This is how I solved the Halting Problem

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peteolcott

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Jun 3, 2019, 12:19:33 AM6/3/19
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https://medium.com/the-mission/elon-musks-3-step-first-principles-thinking-how-to-think-and-solve-difficult-problems-like-a-ba1e73a9f6c0

(1) I deduce a decision tree of very broad categories of possible solutions to analytical problems.

(2) I eliminate whole categories as either infeasible or sub-optimal.

(3) I divide the remaining category into its next increment of specificity
goto (2).

--
Copyright 2019 Pete Olcott All rights reserved

"Great spirits have always encountered violent
opposition from mediocre minds." Albert Einstein

Franz Gnaedinger

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Jun 4, 2019, 2:50:35 AM6/4/19
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On Monday, June 3, 2019 at 6:19:33 AM UTC+2, peteolcott wrote:
>
> "Great spirits have always encountered violent
> opposition from mediocre minds." Albert Einstein


formulate a hypothesis that doesn't violate proven theorems,
otherwise you fail, and if you repeted your claims a million
billion times

(Allgod, mathematical and natural logic, liar paradox, conclusion;
ambiguity or better flexibility, Einstein and Goedel; by the way,
Athel Cornish-Bowden; triangle of language)

Meanwhile Peter Olcott officially announced that he is God. Being God,
and the only one, he can dismiss the proven theorems of Goedel and Turing
and suffocate sci.logic and sci.lang and other fora by starting ever more
parallel threads.

I see the main problem in academe that has no clear idea of logic, or rather
a one-sided one, regarding mathematical logic as logic per se. Mathematical
logic is the logic of building and maintaining based on the formula a = a
while there is a wider logic formulated by Goethe: All is equal, all unequal ...,
known to artists of all times.

Goedel is very hard to understand for laymen when you consider mathematical
logic the only real logic, but most easy when you have a look at both sides.
Goedel proved that mathematics can't really and completely be separated from
general logic and the principle of equal unequal, it can only be secured
from case to case, for example divisions by zero are forbidden. Why? these
divisions yield infinite, which is equal unequal in itself. If you restrict logic
to mathematical logic you encounter paradoxa, which are quite natural
in the real world.

The problem is academe. Universities are not really universal. Allgod tries
to solve the problem by cramming the realm of wider logic (that includes
for example language) into mathematical logic, hoping he will thus regain
totality and completeness - absolute and complete and total being his
mantra words - and does it for the price of his career and sanity.

If only he would stop cross-posting to sci.lang! (he promised to do so,
but he doesn't stand by his word).

The logic of equal unequal blossoms in language. Allgod can't have that,
He tries to force language into the logic of a = a with his "mathematics
of the meaning of words" that led him nowhere. He castrates language
in the name of mathematical logic, and mathematical logic by dismissing
proven theorems.

I feel entitled to defend sci.lang from those who suffocate it with ever
more parallel threads.

(on the liar paradox)

A Cretan says all Cretans are liars. He is right. Psychologists found that
we are lying many times a day, and in different ways. We humans are liars,
Cretans are humans, ergo they are liars. QED. The famous liar paradox arises
when the natural logic of equal unequal is reduced to the mathematical logic
of a = a. A liar is a liar, alaways lying, only ever lying. But such a person
does not exist in the real world, on the contrary, a professional liar cares
to tell the truth as often as ever possible in order to gain the confidence
of a potential victim.

(conclusion, rigid denial vs Goedel's rigor)

Allgod tries to reduce natural logic to mathematical logic, however,
he can't escape the equal unequal, it haunts him in the form of
proven = proven = not proven. He replaces Goedel's rigor with
his naive but rigid denial. Every advice to come down from his trip
and write a modest but useful program that may then be extended
was in vain. He is a satellite that flies too low, destined to burn out
in the atmosphere. All warning failed.

(ambiguity or better flexibility)

The end of the world is near! This may be the warning of a preacher:
prepare yourself. Or it may be the exclamation of a housewife
addressing her hubby: How many times did I tell you to screw
back on the lid of the toothpaste tube after brushing your teeth?
I told you so for years. Now, finally, I see that you oblige. The end
of the world is near!

The same exclamation can have very different meanings. In the first
case it expresses a secret hope: if the apocalypse arrives in our
lifetime we shall go to heaven directly, without having to die,
so prepare yourself. And in the second case it formulates a reproach
in an exaggerated manner that makes it funny: you are so incredibly
obstinate that only a shockwave can move you, must be the approaching
end of the world ...

Ambiguity or better flexibility is the genius of natural language
that escapes from the cage of any formal system.

(Einstein and Goedel)

Einstein and Goedel were good friends who held each other's work
in high esteem. What would Einstein say about a naive Goedel denier?

(by the way)

I defend sci.lang also against those who can only argue on meta-levels
and drop verdicts from above instead of leading a topic discussion.
Kooks are also found on the academic side of the fence. One of them
suggested that proven theorems of mathematics and mathematical
logic can be dismissed. Allgod thanke3d him for confirming the Truth.
Good night.

(Athel Cornish-Bowden)

Athel Cornish-Bowden is the one who suggested that proven theorems
of mathematics and mathematical logic can be dismissed. Kooks are
also found on the academic side of the fence.

(triangle of language)

Word language can be seen as a triangle whose corners are life with
needs and wishes / mathematics as logic of building and maintaining
based on a = a / and art as human measure in a technical world,
based on Goethe's world formula and ever turning key 'All is equal,
all unequal ...', a formula known to artists of all times.

Athel Cornish-Bowden

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Jun 4, 2019, 5:02:43 AM6/4/19
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On 2019-06-04 06:50:33 +0000, Franz Gnaedinger said:

> On Monday, June 3, 2019 at 6:19:33 AM UTC+2, peteolcott wrote:
>>
>> "Great spirits have always encountered violent
>> opposition from mediocre minds." Albert Einstein
>
>
> formulate a hypothesis that doesn't violate proven theorems,
> otherwise you fail, and if you repeted your claims a million
> billion times
>
> (Allgod, mathematical and natural logic, liar paradox, conclusion;
> ambiguity or better flexibility, Einstein and Goedel; by the way,
> Athel Cornish-Bowden; triangle of language)
>
> Meanwhile Peter Olcott officially announced that he is God.

