A proof of an erroneous theory is, by implication, also erroneous. The
halting problem as stated is erroneous ergo all currently extant
halting problem proofs are, by implication, also erroneous and do not
require formal refutation to be considered invalid.

Fix the halting problem itself before trying to refute Olcott, you
shower.

https://en.wikipedia.org/wiki/Category_mistake

/Flibble

On 2022-04-29 14:07:07 +0000, Mr Flibble said:

> A proof of an erroneous theory is, by implication, also erroneous. The
> halting problem as stated is erroneous ergo all currently extant
> halting problem proofs are, by implication, also erroneous and do not
> require formal refutation to be considered invalid.
>
> Fix the halting problem itself before trying to refute Olcott, you
> shower.

Apparently Mr Flibble does not know what "erroneous" mean. Otherwise he
would tell.

There is a common meaning that can be applied proofs: an "erroneous proof"
is not a proof although it may look like one. Does this extend to problems
or theories? Does "erroneous theory" mean something that looks like a
theory but isn't? Is Mr Flibble trying to say that the halting problem
is nor really any problem?

Mikko

On 4/29/22 10:07 AM, Mr Flibble wrote:
> A proof of an erroneous theory is, by implication, also erroneous. The
> halting problem as stated is erroneous ergo all currently extant
> halting problem proofs are, by implication, also erroneous and do not
> require formal refutation to be considered invalid.
>
> Fix the halting problem itself before trying to refute Olcott, you
> shower.
>
> https://en.wikipedia.org/wiki/Category_mistake
>
> /Flibble
>

Your argument that the Halting Problem is erroneous, is in fact, itself
erroneous, so invalid.

There is NOT a "Category Mistake" in the Halting Problem, so your claim
itself is sort of a category error itself.

The Halting Problem is about the computability of a Mapping of
Computations to a binary Halting Value.

There is no category error in that statement.

To see if it is computable, we create a representation of the
computation and provide that to the decider.

All Computations have a representation, so this is not a category error.

If the Halting Function IS computable, then by definition, there will be
Turing Machine that takes that representation and maps it to an answer
that represent Halting or Non-Halting.

SO that is not a category error.

The category error is thinking that the decider needs to take in the
exact thing that the mapping uses. THAT is a category error.

By THAT definition, Primality is uncomputable, because we can't give an
arbitrary number to a Turing Machine to ask if it is prime, only the
representation of that number.

Just as we convert a number to a "string" representation to allow the
Turing Machine to test if it is prime, we convert the Computation to a
representation to ask if it is halting.

Just as giving a Prime testing Turing Machine expecting decimal notation
the value 1001 to test 9 for being prime, if giving H the input
described by <H^> <H^> doesn't mean H^ applied to <H^>, then that input
was formed incorrectly, since the < > notation means the representation
defined by this particular machine.

If there isn't an actual representation of the computation H^ applied to
<H^> that we can give to H, then H has failed the requirement, just like
a prime testing decider that wants decimal encoded numbers but doesn't
allow the digit 0 in the representation.

On 4/29/2022 9:07 AM, Mr Flibble wrote:
> A proof of an erroneous theory is, by implication, also erroneous. The
> halting problem as stated is erroneous ergo all currently extant
> halting problem proofs are, by implication, also erroneous and do not
> require formal refutation to be considered invalid.
>
> Fix the halting problem itself before trying to refute Olcott, you
> shower.
>
> https://en.wikipedia.org/wiki/Category_mistake
>
> /Flibble
>

You are not using the conventional computer science terminology exactly
correctly, yet the gist of what you are saying is exactly correct:
category error.

The exact same issue arises with Gödel's 1931 Incompleteness theorem and
the 1936 Tarski Undefinability theorem.

https://liarparadox.org/Tarski_247_248.pdf
https://liarparadox.org/Tarski_275_276.pdf

Tarski "proved" that the notion of truth cannot be mathematically
formalized entirely on the basis that he could not prove that the liar
paradox is true. It never occurred to Tarski that the Liar Paradox is
not a truth bearer. I had to define "truth bearer" myself because all of
the existing definitions are pretty crappy.

*Expressions of (formal or natural) language that can possibly be
resolved to a truth value* are [truth bearers].

There are only two ways that an expression of language can be resolved
to a truth value:
(1) An expression of language is assigned a truth value such as "cats
are animals" is defined to be true.

(2) Truth preserving operations are applied to expressions of language
that are known to be true. {cats are animals} and {animals are living
things} therefore {cats are living things}. copyright 2021 PL Olcott

The above only focuses on analytic truth (verified as true entirely on
the basis of the meaning of the expression of language) and thus
excludes empirical truth that requires sense data from the sense organs.

--
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 4/29/2022 9:07 AM, Mr Flibble wrote:
> A proof of an erroneous theory is, by implication, also erroneous. The
> halting problem as stated is erroneous ergo all currently extant
> halting problem proofs are, by implication, also erroneous and do not
> require formal refutation to be considered invalid.
>
> Fix the halting problem itself before trying to refute Olcott, you
> shower.
>
> https://en.wikipedia.org/wiki/Category_mistake
>
> /Flibble
>

I also count your idea of calling this a category error a brilliant new
insight that encapsulates the key issue in a single well-defined concept.

--
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 4/29/2022 10:21 AM, Mikko wrote:
> On 2022-04-29 14:07:07 +0000, Mr Flibble said:
>
>> A proof of an erroneous theory is, by implication, also erroneous. The
>> halting problem as stated is erroneous ergo all currently extant
>> halting problem proofs are, by implication, also erroneous and do not
>> require formal refutation to be considered invalid.
>>
>> Fix the halting problem itself before trying to refute Olcott, you
>> shower.
>
> Apparently Mr Flibble does not know what "erroneous" mean. Otherwise he
> would tell.
>
> There is a common meaning that can be applied proofs: an "erroneous proof"
> is not a proof although it may look like one. Does this extend to problems
> or theories? Does "erroneous theory" mean something that looks like a
> theory but isn't? Is Mr Flibble trying to say that the halting problem
> is nor really any problem?
>
> Mikko
>

A person that only cares about rebuttal and does not give a rat's ass
about truth would say that. You don't pay attention to what he says you
merely pick out some fake excuse for a rebuttal.

Flibble perfectly defined "erroneous proof" and "erroneous theory" in
that their basis is anchored in the well defined concept of [category
error]:

[category error]
a semantic or ontological error in which things belonging to a
particular category are presented as if they belong to a different
category,[1] or, alternatively, a property is ascribed to a thing that
could not possibly have that property.
https://en.wikipedia.org/wiki/Category_mistake

--
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 4/29/22 3:30 PM, olcott wrote:
> On 4/29/2022 10:21 AM, Mikko wrote:
>> On 2022-04-29 14:07:07 +0000, Mr Flibble said:
>>
>>> A proof of an erroneous theory is, by implication, also erroneous. The
>>> halting problem as stated is erroneous ergo all currently extant
>>> halting problem proofs are, by implication, also erroneous and do not
>>> require formal refutation to be considered invalid.
>>>
>>> Fix the halting problem itself before trying to refute Olcott, you
>>> shower.
>>
>> Apparently Mr Flibble does not know what "erroneous" mean. Otherwise he
>> would tell.
>>
>> There is a common meaning that can be applied proofs: an "erroneous
>> proof"
>> is not a proof although it may look like one. Does this extend to
>> problems
>> or theories? Does "erroneous theory" mean something that looks like a
>> theory but isn't? Is Mr Flibble trying to say that the halting problem
>> is nor really any problem?
>>
>> Mikko
>>
>
> A person that only cares about rebuttal and does not give a rat's ass
> about truth would say that. You don't pay attention to what he says you
> merely pick out some fake excuse for a rebuttal.
>
> Flibble perfectly defined "erroneous proof" and "erroneous theory" in
> that their basis is anchored in the well defined concept of [category
> error]:
>
> [category error]
> a semantic or ontological error in which things belonging to a
> particular category are presented as if they belong to a different
> category,[1] or, alternatively, a property is ascribed to a thing that
> could not possibly have that property.
> https://en.wikipedia.org/wiki/Category_mistake
>
And exactly WHAT is the category error in the Halting Problem.

What is given the wrong category, and what category is it incorrectly
being given.

If you can't state what the error is, you are just proving that YOU are
just in "Rebuttal Mode" and not caring about what is the actual truth.

On Fri, 29 Apr 2022 15:42:49 -0400
Richard Damon <Richard@Damon-Family.org> wrote:

> On 4/29/22 3:30 PM, olcott wrote:
> > On 4/29/2022 10:21 AM, Mikko wrote:
> >> On 2022-04-29 14:07:07 +0000, Mr Flibble said:
> >>
> >>> A proof of an erroneous theory is, by implication, also
> >>> erroneous. The halting problem as stated is erroneous ergo all
> >>> currently extant halting problem proofs are, by implication, also
> >>> erroneous and do not require formal refutation to be considered
> >>> invalid.
> >>>
> >>> Fix the halting problem itself before trying to refute Olcott, you
> >>> shower.
> >>
> >> Apparently Mr Flibble does not know what "erroneous" mean.
> >> Otherwise he would tell.
> >>
> >> There is a common meaning that can be applied proofs: an
> >> "erroneous proof"
> >> is not a proof although it may look like one. Does this extend to
> >> problems
> >> or theories? Does "erroneous theory" mean something that looks
> >> like a theory but isn't? Is Mr Flibble trying to say that the
> >> halting problem is nor really any problem?
> >>
> >> Mikko
> >>
> >
> > A person that only cares about rebuttal and does not give a rat's
> > ass about truth would say that. You don't pay attention to what he
> > says you merely pick out some fake excuse for a rebuttal.
> >
> > Flibble perfectly defined "erroneous proof" and "erroneous theory"
> > in that their basis is anchored in the well defined concept of
> > [category error]:
> >
> > [category error]
> > a semantic or ontological error in which things belonging to a
> > particular category are presented as if they belong to a different
> > category,[1] or, alternatively, a property is ascribed to a thing
> > that could not possibly have that property.
> > https://en.wikipedia.org/wiki/Category_mistake
> >
> And exactly WHAT is the category error in the Halting Problem.

The infinitely recursive definition.

