Category error

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Mr Flibble

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May 14, 2022, 12:05:58 PMMay 14
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The other day I claimed there was a category error in the halting
theorem proof but I was mistaken: the category error actually exists in
Pete Olcott's understanding of the proof which manifests as an infinite
recursion in his simulation; his simulation is thus invalid and doesn't
refute anything of substance.

/Flibble

olcott

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May 14, 2022, 12:56:33 PMMay 14
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I stand by my claim that your use of the term: "category error" was a
brilliant new insight into Gödel's 1931 incompleteness and Tarski 1936
undefinability.

I refer to this same thing as a type mismatch error in that neither
Gödel's G nor Tarski's x are truth bearers thus cannot be proven because
they are semantically ill-formed propositions.

--
Copyright 2022 Pete Olcott

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

wij

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May 14, 2022, 1:22:36 PMMay 14
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Pete Olcott lied. There has never ever been a real simulation program.
All rebuttals are (finally) made against nothing.

Pete Olcott's brain is fossilized. All he says have no basis, just 'talk':
1. Rebuttal the HP -> No real H to rebuttal !
2. Various kind of claims based on POOH (or tautology)
3. deque implement -> No real codes allow him to claim anything !
4. ...His brain seems now further fossilizing by starting to redefine his logic !

But PO is very well enjoying his belief that he is THE talented/genius who can
hit/see others cannot.
Any rebuttal only strengthens his belief. (IOW, everybody else is idiot).

As to the title "Category error", is that another 'theory' ?

Mr Flibble

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May 14, 2022, 1:24:09 PMMay 14
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On Sat, 14 May 2022 10:22:35 -0700 (PDT)
wij <wyni...@gmail.com> wrote:

> As to the title "Category error", is that another 'theory' ?

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

/Flibble

olcott

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May 14, 2022, 1:27:31 PMMay 14
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*A category mistake* or
*category error* or
*categorical mistake* or
*mistake of category*
is 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.

Richard Damon

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May 14, 2022, 5:04:30 PMMay 14
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On 5/14/22 12:56 PM, olcott wrote:
> On 5/14/2022 11:05 AM, Mr Flibble wrote:
>> The other day I claimed there was a category error in the halting
>> theorem proof but I was mistaken: the category error actually exists in
>> Pete Olcott's understanding of the proof which manifests as an infinite
>> recursion in his simulation; his simulation is thus invalid and doesn't
>> refute anything of substance.
>>
>> /Flibble
>>
>
> I stand by my claim that your use of the term: "category error" was a
> brilliant new insight into Gödel's 1931 incompleteness and Tarski 1936
> undefinability.
>
> I refer to this same thing as a type mismatch error in that neither
> Gödel's G nor Tarski's x are truth bearers thus cannot be proven because
> they are semantically ill-formed propositions.
>

Except that they are, but you don't want to accept that, because you
define "Truth" as something it isn't

I will also point out that your statement is in contradiction to
something you said recently that you only talk about "Analytical Truth",
because "Truth Bearing" is NOT tied to being an Analytical Truth, but to
Truth in General. Every time you use that word, you prove your statement
to be a LIE.

An unprovable statement is still a Truth Bearer if the only possible
Truth Values for the statement are True or False.

The statement of the Collatz Conjecture is a Truth Bearer, even if it
turns out that the Collatz COnjecture is True but Unprovable.

You might not like that, But if it turns out that there is no actual N
that is a counter example, then it is True, even if the statement can
not be proven based on the existing axioms of the system.

olcott

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May 14, 2022, 5:16:00 PMMay 14
to
On 5/14/2022 4:04 PM, Richard Damon wrote:
> On 5/14/22 12:56 PM, olcott wrote:
>> On 5/14/2022 11:05 AM, Mr Flibble wrote:
>>> The other day I claimed there was a category error in the halting
>>> theorem proof but I was mistaken: the category error actually exists in
>>> Pete Olcott's understanding of the proof which manifests as an infinite
>>> recursion in his simulation; his simulation is thus invalid and doesn't
>>> refute anything of substance.
>>>
>>> /Flibble
>>>
>>
>> I stand by my claim that your use of the term: "category error" was a
>> brilliant new insight into Gödel's 1931 incompleteness and Tarski 1936
>> undefinability.
>>
>> I refer to this same thing as a type mismatch error in that neither
>> Gödel's G nor Tarski's x are truth bearers thus cannot be proven
>> because they are semantically ill-formed propositions.
>>
>
> Except that they are, but you don't want to accept that, because you
> define "Truth" as something it isn't
>

G is not provable in F only because G is semantically incorrect in F.

