category error.

FAIL.

On Friday, 15 April 2022 at 02:57:19 UTC+8, olcott wrote:
> On 4/14/2022 1:52 PM, Mr Flibble wrote:
> > On Thu, 14 Apr 2022 13:41:50 -0500
> > olcott <No...@NoWhere.com> wrote:
> >
> >> On 4/14/2022 1:34 PM, Mr Flibble wrote:
> >>> * The halting problem is trivially "disproven" by recognizing the
> >>> infinite recursion in its definition: a category error.
> >>> * Ergo, the halting problem as defined is erroneous.
> >>> * Ergo, the halting problem as defined is "solved". QED.
> >>>
> >>> /Flibble
> >>>
> >>
> >> I used to say it that way too. It is not that the halting problem is
> >> solved. It is that the proofs that it cannot be solved are refuted.
> >>
> >> My halt decider recognizes this infinite recursion and correctly
> >> reports non-halting.
> >
> > Unfortunately (and this is also a reason why your argument with others
> > in this forum will never end) you have also created another
> > completely different category error: my use of the word "recognizing"
> > refers to someone analyzing the halting problem itself and seeing the
> > infinite recursion (category 1) and not a halt decider deciding some
> > input (category 2).
> >
> > /Flibble
> >
> You are saying that the halting problem counter-example is like the liar
> paradox and has no correct Boolean value. I used to think this way for
> many years. The actual truth is H(P,P) == false.
>
> The simulated input to H(P,P) cannot possibly reach its own final state
> it keeps repeating [00000956] to [00000961] until aborted.
>
> _P()
> [00000956](01) 55 push ebp
> [00000957](02) 8bec mov ebp,esp
> [00000959](03) 8b4508 mov eax,[ebp+08]
> [0000095c](01) 50 push eax // push P
> [0000095d](03) 8b4d08 mov ecx,[ebp+08]
> [00000960](01) 51 push ecx // push P
> [00000961](05) e8c0feffff call 00000826 // call H(P,P)
> The above keeps repeating until aborted
>
> [00000966](03) 83c408 add esp,+08
> [00000969](02) 85c0 test eax,eax
> [0000096b](02) 7402 jz 0000096f
> [0000096d](02) ebfe jmp 0000096d
> [0000096f](01) 5d pop ebp
> [00000970](01) c3 ret // final state.
> Size in bytes:(0027) [00000970]
> --
> Copyright 2022 Pete Olcott
>
> "Talent hits a target no one else can hit;
> Genius hits a target no one else can see."
> Arthur Schopenhauer

You just confirmed the Halting Problem: H(P,P) is non-halting (never reaches its
final states). HP is thus referred to as undecidable.

"HP is undecidable, therefore HP is decidable" may be your appeal.
The Halting Problem asks the execution result of H(P,P), not your opinion.

On 4/14/2022 5:52 PM, wij wrote:
> On Friday, 15 April 2022 at 02:57:19 UTC+8, olcott wrote:
>> On 4/14/2022 1:52 PM, Mr Flibble wrote:
>>> On Thu, 14 Apr 2022 13:41:50 -0500
>>> olcott <No...@NoWhere.com> wrote:
>>>
>>>> On 4/14/2022 1:34 PM, Mr Flibble wrote:
>>>>> * The halting problem is trivially "disproven" by recognizing the
>>>>> infinite recursion in its definition: a category error.
>>>>> * Ergo, the halting problem as defined is erroneous.
>>>>> * Ergo, the halting problem as defined is "solved". QED.
>>>>>
>>>>> /Flibble
>>>>>
>>>>
>>>> I used to say it that way too. It is not that the halting problem is
>>>> solved. It is that the proofs that it cannot be solved are refuted.
>>>>
>>>> My halt decider recognizes this infinite recursion and correctly
>>>> reports non-halting.
>>>
>>> Unfortunately (and this is also a reason why your argument with others
>>> in this forum will never end) you have also created another
>>> completely different category error: my use of the word "recognizing"
>>> refers to someone analyzing the halting problem itself and seeing the
>>> infinite recursion (category 1) and not a halt decider deciding some
>>> input (category 2).
>>>
>>> /Flibble
>>>
>> You are saying that the halting problem counter-example is like the liar
>> paradox and has no correct Boolean value. I used to think this way for
>> many years. The actual truth is H(P,P) == false.
>>
>> The simulated input to H(P,P) cannot possibly reach its own final state
>> it keeps repeating [00000956] to [00000961] until aborted.
>>
>> _P()
>> [00000956](01) 55 push ebp
>> [00000957](02) 8bec mov ebp,esp
>> [00000959](03) 8b4508 mov eax,[ebp+08]
>> [0000095c](01) 50 push eax // push P
>> [0000095d](03) 8b4d08 mov ecx,[ebp+08]
>> [00000960](01) 51 push ecx // push P
>> [00000961](05) e8c0feffff call 00000826 // call H(P,P)
>> The above keeps repeating until aborted
>>
>> [00000966](03) 83c408 add esp,+08
>> [00000969](02) 85c0 test eax,eax
>> [0000096b](02) 7402 jz 0000096f
>> [0000096d](02) ebfe jmp 0000096d
>> [0000096f](01) 5d pop ebp
>> [00000970](01) c3 ret // final state.
>> Size in bytes:(0027) [00000970]
>> --
>> Copyright 2022 Pete Olcott
>>
>> "Talent hits a target no one else can hit;
>> Genius hits a target no one else can see."
>> Arthur Schopenhauer
>
> You just confirmed the Halting Problem: H(P,P) is non-halting (never reaches its
> final states). HP is thus referred to as undecidable.
>

That is the opposite of what I said:

The simulated input to H(P,P) cannot possibly reach its own final state
therefore H is correct to abort this simulation and reject this input.