>
> What is given the wrong category, and what category is it incorrectly
> being given.

The two categories are the decider and that which is being decided.

>
> If you can't state what the error is, you are just proving that YOU
> are just in "Rebuttal Mode" and not caring about what is the actual
> truth.

/Flibble

On 4/29/2022 3:17 PM, Mr Flibble wrote:
> On Fri, 29 Apr 2022 15:42:49 -0400
> Richard Damon <Richard@Damon-Family.org> wrote:
>
>> On 4/29/22 3:30 PM, olcott wrote:
>>> On 4/29/2022 10:21 AM, Mikko wrote:
>>>> On 2022-04-29 14:07:07 +0000, Mr Flibble said:
>>>>
>>>>> A proof of an erroneous theory is, by implication, also
>>>>> erroneous. The halting problem as stated is erroneous ergo all
>>>>> currently extant halting problem proofs are, by implication, also
>>>>> erroneous and do not require formal refutation to be considered
>>>>> invalid.
>>>>>
>>>>> Fix the halting problem itself before trying to refute Olcott, you
>>>>> shower.
>>>>
>>>> Apparently Mr Flibble does not know what "erroneous" mean.
>>>> Otherwise he would tell.
>>>>
>>>> There is a common meaning that can be applied proofs: an
>>>> "erroneous proof"
>>>> is not a proof although it may look like one. Does this extend to
>>>> problems
>>>> or theories? Does "erroneous theory" mean something that looks
>>>> like a theory but isn't? Is Mr Flibble trying to say that the
>>>> halting problem is nor really any problem?
>>>>
>>>> Mikko
>>>>
>>>
>>> A person that only cares about rebuttal and does not give a rat's
>>> ass about truth would say that. You don't pay attention to what he
>>> says you merely pick out some fake excuse for a rebuttal.
>>>
>>> Flibble perfectly defined "erroneous proof" and "erroneous theory"
>>> in that their basis is anchored in the well defined concept of
>>> [category error]:
>>>
>>> [category error]
>>> a semantic or ontological error in which things belonging to a
>>> particular category are presented as if they belong to a different
>>> category,[1] or, alternatively, a property is ascribed to a thing
>>> that could not possibly have that property.
>>> https://en.wikipedia.org/wiki/Category_mistake
>>>
>> And exactly WHAT is the category error in the Halting Problem.
>
> The infinitely recursive definition.
>
>>
>> What is given the wrong category, and what category is it incorrectly
>> being given.
>
> The two categories are the decider and that which is being decided.
>
>>
>> If you can't state what the error is, you are just proving that YOU
>> are just in "Rebuttal Mode" and not caring about what is the actual
>> truth.
>
> /Flibble
>

The Liar Paradox and Gödel's G are examples of infinitely recursive
definition.

LP := ~True(LP)
G := ~Provable(G)

This is totally obvious when they are encoded in Prolog.

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

On 4/29/22 4:17 PM, Mr Flibble wrote:
> On Fri, 29 Apr 2022 15:42:49 -0400
> Richard Damon <Richard@Damon-Family.org> wrote:
>
>> On 4/29/22 3:30 PM, olcott wrote:
>>> On 4/29/2022 10:21 AM, Mikko wrote:
>>>> On 2022-04-29 14:07:07 +0000, Mr Flibble said:
>>>>
>>>>> A proof of an erroneous theory is, by implication, also
>>>>> erroneous. The halting problem as stated is erroneous ergo all
>>>>> currently extant halting problem proofs are, by implication, also
>>>>> erroneous and do not require formal refutation to be considered
>>>>> invalid.
>>>>>
>>>>> Fix the halting problem itself before trying to refute Olcott, you
>>>>> shower.
>>>>
>>>> Apparently Mr Flibble does not know what "erroneous" mean.
>>>> Otherwise he would tell.
>>>>
>>>> There is a common meaning that can be applied proofs: an
>>>> "erroneous proof"
>>>> is not a proof although it may look like one. Does this extend to
>>>> problems
>>>> or theories? Does "erroneous theory" mean something that looks
>>>> like a theory but isn't? Is Mr Flibble trying to say that the
>>>> halting problem is nor really any problem?
>>>>
>>>> Mikko
>>>>
>>>
>>> A person that only cares about rebuttal and does not give a rat's
>>> ass about truth would say that. You don't pay attention to what he
>>> says you merely pick out some fake excuse for a rebuttal.
>>>
>>> Flibble perfectly defined "erroneous proof" and "erroneous theory"
>>> in that their basis is anchored in the well defined concept of
>>> [category error]:
>>>
>>> [category error]
>>> a semantic or ontological error in which things belonging to a
>>> particular category are presented as if they belong to a different
>>> category,[1] or, alternatively, a property is ascribed to a thing
>>> that could not possibly have that property.
>>> https://en.wikipedia.org/wiki/Category_mistake
>>>
>> And exactly WHAT is the category error in the Halting Problem.
>
> The infinitely recursive definition.

There IS no "Infinite Recursion" In the definiton of the Halting Problem.

FAIL.

The DEFINITION of the Problem is:

H needs to be able to report, in a finite number of steps, if a given
Turing Machine (or more generally a given algorithm) when applied to a
given input will Halt in finite time or not, by being given a
representation of that Machine and Input.

Not a single bit of recursion.

>
>>
>> What is given the wrong category, and what category is it incorrectly
>> being given.
>
> The two categories are the decider and that which is being decided.

So you are making a category error, because those are not CATEGORIES.

And no one says the "Halt Decider" IS the "Halting Property"

FAIL

>
>>
>> If you can't state what the error is, you are just proving that YOU
>> are just in "Rebuttal Mode" and not caring about what is the actual
>> truth.
>
> /Flibble
>

On 4/29/22 4:25 PM, olcott wrote:
> On 4/29/2022 3:17 PM, Mr Flibble wrote:
>> On Fri, 29 Apr 2022 15:42:49 -0400
>> Richard Damon <Richard@Damon-Family.org> wrote:
>>
>>> On 4/29/22 3:30 PM, olcott wrote:
>>>> On 4/29/2022 10:21 AM, Mikko wrote:
>>>>> On 2022-04-29 14:07:07 +0000, Mr Flibble said:
>>>>>> A proof of an erroneous theory is, by implication, also
>>>>>> erroneous. The halting problem as stated is erroneous ergo all
>>>>>> currently extant halting problem proofs are, by implication, also
>>>>>> erroneous and do not require formal refutation to be considered
>>>>>> invalid.
>>>>>>
>>>>>> Fix the halting problem itself before trying to refute Olcott, you
>>>>>> shower.
>>>>>
>>>>> Apparently Mr Flibble does not know what "erroneous" mean.
>>>>> Otherwise he would tell.
>>>>>
>>>>> There is a common meaning that can be applied proofs: an
>>>>> "erroneous proof"
>>>>> is not a proof although it may look like one. Does this extend to
>>>>> problems
>>>>> or theories? Does "erroneous theory" mean something that looks
>>>>> like a theory but isn't? Is Mr Flibble trying to say that the
>>>>> halting problem is nor really any problem?
>>>>>
>>>>> Mikko
>>>>
>>>> A person that only cares about rebuttal and does not give a rat's
>>>> ass about truth would say that. You don't pay attention to what he
>>>> says you merely pick out some fake excuse for a rebuttal.
>>>>
>>>> Flibble perfectly defined "erroneous proof" and "erroneous theory"
>>>> in that their basis is anchored in the well defined concept of
>>>> [category error]:
>>>>
>>>> [category error]
>>>> a semantic or ontological error in which things belonging to a
>>>> particular category are presented as if they belong to a different
>>>> category,[1] or, alternatively, a property is ascribed to a thing
>>>> that could not possibly have that property.
>>>> https://en.wikipedia.org/wiki/Category_mistake
>>> And exactly WHAT is the category error in the Halting Problem.
>>
>> The infinitely recursive definition.
>>
>>>
>>> What is given the wrong category, and what category is it incorrectly
>>> being given.
>>
>> The two categories are the decider and that which is being decided.
>>
>>>
>>> If you can't state what the error is, you are just proving that YOU
>>> are just in "Rebuttal Mode" and not caring about what is the actual
>>> truth.
>>
>> /Flibble
>>
>
> The Liar Paradox and Gödel's G are examples of infinitely recursive
> definition.
>
> LP := ~True(LP)
> G := ~Provable(G)
>
> This is totally obvious when they are encoded in Prolog.
>
> https://www.researchgate.net/publication/350789898_Prolog_detects_and_rejects_pathological_self_reference_in_the_Godel_sentence
>
>

Except that isn't the actual statement of G, and G can't be written in
Prolog because Prolog only handles first order logic and G uses Higher
Order logic.

FAIL.