84

--
athel

Arnaud Fournet

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Jun 4, 2019, 5:12:36 AM6/4/19
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When your meter reaches 666
I expect something big to happen !?

Peter T. Daniels

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Jun 4, 2019, 8:05:37 AM6/4/19
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On Tuesday, June 4, 2019 at 5:02:43 AM UTC-4, Athel Cornish-Bowden wrote:

> 84

Cornish-Bowden continues to pollute the newsgroup with his inaccurate
and pointless series of integers.

peteolcott

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Jun 10, 2019, 1:29:53 PM6/10/19
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On 6/10/2019 11:04 AM, Ben Bacarisse wrote:
> peteolcott <Here@Home> writes:
>
>> On 6/10/2019 8:37 AM, Ben Bacarisse wrote:
>>> peteolcott <Here@Home> writes:
>>>> On 6/9/2019 7:16 AM, Ben Bacarisse wrote:
>>>>> peteolcott <Here@Home> writes:
>>>>>> On 6/8/2019 7:09 PM, Ben Bacarisse wrote:
> <cut>
>>>>> It's fascinating to see how many excuses you will come up with for not
>>>>> posting two numbers that you claim to have had for six months!
>>>>
>>>> I don't know how many states it has I only encoded the source-code
>>>> I did not totally create every detail of the corresponding machine
>>>> language yet.
>>>
>>> Ah, now the truth comes out! You don't have a TM. I thought not. If,
>>> as you apparently false claimed on Dec 15th, you had the TM "fully
>>> encoded", you could simply count the states.
>>>
>>>> As I already said: It has 32-bit characters intended to at least
>>>> specify the whole Unicode set.
>>>
>>> And now it seems you don't know what a TM's tape alphabet is either.
>>> That's not surprising.
>>>
>>> Since you don't have a TM as you claimed, why not post whatever it is
>>> you do have so you can find out what it is? You clearly don't know.
>>> Maybe you don't want to know...
>>
>> Interactions with you have hardly every had more than the zero fruitfulness
>> of George.
>
> Then I strongly advise you not to interact with me. Unless you ask me
> intelligent questions, I am likely to just point out your mistakes.
>
> Of course you could prove me utterly wrong by posting the TM that does
> that impossible thing you claimed last year.

You and I both know that even if it was utterly infallible in every
possible way you and most everyone that has interacted with me on
this USENET forum would utterly denigrate it anyway.

I am probably going to cease using USENET for discussions and only
post for the purpose of establishing copyright ownership. I will
continue to read replies for a while yet cease responding to any
reply that is an utterly baseless rebuttal as nearly all the replies
have been recently.

> You won't of course.
> Instead, why don't you fantasise about how great it will be when you
> do? That fantasy can last for years if you never actually post what you
> have!
>
> Hey, here's another option... Why don't you ask me what the tape
> alphabet of a TM is so you can see why saying "it's Unicode" is a silly
> answer? The trouble is, if you understand my answer, you might realise
> you've been mistaken all these years.
>

I have adapted the concept of a TM so that it retains an isomorphism
to the original concept and examines most of the tedious details at
a much higher level of abstraction. Examining these things at much
higher levels of abstraction provides enormous cognitive leverage.

Key relations that could not be seen when buried in thousands of
details become enormously easier to see when the extraneous complexity
is stripped away.

Now that I have Ludwig Wittgenstein's perfect agreement on my verbatim
basis for refuting the 1931 Incompleteness Theorem
http://wab.uib.no/agora/tools/alws/collection-6-issue-1-article-6.annotate
The idea of examining these things at very high levels of abstraction
and my 1931 GIT refutation basis are no longer rejected out-of-hand.

Honest people that actually understand these things will understand
that it is perfectly legitimate to examine things at much higher
levels of abstraction as long as the isomorphism to the original is
maintained.

Dishonest people will say that if it diverges from the original verbatim
concept of a TM to the slightest degree that it says nothing about TM's
at all even if the isomorphism is perfect.

To the best of my current knowledge there are only two people on any of
these forums that sufficiently understand halting problem related concepts
and only one of those is honest. Mike Terry is the honest one.

Several other people that know that their understanding is woefully insufficient
dishonestly provide baseless denigration anyway.

Mścisław Wojna-Bojewski

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Jun 10, 2019, 9:00:13 PM6/10/19
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I understand why you find it pointless, but inaccurate...? Does it mean he has overlooked some instance of Fränzeli's megillah?

Peter T. Daniels

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Jun 11, 2019, 9:36:08 AM6/11/19
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I think it was the first day he was doing it: he typed the same number
in two successive messages, so ever since, the count has been 1 too low
(assuming that he somehow counted the first 60-odd occurrences accurately
in the first place).

skpf...@gmail.com

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Jun 11, 2019, 9:50:12 AM6/11/19
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peteolcott

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Jun 11, 2019, 2:16:58 PM6/11/19
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I am God and everyone knows it because everyone knows that they are me.
Can we quit pretending otherwise now?

--
Copyright 2019 Pete Olcott All rights reserved

peteolcott

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Jun 12, 2019, 1:09:07 PM6/12/19
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On 6/12/2019 11:09 AM, Fred wrote:
> On 12/06/2019 16:47, peteolcott wrote:
>> On 6/12/2019 9:04 AM, George Greene wrote:
>>> On Tuesday, June 11, 2019 at 11:23:20 PM UTC-4, peteolcott wrote:
>>>
>>>> Both Gödel and Tarski can be refuted as long as we understand that True
>>>> and False are relative to a formal system.
>>>
>>> Which NOBODY WILL EVER understand because MODEL THEORY EXISTS and we have
>>> THIS WHOLE FIELD FOUNDED UPON KNOWING that truth and falsity exist IN MODELS
>>> AND NOT just in theories!
>>
>> That following is specified AFTER INTERPRETATION thus it is false in all models
>> // Wittgenstein verbatim quote
>>     “I have constructed a proposition (I will use ‘P’ to designate it)
>>     in Russell’s symbolism, and by means of certain definitions and
>>     transformations it can be so interpreted that it says ‘P is not
>>     provable in Russell’s system’.
>> P ↔ (RS ⊬ P)  // Minimal essence of 1931 Incompleteness Theorem conclusion
>
>     P says ‘P is not provable in Russell’s system’
>
> *isn't* reasonably translated as
>
>     P ↔ ‘P is not provable in Russell’s system’
>
> because ↔ only means that the L & RHS have the same truth value.
>

You are certainly correct.
I had to correct Wittgenstein so that his specification more closely
corresponded to the actual Incompleteness Theorem.