> "HP is undecidable, therefore HP is decidable" may be your appeal.
> The Halting Problem asks the execution result of H(P,P), not your opinion.

--
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 4/14/22 6:58 PM, olcott wrote:
> On 4/14/2022 5:52 PM, wij wrote:
>> On Friday, 15 April 2022 at 02:57:19 UTC+8, olcott wrote:
>>> On 4/14/2022 1:52 PM, Mr Flibble wrote:
>>>> On Thu, 14 Apr 2022 13:41:50 -0500
>>>> olcott <No...@NoWhere.com> wrote:
>>>>
>>>>> On 4/14/2022 1:34 PM, Mr Flibble wrote:
>>>>>> * The halting problem is trivially "disproven" by recognizing the
>>>>>> infinite recursion in its definition: a category error.
>>>>>> * Ergo, the halting problem as defined is erroneous.
>>>>>> * Ergo, the halting problem as defined is "solved". QED.
>>>>>>
>>>>>> /Flibble
>>>>>>
>>>>>
>>>>> I used to say it that way too. It is not that the halting problem is
>>>>> solved. It is that the proofs that it cannot be solved are refuted.
>>>>>
>>>>> My halt decider recognizes this infinite recursion and correctly
>>>>> reports non-halting.
>>>>
>>>> Unfortunately (and this is also a reason why your argument with others
>>>> in this forum will never end) you have also created another
>>>> completely different category error: my use of the word "recognizing"
>>>> refers to someone analyzing the halting problem itself and seeing the
>>>> infinite recursion (category 1) and not a halt decider deciding some
>>>> input (category 2).
>>>>
>>>> /Flibble
>>>>
>>> You are saying that the halting problem counter-example is like the liar
>>> paradox and has no correct Boolean value. I used to think this way for
>>> many years. The actual truth is H(P,P) == false.
>>>
>>> The simulated input to H(P,P) cannot possibly reach its own final state
>>> it keeps repeating [00000956] to [00000961] until aborted.
>>>
>>> _P()
>>> [00000956](01) 55 push ebp
>>> [00000957](02) 8bec mov ebp,esp
>>> [00000959](03) 8b4508 mov eax,[ebp+08]
>>> [0000095c](01) 50 push eax // push P
>>> [0000095d](03) 8b4d08 mov ecx,[ebp+08]
>>> [00000960](01) 51 push ecx // push P
>>> [00000961](05) e8c0feffff call 00000826 // call H(P,P)
>>> The above keeps repeating until aborted
>>>
>>> [00000966](03) 83c408 add esp,+08
>>> [00000969](02) 85c0 test eax,eax
>>> [0000096b](02) 7402 jz 0000096f
>>> [0000096d](02) ebfe jmp 0000096d
>>> [0000096f](01) 5d pop ebp
>>> [00000970](01) c3 ret // final state.
>>> Size in bytes:(0027) [00000970]
>>> --
>>> Copyright 2022 Pete Olcott
>>>
>>> "Talent hits a target no one else can hit;
>>> Genius hits a target no one else can see."
>>> Arthur Schopenhauer
>>
>> You just confirmed the Halting Problem: H(P,P) is non-halting (never
>> reaches its
>> final states). HP is thus referred to as undecidable.
>>
>
> That is the opposite of what I said:
>
> The simulated input to H(P,P) cannot possibly reach its own final state
> therefore H is correct to abort this simulation and reject this input.

You say that, but that is a lie, since even YOU have posted a correct
simulation of the input that does reach its own final state.

Was that a lie?

>
>> "HP is undecidable, therefore HP is decidable" may be your appeal.
>> The Halting Problem asks the execution result of H(P,P), not your
>> opinion.
>
>

On 2022-04-14 18:34:49 +0000, Mr Flibble said:

> * The halting problem is trivially "disproven" by recognizing the
> infinite recursion in its definition: a category error.

An infinite recursion is not a category error. An example of category
error is to say "The halting problem is trivially 'disproven'":
the word "disproven" is not applicable to a problem. A claim can
be disproven but the halting problem does not claim anything.

Mikko

On Fri, 15 Apr 2022 11:53:51 +0300
Mikko <mikko.levanto@iki.fi> wrote:

> On 2022-04-14 18:34:49 +0000, Mr Flibble said:
>
> > * The halting problem is trivially "disproven" by recognizing the
> > infinite recursion in its definition: a category error.
>
> An infinite recursion is not a category error. An example of category
> error is to say "The halting problem is trivially 'disproven'":
> the word "disproven" is not applicable to a problem. A claim can
> be disproven but the halting problem does not claim anything.

"disproven" was in "quotes" for a reason, mate, and an infinite
recursion in a definition is a type of category error if it is the
presence of two categories that is causing the recursion; in this case
the two categories in question here are the halt decider and that which
is being decided.

