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 4/29/2022 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 4/29/2022 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