On 4/29/2022 4:42 PM, Richard Damon wrote:
> On 4/29/22 4:25 PM, olcott wrote:
>> On 4/29/2022 3:17 PM, Mr Flibble wrote:
>>> On Fri, 29 Apr 2022 15:42:49 -0400
>>> Richard Damon <Richard@Damon-Family.org> wrote:
>>>
>>>> On 4/29/22 3:30 PM, olcott wrote:
>>>>> On 4/29/2022 10:21 AM, Mikko wrote:
>>>>>> On 2022-04-29 14:07:07 +0000, Mr Flibble said:
>>>>>>> A proof of an erroneous theory is, by implication, also
>>>>>>> erroneous. The halting problem as stated is erroneous ergo all
>>>>>>> currently extant halting problem proofs are, by implication, also
>>>>>>> erroneous and do not require formal refutation to be considered
>>>>>>> invalid.
>>>>>>>
>>>>>>> Fix the halting problem itself before trying to refute Olcott, you
>>>>>>> shower.
>>>>>>
>>>>>> Apparently Mr Flibble does not know what "erroneous" mean.
>>>>>> Otherwise he would tell.
>>>>>>
>>>>>> There is a common meaning that can be applied proofs: an
>>>>>> "erroneous proof"
>>>>>> is not a proof although it may look like one. Does this extend to
>>>>>> problems
>>>>>> or theories? Does "erroneous theory" mean something that looks
>>>>>> like a theory but isn't? Is Mr Flibble trying to say that the
>>>>>> halting problem is nor really any problem?
>>>>>>
>>>>>> Mikko
>>>>>
>>>>> A person that only cares about rebuttal and does not give a rat's
>>>>> ass about truth would say that. You don't pay attention to what he
>>>>> says you merely pick out some fake excuse for a rebuttal.
>>>>>
>>>>> Flibble perfectly defined "erroneous proof" and "erroneous theory"
>>>>> in that their basis is anchored in the well defined concept of
>>>>> [category error]:
>>>>>
>>>>> [category error]
>>>>> a semantic or ontological error in which things belonging to a
>>>>> particular category are presented as if they belong to a different
>>>>> category,[1] or, alternatively, a property is ascribed to a thing
>>>>> that could not possibly have that property.
>>>>> https://en.wikipedia.org/wiki/Category_mistake
>>>> And exactly WHAT is the category error in the Halting Problem.
>>>
>>> The infinitely recursive definition.
>>>
>>>>
>>>> What is given the wrong category, and what category is it incorrectly
>>>> being given.
>>>
>>> The two categories are the decider and that which is being decided.
>>>
>>>>
>>>> If you can't state what the error is, you are just proving that YOU
>>>> are just in "Rebuttal Mode" and not caring about what is the actual
>>>> truth.
>>>
>>> /Flibble
>>>
>>
>> The Liar Paradox and Gödel's G are examples of infinitely recursive
>> definition.
>>
>> LP := ~True(LP)
>> G := ~Provable(G)
>>
>> This is totally obvious when they are encoded in Prolog.
>>
>> https://www.researchgate.net/publication/350789898_Prolog_detects_and_rejects_pathological_self_reference_in_the_Godel_sentence
>>
>>
>
> Except that isn't the actual statement of G, and G can't be written in
> Prolog because Prolog only handles first order logic and G uses Higher
> Order logic.
>
> FAIL.
>

DIRECT QUOTE FROM page 40/43 OF Gödel's PAPER
The analogy between this result and Richard’s antinomy leaps to the eye;
there is also a close relationship with the “liar” antinomy,^14 since
the undecidable proposition [R(q); q] states precisely that q belongs to
K, i.e. according to (1), that [R(q); q] is not provable. We are
therefore confronted with a proposition which asserts its own unprovability.

14 Every epistemological antinomy can likewise be used for a similar
undecidability proof

https://mavdisk.mnsu.edu/pj2943kt/Fall%202015/Promotion%20Application/Previous%20Years%20Article%2022%20Materials/godel-1931.pdf

Thus: G ⟷ ~Provable(G)
is sufficiently equivalent to Gödel's G.

When this is encoded in Prolog it is rejected as an infinite term as my
paper clearly shows.

--
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 4/29/22 6:30 PM, olcott wrote:
> On 4/29/2022 4:42 PM, Richard Damon wrote:
>> On 4/29/22 4:25 PM, olcott wrote:
>>> On 4/29/2022 3:17 PM, Mr Flibble wrote:
>>>> On Fri, 29 Apr 2022 15:42:49 -0400
>>>> Richard Damon <Richard@Damon-Family.org> wrote:
>>>>
>>>>> On 4/29/22 3:30 PM, olcott wrote:
>>>>>> On 4/29/2022 10:21 AM, Mikko wrote:
>>>>>>> On 2022-04-29 14:07:07 +0000, Mr Flibble said:
>>>>>>>> A proof of an erroneous theory is, by implication, also
>>>>>>>> erroneous. The halting problem as stated is erroneous ergo all
>>>>>>>> currently extant halting problem proofs are, by implication, also
>>>>>>>> erroneous and do not require formal refutation to be considered
>>>>>>>> invalid.
>>>>>>>>
>>>>>>>> Fix the halting problem itself before trying to refute Olcott, you
>>>>>>>> shower.
>>>>>>>
>>>>>>> Apparently Mr Flibble does not know what "erroneous" mean.
>>>>>>> Otherwise he would tell.
>>>>>>>
>>>>>>> There is a common meaning that can be applied proofs: an
>>>>>>> "erroneous proof"
>>>>>>> is not a proof although it may look like one. Does this extend to
>>>>>>> problems
>>>>>>> or theories? Does "erroneous theory" mean something that looks
>>>>>>> like a theory but isn't? Is Mr Flibble trying to say that the
>>>>>>> halting problem is nor really any problem?
>>>>>>>
>>>>>>> Mikko
>>>>>>
>>>>>> A person that only cares about rebuttal and does not give a rat's
>>>>>> ass about truth would say that. You don't pay attention to what he
>>>>>> says you merely pick out some fake excuse for a rebuttal.
>>>>>>
>>>>>> Flibble perfectly defined "erroneous proof" and "erroneous theory"
>>>>>> in that their basis is anchored in the well defined concept of
>>>>>> [category error]:
>>>>>>
>>>>>> [category error]
>>>>>> a semantic or ontological error in which things belonging to a
>>>>>> particular category are presented as if they belong to a different
>>>>>> category,[1] or, alternatively, a property is ascribed to a thing
>>>>>> that could not possibly have that property.
>>>>>> https://en.wikipedia.org/wiki/Category_mistake
>>>>> And exactly WHAT is the category error in the Halting Problem.
>>>>
>>>> The infinitely recursive definition.
>>>>
>>>>>
>>>>> What is given the wrong category, and what category is it incorrectly
>>>>> being given.
>>>>
>>>> The two categories are the decider and that which is being decided.
>>>>
>>>>>
>>>>> If you can't state what the error is, you are just proving that YOU
>>>>> are just in "Rebuttal Mode" and not caring about what is the actual
>>>>> truth.
>>>>
>>>> /Flibble
>>>>
>>>
>>> The Liar Paradox and Gödel's G are examples of infinitely recursive
>>> definition.
>>>
>>> LP := ~True(LP)
>>> G := ~Provable(G)
>>>
>>> This is totally obvious when they are encoded in Prolog.
>>>
>>> https://www.researchgate.net/publication/350789898_Prolog_detects_and_rejects_pathological_self_reference_in_the_Godel_sentence
>>>
>>>
>>
>> Except that isn't the actual statement of G, and G can't be written in
>> Prolog because Prolog only handles first order logic and G uses Higher
>> Order logic.
>>
>> FAIL.
>>
>
> DIRECT QUOTE FROM page 40/43 OF Gödel's PAPER
> The analogy between this result and Richard’s antinomy leaps to the eye;
> there is also a close relationship with the “liar” antinomy,^14 since
> the undecidable proposition [R(q); q] states precisely that q belongs to
> K, i.e. according to (1), that [R(q); q] is not provable. We are
> therefore confronted with a proposition which asserts its own
> unprovability.

"Close Relationship" is not the same thing as "Same as".

Yes, there is some similarity in how G is built to the liar's paradox,
but G includes some extra indirection that makes it so it does still
have a truth value, and then it is about something being Provable, and
for ALL statements, the provability of that statement is ALWAYS a
truth-bearer, as statements which are not truth bearers are by
definition not provable.

>
> 14 Every epistemological antinomy can likewise be used for a similar
> undecidability proof

Right, by the same transformation used with the liars paradox, you can
transform another antinomy to build a similar contradiction that makes G
unprovable but true.

That doesn't mean G's truth value is the same as that antinomy.

>
> https://mavdisk.mnsu.edu/pj2943kt/Fall%202015/Promotion%20Application/Previous%20Years%20Article%2022%20Materials/godel-1931.pdf
>
>
> Thus: G ⟷ ~Provable(G)
> is sufficiently equivalent to Gödel's G.
>

Nope. Just shows you don't understand G.

> When this is encoded in Prolog it is rejected as an infinite term as my
> paper clearly shows.
>
>
>

As it should, since G uses Higher Order Logic which can NOT be properly
expressed in the first order logic of Prolog.