/Flibble

Mr Flibble <flibble@reddwarf.jmc> writes:

> * The halting problem is trivially "disproven" by recognizing the
> infinite recursion in its definition: a category error.
> * Ergo, the halting problem as defined is erroneous.
> * Ergo, the halting problem as defined is "solved".

What about the other undecidable problems like spotting ambiguous
context free grammars, Post's correspondence problem and the word
problem for groups? Are they "category errors" too?

> QED.

I think "QED" should be in scare quotes as well.

--
Ben.

On 4/15/2022 11:55 AM, Ben wrote:
> Mr Flibble <flibble@reddwarf.jmc> writes:
>
>> * The halting problem is trivially "disproven" by recognizing the
>> infinite recursion in its definition: a category error.
>> * Ergo, the halting problem as defined is erroneous.
>> * Ergo, the halting problem as defined is "solved".
>
> What about the other undecidable problems like spotting ambiguous
> context free grammars, Post's correspondence problem and the word
> problem for groups? Are they "category errors" too?

Any problem that can be reduced to a halting problem counter-example can
be reduced to this counter-example's correct refutation.

--
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 4/15/22 12:25 PM, Mr Flibble wrote:
> On Fri, 15 Apr 2022 11:53:51 +0300
> Mikko <mikko.levanto@iki.fi> wrote:
>
>> On 2022-04-14 18:34:49 +0000, Mr Flibble said:
>>
>>> * The halting problem is trivially "disproven" by recognizing the
>>> infinite recursion in its definition: a category error.
>>
>> An infinite recursion is not a category error. An example of category
>> error is to say "The halting problem is trivially 'disproven'":
>> the word "disproven" is not applicable to a problem. A claim can
>> be disproven but the halting problem does not claim anything.
>
> "disproven" was in "quotes" for a reason, mate, and an infinite
> recursion in a definition is a type of category error if it is the
> presence of two categories that is causing the recursion; in this case
> the two categories in question here are the halt decider and that which
> is being decided.
>
> /Flibble
>

Except there isn't recursion in the definition.

The DEFINITION is that:

H applied to <M> w needs to -> Qy iff M applied to w Halts, and -> Qn
iff M applied to w never Halts.

There is no recursion in that definition.

If you mean that you can build an example that has 'infinite' recursion
from the definition, then you rule is invalid as this is a common
occurance in mathematics, so you are just showing that your logic is
unable to handle mathematics.

It has been established that logics that require all truth to be
provable fail to be 'expresive' enough to handle mathematics.

On Fri, 15 Apr 2022 15:45:11 -0400
Richard Damon <Richard@Damon-Family.org> wrote:

> On 4/15/22 12:25 PM, Mr Flibble wrote:
> > On Fri, 15 Apr 2022 11:53:51 +0300
> > Mikko <mikko.levanto@iki.fi> wrote:
> >
> >> On 2022-04-14 18:34:49 +0000, Mr Flibble said:
> >>
> >>> * The halting problem is trivially "disproven" by recognizing the
> >>> infinite recursion in its definition: a category error.
> >>
> >> An infinite recursion is not a category error. An example of
> >> category error is to say "The halting problem is trivially
> >> 'disproven'": the word "disproven" is not applicable to a problem.
> >> A claim can be disproven but the halting problem does not claim
> >> anything.
> >
> > "disproven" was in "quotes" for a reason, mate, and an infinite
> > recursion in a definition is a type of category error if it is the
> > presence of two categories that is causing the recursion; in this
> > case the two categories in question here are the halt decider and
> > that which is being decided.
> >
> > /Flibble
> >
>
> Except there isn't recursion in the definition.
>
> The DEFINITION is that:
>
> H applied to <M> w needs to -> Qy iff M applied to w Halts, and -> Qn
> iff M applied to w never Halts.
>
> There is no recursion in that definition.
>
> If you mean that you can build an example that has 'infinite'
> recursion from the definition, then you rule is invalid as this is a
> common occurance in mathematics, so you are just showing that your
> logic is unable to handle mathematics.
>
> It has been established that logics that require all truth to be
> provable fail to be 'expresive' enough to handle mathematics.

This is the definition of the halting problem:

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.

The definition is infinitely recursive: if you cannot see that then
English mustn't be your first language.

/Flibble

On 4/15/22 3:51 PM, Mr Flibble wrote:
> On Fri, 15 Apr 2022 15:45:11 -0400
> Richard Damon <Richard@Damon-Family.org> wrote:
>
>> On 4/15/22 12:25 PM, Mr Flibble wrote:
>>> On Fri, 15 Apr 2022 11:53:51 +0300
>>> Mikko <mikko.levanto@iki.fi> wrote:
>>>
>>>> On 2022-04-14 18:34:49 +0000, Mr Flibble said:
>>>>
>>>>> * The halting problem is trivially "disproven" by recognizing the
>>>>> infinite recursion in its definition: a category error.
>>>>
>>>> An infinite recursion is not a category error. An example of
>>>> category error is to say "The halting problem is trivially
>>>> 'disproven'": the word "disproven" is not applicable to a problem.
>>>> A claim can be disproven but the halting problem does not claim
>>>> anything.
>>>
>>> "disproven" was in "quotes" for a reason, mate, and an infinite
>>> recursion in a definition is a type of category error if it is the
>>> presence of two categories that is causing the recursion; in this
>>> case the two categories in question here are the halt decider and
>>> that which is being decided.
>>>
>>> /Flibble
>>>
>>
>> Except there isn't recursion in the definition.
>>
>> The DEFINITION is that:
>>
>> H applied to <M> w needs to -> Qy iff M applied to w Halts, and -> Qn
>> iff M applied to w never Halts.
>>
>> There is no recursion in that definition.
>>
>> If you mean that you can build an example that has 'infinite'
>> recursion from the definition, then you rule is invalid as this is a
>> common occurance in mathematics, so you are just showing that your
>> logic is unable to handle mathematics.
>>
>> It has been established that logics that require all truth to be
>> provable fail to be 'expresive' enough to handle mathematics.
>
> This is the definition of the halting problem:
>
> 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.
>
> The definition is infinitely recursive: if you cannot see that then
> English mustn't be your first language.
>
> /Flibble
>