> I will also point out that your statement is in contradiction to
> something you said recently that you only talk about "Analytical Truth",
> because "Truth Bearing" is NOT tied to being an Analytical Truth, but to
> Truth in General. Every time you use that word, you prove your statement
> to be a LIE.
>
> An unprovable statement is still a Truth Bearer if the only possible
> Truth Values for the statement are True or False.
>
> The statement of the Collatz Conjecture is a Truth Bearer, even if it
> turns out that the Collatz COnjecture is True but Unprovable.
>
> You might not like that, But if it turns out that there is no actual N
> that is a counter example, then it is True, even if the statement can
> not be proven based on the existing axioms of the system.


Richard Damon

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May 14, 2022, 5:31:34 PMMay 14
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On 5/14/22 5:15 PM, olcott wrote:
> On 5/14/2022 4:04 PM, Richard Damon wrote:
>> On 5/14/22 12:56 PM, olcott wrote:
>>> On 5/14/2022 11:05 AM, Mr Flibble wrote:
>>>> The other day I claimed there was a category error in the halting
>>>> theorem proof but I was mistaken: the category error actually exists in
>>>> Pete Olcott's understanding of the proof which manifests as an infinite
>>>> recursion in his simulation; his simulation is thus invalid and doesn't
>>>> refute anything of substance.
>>>>
>>>> /Flibble
>>>>
>>>
>>> I stand by my claim that your use of the term: "category error" was a
>>> brilliant new insight into Gödel's 1931 incompleteness and Tarski
>>> 1936 undefinability.
>>>
>>> I refer to this same thing as a type mismatch error in that neither
>>> Gödel's G nor Tarski's x are truth bearers thus cannot be proven
>>> because they are semantically ill-formed propositions.
>>>
>>
>> Except that they are, but you don't want to accept that, because you
>> define "Truth" as something it isn't
>>
>
> G is not provable in F only because G is semantically incorrect in F.

Nope, I don't thnk you have actually read what G is.G actually is a
fairly innocuous, if complected, mathematical formula asking if there
exsit interger roots (If I am remembering it correctly).

olcott

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May 14, 2022, 5:59:47 PMMay 14
to
Gödel says:
We are therefore confronted with a proposition which asserts its own
unprovability.

Which is the same self-contradictory bullshit as the liar paradox.

>>
>>> I will also point out that your statement is in contradiction to
>>> something you said recently that you only talk about "Analytical
>>> Truth", because "Truth Bearing" is NOT tied to being an Analytical
>>> Truth, but to Truth in General. Every time you use that word, you
>>> prove your statement to be a LIE.
>>>
>>> An unprovable statement is still a Truth Bearer if the only possible
>>> Truth Values for the statement are True or False.
>>>
>>> The statement of the Collatz Conjecture is a Truth Bearer, even if it
>>> turns out that the Collatz COnjecture is True but Unprovable.
>>>
>>> You might not like that, But if it turns out that there is no actual
>>> N that is a counter example, then it is True, even if the statement
>>> can not be proven based on the existing axioms of the system.
>>
>>
>


André G. Isaak

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May 14, 2022, 6:07:40 PMMay 14
to
On 2022-05-14 15:59, olcott wrote:
> On 5/14/2022 4:31 PM, Richard Damon wrote:
>> On 5/14/22 5:15 PM, olcott wrote:

>>> G is not provable in F only because G is semantically incorrect in F.
>>
>> Nope, I don't thnk you have actually read what G is.G actually is a
>> fairly innocuous, if complected, mathematical formula asking if there
>> exsit interger roots (If I am remembering it correctly).
>>
>
> Gödel says:
> We are therefore confronted with a proposition which asserts its own
> unprovability.

That's Gödel's commentary, not the actual content of G.

> Which is the same self-contradictory bullshit as the liar paradox.