>>> In formal theories (NOT "formal systems"), we have
>> Because of the inconsistent way that these terms are conventionally
>> used you cannot even say that my use is unconventional.
>> https://en.wikipedia.org/wiki/Formal_system
>>
>> They had a whole thing on Quora about this providing numerous examples
>> of inconsistent standard conventions.
>>
>>
>>> something MORE THAN truth and falsity!  Theorems or their denials ARE MODALLY
>>> true or false!  Theorems are true IN ALL models of the axioms and their denials are false IN ALL models of the axioms!  THERE IS A THIRD
>>
>> Great. That was useful. I already thought of it that way.
>>
>>> collection OF SENTENCES (over the first-order language of the axioms) that are true in some models and false in others.  All of the sentences in this third collection are unprovable, but THEIR DENIALS ARE ALSO UNPROVABLE AND ARE ALSO IN this collection
>>> (you could say that the  > collection is "closed under negation").
>>
>> Yet and what no one ever bothered to ever notice before and are
>> refusing to notice now when pointed out is that these sentences
>> are neither provable nor unprovable only because they are self-contradictory.
>
> The undecided sentences are formulae of arithmetic. What does it mean to say of a formula of arithmetic that it is self-contradictory?

The exact same sort of thing that it says when it says that
it is true that it is unprovable.

Its the whole rat's nest of humongous extraneous complexity that
faking a provability predicate with Gödel numbers and diagonalization
brings with this.

When we strip away this 1,000,000-fold extraneous complexity we end up
with this: P ↔ (F ⊬ P)

Which gives us the exact same:
statements of the language of F which can neither be proved nor
disproved in F shown in this paragraph:

https://plato.stanford.edu/entries/goedel-incompleteness/
The first incompleteness theorem states that in any consistent
formal system F within which a certain amount of arithmetic can
be carried out, there are statements of the language of F
which can neither be proved nor disproved in F.


>
>> "This sentence is not true" is not true AND THAT DOES NOT MAKE IT TRUE.
>>
>>>
>>> Since both the sentence and its denial are unprovable,
>>
>> Unprovable when its context is self-contradiction (Tarski's theory)
>> and provable when the context been changed (Tarski's meta-theory).
>>
>> Tarski thought that it became decidable in his meta-theory because
>> his meta-theory was more powerful than his theory. It actually
>> became decidable in his meta-theory because the context had been
>> changed from self-contradictory to not self-contradictory.
>>
>> Tarski knew that if the Liar Paradox was stated directly in his meta-theory
>> and evaluated in this same meta-theory that he would need a more powerful
>> theory to correctly decide this sentence. He posited an infinite hierarchy
>> of increasingly more "powerful" theories.
>>
>> Because I am correct and he is incorrect we could simply have two
>> theories of identical power decide the undecidable sentences for the other.
>>
>> We assume that theory F and theory RS are identical except for their names.
>> When we add theory F to theory RS we create theory F'
>
> Who knows what you mean by adding one theory to another.

see pages 275-276 and 247-248
http://www.thatmarcusfamily.org/philosophy/Course_Websites/Readings/Tarski%20-%20The%20Concept%20of%20Truth%20in%20Formalized%20Languages.pdf

> I doubt that you know yourself.  If 'theory' means set of sentences closed under logical consequence, and if theory T plus theory S is T union S closed under logical consequence, then your F, RS, F'
> and RS' are all the same.
>
>> or we add theory RS to theory F we create theory RS'
>> F' and RS' are theories of identical power but different scope.
>> F' can decide the undecidable sentences of RS
>> RS' can decide the undecidable sentences of F
>> because the self-contradictory context has been removed.
>
> Could you explain how your adding of theories removes anything?

It was Tarski's whole basis and I gave you Tarski's whole paper along
with references to these pages 275-276 and 247-248
P ↔ (RS ⊬ P) // P in RS cannot prove that P is not provable in RS because that would be self-contradictory.
(F' ⊢ P) // F' proves that P in RS is not provable in RS

>
>>> BY YOUR "logic", they would have TO BOTH BE FALSE, but THIS IS NOT POSSIBLE, since if a sentence's denial is false, THE SENTENCE MUST BE TRUE.  Your take leads immediately TO CONTRADICTION here.  We just derived a contradiction from what you said,
>>> so in this room, that constitutes a proof that you are full of shit.
>>> Thanks for playing!

peteolcott

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Jun 12, 2019, 2:04:51 PM6/12/19
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> How is that a formula of arithmetic?

By doing this in arithmetic rather than a formal language
having its own provability operator we add a million-fold
extraneous complexity.

ONLY by stripping away this purely extraneous complexity can
we see what is really going on.

Tarski openly admitted that he was directly using the Liar Paradox.
Gödel openly admitted that the Liar Paradox would prove his same point.

ON FORMALLY UNDECIDABLE PROPOSITIONS
OF PRINCIPIA MATHEMATICA AND RELATED SYSTEMS I
by Kurt Godel Vienna
The analogy between this result and Richard’s antinomy leaps to the eye; there is also a
close relationship with the “liar” antinomy,14

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

By: "epistemological antinomy" he means any self-contradictory sentence.
The the "great" work of Godel and Tarski simply boils down to their
"miraculous" discovery that self-contradictory sentences are not true, or provable.
I say WELL DUH !!!