That is NOT the DEFINITION of the problem.

The PROBLEM statement is to attempt to construct a Turing Machine H such
that:

H applied to <M> w -> Qy iff M applied to w Halts, and
H applied to <M> w -> Qy iff M applied to w never Hals.

Then there is the question of if such an H can possible exist.

That is ALL that the problem is.

What you give is one example that proves that the problem can't be solved.

You don't understand what it means to provide a DEFINITION.

On Fri, 15 Apr 2022 16:01:32 -0400
Richard Damon <Richard@Damon-Family.org> wrote:

> On 4/15/22 3:51 PM, Mr Flibble wrote:
> > On Fri, 15 Apr 2022 15:45:11 -0400
> > Richard Damon <Richard@Damon-Family.org> wrote:
> >
> >> On 4/15/22 12:25 PM, Mr Flibble wrote:
> >>> On Fri, 15 Apr 2022 11:53:51 +0300
> >>> Mikko <mikko.levanto@iki.fi> wrote:
> >>>
> >>>> On 2022-04-14 18:34:49 +0000, Mr Flibble said:
> >>>>
> >>>>> * The halting problem is trivially "disproven" by recognizing
> >>>>> the infinite recursion in its definition: a category error.
> >>>>
> >>>> An infinite recursion is not a category error. An example of
> >>>> category error is to say "The halting problem is trivially
> >>>> 'disproven'": the word "disproven" is not applicable to a
> >>>> problem. A claim can be disproven but the halting problem does
> >>>> not claim anything.
> >>>
> >>> "disproven" was in "quotes" for a reason, mate, and an infinite
> >>> recursion in a definition is a type of category error if it is the
> >>> presence of two categories that is causing the recursion; in this
> >>> case the two categories in question here are the halt decider and
> >>> that which is being decided.
> >>>
> >>> /Flibble
> >>>
> >>
> >> Except there isn't recursion in the definition.
> >>
> >> The DEFINITION is that:
> >>
> >> H applied to <M> w needs to -> Qy iff M applied to w Halts, and ->
> >> Qn iff M applied to w never Halts.
> >>
> >> There is no recursion in that definition.
> >>
> >> If you mean that you can build an example that has 'infinite'
> >> recursion from the definition, then you rule is invalid as this is
> >> a common occurance in mathematics, so you are just showing that
> >> your logic is unable to handle mathematics.
> >>
> >> It has been established that logics that require all truth to be
> >> provable fail to be 'expresive' enough to handle mathematics.
> >
> > This is the definition of the halting problem:
> >
> > 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.
> >
> > The definition is infinitely recursive: if you cannot see that then
> > English mustn't be your first language.
> >
> > /Flibble
> >
>
> That is NOT the DEFINITION of the problem.

Yes it is; see the second paragraph of
https://en.wikipedia.org/wiki/Halting_problem

[snip]

/Flibble

On 4/15/2022 2:51 PM, Mr Flibble wrote:
> On Fri, 15 Apr 2022 15:45:11 -0400
> Richard Damon <Richard@Damon-Family.org> wrote:
>
>> On 4/15/22 12:25 PM, Mr Flibble wrote:
>>> On Fri, 15 Apr 2022 11:53:51 +0300
>>> Mikko <mikko.levanto@iki.fi> wrote:
>>>
>>>> On 2022-04-14 18:34:49 +0000, Mr Flibble said:
>>>>
>>>>> * The halting problem is trivially "disproven" by recognizing the
>>>>> infinite recursion in its definition: a category error.
>>>>
>>>> An infinite recursion is not a category error. An example of
>>>> category error is to say "The halting problem is trivially
>>>> 'disproven'": the word "disproven" is not applicable to a problem.
>>>> A claim can be disproven but the halting problem does not claim
>>>> anything.
>>>
>>> "disproven" was in "quotes" for a reason, mate, and an infinite
>>> recursion in a definition is a type of category error if it is the
>>> presence of two categories that is causing the recursion; in this
>>> case the two categories in question here are the halt decider and
>>> that which is being decided.
>>>
>>> /Flibble
>>>
>>
>> Except there isn't recursion in the definition.
>>
>> The DEFINITION is that:
>>
>> H applied to <M> w needs to -> Qy iff M applied to w Halts, and -> Qn
>> iff M applied to w never Halts.
>>
>> There is no recursion in that definition.
>>
>> If you mean that you can build an example that has 'infinite'
>> recursion from the definition, then you rule is invalid as this is a
>> common occurance in mathematics, so you are just showing that your
>> logic is unable to handle mathematics.
>>
>> It has been established that logics that require all truth to be
>> provable fail to be 'expresive' enough to handle mathematics.
>
> This is the definition of the halting problem:
>
> 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.
>
> The definition is infinitely recursive: if you cannot see that then
> English mustn't be your first language.
>
> /Flibble
>

I used to think that exact same thing for about 15 years.