On 4/29/2022 6:10 PM, Richard Damon wrote:
> On 4/29/22 6:30 PM, olcott wrote:
>> On 4/29/2022 4:42 PM, Richard Damon wrote:
>>> On 4/29/22 4:25 PM, olcott wrote:
>>>> On 4/29/2022 3:17 PM, Mr Flibble wrote:
>>>>> On Fri, 29 Apr 2022 15:42:49 -0400
>>>>> Richard Damon <Richard@Damon-Family.org> wrote:
>>>>>
>>>>>> On 4/29/22 3:30 PM, olcott wrote:
>>>>>>> On 4/29/2022 10:21 AM, Mikko wrote:
>>>>>>>> On 2022-04-29 14:07:07 +0000, Mr Flibble said:
>>>>>>>>> A proof of an erroneous theory is, by implication, also
>>>>>>>>> erroneous. The halting problem as stated is erroneous ergo all
>>>>>>>>> currently extant halting problem proofs are, by implication, also
>>>>>>>>> erroneous and do not require formal refutation to be considered
>>>>>>>>> invalid.
>>>>>>>>>
>>>>>>>>> Fix the halting problem itself before trying to refute Olcott, you
>>>>>>>>> shower.
>>>>>>>>
>>>>>>>> Apparently Mr Flibble does not know what "erroneous" mean.
>>>>>>>> Otherwise he would tell.
>>>>>>>>
>>>>>>>> There is a common meaning that can be applied proofs: an
>>>>>>>> "erroneous proof"
>>>>>>>> is not a proof although it may look like one. Does this extend to
>>>>>>>> problems
>>>>>>>> or theories? Does "erroneous theory" mean something that looks
>>>>>>>> like a theory but isn't? Is Mr Flibble trying to say that the
>>>>>>>> halting problem is nor really any problem?
>>>>>>>>
>>>>>>>> Mikko
>>>>>>>
>>>>>>> A person that only cares about rebuttal and does not give a rat's
>>>>>>> ass about truth would say that. You don't pay attention to what he
>>>>>>> says you merely pick out some fake excuse for a rebuttal.
>>>>>>>
>>>>>>> Flibble perfectly defined "erroneous proof" and "erroneous theory"
>>>>>>> in that their basis is anchored in the well defined concept of
>>>>>>> [category error]:
>>>>>>>
>>>>>>> [category error]
>>>>>>> a semantic or ontological error in which things belonging to a
>>>>>>> particular category are presented as if they belong to a different
>>>>>>> category,[1] or, alternatively, a property is ascribed to a thing
>>>>>>> that could not possibly have that property.
>>>>>>> https://en.wikipedia.org/wiki/Category_mistake
>>>>>> And exactly WHAT is the category error in the Halting Problem.
>>>>>
>>>>> The infinitely recursive definition.
>>>>>
>>>>>>
>>>>>> What is given the wrong category, and what category is it incorrectly
>>>>>> being given.
>>>>>
>>>>> The two categories are the decider and that which is being decided.
>>>>>
>>>>>>
>>>>>> If you can't state what the error is, you are just proving that YOU
>>>>>> are just in "Rebuttal Mode" and not caring about what is the actual
>>>>>> truth.
>>>>>
>>>>> /Flibble
>>>>>
>>>>
>>>> The Liar Paradox and Gödel's G are examples of infinitely recursive
>>>> definition.
>>>>
>>>> LP := ~True(LP)
>>>> G := ~Provable(G)
>>>>
>>>> This is totally obvious when they are encoded in Prolog.
>>>>
>>>> https://www.researchgate.net/publication/350789898_Prolog_detects_and_rejects_pathological_self_reference_in_the_Godel_sentence
>>>>
>>>>
>>>
>>> Except that isn't the actual statement of G, and G can't be written
>>> in Prolog because Prolog only handles first order logic and G uses
>>> Higher Order logic.
>>>
>>> FAIL.
>>>
>>
>> DIRECT QUOTE FROM page 40/43 OF Gödel's PAPER
>> The analogy between this result and Richard’s antinomy leaps to the
>> eye; there is also a close relationship with the “liar” antinomy,^14
>> since the undecidable proposition [R(q); q] states precisely that q
>> belongs to K, i.e. according to (1), that [R(q); q] is not provable.
>> We are therefore confronted with a proposition which asserts its own
>> unprovability.
>
> "Close Relationship" is not the same thing as "Same as".
>
> Yes, there is some similarity in how G is built to the liar's paradox,
> but G includes some extra indirection that makes it so it does still
> have a truth value, and then it is about something being Provable, and
> for ALL statements, the provability of that statement is ALWAYS a
> truth-bearer, as statements which are not truth bearers are by
> definition not provable.
>
>>
>> 14 Every epistemological antinomy can likewise be used for a similar
>> undecidability proof
>
> Right, by the same transformation used with the liars paradox, you can
> transform another antinomy to build a similar contradiction that makes G
> unprovable but true.
>
> That doesn't mean G's truth value is the same as that antinomy.
>
>
>>
>> https://mavdisk.mnsu.edu/pj2943kt/Fall%202015/Promotion%20Application/Previous%20Years%20Article%2022%20Materials/godel-1931.pdf
>>
>>
>> Thus: G ⟷ ~Provable(G)
>> is sufficiently equivalent to Gödel's G.
>>
>
> Nope. Just shows you don't understand G.
>
>> When this is encoded in Prolog it is rejected as an infinite term as
>> my paper clearly shows.
>>
>>
>>
>
> As it should, since G uses Higher Order Logic which can NOT be properly
> expressed in the first order logic of Prolog.

14 Every epistemological antinomy can likewise be used for a similar
undecidability proof

Thus this {epistemological antinomy} is sufficiently equivalent
G ⟷ ~Provable(G)

"We are therefore confronted with a proposition which asserts its own
unprovability." Which is exactly formalized above.
Which is correctly rejected by Prolog.

--
Copyright 2022 Pete Olcott "Talent hits a target no one else can hit;
Genius hits a target no one else can see." Arthur Schopenhauer

Richard Damon wrote:
> On 4/29/22 10:07 AM, Mr Flibble wrote:
>> A proof of an erroneous theory is, by implication, also erroneous. The
>> halting problem as stated is erroneous ergo all currently extant
>> halting problem proofs are, by implication, also erroneous and do not
>> require formal refutation to be considered invalid.
>>
>> Fix the halting problem itself before trying to refute Olcott, you
>> shower.
>>
>> https://en.wikipedia.org/wiki/Category_mistake
>>
>> /Flibble
>>
>
> Your argument that the Halting Problem is erroneous, is in fact, itself
> erroneous, so invalid.
>
> There is NOT a "Category Mistake" in the Halting Problem, so your claim
> itself is sort of a category error itself.
>
> The Halting Problem is about the computability of a Mapping of
> Computations to a binary Halting Value.
>
> There is no category error in that statement.
>
> To see if it is computable, we create a representation of the
> computation and provide that to the decider.
>
> All Computations have a representation, so this is not a category error.
>
> If the Halting Function IS computable, then by definition, there will be
> Turing Machine that takes that representation and maps it to an answer
> that represent Halting or Non-Halting.
>
> SO that is not a category error.
>
> The category error is thinking that the decider needs to take in the
> exact thing that the mapping uses. THAT is a category error.
>
> By THAT definition, Primality is uncomputable, because we can't give an
> arbitrary number to a Turing Machine to ask if it is prime, only the
> representation of that number.
>
> Just as we convert a number to a "string" representation to allow the
> Turing Machine to test if it is prime, we convert the Computation to a
> representation to ask if it is halting.
>
> Just as giving a Prime testing Turing Machine expecting decimal notation
> the value 1001 to test 9 for being prime, if giving H the input
> described by <H^> <H^> doesn't mean H^ applied to <H^>, then that input
> was formed incorrectly, since the < > notation means the representation
> defined by this particular machine.
>
> If there isn't an actual representation of the computation H^ applied to
> <H^> that we can give to H, then H has failed the requirement, just like
> a prime testing decider that wants decimal encoded numbers but doesn't
> allow the digit 0 in the representation.

I wonder why is a programmer, Mr Fibble, so eager to reject the most
profound and interesting part of Computer Science?

On 4/29/2022 5:10 PM, Richard Damon wrote:
> On 4/29/22 6:30 PM, olcott wrote:

<SNIP>

>> When this is encoded in Prolog it is rejected as an infinite term as
>> my paper clearly shows.
>>
>>
>>
>
> As it should, since G uses Higher Order Logic which can NOT be properly
> expressed in the first order logic of Prolog.

Unless Prolog has changed wildly in the last several years, it isn't
even close to FOL. I remember it as a toy that could only represent and
reason with Horn clauses. Can Prolog now deal with quantifiers and
negation on both sides of an implication? That would be very impressive.

As a side note, I think it was this paucity of power that caused many
folks to not understand that "A -> B" could be true when "B" was false.
--
Jeff Barnett

On 4/29/2022 8:15 PM, Python wrote:
> Richard Damon wrote:
>> On 4/29/22 10:07 AM, Mr Flibble wrote:
>>> A proof of an erroneous theory is, by implication, also erroneous. The
>>> halting problem as stated is erroneous ergo all currently extant
>>> halting problem proofs are, by implication, also erroneous and do not
>>> require formal refutation to be considered invalid.
>>>
>>> Fix the halting problem itself before trying to refute Olcott, you
>>> shower.
>>>
>>> https://en.wikipedia.org/wiki/Category_mistake
>>>
>>> /Flibble
>>>
>>
>> Your argument that the Halting Problem is erroneous, is in fact,
>> itself erroneous, so invalid.
>>
>> There is NOT a "Category Mistake" in the Halting Problem, so your
>> claim itself is sort of a category error itself.
>>
>> The Halting Problem is about the computability of a Mapping of
>> Computations to a binary Halting Value.
>>
>> There is no category error in that statement.
>>
>> To see if it is computable, we create a representation of the
>> computation and provide that to the decider.
>>
>> All Computations have a representation, so this is not a category error.
>>
>> If the Halting Function IS computable, then by definition, there will
>> be Turing Machine that takes that representation and maps it to an
>> answer that represent Halting or Non-Halting.
>>
>> SO that is not a category error.
>>
>> The category error is thinking that the decider needs to take in the
>> exact thing that the mapping uses. THAT is a category error.
>>
>> By THAT definition, Primality is uncomputable, because we can't give
>> an arbitrary number to a Turing Machine to ask if it is prime, only
>> the representation of that number.
>>
>> Just as we convert a number to a "string" representation to allow the
>> Turing Machine to test if it is prime, we convert the Computation to a
>> representation to ask if it is halting.
>>
>> Just as giving a Prime testing Turing Machine expecting decimal
>> notation the value 1001 to test 9 for being prime, if giving H the
>> input described by <H^> <H^> doesn't mean H^ applied to <H^>, then
>> that input was formed incorrectly, since the < > notation means the
>> representation defined by this particular machine.
>>
>> If there isn't an actual representation of the computation H^ applied
>> to <H^> that we can give to H, then H has failed the requirement, just
>> like a prime testing decider that wants decimal encoded numbers but
>> doesn't allow the digit 0 in the representation.
>
> I wonder why is a programmer, Mr Fibble, so eager to reject the most
> profound and interesting part of Computer Science?

I spent two decades on self-reference paradox of the
(1) Halting Problem proofs
(2) The 1931 Gödel Incompleteness theorem
(3) Liar Paradox (I own LiarParadox.org)

In recent years I added the 1936 Tarski undefinability theorem.

https://liarparadox.org/Tarski_247_248.pdf
https://liarparadox.org/Tarski_275_276.pdf

Tarski "proved" that the notion of truth cannot be mathematically
formalized entirely on the basis that he could not prove that the liar
paradox is true. It never occurred to Tarski that the Liar Paradox is
not a truth bearer. I had to define "truth bearer" myself because all of
the existing definitions are pretty crappy.

Expressions of (formal or natural) language that can possibly be
resolved to a truth value are [truth bearers].

--
Copyright 2022 Pete Olcott

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

Python <python@example.invalid> writes:

> I wonder why is a programmer, Mr Fibble, so eager to reject the most
> profound and interesting part of Computer Science?

It's profound and banal at the same time. It's banal because there are
uncountably many subsets of finite strings, and only countably many
Turing machines, so almost all sets of strings are undecidable.

--
Ben.