> Put to one side the theory P that Gödel worked with (a simplification of Principia's type theory).  Modern text book accounts are about first-order theories of arithmetic, the non-logical symbols are which are 0,
> s(uccessor), + and *, and maybe an order relation (i.e., one of <, >, <=, >=).  How do you express P ↔ (F ⊬ P) using them?
> I see no definition of adding one theory to another.

If you carefully study the referenced pages you will see that this
is what Tarski is doing. He may never get around to explaining how
he is doing it.

>
>>>  I doubt that you know yourself.  If 'theory' means set of sentences closed under logical consequence, and if theory T plus theory S is T union S closed under logical consequence, then your F, RS, F' and RS' are all the same.
>>>
>>>> or we add theory RS to theory F we create theory RS'
>>>> F' and RS' are theories of identical power but different scope.
>>>> F' can decide the undecidable sentences of RS
>>>> RS' can decide the undecidable sentences of F
>>>> because the self-contradictory context has been removed.
>>>
>>> Could you explain how your adding of theories removes anything?
>>
>> It was Tarski's whole basis and I gave you Tarski's whole paper along
>> with references to these pages 275-276 and 247-248
>> P ↔ (RS ⊬ P) // P in RS cannot prove that P is not provable in RS because that would be self-contradictory.
>> (F' ⊢ P)     // F' proves that P in RS is not provable in RS
>>
>
>


peteolcott

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Jun 13, 2019, 11:32:56 PM6/13/19
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On 6/13/2019 10:13 PM, André G. Isaak wrote:
> On 2019-06-13 8:54 p.m., peteolcott wrote:
>> On 6/13/2019 9:34 PM, André G. Isaak wrote:
>>> On 2019-06-13 6:27 p.m., peteolcott wrote:
>>>> On 6/3/2019 11:20 AM, André G. Isaak wrote:
>>>>> void DoIHalt {
>>>>>
>>>>>    unsigned long x = 14;
>>>>>
>>>>>    while (x != 982353739) {
>>>>>
>>>>>      x = x * 144;
>>>>>      x += 17;
>>>>>      x = x/57;
>>>>>
>>>>>    };
>>>>>
>>>>>    return;
>>>>>
>>>>> };
>>>>
>>>>
>>>> The termination condition was intentionally chosen to never be met
>>>> from the above pattern. Now that I am actually back to work on halting
>>>> this became relevant. That the termination condition was intentionally
>>>> chosen to never be met proves that at least some of these non terminating
>>>> termination conditions can be detected.
>>>
>>> Actually, it was chosen purely at random. I did not attempt to establish whether it would terminate or not. Establishing whether this particular program would or would not halt is a fairly trivial task, but I'd asked you to show how the general method
>>> which you'd earlier described would be applied to this particular case.  Thus far you haven't attempted to answer this.
>>>
>>> In case you've forgotten, that 'general method' was as follows:
>>>
>>>> (1) I deduce a decision tree of very broad categories of possible solutions to analytical problems.
>>>>
>>>> (2) I eliminate whole categories as either infeasible or sub-optimal.
>>>>
>>>> (3) I divide the remaining category into its next increment of specificity goto (2).
>>>
>>
>> Yes and for taking decades to refute all the conventional halting
>> problem proofs it is very cost-effective.
>
> So why don't you actually answer the question and illustrate how this 'method' works with respect to the above problem?

It is not cost-effective for me to do this.

> What does your 'decision tree' look like and how exactly is it deduced? Which categories are eliminated and how?
>

To refute Tarski and Gödel I had to boil down their conclusions to
their barest possible essence. The incompleteness aspect and the
undefinability aspect are both derived entirely from self-contradictory
sentences. Tarski documented that he specifically used the actual Liar Paradox
and Gödel specifically documented that the Lair Paradox would have just as well
to prove his point.

ON FORMALLY UNDECIDABLE PROPOSITIONS
OF PRINCIPIA MATHEMATICA AND RELATED SYSTEMS I
by Kurt Godel Vienna
The analogy between this result and Richard’s antinomy leaps to the eye; there is also a
close relationship with the “liar” antinomy,14

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

> Show your work.

USENET since 1998 shows my work. This is my very first published work:
https://groups.google.com/forum/#!original/alt.philosophy/g13n38LcCO0/7QGb7JXGn-4J

From: "GOD" <iam...@home.com>
Subject: Re: GOD is...
Date: 1998/12/20

The one directional mathematical mapping from representations of actuality
(within language or memories of physical sensations) to actuality itself is
TRUTH Copyright 1997 by Pete Olcott

>
> André
>
>> I am right on the verge of refuting Tarski and Gödel the last step
>> to refuting them appears to be establishing that conceptual truth
>> represented in (formal or natural) language is defined relations
>> between finite strings.
>>
>> There is no conceptual truth represented in language that does not
>> exactly fit that model.

André G. Isaak

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Jun 14, 2019, 12:11:05 AM6/14/19
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Which is shorthand for 'I can't'.

>
>> What does your 'decision tree' look like and how exactly is it
>> deduced? Which categories are eliminated and how?
>>
>
> To refute Tarski and Gödel I had to boil down their conclusions to
> their barest possible essence. The incompleteness aspect and the
> undefinability aspect are both derived entirely from self-contradictory
> sentences. Tarski documented that he specifically used the actual Liar
> Paradox
> and Gödel specifically documented that the Lair Paradox would have just
> as well
> to prove his point.
>
>     ON FORMALLY UNDECIDABLE PROPOSITIONS
>     OF PRINCIPIA MATHEMATICA AND RELATED SYSTEMS I
>     by Kurt Godel Vienna
>     The analogy between this result and Richard’s antinomy leaps to the
> eye; there is also a
>     close relationship with the “liar” antinomy,14
>
>     14 Every epistemological antinomy can likewise be used for a
> similar undecidability proof.

None of the above has anything to do with my question.

>> Show your work.
>
> USENET since 1998 shows my work. This is my very first published work:
> https://groups.google.com/forum/#!original/alt.philosophy/g13n38LcCO0/7QGb7JXGn-4J

Posting to usenet hardly qualifies as 'publishing'.