Even if G did assert its own unprovability, there would be nothing
self-contradictory about this. A sentence which asserts its own falsity
is self-contradictory, one that asserts its own unprovability is not.

The big problem here is that you are clearly not Gödel's intended
audience. Gödel makes three crucial assumptions, none of which apply to you.

First, he assumes a certain minimal background in the field on the part
of his readership.

Second, he assumes that people reading his commentary are also following
along with the actual math.

And thirdly, he assumes his audience is actually making a good-faith
effort to actually understand what he is saying and will interpret his
comments accordingly rather than seizing on some misguided
interpretation which clearly does not match the actual math.

André

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

olcott

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May 14, 2022, 6:21:16 PMMay 14
to
On 5/14/2022 5:07 PM, André G. Isaak wrote:
> On 2022-05-14 15:59, olcott wrote:
>> On 5/14/2022 4:31 PM, Richard Damon wrote:
>>> On 5/14/22 5:15 PM, olcott wrote:
>
>>>> G is not provable in F only because G is semantically incorrect in F.
>>>
>>> Nope, I don't thnk you have actually read what G is.G actually is a
>>> fairly innocuous, if complected, mathematical formula asking if there
>>> exsit interger roots (If I am remembering it correctly).
>>>
>>
>> Gödel says:
>> We are therefore confronted with a proposition which asserts its own
>> unprovability.
>
> That's Gödel's commentary, not the actual content of G.
>
>> Which is the same self-contradictory bullshit as the liar paradox.
>
> Even if G did assert its own unprovability, there would be nothing
> self-contradictory about this.


8. 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 it 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. If you
assume that the proposition is true in the Russell sense, the same thing
follows...

Wittgenstein, Ludwig 1983. Remarks on the Foundations of Mathematics
(Appendix III), 118-119.Cambridge, Massachusetts and London, England:
The MIT Press


> A sentence which asserts its own falsity
> is self-contradictory, one that asserts its own unprovability is not.
>

When an expression of language is asserting its own unprovability it is
also asserting that it is untrue in the same system that it is
unprovable. This means that F is not incomplete, it is merely that G is
untrue.

> The big problem here is that you are clearly not Gödel's intended
> audience. Gödel makes three crucial assumptions, none of which apply to
> you.
>
> First, he assumes a certain minimal background in the field on the part
> of his readership.
>
> Second, he assumes that people reading his commentary are also following
> along with the actual math.
>
> And thirdly, he assumes his audience is actually making a good-faith
> effort to actually understand what he is saying and will interpret his
> comments accordingly rather than seizing on some misguided
> interpretation which clearly does not match the actual math.
>
> André
>


--

Richard Damon

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May 14, 2022, 7:00:38 PMMay 14
to
And, my understanding is that Wittgestein hadn't read Godel's paper at
this point either, so he makes the same error you do of know knowing
what he is talking about.

>
>> A sentence which asserts its own falsity is self-contradictory, one
>> that asserts its own unprovability is not.
>>
>
> When an expression of language is asserting its own unprovability it is
> also asserting that it is untrue in the same system that it is
> unprovable. This means that F is not incomplete, it is merely that G is
> untrue.

What rule is that?

The PRESUMES that True -> Provable, which has NOT been proven (so isnt'
True by its own words), and only applies in a system that accepts it as
a basis, so it can be true.

FAIL.

André G. Isaak

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May 14, 2022, 7:21:09 PMMay 14
to
On 2022-05-14 17:00, Richard Damon wrote:
> On 5/14/22 6:21 PM, olcott wrote:

>> Wittgenstein, Ludwig 1983. Remarks on the Foundations of Mathematics
>> (Appendix III), 118-119.Cambridge, Massachusetts and London, England:
>> The MIT Press
>>
> And, my understanding is that Wittgestein hadn't read Godel's paper at
> this point either, so he makes the same error you do of know knowing
> what he is talking about.

There is one crucial difference -- Wittgenstein recorded his initial
reactions to first hearing of Gödel's proof in a private journal which
was never intended for publication (which explains why he never bothered
to retract this remark once the error became clear to him).