You are correct that it has the same infinitely recursive pattern that
makes Gödel's incompleteness, Tarski Undefinability and the Liar paradox
all invalid.

The difference is that a Turing Machine has intelligence that can spot
and reject this infinite recursion.

--
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 4/15/22 4:08 PM, Mr Flibble wrote:
> On Fri, 15 Apr 2022 16:01:32 -0400
> Richard Damon <Richard@Damon-Family.org> wrote:
>
>> On 4/15/22 3:51 PM, Mr Flibble wrote:
>>> On Fri, 15 Apr 2022 15:45:11 -0400
>>> Richard Damon <Richard@Damon-Family.org> wrote:
>>>
>>>> On 4/15/22 12:25 PM, Mr Flibble wrote:
>>>>> On Fri, 15 Apr 2022 11:53:51 +0300
>>>>> Mikko <mikko.levanto@iki.fi> wrote:
>>>>>
>>>>>> On 2022-04-14 18:34:49 +0000, Mr Flibble said:
>>>>>>
>>>>>>> * The halting problem is trivially "disproven" by recognizing
>>>>>>> the infinite recursion in its definition: a category error.
>>>>>>
>>>>>> An infinite recursion is not a category error. An example of
>>>>>> category error is to say "The halting problem is trivially
>>>>>> 'disproven'": the word "disproven" is not applicable to a
>>>>>> problem. A claim can be disproven but the halting problem does
>>>>>> not claim anything.
>>>>>
>>>>> "disproven" was in "quotes" for a reason, mate, and an infinite
>>>>> recursion in a definition is a type of category error if it is the
>>>>> presence of two categories that is causing the recursion; in this
>>>>> case the two categories in question here are the halt decider and
>>>>> that which is being decided.
>>>>>
>>>>> /Flibble
>>>>>
>>>>
>>>> Except there isn't recursion in the definition.
>>>>
>>>> The DEFINITION is that:
>>>>
>>>> H applied to <M> w needs to -> Qy iff M applied to w Halts, and ->
>>>> Qn iff M applied to w never Halts.
>>>>
>>>> There is no recursion in that definition.
>>>>
>>>> If you mean that you can build an example that has 'infinite'
>>>> recursion from the definition, then you rule is invalid as this is
>>>> a common occurance in mathematics, so you are just showing that
>>>> your logic is unable to handle mathematics.
>>>>
>>>> It has been established that logics that require all truth to be
>>>> provable fail to be 'expresive' enough to handle mathematics.
>>>
>>> This is the definition of the halting problem:
>>>
>>> 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.
>>>
>>> The definition is infinitely recursive: if you cannot see that then
>>> English mustn't be your first language.
>>>
>>> /Flibble
>>>
>>
>> That is NOT the DEFINITION of the problem.
>
> Yes it is; see the second paragraph of
> https://en.wikipedia.org/wiki/Halting_problem
>
> [snip]
>
> /Flibble
>

Nope, just shows that you don't know how to read an article.

In that article, the FIRST paragraph begins with the problem definition.

That second paragraph, isn't the problem definition any more, but a
summary of the proof that such a program can't exist. (As lead into by
the last sentence of the first paragraph).

On 4/15/22 4:10 PM, olcott wrote:
> On 4/15/2022 2:51 PM, Mr Flibble wrote:
>> On Fri, 15 Apr 2022 15:45:11 -0400
>> Richard Damon <Richard@Damon-Family.org> wrote:
>>
>>> On 4/15/22 12:25 PM, Mr Flibble wrote:
>>>> On Fri, 15 Apr 2022 11:53:51 +0300
>>>> Mikko <mikko.levanto@iki.fi> wrote:
>>>>> On 2022-04-14 18:34:49 +0000, Mr Flibble said:
>>>>>> * The halting problem is trivially "disproven" by recognizing the
>>>>>> infinite recursion in its definition: a category error.
>>>>>
>>>>> An infinite recursion is not a category error. An example of
>>>>> category error is to say "The halting problem is trivially
>>>>> 'disproven'": the word "disproven" is not applicable to a problem.
>>>>> A claim can be disproven but the halting problem does not claim
>>>>> anything.
>>>>
>>>> "disproven" was in "quotes" for a reason, mate, and an infinite
>>>> recursion in a definition is a type of category error if it is the
>>>> presence of two categories that is causing the recursion; in this
>>>> case the two categories in question here are the halt decider and
>>>> that which is being decided.
>>>>
>>>> /Flibble
>>>
>>> Except there isn't recursion in the definition.
>>>
>>> The DEFINITION is that:
>>>
>>> H applied to <M> w needs to -> Qy iff M applied to w Halts, and -> Qn
>>> iff M applied to w never Halts.
>>>
>>> There is no recursion in that definition.
>>>
>>> If you mean that you can build an example that has 'infinite'
>>> recursion from the definition, then you rule is invalid as this is a
>>> common occurance in mathematics, so you are just showing that your
>>> logic is unable to handle mathematics.
>>>
>>> It has been established that logics that require all truth to be
>>> provable fail to be 'expresive' enough to handle mathematics.
>>
>> This is the definition of the halting problem:
>>
>> 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.
>>
>> The definition is infinitely recursive: if you cannot see that then
>> English mustn't be your first language.
>>
>> /Flibble
>>
>
> I used to think that exact same thing for about 15 years.
>
> You are correct that it has the same infinitely recursive pattern that
> makes Gödel's incompleteness, Tarski Undefinability and the Liar paradox
> all invalid.
>
> The difference is that a Turing Machine has intelligence that can spot
> and reject this infinite recursion.
>
>