>
> From: "GOD" <iam...@home.com>
> Subject: Re: GOD is...
> Date: 1998/12/20
>
> The one directional mathematical mapping from representations of actuality
> (within language or memories of physical sensations) to actuality itself is
> TRUTH Copyright 1997 by Pete Olcott

Again, this has nothing to do with my question.

André

--
To email remove 'invalid' & replace 'gm' with well known Google mail
service.

peteolcott

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Jun 14, 2019, 12:37:08 AM6/14/19
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According to copyright law it does count as publishing.
I have an intellectual property trail all the way back to 1997.

>
>>
>> From: "GOD" <iam...@home.com>
>> Subject: Re: GOD is...
>> Date: 1998/12/20
>>
>> The one directional mathematical mapping from representations of actuality
>> (within language or memories of physical sensations) to actuality itself is
>> TRUTH Copyright 1997 by Pete Olcott
>
> Again, this has nothing to do with my question.
>
> André
>

I am not going to answer your question your way.
I answered your question my way.

peteolcott

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Jun 14, 2019, 12:55:02 AM6/14/19
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You said it was just something that you came up with on the spur of the moment.
I don't really believe that.
I was actually working on it when I got your message.
I found that after a billion iterations all the numbers were less than 90%
of your test number.

André G. Isaak

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Jun 14, 2019, 1:57:27 AM6/14/19
to
Well, obviously I wanted something that, if it halts, will take a long
time to halt - that's why I chose a largish number to the while test.
But I didn't design it specifically to halt or not halt.

The point is that a solution to the halting problem shouldn't have to
actually run the program.

peteolcott

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Jun 14, 2019, 2:27:14 AM6/14/19
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I am too close to complete to divulge any details of what a solution
to the halting problem actually does involve.

André G. Isaak

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Jun 14, 2019, 9:40:14 AM6/14/19
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I thought you said you already had a solution to the halting problem.

Do you actually understand what the halting problem is? Maybe you could
state it in your own words (no quotes from textbooks or other sources).

peteolcott

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Jun 14, 2019, 11:29:34 AM6/14/19
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I have the source code for H/H^. The compiler is mostly written
The UTM interpreter is not written at all.

peteolcott

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Jun 16, 2019, 12:20:03 PM6/16/19
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On 6/16/2019 11:00 AM, peteolcott wrote:
> On 6/16/2019 10:53 AM, Ben Bacarisse wrote:
>> peteolcott <Here@Home> writes:
>>
>>> On 6/15/2019 9:38 PM, Ben Bacarisse wrote:
>>>> peteolcott <Here@Home> writes:
>>>>
>>>>> What I mean by "solved the halting problem" is that I know how
>>>>> to refute the Peter Linz proof of the halting problem such that
>>>>> this way can be generalized to all of the conventional halting
>>>>> problem proofs thereby refuting every proof that shows solving
>>>>> the halting problem is impossible.
>>>>
>>>> But there are other proofs that use other methods.  Your "lazer-like
>>>> focus", otherwise known as wilful ignorance, means that you are unaware
>>>> of the vast body of work that puts limits on what can be computed.
>>>
>>> To the best of my knowledge none of the other proofs show that
>>> halting is impossibly decidable, they merely rely on not currently
>>> having the answer to certain decision problems.
>>
>> You set the bar too low.  I know very few CS people with less knowledge
>> of this field than you.
>
> My knowledge has a very specific focus.
> Since all human knowledge is merely tautological connections between
> concepts: Gödel/Tarski/HP/Liar Paradox are necessarily incorrect.

Since true is verifying the semantic relation between concepts
and provable is verifying the corresponding syntactic relation
between finite strings, true and provable mutually define each
other and are therefore utterly inseparable.

Taking provability away from true is like removing {wet} from liquid water.
I have known this for thirty years yet only now have the words to express it.

>
>> After an undergraduate course on this topic,
>> I'd expect all but the students who are in real difficulties to be able
>> to prove the "halting theorem" in at least two totally different ways.
>>
>>> I just did a quick search and found no alternates.
>>> [alternative halting problem proof]
>>>
>>> https://cstheory.stackexchange.com/questions/3810/is-there-an-alternative-proof-of-the-tm-halting-problem-other-than-the-standard
>>> I would guess that you might have a more comprehensive answer.
>>
>> I am not an expert in the field, but yes, I could give a more
>> comprehensive answer.  I've suggested alternative work that you should
>> look at many times in the past.

peteolcott

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Jun 16, 2019, 2:43:43 PM6/16/19
to
On 6/16/2019 12:22 PM, pete_olcott wrote:
> That is the architectural framework of exactly how and why
> those things:
Gödel/Tarski/HP/Liar Paradox

> are incorrect. The precise details of these refutations
> are logically entailed by that architectural overview. So far only
> Ludwig Wittgenstein had understood these specific details.
>

“I have constructed a proposition (I will use ‘P’ to designate it)
in Russell’s symbolism, and by means of certain definitions and
transformations it can be so interpreted that it says ‘P is not
provable in Russell’s system’.

‘True in Russell’s system’ means, as was said: proved in Russell’s
system; and ‘false in Russell’s system’ means: the opposite has
been proved in Russell’s system.

Formalizing Wittgenstein's words:
P ↔ (RS ⊬ P)
∀x (True(RS, x) ↔ (RS ⊢ x))
∀x (False(RS, x) ↔ (RS ⊢ ¬x))

MY PROOF THAT WITTGENSTEIN IS CORRECT
If G is not provable in PA then G is not true in PA. If G is provable
in the Gödelization of PA then G is true in the Gödelization of PA.
Diagonalization is an alternative form of provability.

The Gödelization of PA is a distinctly different formal system than
PA as shown by the difference of the provability of G.

The key difference between PA and the Gödelization of PA is that
G is inside the scope of self-contradiction in PA and G is outside
the scope of self-contradiction in the Gödelization of PA.

THAT GÖDEL SAID THAT G IS NOT PROVABLE AT ALL INSTEAD OF SAYING
THAT G IS NOT PROVABLE IN PA AND IS PROVABLE IN THE GÖDELIZATION
OF PA IS THE ENTIRE MISTAKE THAT GÖDEL MADE.

