On 4/16/22 5:03 PM, olcott wrote:
> 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 ⊢ ...) ) ) ) ) ) )
>
>

But that isnt' the definition of the Problem.

You are just proving that your logic can't handle mathematics.

FAIL.

On Sat, 16 Apr 2022 17:31:36 -0400
Richard Damon <Richard@Damon-Family.org> wrote:

> 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.

Nope.

The "proof" that the halting problem is insolvable is what makes the
halting problem a problem, by definition. The problem and its so
called proof are intrinsically linked to each other which is why if the
proof is erroneous then so is the halting problem itself, which it is.

/Flibble

On Sat, 16 Apr 2022 17:33:08 -0400
Richard Damon <Richard@Damon-Family.org> wrote:

> On 4/16/22 5:03 PM, olcott wrote:
> > 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 ⊢ ...) ) ) ) ) ) )
> >
> >
>
> But that isnt' the definition of the Problem.
>
> You are just proving that your logic can't handle mathematics.
>
> FAIL.

You are the one who is failing, not Olcott. As I mentioned elsewhere
the erroneous infinitely recursive "proof" and the halting problem
according to your definition are intrinsically linked to each other: if
one is erroneous then so is the other.

/Flibble

On 4/17/22 7:13 AM, Mr Flibble wrote:
> On Sat, 16 Apr 2022 17:31:36 -0400
> Richard Damon <Richard@Damon-Family.org> wrote:
>
>> 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.
>
> Nope.
>
> The "proof" that the halting problem is insolvable is what makes the
> halting problem a problem, by definition. The problem and its so
> called proof are intrinsically linked to each other which is why if the
> proof is erroneous then so is the halting problem itself, which it is.
>
> /Flibble
>

So, you also fail to understand how logic works.

The definition of a problem does not include what is done with it.

FAIL.

On 4/17/22 7:16 AM, Mr Flibble wrote:
> On Sat, 16 Apr 2022 17:33:08 -0400
> Richard Damon <Richard@Damon-Family.org> wrote:
>
>> On 4/16/22 5:03 PM, olcott wrote:
>>> 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 ⊢ ...) ) ) ) ) ) )
>>>
>>>
>>
>> But that isnt' the definition of the Problem.
>>
>> You are just proving that your logic can't handle mathematics.
>>
>> FAIL.
>
> You are the one who is failing, not Olcott. As I mentioned elsewhere
> the erroneous infinitely recursive "proof" and the halting problem
> according to your definition are intrinsically linked to each other: if
> one is erroneous then so is the other.
>
> /Flibble
>

Nope. Can you actually cite a source about this 'infinite recursion'
rule, that is applicable to this case?

There is no such basic rule of logic, so invoking it is a logic error.

If you just make up rules, then you are not actually doing logical
analysis, but something illogical.

On 4/17/2022 6:16 AM, Mr Flibble wrote:
> On Sat, 16 Apr 2022 17:33:08 -0400
> Richard Damon <Richard@Damon-Family.org> wrote:
>
>> On 4/16/22 5:03 PM, olcott wrote:
>>> 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 ⊢ ...) ) ) ) ) ) )
>>>
>>>
>>
>> But that isnt' the definition of the Problem.
>>
>> You are just proving that your logic can't handle mathematics.
>>
>> FAIL.
>
> You are the one who is failing, not Olcott. As I mentioned elsewhere
> the erroneous infinitely recursive "proof" and the halting problem
> according to your definition are intrinsically linked to each other: if
> one is erroneous then so is the other.
>
> /Flibble
>

Likewize with the defintion of the incompleteness theorem
G := ~(F ⊢ G)
G is not provable in 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 2022-04-16 20:50:01 +0000, Mr Flibble said:

> 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:

>>> 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.

No. A category error is, as defined on
https://en.wikipedia.org/wiki/Category_mistake
a semantic or ontological error in which things belonging to a particular
category are presented as if they belong to a different category, or,
alternatively, a property is ascribed to a thing that could not possibly
have that property. You cannot point a word used as if it were what it
is not.

Mikko

On 4/17/2022 9:20 AM, Mikko wrote:
> On 2022-04-16 20:50:01 +0000, Mr Flibble said:
>
>> 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:
>
>>>> 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.
>
> No. A category error is, as defined on
>   https://en.wikipedia.org/wiki/Category_mistake
> a semantic or ontological error in which things belonging to a particular
> category are presented as if they belong to a different category, or,
> alternatively, a property is ascribed to a thing that could not possibly
> have that property. You cannot point a word used as if it were what it
> is not.
>
> Mikko
>
>

Gödel's G cannot have a Boolean property because it is not a truth
bearer: G := ~(F ⊢ G)

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

--
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 "proof" that the halting problem is insolvable is what makes the
> halting problem a problem, by definition.

No, it's an example of a class of problems called decision problems.
The word problem here does not mean problematic but is being used in the
more general "a question to be answered" sense.

> The problem and its so
> called proof are intrinsically linked to each other which is why if the
> proof is erroneous then so is the halting problem itself, which it is.

The proofs (of which there are many) are so called because they are
proofs.

--
Ben.