I think you over estimate the power of a Turing Machine or underestimate
what it means to be intelligent. (It that your problem, you are only as
smart as a Turing Machine?)

A Turing Machine can do NOTHING it hasn't been programmed to do in
detailed instructions.

On 2022-04-15 16:25:14 +0000, Mr Flibble said:

> On Fri, 15 Apr 2022 11:53:51 +0300
> Mikko <mikko.levanto@iki.fi> wrote:
>
>> On 2022-04-14 18:34:49 +0000, Mr Flibble said:
>>
>>> * The halting problem is trivially "disproven" by recognizing the
>>> infinite recursion in its definition: a category error.
>>
>> An infinite recursion is not a category error. An example of category
>> error is to say "The halting problem is trivially 'disproven'":
>> the word "disproven" is not applicable to a problem. A claim can
>> be disproven but the halting problem does not claim anything.
>
> "disproven" was in "quotes" for a reason, mate,

No reasonable reason can be seen.

> and an infinite recursion in a definition is a type of category error

No, it isn't, not even close. An infinite recursion is not necessarily
an error at all, and never a category error. Neither "category" nor
"error" was in quotes.

Mikko

On Sat, 16 Apr 2022 12:39:13 +0300
Mikko <mikko.levanto@iki.fi> wrote:

> On 2022-04-15 16:25:14 +0000, Mr Flibble said:
>
> > On Fri, 15 Apr 2022 11:53:51 +0300
> > Mikko <mikko.levanto@iki.fi> wrote:
> >
> >> On 2022-04-14 18:34:49 +0000, Mr Flibble said:
> >>
> >>> * The halting problem is trivially "disproven" by recognizing the
> >>> infinite recursion in its definition: a category error.
> >>
> >> An infinite recursion is not a category error. An example of
> >> category error is to say "The halting problem is trivially
> >> 'disproven'": the word "disproven" is not applicable to a problem.
> >> A claim can be disproven but the halting problem does not claim
> >> anything.
> >
> > "disproven" was in "quotes" for a reason, mate,
>
> No reasonable reason can be seen.
>
> > and an infinite recursion in a definition is a type of category
> > error
>
> No, it isn't, not even close. An infinite recursion is not necessarily
> an error at all, and never a category error. Neither "category" nor
> "error" was in quotes.

In the case of the halting problem AS DEFINED it *is* a category error.

/Flibble

On Fri, 15 Apr 2022 16:29:26 -0400
Richard Damon <Richard@Damon-Family.org> wrote:

> On 4/15/22 4:08 PM, Mr Flibble wrote:
> > On Fri, 15 Apr 2022 16:01:32 -0400
> > Richard Damon <Richard@Damon-Family.org> wrote:
> >
> >> On 4/15/22 3:51 PM, Mr Flibble wrote:
> >>> On Fri, 15 Apr 2022 15:45:11 -0400
> >>> Richard Damon <Richard@Damon-Family.org> wrote:
> >>>
> >>>> On 4/15/22 12:25 PM, Mr Flibble wrote:
> >>>>> On Fri, 15 Apr 2022 11:53:51 +0300
> >>>>> Mikko <mikko.levanto@iki.fi> wrote:
> >>>>>
> >>>>>> On 2022-04-14 18:34:49 +0000, Mr Flibble said:
> >>>>>>
> >>>>>>> * The halting problem is trivially "disproven" by recognizing
> >>>>>>> the infinite recursion in its definition: a category error.
> >>>>>>
> >>>>>> An infinite recursion is not a category error. An example of
> >>>>>> category error is to say "The halting problem is trivially
> >>>>>> 'disproven'": the word "disproven" is not applicable to a
> >>>>>> problem. A claim can be disproven but the halting problem does
> >>>>>> not claim anything.
> >>>>>
> >>>>> "disproven" was in "quotes" for a reason, mate, and an infinite
> >>>>> recursion in a definition is a type of category error if it is
> >>>>> the presence of two categories that is causing the recursion;
> >>>>> in this case the two categories in question here are the halt
> >>>>> decider and that which is being decided.
> >>>>>
> >>>>> /Flibble
> >>>>>
> >>>>
> >>>> Except there isn't recursion in the definition.
> >>>>
> >>>> The DEFINITION is that:
> >>>>
> >>>> H applied to <M> w needs to -> Qy iff M applied to w Halts, and
> >>>> -> Qn iff M applied to w never Halts.
> >>>>
> >>>> There is no recursion in that definition.
> >>>>
> >>>> If you mean that you can build an example that has 'infinite'
> >>>> recursion from the definition, then you rule is invalid as this
> >>>> is a common occurance in mathematics, so you are just showing
> >>>> that your logic is unable to handle mathematics.
> >>>>
> >>>> It has been established that logics that require all truth to be
> >>>> provable fail to be 'expresive' enough to handle mathematics.
> >>>
> >>> This is the definition of the halting problem:
> >>>
> >>> 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.
> >>>
> >>> The definition is infinitely recursive: if you cannot see that
> >>> then English mustn't be your first language.
> >>>
> >>> /Flibble
> >>>
> >>
> >> That is NOT the DEFINITION of the problem.
> >
> > Yes it is; see the second paragraph of
> > https://en.wikipedia.org/wiki/Halting_problem
> >
> > [snip]
> >
> > /Flibble
> >
>
> Nope, just shows that you don't know how to read an article.
>
> In that article, the FIRST paragraph begins with the problem
> definition.
>
> That second paragraph, isn't the problem definition any more, but a
> summary of the proof that such a program can't exist. (As lead into
> by the last sentence of the first paragraph).