THERE REALLY IS NO SUCH THING AS TRUE AND UNPROVABLE BECAUSE
PROVABLE AND TRUE ARE EXACTLY THE SAME THING.

TO MORE CLEARLY UNDERSTAND THIS MISTAKE REQUIRES THE NOTION OF
PROVABILITY TO BE UNDERSTOOD IN THE BROADER CONTEXT OF VERIFYING
THAT RELATIONS EXIST BETWEEN FINITE STRINGS.

THE ABOVE COMPLETE REFUTATION IS LOGICALLY ENTAILED BY THIS
All human knowledge is merely tautological connections between concepts
forming an isomorphism to relations between finite strings.

peteolcott

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Jul 10, 2019, 2:44:49 PM7/10/19
to
On 7/9/2019 3:11 AM, André G. Isaak wrote:
> On 2019-07-08 7:30 p.m., peteolcott wrote:
>
>> It does not frigging depend on its implementation. I spent a bunch of
>> hours on that code and found that it specifies a repeating sequence of
>> integers. After I solved it the author rewrote it with integers too
>> large to test.
>
> I'm a bit mystified that you had to spend 'a bunch of hours' on that code. That program (minus the syntax errors which Keith pointed out -- it's been awhile since I've coded in C) was designed with two very simple desiderata in mind:
>
> (1) it should be trivially easy to determine whether it halts, and
> (2) it should not be apparent whether it halts based on just a cursory examination.
>

This apparently does not effect my claim at all:
I have a fully encoded the computational equivalent to a Peter Linz
H deciding halting for exactly one instance of a Peter Linz H^.

The actual final result will be much more robust than this
and decide halting for two whole classes of Peter Linx H^.

> The whole point here was for you to demonstrate how your 'general method works'. Instead, you fight with code for hours without even figuring out the basics of how the code worked (i.e. the integer overflow induced loop).
>
> This really doesn't bode well for your claims of having a 'general method' involving 'eliminating whole categories of solutions'. As far as I can tell, no categories of solutions were even identified, let alone eliminated.
>
> André
>
>

Almost everyone continues to make the same mistake of precisely
equating totally unbelievable with false never realizing that
this implicitly presumes infallibility upon woefully fallible humans.

This logically unjustified self-certainty (if not corrected) could
otherwise directly cause the extinction of humanity through issues
such as climate change.

https://www.climatecentral.org/news/the-last-time-co2-was-this-high-humans-didnt-exist-15938

https://climate.nasa.gov/climate_resources/24/graphic-the-relentless-rise-of-carbon-dioxide/

https://www.ipcc.ch/site/assets/uploads/sites/2/2019/05/SR15_SPM_version_report_LR.pdf

peteolcott

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Jul 10, 2019, 3:50:24 PM7/10/19
to
On 7/10/2019 2:11 PM, Ben Bacarisse wrote:
> peteolcott <Here@Home> writes:
> <cut>
>> I have a fully encoded the computational equivalent to a Peter Linz
>> H deciding halting for exactly one instance of a Peter Linz H^.
>
> No you don't. That's impossible (provided you meant to say "correctly
> decides"). We may never know what it is you have since you won't post
> it, but can't be what you say here. And just to remind readers, it
> certainly is not what you originally lied about having more than six
> months ago:
>

If one is careful to think through every possible combination of ideas
pertaining to the halting problem there is at least one of these ideas
where the computational equivalent of a Peter Linz H correctly deciding
halting for the computational equivalent of a Peter Linz H^ is not impossible.

In other words with limited subject domain omniscience such that
the subject is limited to the halting problem there are key aspects
that have never been examined before such that the conclusion is
refuted.

As of today I can also explain exactly how the direct contradiction
of the existence of such a solution can be addressed and conquered.

Genius is 1% inspiration and 99% perspiration:
It only took me about ten thousand hours over 21 years studying the
details again and again over and over to see these things a little more
deeply than anyone has ever seen them before.

It was very helpful to see these issues from the differing perspectives
of (a) The Liar Paradox, (b) 1931 Incompleteness Theorem (c) Tarski Undefinability
and finally (d) The Halting Problem.


> | Date: Sat, 15 Dec 2018 11:03:21 -0600
> | Message-ID: <JbydneYGrrpProjB...@giganews.com>
> |
> | Everyone has claimed that H on input pair (Ĥ, Ĥ) meeting the Linz specs
> | does not exist. I now have a fully encoded pair of Turing Machines H / Ĥ
> | proving them wrong.
> |
> | Date: Sat, 15 Dec 2018 01:28:22 -0600
> | Message-ID: <YdidnYrC-duNMInB...@giganews.com>
> |
> | I now have an actual H that decides actual halting for an actual (Ĥ,
> | Ĥ) input pair. I have to write the UTM to execute this code, that
> | should not take very long. The key thing is the H and Ĥ are 100%
> | fully encoded as actual Turing machines.
>

I am reducing this claim such that every subtle trace of what could
possibly be construed as exaggeration is explicitly eliminated.

I have the computational equivalent of a Peter Linz H correctly
deciding halting for exactly one instance of the computational
equivalent of a Peter Linz H^.

peteolcott

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Jul 11, 2019, 10:56:19 AM7/11/19
to
On 7/11/2019 7:47 AM, Fred wrote:
> On 11/07/2019 03:49, peteolcott wrote:
>
>>
>> I had this problem with my refutation of the Incompleteness Theorem. No one
>> would give it a fair review for two years until I found that Wittgenstein
>> had a verbatim solution. They finally gave MY solution a fair review ONLY
>> after I leapt over the credibility gap by attributing my exact solution to
>> Wittgenstein.
>
> You haven't refuted the incompleteness theorem (you don't even know what the incompleteness theorem says).

Your counter-factual opinion carries zero weight because it is counter-factual.
My refutation of Gödel's 1931 Incompleteness theorem has been validated as
Wittgenstein's refutation up to but not including the last step.

THIS PHILOSOPHY OF LOGIC WILL SHORT-CIRCUIT IN THE MINDS OF LEARNED BY ROTE
The last step is comprehending that by what-so-ever means we verify that
a statement of conceptual truth is true <is> this statement's formal proof.