On 4/29/2022 8:29 PM, Jeff Barnett wrote:
> On 4/29/2022 5:10 PM, Richard Damon wrote:
>> On 4/29/22 6:30 PM, olcott wrote:
>
>   <SNIP>
>
>>> When this is encoded in Prolog it is rejected as an infinite term as
>>> my paper clearly shows.
>>>
>>>
>>>
>>
>> As it should, since G uses Higher Order Logic which can NOT be
>> properly expressed in the first order logic of Prolog.
>
> Unless Prolog has changed wildly in the last several years, it isn't
> even close to FOL. I remember it as a toy that could only represent and
> reason with Horn clauses. Can Prolog now deal with quantifiers and
> negation on both sides of an implication? That would be very impressive.
>
> As a side note, I think it was this paucity of power that caused many
> folks to not understand that "A -> B" could be true when "B" was false.

It resolves the Liar Paradox to semantically malformed:

?- LP = not(true(LP)).
LP = not(true(LP)).

?- unify_with_occurs_check(LP, not(true(LP))).
false.

(SWI-Prolog (threaded, 64 bits, version 7.6.4)

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

On 4/29/22 8:49 PM, olcott wrote:
> On 4/29/2022 6:10 PM, Richard Damon wrote:
>> On 4/29/22 6:30 PM, olcott wrote:
>>> On 4/29/2022 4:42 PM, Richard Damon wrote:
>>>> On 4/29/22 4:25 PM, olcott wrote:
>>>>> On 4/29/2022 3:17 PM, Mr Flibble wrote:
>>>>>> On Fri, 29 Apr 2022 15:42:49 -0400
>>>>>> Richard Damon <Richard@Damon-Family.org> wrote:
>>>>>>
>>>>>>> On 4/29/22 3:30 PM, olcott wrote:
>>>>>>>> On 4/29/2022 10:21 AM, Mikko wrote:
>>>>>>>>> On 2022-04-29 14:07:07 +0000, Mr Flibble said:
>>>>>>>>>> A proof of an erroneous theory is, by implication, also
>>>>>>>>>> erroneous. The halting problem as stated is erroneous ergo all
>>>>>>>>>> currently extant halting problem proofs are, by implication, also
>>>>>>>>>> erroneous and do not require formal refutation to be considered
>>>>>>>>>> invalid.
>>>>>>>>>>
>>>>>>>>>> Fix the halting problem itself before trying to refute Olcott,
>>>>>>>>>> you
>>>>>>>>>> shower.
>>>>>>>>>
>>>>>>>>> Apparently Mr Flibble does not know what "erroneous" mean.
>>>>>>>>> Otherwise he would tell.
>>>>>>>>>
>>>>>>>>> There is a common meaning that can be applied proofs: an
>>>>>>>>> "erroneous proof"
>>>>>>>>> is not a proof although it may look like one. Does this extend to
>>>>>>>>> problems
>>>>>>>>> or theories? Does "erroneous theory" mean something that looks
>>>>>>>>> like a theory but isn't? Is Mr Flibble trying to say that the
>>>>>>>>> halting problem is nor really any problem?
>>>>>>>>>
>>>>>>>>> Mikko
>>>>>>>>
>>>>>>>> A person that only cares about rebuttal and does not give a rat's
>>>>>>>> ass about truth would say that. You don't pay attention to what he
>>>>>>>> says you merely pick out some fake excuse for a rebuttal.
>>>>>>>>
>>>>>>>> Flibble perfectly defined "erroneous proof" and "erroneous theory"
>>>>>>>> in that their basis is anchored in the well defined concept of
>>>>>>>> [category error]:
>>>>>>>>
>>>>>>>> [category error]
>>>>>>>> a semantic or ontological error in which things belonging to a
>>>>>>>> particular category are presented as if they belong to a different
>>>>>>>> category,[1] or, alternatively, a property is ascribed to a thing
>>>>>>>> that could not possibly have that property.
>>>>>>>> https://en.wikipedia.org/wiki/Category_mistake
>>>>>>> And exactly WHAT is the category error in the Halting Problem.
>>>>>>
>>>>>> The infinitely recursive definition.
>>>>>>
>>>>>>>
>>>>>>> What is given the wrong category, and what category is it
>>>>>>> incorrectly
>>>>>>> being given.
>>>>>>
>>>>>> The two categories are the decider and that which is being decided.
>>>>>>
>>>>>>>
>>>>>>> If you can't state what the error is, you are just proving that YOU
>>>>>>> are just in "Rebuttal Mode" and not caring about what is the actual
>>>>>>> truth.
>>>>>>
>>>>>> /Flibble
>>>>>>
>>>>>
>>>>> The Liar Paradox and Gödel's G are examples of infinitely recursive
>>>>> definition.
>>>>>
>>>>> LP := ~True(LP)
>>>>> G := ~Provable(G)
>>>>>
>>>>> This is totally obvious when they are encoded in Prolog.
>>>>>
>>>>> https://www.researchgate.net/publication/350789898_Prolog_detects_and_rejects_pathological_self_reference_in_the_Godel_sentence
>>>>>
>>>>>
>>>>
>>>> Except that isn't the actual statement of G, and G can't be written
>>>> in Prolog because Prolog only handles first order logic and G uses
>>>> Higher Order logic.
>>>>
>>>> FAIL.
>>>>
>>>
>>> DIRECT QUOTE FROM page 40/43 OF Gödel's PAPER
>>> The analogy between this result and Richard’s antinomy leaps to the
>>> eye; there is also a close relationship with the “liar” antinomy,^14
>>> since the undecidable proposition [R(q); q] states precisely that q
>>> belongs to K, i.e. according to (1), that [R(q); q] is not provable.
>>> We are therefore confronted with a proposition which asserts its own
>>> unprovability.
>>
>> "Close Relationship" is not the same thing as "Same as".
>>
>> Yes, there is some similarity in how G is built to the liar's paradox,
>> but G includes some extra indirection that makes it so it does still
>> have a truth value, and then it is about something being Provable, and
>> for ALL statements, the provability of that statement is ALWAYS a
>> truth-bearer, as statements which are not truth bearers are by
>> definition not provable.
>>
>>>
>>> 14 Every epistemological antinomy can likewise be used for a similar
>>> undecidability proof
>>
>> Right, by the same transformation used with the liars paradox, you can
>> transform another antinomy to build a similar contradiction that makes
>> G unprovable but true.
>>
>> That doesn't mean G's truth value is the same as that antinomy.
>>
>>
>>>
>>> https://mavdisk.mnsu.edu/pj2943kt/Fall%202015/Promotion%20Application/Previous%20Years%20Article%2022%20Materials/godel-1931.pdf
>>>
>>>
>>> Thus: G ⟷ ~Provable(G)
>>> is sufficiently equivalent to Gödel's G.
>>>
>>
>> Nope. Just shows you don't understand G.
>>
>>> When this is encoded in Prolog it is rejected as an infinite term as
>>> my paper clearly shows.
>>>
>>>
>>>
>>
>> As it should, since G uses Higher Order Logic which can NOT be
>> properly expressed in the first order logic of Prolog.
>
>
> 14 Every epistemological antinomy can likewise be used for a similar
> undecidability proof
>
> Thus this {epistemological antinomy} is sufficiently equivalent
> G ⟷ ~Provable(G)

Since that isn't G, you havn't made you point.

Note also, that Provable(x) is ALWAYS a Truth Bearer, as if x is not a
Truth Bearer, then it is not Provable, by definition.

So, if you can actually establish that X is true if Y is not provable,
then if Y is not a trurh bearer, you have established that X is true,
and thus must be a Truth Bearer, if X was NOT a truth bearer, then you
couldn't establish the implication.

>
> "We are therefore confronted with a proposition which asserts its own
> unprovability." Which is exactly formalized above.
> Which is correctly rejected by Prolog.
>
>

Right, G is a proposition, that when you work through all the details,
asserts the unprovability of itself without mentioning itself.

It is more based on the concept that the accepted properties of
Mathematics allow a statement to refer to itself via a formula that
doesn't actually directly refer to itself.