The first and second paragraphs taken together define the halting
problem as viewed in all academic/CompSci circles.

/Flibble

On 4/16/2022 3:50 PM, Mr Flibble wrote:
> On Sat, 16 Apr 2022 12:39:13 +0300
> Mikko <mikko.levanto@iki.fi> wrote:
>
>> On 2022-04-15 16:25:14 +0000, Mr Flibble said:
>>
>>> On Fri, 15 Apr 2022 11:53:51 +0300
>>> Mikko <mikko.levanto@iki.fi> wrote:
>>>
>>>> On 2022-04-14 18:34:49 +0000, Mr Flibble said:
>>>>
>>>>> * The halting problem is trivially "disproven" by recognizing the
>>>>> infinite recursion in its definition: a category error.
>>>>
>>>> An infinite recursion is not a category error. An example of
>>>> category error is to say "The halting problem is trivially
>>>> 'disproven'": the word "disproven" is not applicable to a problem.
>>>> A claim can be disproven but the halting problem does not claim
>>>> anything.
>>>
>>> "disproven" was in "quotes" for a reason, mate,
>>
>> No reasonable reason can be seen.
>>
>>> and an infinite recursion in a definition is a type of category
>>> error
>>
>> No, it isn't, not even close. An infinite recursion is not necessarily
>> an error at all, and never a category error. Neither "category" nor
>> "error" was in quotes.
>
> In the case of the halting problem AS DEFINED it *is* a category error.
>
> /Flibble
>
>

G := ~(F ⊢ G) expands to
~(F ⊢ ~(F ⊢ ~(F ⊢ ~(F ⊢ ~(F ⊢ ~(F ⊢ ~(F ⊢ ...) ) ) ) ) ) )

--
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 4/16/2022 3:51 PM, Mr Flibble wrote:
> On Fri, 15 Apr 2022 16:29:26 -0400
> Richard Damon <Richard@Damon-Family.org> wrote:
>
>> On 4/15/22 4:08 PM, Mr Flibble wrote:
>>> On Fri, 15 Apr 2022 16:01:32 -0400
>>> Richard Damon <Richard@Damon-Family.org> wrote:
>>>
>>>> On 4/15/22 3:51 PM, Mr Flibble wrote:
>>>>> On Fri, 15 Apr 2022 15:45:11 -0400
>>>>> Richard Damon <Richard@Damon-Family.org> wrote:
>>>>>
>>>>>> On 4/15/22 12:25 PM, Mr Flibble wrote:
>>>>>>> On Fri, 15 Apr 2022 11:53:51 +0300
>>>>>>> Mikko <mikko.levanto@iki.fi> wrote:
>>>>>>>
>>>>>>>> On 2022-04-14 18:34:49 +0000, Mr Flibble said:
>>>>>>>>
>>>>>>>>> * The halting problem is trivially "disproven" by recognizing
>>>>>>>>> the infinite recursion in its definition: a category error.
>>>>>>>>
>>>>>>>> An infinite recursion is not a category error. An example of
>>>>>>>> category error is to say "The halting problem is trivially
>>>>>>>> 'disproven'": the word "disproven" is not applicable to a
>>>>>>>> problem. A claim can be disproven but the halting problem does
>>>>>>>> not claim anything.
>>>>>>>
>>>>>>> "disproven" was in "quotes" for a reason, mate, and an infinite
>>>>>>> recursion in a definition is a type of category error if it is
>>>>>>> the presence of two categories that is causing the recursion;
>>>>>>> in this case the two categories in question here are the halt
>>>>>>> decider and that which is being decided.
>>>>>>>
>>>>>>> /Flibble
>>>>>>>
>>>>>>
>>>>>> Except there isn't recursion in the definition.
>>>>>>
>>>>>> The DEFINITION is that:
>>>>>>
>>>>>> H applied to <M> w needs to -> Qy iff M applied to w Halts, and
>>>>>> -> Qn iff M applied to w never Halts.
>>>>>>
>>>>>> There is no recursion in that definition.
>>>>>>
>>>>>> If you mean that you can build an example that has 'infinite'
>>>>>> recursion from the definition, then you rule is invalid as this
>>>>>> is a common occurance in mathematics, so you are just showing
>>>>>> that your logic is unable to handle mathematics.
>>>>>>
>>>>>> It has been established that logics that require all truth to be
>>>>>> provable fail to be 'expresive' enough to handle mathematics.
>>>>>
>>>>> This is the definition of the halting problem:
>>>>>
>>>>> 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.
>>>>>
>>>>> The definition is infinitely recursive: if you cannot see that
>>>>> then English mustn't be your first language.
>>>>>
>>>>> /Flibble
>>>>>
>>>>
>>>> That is NOT the DEFINITION of the problem.
>>>
>>> Yes it is; see the second paragraph of
>>> https://en.wikipedia.org/wiki/Halting_problem
>>>
>>> [snip]
>>>
>>> /Flibble
>>>
>>
>> Nope, just shows that you don't know how to read an article.
>>
>> In that article, the FIRST paragraph begins with the problem
>> definition.
>>
>> That second paragraph, isn't the problem definition any more, but a
>> summary of the proof that such a program can't exist. (As lead into
>> by the last sentence of the first paragraph).
>
> The first and second paragraphs taken together define the halting
> problem as viewed in all academic/CompSci circles.
>
> /Flibble
>