Another way to say this is that every sound deductive inference chain
has a corresponding formal proof because every relation between concepts
has a corresponding relation between finite strings.

Sound deduction and formal proofs are isomorphic and mutually define
each other making them inseparable.

FOR ALL LEARNED-BY-ROTE PEOPLE THAT CAN'T IMAGINE ANYTHING BEYOND THEIR
LEARNED-BY-ROTE THE FACT THAT "THIS IS JUST NOT THE WAY WE DO THESE THINGS"
PROVIDES ZERO REFUTATION WHAT-SO-EVER.

> Your errors before you read a snippet of Wittgenstein and your errors after you read it are the same.  That credibility gap might be narrowed if you
> didn't continually make elementary errors of logic.
>

Only because I independently derived the exact same refutation myself
(as the sci.logic record shows)
long before I ever heard of Wittgenstein do I know that his "snippet"
is entirely complete and correct on its own, thus not a snippet at all.

Wittgenstein's refutation of Gödel
I imagine someone asking my advice; he says: “I have constructed a proposition (I will use ‘P’ to designate it) in Russell’s symbolism, and by means of certain definitions and transformations it can be so interpreted that it says ‘P is not provable in
Russell’s system’. Must I not say that this proposition on the one hand is true, and on the other hand is unprovable? For suppose it were false; then it is true that it is provable. And that surely cannot be! And if it is proved, then it is proved that is
not provable. Thus it can only be true, but unprovable.”

Just as we ask, “‘Provable’ in what system?”, so we must also ask, “‘true’ in what system?” ‘True in Russell’s system’ means, as was said: proved in Russell’s system; and ‘false in Russell’s system’ means: the opposite has been proved in Russell’s system.
– Now what does your “suppose it is false” mean? In the Russell sense it means ‘suppose the opposite is proved in Russell’s system’; if that is your assumption you will now presumably give up the interpretation that it is unprovable. And by ‘this
interpretation’ I understand the translation into this English sentence. – If you assume that the proposition is provable in Russell’s system, that means it is true in the Russell sense, and the interpretation “P is not provable” again has to be given up.[…]

peteolcott

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Jul 11, 2019, 11:33:45 AM7/11/19
to
On 7/11/2019 10:07 AM, Fred wrote:
> On 11/07/2019 15:56, peteolcott wrote:
>> On 7/11/2019 7:47 AM, Fred wrote:
>>> On 11/07/2019 03:49, peteolcott wrote:
>>>
>>>>
>>>> I had this problem with my refutation of the Incompleteness Theorem. No one
>>>> would give it a fair review for two years until I found that Wittgenstein
>>>> had a verbatim solution. They finally gave MY solution a fair review ONLY
>>>> after I leapt over the credibility gap by attributing my exact solution to
>>>> Wittgenstein.
>>>
>>> You haven't refuted the incompleteness theorem (you don't even know what the incompleteness theorem says).
>>
>> Your counter-factual opinion carries zero weight because it is counter-factual.
>> My refutation of Gödel's 1931 Incompleteness theorem has been validated as
>> Wittgenstein's refutation up to but not including the last step.
>
> Not at all.  You have a bit of Wittgenstein that expresses (more or less) what you have claimed.  "I agree (more or less) with Wittgenstein" is *not* a validation of your claim.  You and he might be equally mistaken.
>
>> THIS PHILOSOPHY OF LOGIC WILL SHORT-CIRCUIT IN THE MINDS OF LEARNED BY ROTE
>> The last step is comprehending that by what-so-ever means we verify that
>> a statement of conceptual truth is true <is> this statement's formal proof.
>>
>> Another way to say this is that every sound deductive inference chain
>> has a corresponding formal proof because every relation between concepts
>> has a corresponding relation between finite strings.
>>
>> Sound deduction and formal proofs are isomorphic and mutually define
>> each other making them inseparable.
>>
>> FOR ALL LEARNED-BY-ROTE PEOPLE THAT CAN'T IMAGINE ANYTHING BEYOND THEIR
>> LEARNED-BY-ROTE THE FACT THAT "THIS IS JUST NOT THE WAY WE DO THESE THINGS"
>> PROVIDES ZERO REFUTATION WHAT-SO-EVER.
>>
>>>  Your errors before you read a snippet of Wittgenstein and your errors after you read it are the same.  That credibility gap might be narrowed if you didn't continually make elementary errors of logic.
>>>
>>
>> Only because I independently derived the exact same refutation myself
>> (as the sci.logic record shows)
>> long before I ever heard of Wittgenstein do I know that his "snippet"
>> is entirely complete and correct on its own, thus not a snippet at all.
>>
>> Wittgenstein's refutation of Gödel
>
> Wittgenstein's mistake was to think that Gödel's incompleteness theorem said something like "there are truths unprovable in 'Russell's system'", where "truths" means something like "things provable in 'Russell's system'".  That is obviously not right.  To
> find fault (if there is any to be found) with Gödel's incompleteness theorem you'll need to do one of two things
> i) read Gödel's paper (in English translation, presumably); or
> ii) read a modern textbook account of the incompleteness theorem.
> ii) is preferable, but you'll do neither.
>
>> I imagine someone asking my advice; he says: “I have constructed a proposition (I will use ‘P’ to designate it) in Russell’s symbolism, and by means of certain definitions and transformations it can be so interpreted that it says ‘P is not provable in
>> Russell’s system’. Must I not say that this proposition on the one hand is true, and on the other hand is unprovable? For suppose it were false; then it is true that it is provable. And that surely cannot be! And if it is proved, then it is proved that
>> is not provable. Thus it can only be true, but unprovable.”
>>
>> Just as we ask, “‘Provable’ in what system?”, so we must also ask, “‘true’ in what system?” ‘True in Russell’s system’ means, as was said: proved in Russell’s system; and ‘false in Russell’s system’ means: the opposite has been proved in Russell’s
>> system. – Now what does your “suppose it is false” mean? In the Russell sense it means ‘suppose the opposite is proved in Russell’s system’; if that is your assumption you will now presumably give up the interpretation that it is unprovable. And by ‘this
>> interpretation’ I understand the translation into this English sentence. – If you assume that the proposition is provable in Russell’s system, that means it is true in the Russell sense, and the interpretation “P is not provable” again has to be given
>> up.[…]
>>
>

https://plato.stanford.edu/entries/goedel-incompleteness/
The first incompleteness theorem states that in any consistent
formal system F within which a certain amount of arithmetic
can be carried out, there are statements of the language of F
which can neither be proved nor disproved in F.
Raatikainen, Panu, (Fall 2018)


I have told you this already hundreds of times, you must be a little
slow on the uptake.