On 4/29/2022 8:59 PM, Richard Damon wrote:
> On 4/29/22 8:49 PM, olcott wrote:
>> On 4/29/2022 6:10 PM, Richard Damon wrote:
>>> On 4/29/22 6:30 PM, olcott wrote:
>>>> On 4/29/2022 4:42 PM, Richard Damon wrote:
>>>>> On 4/29/22 4:25 PM, olcott wrote:
>>>>>> On 4/29/2022 3:17 PM, Mr Flibble wrote:
>>>>>>> On Fri, 29 Apr 2022 15:42:49 -0400
>>>>>>> Richard Damon <Richard@Damon-Family.org> wrote:
>>>>>>>
>>>>>>>> On 4/29/22 3:30 PM, olcott wrote:
>>>>>>>>> On 4/29/2022 10:21 AM, Mikko wrote:
>>>>>>>>>> On 2022-04-29 14:07:07 +0000, Mr Flibble said:
>>>>>>>>>>> A proof of an erroneous theory is, by implication, also
>>>>>>>>>>> erroneous. The halting problem as stated is erroneous ergo all
>>>>>>>>>>> currently extant halting problem proofs are, by implication,
>>>>>>>>>>> also
>>>>>>>>>>> erroneous and do not require formal refutation to be considered
>>>>>>>>>>> invalid.
>>>>>>>>>>>
>>>>>>>>>>> Fix the halting problem itself before trying to refute
>>>>>>>>>>> Olcott, you
>>>>>>>>>>> shower.
>>>>>>>>>>
>>>>>>>>>> Apparently Mr Flibble does not know what "erroneous" mean.
>>>>>>>>>> Otherwise he would tell.
>>>>>>>>>>
>>>>>>>>>> There is a common meaning that can be applied proofs: an
>>>>>>>>>> "erroneous proof"
>>>>>>>>>> is not a proof although it may look like one. Does this extend to
>>>>>>>>>> problems
>>>>>>>>>> or theories? Does "erroneous theory" mean something that looks
>>>>>>>>>> like a theory but isn't? Is Mr Flibble trying to say that the
>>>>>>>>>> halting problem is nor really any problem?
>>>>>>>>>>
>>>>>>>>>> Mikko
>>>>>>>>>
>>>>>>>>> A person that only cares about rebuttal and does not give a rat's
>>>>>>>>> ass about truth would say that. You don't pay attention to what he
>>>>>>>>> says you merely pick out some fake excuse for a rebuttal.
>>>>>>>>>
>>>>>>>>> Flibble perfectly defined "erroneous proof" and "erroneous theory"
>>>>>>>>> in that their basis is anchored in the well defined concept of
>>>>>>>>> [category error]:
>>>>>>>>>
>>>>>>>>> [category error]
>>>>>>>>> a semantic or ontological error in which things belonging to a
>>>>>>>>> particular category are presented as if they belong to a different
>>>>>>>>> category,[1] or, alternatively, a property is ascribed to a thing
>>>>>>>>> that could not possibly have that property.
>>>>>>>>> https://en.wikipedia.org/wiki/Category_mistake
>>>>>>>> And exactly WHAT is the category error in the Halting Problem.
>>>>>>>
>>>>>>> The infinitely recursive definition.
>>>>>>>
>>>>>>>>
>>>>>>>> What is given the wrong category, and what category is it
>>>>>>>> incorrectly
>>>>>>>> being given.
>>>>>>>
>>>>>>> The two categories are the decider and that which is being decided.
>>>>>>>
>>>>>>>>
>>>>>>>> If you can't state what the error is, you are just proving that YOU
>>>>>>>> are just in "Rebuttal Mode" and not caring about what is the actual
>>>>>>>> truth.
>>>>>>>
>>>>>>> /Flibble
>>>>>>>
>>>>>>
>>>>>> The Liar Paradox and Gödel's G are examples of infinitely
>>>>>> recursive definition.
>>>>>>
>>>>>> LP := ~True(LP)
>>>>>> G := ~Provable(G)
>>>>>>
>>>>>> This is totally obvious when they are encoded in Prolog.
>>>>>>
>>>>>> https://www.researchgate.net/publication/350789898_Prolog_detects_and_rejects_pathological_self_reference_in_the_Godel_sentence
>>>>>>
>>>>>>
>>>>>
>>>>> Except that isn't the actual statement of G, and G can't be written
>>>>> in Prolog because Prolog only handles first order logic and G uses
>>>>> Higher Order logic.
>>>>>
>>>>> FAIL.
>>>>>
>>>>
>>>> DIRECT QUOTE FROM page 40/43 OF Gödel's PAPER
>>>> The analogy between this result and Richard’s antinomy leaps to the
>>>> eye; there is also a close relationship with the “liar” antinomy,^14
>>>> since the undecidable proposition [R(q); q] states precisely that q
>>>> belongs to K, i.e. according to (1), that [R(q); q] is not provable.
>>>> We are therefore confronted with a proposition which asserts its own
>>>> unprovability.
>>>
>>> "Close Relationship" is not the same thing as "Same as".
>>>
>>> Yes, there is some similarity in how G is built to the liar's
>>> paradox, but G includes some extra indirection that makes it so it
>>> does still have a truth value, and then it is about something being
>>> Provable, and for ALL statements, the provability of that statement
>>> is ALWAYS a truth-bearer, as statements which are not truth bearers
>>> are by definition not provable.
>>>
>>>>
>>>> 14 Every epistemological antinomy can likewise be used for a similar
>>>> undecidability proof
>>>
>>> Right, by the same transformation used with the liars paradox, you
>>> can transform another antinomy to build a similar contradiction that
>>> makes G unprovable but true.
>>>
>>> That doesn't mean G's truth value is the same as that antinomy.
>>>
>>>
>>>>
>>>> https://mavdisk.mnsu.edu/pj2943kt/Fall%202015/Promotion%20Application/Previous%20Years%20Article%2022%20Materials/godel-1931.pdf
>>>>
>>>>
>>>> Thus: G ⟷ ~Provable(G)
>>>> is sufficiently equivalent to Gödel's G.
>>>>
>>>
>>> Nope. Just shows you don't understand G.
>>>
>>>> When this is encoded in Prolog it is rejected as an infinite term as
>>>> my paper clearly shows.
>>>>
>>>>
>>>>
>>>
>>> As it should, since G uses Higher Order Logic which can NOT be
>>> properly expressed in the first order logic of Prolog.
>>
>>
>> 14 Every epistemological antinomy can likewise be used for a similar
>> undecidability proof
>>
>> Thus this {epistemological antinomy} is sufficiently equivalent
>> G ⟷ ~Provable(G)
>
> Since that isn't G, you havn't made you point.
>

Gödel said it does not have to be G:

14 Every epistemological antinomy can likewise be used for a similar
undecidability proof

Prolog is smart enough to detect the same infinitely recursive
definition that Flibble referred to:

?- LP = not(true(LP)).
LP = not(true(LP)).

?- unify_with_occurs_check(LP, not(true(LP))).
false.

(SWI-Prolog (threaded, 64 bits, version 7.6.4)

All of the detail including quotes from a Prolog textbook are included here:

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

> Note also, that Provable(x) is ALWAYS a Truth Bearer, as if x is not a
> Truth Bearer, then it is not Provable, by definition.

Not when the expression it is trying to prove is semantically malformed
by infinitely recursive definition.

--
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 4/29/22 10:10 PM, olcott wrote:
> On 4/29/2022 8:59 PM, Richard Damon wrote:
>> On 4/29/22 8:49 PM, olcott wrote:
>>> On 4/29/2022 6:10 PM, Richard Damon wrote:
>>>> On 4/29/22 6:30 PM, olcott wrote:
>>>>> On 4/29/2022 4:42 PM, Richard Damon wrote:
>>>>>> On 4/29/22 4:25 PM, olcott wrote:
>>>>>>> On 4/29/2022 3:17 PM, Mr Flibble wrote:
>>>>>>>> On Fri, 29 Apr 2022 15:42:49 -0400
>>>>>>>> Richard Damon <Richard@Damon-Family.org> wrote:
>>>>>>>>
>>>>>>>>> On 4/29/22 3:30 PM, olcott wrote:
>>>>>>>>>> On 4/29/2022 10:21 AM, Mikko wrote:
>>>>>>>>>>> On 2022-04-29 14:07:07 +0000, Mr Flibble said:
>>>>>>>>>>>> A proof of an erroneous theory is, by implication, also
>>>>>>>>>>>> erroneous. The halting problem as stated is erroneous ergo all
>>>>>>>>>>>> currently extant halting problem proofs are, by implication,
>>>>>>>>>>>> also
>>>>>>>>>>>> erroneous and do not require formal refutation to be considered
>>>>>>>>>>>> invalid.
>>>>>>>>>>>>
>>>>>>>>>>>> Fix the halting problem itself before trying to refute
>>>>>>>>>>>> Olcott, you
>>>>>>>>>>>> shower.
>>>>>>>>>>>
>>>>>>>>>>> Apparently Mr Flibble does not know what "erroneous" mean.
>>>>>>>>>>> Otherwise he would tell.
>>>>>>>>>>>
>>>>>>>>>>> There is a common meaning that can be applied proofs: an
>>>>>>>>>>> "erroneous proof"
>>>>>>>>>>> is not a proof although it may look like one. Does this
>>>>>>>>>>> extend to
>>>>>>>>>>> problems
>>>>>>>>>>> or theories? Does "erroneous theory" mean something that looks
>>>>>>>>>>> like a theory but isn't? Is Mr Flibble trying to say that the
>>>>>>>>>>> halting problem is nor really any problem?
>>>>>>>>>>>
>>>>>>>>>>> Mikko
>>>>>>>>>>
>>>>>>>>>> A person that only cares about rebuttal and does not give a rat's
>>>>>>>>>> ass about truth would say that. You don't pay attention to
>>>>>>>>>> what he
>>>>>>>>>> says you merely pick out some fake excuse for a rebuttal.
>>>>>>>>>>
>>>>>>>>>> Flibble perfectly defined "erroneous proof" and "erroneous
>>>>>>>>>> theory"
>>>>>>>>>> in that their basis is anchored in the well defined concept of
>>>>>>>>>> [category error]:
>>>>>>>>>>
>>>>>>>>>> [category error]
>>>>>>>>>> a semantic or ontological error in which things belonging to a
>>>>>>>>>> particular category are presented as if they belong to a
>>>>>>>>>> different
>>>>>>>>>> category,[1] or, alternatively, a property is ascribed to a thing
>>>>>>>>>> that could not possibly have that property.
>>>>>>>>>> https://en.wikipedia.org/wiki/Category_mistake
>>>>>>>>> And exactly WHAT is the category error in the Halting Problem.
>>>>>>>>
>>>>>>>> The infinitely recursive definition.
>>>>>>>>
>>>>>>>>>
>>>>>>>>> What is given the wrong category, and what category is it
>>>>>>>>> incorrectly
>>>>>>>>> being given.
>>>>>>>>
>>>>>>>> The two categories are the decider and that which is being decided.
>>>>>>>>
>>>>>>>>>
>>>>>>>>> If you can't state what the error is, you are just proving that
>>>>>>>>> YOU
>>>>>>>>> are just in "Rebuttal Mode" and not caring about what is the
>>>>>>>>> actual
>>>>>>>>> truth.
>>>>>>>>
>>>>>>>> /Flibble
>>>>>>>>
>>>>>>>
>>>>>>> The Liar Paradox and Gödel's G are examples of infinitely
>>>>>>> recursive definition.
>>>>>>>
>>>>>>> LP := ~True(LP)
>>>>>>> G := ~Provable(G)
>>>>>>>
>>>>>>> This is totally obvious when they are encoded in Prolog.
>>>>>>>
>>>>>>> https://www.researchgate.net/publication/350789898_Prolog_detects_and_rejects_pathological_self_reference_in_the_Godel_sentence
>>>>>>>
>>>>>>>
>>>>>>
>>>>>> Except that isn't the actual statement of G, and G can't be
>>>>>> written in Prolog because Prolog only handles first order logic
>>>>>> and G uses Higher Order logic.
>>>>>>
>>>>>> FAIL.
>>>>>>
>>>>>
>>>>> DIRECT QUOTE FROM page 40/43 OF Gödel's PAPER
>>>>> The analogy between this result and Richard’s antinomy leaps to the
>>>>> eye; there is also a close relationship with the “liar”
>>>>> antinomy,^14 since the undecidable proposition [R(q); q] states
>>>>> precisely that q belongs to K, i.e. according to (1), that [R(q);
>>>>> q] is not provable. We are therefore confronted with a proposition
>>>>> which asserts its own unprovability.
>>>>
>>>> "Close Relationship" is not the same thing as "Same as".
>>>>
>>>> Yes, there is some similarity in how G is built to the liar's
>>>> paradox, but G includes some extra indirection that makes it so it
>>>> does still have a truth value, and then it is about something being
>>>> Provable, and for ALL statements, the provability of that statement
>>>> is ALWAYS a truth-bearer, as statements which are not truth bearers
>>>> are by definition not provable.
>>>>
>>>>>
>>>>> 14 Every epistemological antinomy can likewise be used for a
>>>>> similar undecidability proof
>>>>
>>>> Right, by the same transformation used with the liars paradox, you
>>>> can transform another antinomy to build a similar contradiction that
>>>> makes G unprovable but true.
>>>>
>>>> That doesn't mean G's truth value is the same as that antinomy.
>>>>
>>>>
>>>>>
>>>>> https://mavdisk.mnsu.edu/pj2943kt/Fall%202015/Promotion%20Application/Previous%20Years%20Article%2022%20Materials/godel-1931.pdf
>>>>>
>>>>>
>>>>> Thus: G ⟷ ~Provable(G)
>>>>> is sufficiently equivalent to Gödel's G.
>>>>>
>>>>
>>>> Nope. Just shows you don't understand G.
>>>>
>>>>> When this is encoded in Prolog it is rejected as an infinite term
>>>>> as my paper clearly shows.
>>>>>
>>>>>
>>>>>
>>>>
>>>> As it should, since G uses Higher Order Logic which can NOT be
>>>> properly expressed in the first order logic of Prolog.
>>>
>>>
>>> 14 Every epistemological antinomy can likewise be used for a similar
>>> undecidability proof
>>>
>>> Thus this {epistemological antinomy} is sufficiently equivalent
>>> G ⟷ ~Provable(G)
>>
>> Since that isn't G, you havn't made you point.
>>
>
> Gödel said it does not have to be G:
>
> 14 Every epistemological antinomy can likewise be used for a similar
> undecidability proof
>