YES

--
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 4/16/22 4:51 PM, Mr Flibble wrote:
> On Fri, 15 Apr 2022 16:29:26 -0400
> Richard Damon <Richard@Damon-Family.org> wrote:
>
>> On 4/15/22 4:08 PM, Mr Flibble wrote:
>>> On Fri, 15 Apr 2022 16:01:32 -0400
>>> Richard Damon <Richard@Damon-Family.org> wrote:
>>>
>>>> On 4/15/22 3:51 PM, Mr Flibble wrote:
>>>>> On Fri, 15 Apr 2022 15:45:11 -0400
>>>>> Richard Damon <Richard@Damon-Family.org> wrote:
>>>>>
>>>>>> On 4/15/22 12:25 PM, Mr Flibble wrote:
>>>>>>> On Fri, 15 Apr 2022 11:53:51 +0300
>>>>>>> Mikko <mikko.levanto@iki.fi> wrote:
>>>>>>>
>>>>>>>> On 2022-04-14 18:34:49 +0000, Mr Flibble said:
>>>>>>>>
>>>>>>>>> * The halting problem is trivially "disproven" by recognizing
>>>>>>>>> the infinite recursion in its definition: a category error.
>>>>>>>>
>>>>>>>> An infinite recursion is not a category error. An example of
>>>>>>>> category error is to say "The halting problem is trivially
>>>>>>>> 'disproven'": the word "disproven" is not applicable to a
>>>>>>>> problem. A claim can be disproven but the halting problem does
>>>>>>>> not claim anything.
>>>>>>>
>>>>>>> "disproven" was in "quotes" for a reason, mate, and an infinite
>>>>>>> recursion in a definition is a type of category error if it is
>>>>>>> the presence of two categories that is causing the recursion;
>>>>>>> in this case the two categories in question here are the halt
>>>>>>> decider and that which is being decided.
>>>>>>>
>>>>>>> /Flibble
>>>>>>>
>>>>>>
>>>>>> Except there isn't recursion in the definition.
>>>>>>
>>>>>> The DEFINITION is that:
>>>>>>
>>>>>> H applied to <M> w needs to -> Qy iff M applied to w Halts, and
>>>>>> -> Qn iff M applied to w never Halts.
>>>>>>
>>>>>> There is no recursion in that definition.
>>>>>>
>>>>>> If you mean that you can build an example that has 'infinite'
>>>>>> recursion from the definition, then you rule is invalid as this
>>>>>> is a common occurance in mathematics, so you are just showing
>>>>>> that your logic is unable to handle mathematics.
>>>>>>
>>>>>> It has been established that logics that require all truth to be
>>>>>> provable fail to be 'expresive' enough to handle mathematics.
>>>>>
>>>>> This is the definition of the halting problem:
>>>>>
>>>>> 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.
>>>>>
>>>>> The definition is infinitely recursive: if you cannot see that
>>>>> then English mustn't be your first language.
>>>>>
>>>>> /Flibble
>>>>>
>>>>
>>>> That is NOT the DEFINITION of the problem.
>>>
>>> Yes it is; see the second paragraph of
>>> https://en.wikipedia.org/wiki/Halting_problem
>>>
>>> [snip]
>>>
>>> /Flibble
>>>
>>
>> Nope, just shows that you don't know how to read an article.
>>
>> In that article, the FIRST paragraph begins with the problem
>> definition.
>>
>> That second paragraph, isn't the problem definition any more, but a
>> summary of the proof that such a program can't exist. (As lead into
>> by the last sentence of the first paragraph).
>
> The first and second paragraphs taken together define the halting
> problem as viewed in all academic/CompSci circles.
>
> /Flibble
>

Nope.

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.

And if you look at the Etymology section, we get:

Theorem 2.2 There exists a Turing machine whose halting problem is
recursively unsolvable.

The the "Halting Problem" was the decision, NOT the proof that it was
unsolvable.

So, the DEFINITION of the problem is just the mapping the Halt Decider
needs to answer, and the requirement to try to build a Turing Machine to
compute this mapping.

Just like the DEFINTION of the Pythagorean theorem is just the formula /
geometric defintion of the theorem, and while all the other stuff that
people talk about might be classified as about the theorem, it isn't
part of the defintion of the theorem.