(a) For an expression of language to be a statement (ie logic sentence)
of that language it must be exactly one of: {true, false}.

(b) The ONLY way to know if an expression of language is: {true,false}
is according to Wittgenstein/Olcott this expression of language must
be proved (Wittgenstein's word) or disproved in that same formal system.

(c) Therefore it is impossible for there to be any statement (ie logic sentence)
of any language of any formal system "which can neither be proved nor disproved"
in that formal system.

THIS REALLY IS ALL THERE IS TO IT: IF (1) AND (2) THEN (3)
(1) Raatikainen 2018 Accurately sums up the essence of the 1931 Incompleteness Theorem.
(2) The Wittgenstein/Olcott connection between true/provable is mandatory.
(3) Gödel is wrong.

I HAVE ALREADY TOLD YOU THIS HUNDREDS OF TIMES THE ONLY DIFFERENCE IS
NOW I KNOW THAT WITTGENSTEIN AGREES WITH ME.

Athel Cornish-Bowden

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Sep 11, 2019, 5:13:46 AM9/11/19
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On 2019-06-04 06:50:33 +0000, Franz Gnaedinger said:

>
> Athel Cornish-Bowden is the one who suggested that proven theorems
> of mathematics and mathematical logic can be dismissed.

As I expected, Franz never produced any evidence that I said anything
remotely resembling that. The closest I can find is the following, from
2nd March 2019:

> You've never heard of supposed proofs being found to be faulty? I
> thought you knew more mathematics than that (no linguistics, of course,
> but a certain amount of mathematics). Andrew Wiles's original proof of
> Fermat's last theorem turned out to be wrong (fortunately in time to be
> fixed).

As anyone who can understand English can see immediately, it is not the
same as what Franz claims I said. If he wants to maintain his position
he'll have to find a genuine quotation.

--
athel

peteolcott

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Sep 11, 2019, 10:44:46 AM9/11/19
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Close enough. You said that it is clear that people make mistakes even
on formal mathematical proofs, whereas Franz has always claimed that any
formal mathematical proof is always 100% perfectly infallible.

Peter T. Daniels

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Sep 11, 2019, 11:30:08 AM9/11/19
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On Wednesday, September 11, 2019 at 10:44:46 AM UTC-4, peteolcott wrote:
> On 9/11/2019 4:13 AM, Athel Cornish-Bowden wrote:
> > On 2019-06-04 06:50:33 +0000, Franz Gnaedinger said:

> >> Athel Cornish-Bowden is the one who suggested that proven theorems
> >> of mathematics and mathematical logic can be dismissed.
> > As I expected, Franz never produced any evidence that I said anything remotely resembling that. The closest I can find is the following, from 2nd March 2019:
> >> You've never heard of supposed proofs being found to be faulty? I thought you knew more mathematics than that (no linguistics, of course, but a certain amount of mathematics). Andrew Wiles's original proof of Fermat's last theorem turned out to be wrong
> >> (fortunately in time to be fixed).
> > As anyone who can understand English can see immediately, it is not the same as what Franz claims I said. If he wants to maintain his position he'll have to find a genuine quotation.
>
> Close enough. You said that it is clear that people make mistakes even
> on formal mathematical proofs, whereas Franz has always claimed that any
> formal mathematical proof is always 100% perfectly infallible.

If it isn't, then it isn't a proof. Duh.

Wiles had thought he had a proof but he didn't.

peteolcott

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Sep 11, 2019, 1:08:40 PM9/11/19
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Until it is understood to be incorrect it continues to be misconstrued as a proof.

Peter T. Daniels

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Sep 11, 2019, 1:13:01 PM9/11/19
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That doesn't make it one.

peteolcott

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Sep 11, 2019, 1:24:03 PM9/11/19
to
Once the following is understood it becomes obvious that true and provable
cannot possibly diverge and thus Gödel is necessarily incorrect. Every
expression of language that is unprovable IS ONLY unprovable because it is untrue.

Conceptual knowledge is every statement that can be verified as completely
true entirely based on its meaning without any input from the sense organs.

THIS IS THE SIMPLEST POSSIBLE REFUTATION OF 1931 INCOMPLETENESS
Conceptual truth is always provable because the same relations
between expressions of language that define the truth of an
expression also define the proof of this same expression.

Peter T. Daniels

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Sep 11, 2019, 3:58:13 PM9/11/19
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Which, of course, has absolutely nothing to do with what I or Athel said.

peteolcott

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Sep 11, 2019, 4:03:47 PM9/11/19
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The 1931 Incompleteness Theorem is misconstrued as an actual proof
and in a quote of your words that I was responding to:
"That doesn't make it one."

Peter T. Daniels

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Sep 11, 2019, 4:39:31 PM9/11/19
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If it were construed as a proof it would be called a proof, not a theorem.

At least since Euclid, a theorem is a thing that is set out to be proved.

peteolcott

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Sep 11, 2019, 5:07:06 PM9/11/19
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It looks like you are right.

http://mathworld.wolfram.com/Theorem.html
A theorem is a statement that can be demonstrated to be true
by accepted mathematical operations and arguments. In general,
a theorem is an embodiment of some general principle that makes
it part of a larger theory. The process of showing a theorem
to be correct is called a proof.

So the 1931 Incompleteness Theorem is really the
1931 Incompleteness could be proved.

That makes less sense
(1) 1931 Incompleteness could be proved.
(2) 1931 Incompleteness has been proved.
(3) 1931 Incompleteness considered to be true.
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