On 4/29/2022 9:36 PM, Richard Damon wrote:
>
> On 4/29/22 10:10 PM, olcott wrote:
>> On 4/29/2022 8:59 PM, Richard Damon wrote:
>>> On 4/29/22 8:49 PM, olcott wrote:
>>>> On 4/29/2022 6:10 PM, Richard Damon wrote:
>>>>> On 4/29/22 6:30 PM, olcott wrote:
>>>>>> On 4/29/2022 4:42 PM, Richard Damon wrote:
>>>>>>> On 4/29/22 4:25 PM, olcott wrote:
>>>>>>>> On 4/29/2022 3:17 PM, Mr Flibble wrote:
>>>>>>>>> On Fri, 29 Apr 2022 15:42:49 -0400
>>>>>>>>> Richard Damon <Richard@Damon-Family.org> wrote:
>>>>>>>>>
>>>>>>>>>> On 4/29/22 3:30 PM, olcott wrote:
>>>>>>>>>>> On 4/29/2022 10:21 AM, Mikko wrote:
>>>>>>>>>>>> On 2022-04-29 14:07:07 +0000, Mr Flibble said:
>>>>>>>>>>>>> A proof of an erroneous theory is, by implication, also
>>>>>>>>>>>>> erroneous. The halting problem as stated is erroneous ergo all
>>>>>>>>>>>>> currently extant halting problem proofs are, by
>>>>>>>>>>>>> implication, also
>>>>>>>>>>>>> erroneous and do not require formal refutation to be
>>>>>>>>>>>>> considered
>>>>>>>>>>>>> invalid.
>>>>>>>>>>>>>
>>>>>>>>>>>>> Fix the halting problem itself before trying to refute
>>>>>>>>>>>>> Olcott, you
>>>>>>>>>>>>> shower.
>>>>>>>>>>>>
>>>>>>>>>>>> Apparently Mr Flibble does not know what "erroneous" mean.
>>>>>>>>>>>> Otherwise he would tell.
>>>>>>>>>>>>
>>>>>>>>>>>> There is a common meaning that can be applied proofs: an
>>>>>>>>>>>> "erroneous proof"
>>>>>>>>>>>> is not a proof although it may look like one. Does this
>>>>>>>>>>>> extend to
>>>>>>>>>>>> problems
>>>>>>>>>>>> or theories? Does "erroneous theory" mean something that looks
>>>>>>>>>>>> like a theory but isn't? Is Mr Flibble trying to say that the
>>>>>>>>>>>> halting problem is nor really any problem?
>>>>>>>>>>>>
>>>>>>>>>>>> Mikko
>>>>>>>>>>>
>>>>>>>>>>> A person that only cares about rebuttal and does not give a
>>>>>>>>>>> rat's
>>>>>>>>>>> ass about truth would say that. You don't pay attention to
>>>>>>>>>>> what he
>>>>>>>>>>> says you merely pick out some fake excuse for a rebuttal.
>>>>>>>>>>>
>>>>>>>>>>> Flibble perfectly defined "erroneous proof" and "erroneous
>>>>>>>>>>> theory"
>>>>>>>>>>> in that their basis is anchored in the well defined concept of
>>>>>>>>>>> [category error]:
>>>>>>>>>>>
>>>>>>>>>>> [category error]
>>>>>>>>>>> a semantic or ontological error in which things belonging to a
>>>>>>>>>>> particular category are presented as if they belong to a
>>>>>>>>>>> different
>>>>>>>>>>> category,[1] or, alternatively, a property is ascribed to a
>>>>>>>>>>> thing
>>>>>>>>>>> that could not possibly have that property.
>>>>>>>>>>> https://en.wikipedia.org/wiki/Category_mistake
>>>>>>>>>> And exactly WHAT is the category error in the Halting Problem.
>>>>>>>>>
>>>>>>>>> The infinitely recursive definition.
>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> What is given the wrong category, and what category is it
>>>>>>>>>> incorrectly
>>>>>>>>>> being given.
>>>>>>>>>
>>>>>>>>> The two categories are the decider and that which is being
>>>>>>>>> decided.
>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> If you can't state what the error is, you are just proving
>>>>>>>>>> that YOU
>>>>>>>>>> are just in "Rebuttal Mode" and not caring about what is the
>>>>>>>>>> actual
>>>>>>>>>> truth.
>>>>>>>>>
>>>>>>>>> /Flibble
>>>>>>>>>
>>>>>>>>
>>>>>>>> The Liar Paradox and Gödel's G are examples of infinitely
>>>>>>>> recursive definition.
>>>>>>>>
>>>>>>>> LP := ~True(LP)
>>>>>>>> G := ~Provable(G)
>>>>>>>>
>>>>>>>> This is totally obvious when they are encoded in Prolog.
>>>>>>>>
>>>>>>>> https://www.researchgate.net/publication/350789898_Prolog_detects_and_rejects_pathological_self_reference_in_the_Godel_sentence
>>>>>>>>
>>>>>>>>
>>>>>>>
>>>>>>> Except that isn't the actual statement of G, and G can't be
>>>>>>> written in Prolog because Prolog only handles first order logic
>>>>>>> and G uses Higher Order logic.
>>>>>>>
>>>>>>> FAIL.
>>>>>>>
>>>>>>
>>>>>> DIRECT QUOTE FROM page 40/43 OF Gödel's PAPER
>>>>>> The analogy between this result and Richard’s antinomy leaps to
>>>>>> the eye; there is also a close relationship with the “liar”
>>>>>> antinomy,^14 since the undecidable proposition [R(q); q] states
>>>>>> precisely that q belongs to K, i.e. according to (1), that [R(q);
>>>>>> q] is not provable. We are therefore confronted with a proposition
>>>>>> which asserts its own unprovability.
>>>>>
>>>>> "Close Relationship" is not the same thing as "Same as".
>>>>>
>>>>> Yes, there is some similarity in how G is built to the liar's
>>>>> paradox, but G includes some extra indirection that makes it so it
>>>>> does still have a truth value, and then it is about something being
>>>>> Provable, and for ALL statements, the provability of that statement
>>>>> is ALWAYS a truth-bearer, as statements which are not truth bearers
>>>>> are by definition not provable.
>>>>>
>>>>>>
>>>>>> 14 Every epistemological antinomy can likewise be used for a
>>>>>> similar undecidability proof
>>>>>
>>>>> Right, by the same transformation used with the liars paradox, you
>>>>> can transform another antinomy to build a similar contradiction
>>>>> that makes G unprovable but true.
>>>>>
>>>>> That doesn't mean G's truth value is the same as that antinomy.
>>>>>
>>>>>
>>>>>>
>>>>>> https://mavdisk.mnsu.edu/pj2943kt/Fall%202015/Promotion%20Application/Previous%20Years%20Article%2022%20Materials/godel-1931.pdf
>>>>>>
>>>>>>
>>>>>> Thus: G ⟷ ~Provable(G)
>>>>>> is sufficiently equivalent to Gödel's G.
>>>>>>
>>>>>
>>>>> Nope. Just shows you don't understand G.
>>>>>
>>>>>> When this is encoded in Prolog it is rejected as an infinite term
>>>>>> as my paper clearly shows.
>>>>>>
>>>>>>
>>>>>>
>>>>>
>>>>> As it should, since G uses Higher Order Logic which can NOT be
>>>>> properly expressed in the first order logic of Prolog.
>>>>
>>>>
>>>> 14 Every epistemological antinomy can likewise be used for a similar
>>>> undecidability proof
>>>>
>>>> Thus this {epistemological antinomy} is sufficiently equivalent
>>>> G ⟷ ~Provable(G)
>>>
>>> Since that isn't G, you havn't made you point.
>>>
>>
>> Gödel said it does not have to be G:
>>
>> 14 Every epistemological antinomy can likewise be used for a similar
>> undecidability proof
>>
>
> You don't understand what he is saying, he is saying you can create a
> statement similar to the G he presents based on other antinomies. He
> just presented one based on the simplest version of the Liar's Paradox.
>

On 4/29/2022 10:32 PM, olcott wrote:
> On 4/29/2022 9:36 PM, Richard Damon wrote:
>>
>> On 4/29/22 10:10 PM, olcott wrote:
>>> On 4/29/2022 8:59 PM, Richard Damon wrote:
>>>> On 4/29/22 8:49 PM, olcott wrote:
>>>>> On 4/29/2022 6:10 PM, Richard Damon wrote:
>>>>>> On 4/29/22 6:30 PM, olcott wrote:
>>>>>>> On 4/29/2022 4:42 PM, Richard Damon wrote:
>>>>>>>> On 4/29/22 4:25 PM, olcott wrote:
>>>>>>>>> On 4/29/2022 3:17 PM, Mr Flibble wrote:
>>>>>>>>>> On Fri, 29 Apr 2022 15:42:49 -0400
>>>>>>>>>> Richard Damon <Richard@Damon-Family.org> wrote:
>>>>>>>>>>
>>>>>>>>>>> On 4/29/22 3:30 PM, olcott wrote:
>>>>>>>>>>>> On 4/29/2022 10:21 AM, Mikko wrote:
>>>>>>>>>>>>> On 2022-04-29 14:07:07 +0000, Mr Flibble said:
>>>>>>>>>>>>>> A proof of an erroneous theory is, by implication, also
>>>>>>>>>>>>>> erroneous. The halting problem as stated is erroneous ergo
>>>>>>>>>>>>>> all
>>>>>>>>>>>>>> currently extant halting problem proofs are, by
>>>>>>>>>>>>>> implication, also
>>>>>>>>>>>>>> erroneous and do not require formal refutation to be
>>>>>>>>>>>>>> considered
>>>>>>>>>>>>>> invalid.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Fix the halting problem itself before trying to refute
>>>>>>>>>>>>>> Olcott, you
>>>>>>>>>>>>>> shower.
>>>>>>>>>>>>>
>>>>>>>>>>>>> Apparently Mr Flibble does not know what "erroneous" mean.
>>>>>>>>>>>>> Otherwise he would tell.
>>>>>>>>>>>>>
>>>>>>>>>>>>> There is a common meaning that can be applied proofs: an
>>>>>>>>>>>>> "erroneous proof"
>>>>>>>>>>>>> is not a proof although it may look like one. Does this
>>>>>>>>>>>>> extend to
>>>>>>>>>>>>> problems
>>>>>>>>>>>>> or theories? Does "erroneous theory" mean something that looks
>>>>>>>>>>>>> like a theory but isn't? Is Mr Flibble trying to say that the
>>>>>>>>>>>>> halting problem is nor really any problem?
>>>>>>>>>>>>>
>>>>>>>>>>>>> Mikko
>>>>>>>>>>>>
>>>>>>>>>>>> A person that only cares about rebuttal and does not give a
>>>>>>>>>>>> rat's
>>>>>>>>>>>> ass about truth would say that. You don't pay attention to
>>>>>>>>>>>> what he
>>>>>>>>>>>> says you merely pick out some fake excuse for a rebuttal.
>>>>>>>>>>>>
>>>>>>>>>>>> Flibble perfectly defined "erroneous proof" and "erroneous
>>>>>>>>>>>> theory"
>>>>>>>>>>>> in that their basis is anchored in the well defined concept of
>>>>>>>>>>>> [category error]:
>>>>>>>>>>>>
>>>>>>>>>>>> [category error]
>>>>>>>>>>>> a semantic or ontological error in which things belonging to a
>>>>>>>>>>>> particular category are presented as if they belong to a
>>>>>>>>>>>> different
>>>>>>>>>>>> category,[1] or, alternatively, a property is ascribed to a
>>>>>>>>>>>> thing
>>>>>>>>>>>> that could not possibly have that property.
>>>>>>>>>>>> https://en.wikipedia.org/wiki/Category_mistake
>>>>>>>>>>> And exactly WHAT is the category error in the Halting Problem.
>>>>>>>>>>
>>>>>>>>>> The infinitely recursive definition.
>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> What is given the wrong category, and what category is it
>>>>>>>>>>> incorrectly
>>>>>>>>>>> being given.
>>>>>>>>>>
>>>>>>>>>> The two categories are the decider and that which is being
>>>>>>>>>> decided.
>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> If you can't state what the error is, you are just proving
>>>>>>>>>>> that YOU
>>>>>>>>>>> are just in "Rebuttal Mode" and not caring about what is the
>>>>>>>>>>> actual
>>>>>>>>>>> truth.
>>>>>>>>>>
>>>>>>>>>> /Flibble
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> The Liar Paradox and Gödel's G are examples of infinitely
>>>>>>>>> recursive definition.
>>>>>>>>>
>>>>>>>>> LP := ~True(LP)
>>>>>>>>> G := ~Provable(G)
>>>>>>>>>
>>>>>>>>> This is totally obvious when they are encoded in Prolog.
>>>>>>>>>
>>>>>>>>> https://www.researchgate.net/publication/350789898_Prolog_detects_and_rejects_pathological_self_reference_in_the_Godel_sentence
>>>>>>>>>
>>>>>>>>>
>>>>>>>>
>>>>>>>> Except that isn't the actual statement of G, and G can't be
>>>>>>>> written in Prolog because Prolog only handles first order logic
>>>>>>>> and G uses Higher Order logic.
>>>>>>>>
>>>>>>>> FAIL.
>>>>>>>>
>>>>>>>
>>>>>>> DIRECT QUOTE FROM page 40/43 OF Gödel's PAPER
>>>>>>> The analogy between this result and Richard’s antinomy leaps to
>>>>>>> the eye; there is also a close relationship with the “liar”
>>>>>>> antinomy,^14 since the undecidable proposition [R(q); q] states
>>>>>>> precisely that q belongs to K, i.e. according to (1), that [R(q);
>>>>>>> q] is not provable. We are therefore confronted with a
>>>>>>> proposition which asserts its own unprovability.
>>>>>>
>>>>>> "Close Relationship" is not the same thing as "Same as".
>>>>>>
>>>>>> Yes, there is some similarity in how G is built to the liar's
>>>>>> paradox, but G includes some extra indirection that makes it so it
>>>>>> does still have a truth value, and then it is about something
>>>>>> being Provable, and for ALL statements, the provability of that
>>>>>> statement is ALWAYS a truth-bearer, as statements which are not
>>>>>> truth bearers are by definition not provable.
>>>>>>
>>>>>>>
>>>>>>> 14 Every epistemological antinomy can likewise be used for a
>>>>>>> similar undecidability proof
>>>>>>
>>>>>> Right, by the same transformation used with the liars paradox, you
>>>>>> can transform another antinomy to build a similar contradiction
>>>>>> that makes G unprovable but true.
>>>>>>
>>>>>> That doesn't mean G's truth value is the same as that antinomy.
>>>>>>
>>>>>>
>>>>>>>
>>>>>>> https://mavdisk.mnsu.edu/pj2943kt/Fall%202015/Promotion%20Application/Previous%20Years%20Article%2022%20Materials/godel-1931.pdf
>>>>>>>
>>>>>>>
>>>>>>> Thus: G ⟷ ~Provable(G)
>>>>>>> is sufficiently equivalent to Gödel's G.
>>>>>>>
>>>>>>
>>>>>> Nope. Just shows you don't understand G.
>>>>>>
>>>>>>> When this is encoded in Prolog it is rejected as an infinite term
>>>>>>> as my paper clearly shows.
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>
>>>>>> As it should, since G uses Higher Order Logic which can NOT be
>>>>>> properly expressed in the first order logic of Prolog.
>>>>>
>>>>>
>>>>> 14 Every epistemological antinomy can likewise be used for a similar
>>>>> undecidability proof
>>>>>
>>>>> Thus this {epistemological antinomy} is sufficiently equivalent
>>>>> G ⟷ ~Provable(G)
>>>>
>>>> Since that isn't G, you havn't made you point.
>>>>
>>>
>>> Gödel said it does not have to be G:
>>>
>>> 14 Every epistemological antinomy can likewise be used for a similar
>>> undecidability proof
>>>
>>
>> You don't understand what he is saying, he is saying you can create a
>> statement similar to the G he presents based on other antinomies. He
>> just presented one based on the simplest version of the Liar's Paradox.
>>
>
> Sure when he says: "Every epistemological antinomy can likewise be used
> for a similar undecidability proof"
>
> He must actually mean NOT
> Every epistemological antinomy can likewise be used for a similar
> undecidability proof
>
> Because everyone knows that every X always means NOT every X
>
> Don't you feel a little embarrassed by your bald faced lie?
>
>

On 4/29/2022 7:46 PM, olcott wrote:
> On 4/29/2022 8:29 PM, Jeff Barnett wrote:
>> On 4/29/2022 5:10 PM, Richard Damon wrote:
>>> On 4/29/22 6:30 PM, olcott wrote:
>>
>>    <SNIP>
>>
>>>> When this is encoded in Prolog it is rejected as an infinite term as
>>>> my paper clearly shows.
>>>>
>>>>
>>>>
>>>
>>> As it should, since G uses Higher Order Logic which can NOT be
>>> properly expressed in the first order logic of Prolog.
>>
>> Unless Prolog has changed wildly in the last several years, it isn't
>> even close to FOL. I remember it as a toy that could only represent
>> and reason with Horn clauses. Can Prolog now deal with quantifiers and
>> negation on both sides of an implication? That would be very impressive.
>>
>> As a side note, I think it was this paucity of power that caused many
>> folks to not understand that "A -> B" could be true when "B" was false.
>
> It resolves the Liar Paradox to semantically malformed:
>
> ?- LP = not(true(LP)).
> LP = not(true(LP)).
>
> ?- unify_with_occurs_check(LP, not(true(LP))).
> false.
>
> (SWI-Prolog (threaded, 64 bits, version 7.6.4)
>
> https://www.researchgate.net/publication/350789898_Prolog_detects_and_rejects_pathological_self_reference_in_the_Godel_sentence
I know this is painful for you but 1) it is ill-formed AND 2) it isn't
the liar's paradox; it's just ill-formed like most of your attempts to
express things symbolically.
It's also an extremely poor response. I was hoping that Richard would
inform me if Prolog had extraordinarily extended its representation and
reasoning power. And here you are, a self-proclaimed Prologue expert who
missed a chance to actually pass back useful and correct information.
Instead, as usual, you just crapped on your terminal with non-sense. I
guess you know as little about Prologue as everything else you discuss.
I don't think I'll bother to thank you for your effort.
--
Jeff Barnett