Olcott, on the other hand, is intent on broadcasting his
misunderstanding to the world even after his errors have been pointed
out to him repeatedly.

olcott

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May 14, 2022, 7:28:01 PMMay 14
to
Unprovable(F, G) merely means Untrue(F, G) and not Incomplete(F).
(Untrue(F, G) and Untrue(F, ~G)) means ~Truth_Bearer(G).

André G. Isaak

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May 14, 2022, 7:32:55 PMMay 14
to
On 2022-05-14 17:27, olcott wrote:
> On 5/14/2022 6:21 PM, André G. Isaak wrote:
>> On 2022-05-14 17:00, Richard Damon wrote:
>>> On 5/14/22 6:21 PM, olcott wrote:
>>
>>>> Wittgenstein, Ludwig 1983. Remarks on the Foundations of Mathematics
>>>> (Appendix III), 118-119.Cambridge, Massachusetts and London,
>>>> England: The MIT Press
>>>>
>>> And, my understanding is that Wittgestein hadn't read Godel's paper
>>> at this point either, so he makes the same error you do of know
>>> knowing what he is talking about.
>>
>> There is one crucial difference -- Wittgenstein recorded his initial
>> reactions to first hearing of Gödel's proof in a private journal which
>> was never intended for publication (which explains why he never
>> bothered to retract this remark once the error became clear to him).
>>
>> Olcott, on the other hand, is intent on broadcasting his
>> misunderstanding to the world even after his errors have been pointed
>> out to him repeatedly.
>>
>> André
>>
>
> Unprovable(F, G) merely means Untrue(F, G) and not Incomplete(F).

That's an assertion, not an argument.

> (Untrue(F, G) and Untrue(F, ~G)) means ~Truth_Bearer(G).

That's an assertion, not an argument.

And the logics which Gödel is considering all include the law of the
excluded middle. There is no 'untrue' in these systems; only true and false.

olcott

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May 14, 2022, 7:35:55 PMMay 14
to
This is simply the way that correct reasoning works and when logic
diverges from this it becomes incorrect.

Try and find any example of analytical truth that cannot be proven to be
true.

> FAIL.
>
>>
>>> The big problem here is that you are clearly not Gödel's intended
>>> audience. Gödel makes three crucial assumptions, none of which apply
>>> to you.
>>>
>>> First, he assumes a certain minimal background in the field on the
>>> part of his readership.
>>>
>>> Second, he assumes that people reading his commentary are also
>>> following along with the actual math.
>>>
>>> And thirdly, he assumes his audience is actually making a good-faith
>>> effort to actually understand what he is saying and will interpret
>>> his comments accordingly rather than seizing on some misguided
>>> interpretation which clearly does not match the actual math.
>>>
>>> André
>>>
>>
>>
>


André G. Isaak

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May 14, 2022, 7:39:58 PMMay 14
to
On 2022-05-14 17:35, olcott wrote:
> On 5/14/2022 6:00 PM, Richard Damon wrote:

>> The PRESUMES that True -> Provable, which has NOT been proven (so
>> isnt' True by its own words), and only applies in a system that
>> accepts it as a basis, so it can be true.
>>
>
> This is simply the way that correct reasoning works and when logic
> diverges from this it becomes incorrect.

Where exactly can one read up on this 'correct reasoning'? Can you point
us to a source where its axioms and rules of inference are collected?

Or is this just some vague concept that exists only in your head?

Richard Damon

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May 14, 2022, 8:22:18 PMMay 14
to
Yes, it proves that correct reasoning must be incorrect, because it says
the laws of logic don't apply to the fields that they apply to.
>
> Try and find any example of analytical truth that cannot be proven to be
> true.

Wrong Question, showing you are still stuck in a category error.

You keep on saying that a TRUTH that cannot be proves isn't True.

Your wording has proven your system in inconsistent, because in one set
of words you restrict yourelf to "Analytic Truths", but then you assert
your conclusion on "All Truth"

Your logic is proven inconsistent in definition (which is as close a
system gets to be logically "incorrect"),

Richard Damon

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May 14, 2022, 8:23:45 PMMay 14
to
On 5/14/22 7:32 PM, André G. Isaak wrote:
> On 2022-05-14 17:27, olcott wrote:
>> On 5/14/2022 6:21 PM, André G. Isaak wrote:
>>> On 2022-05-14 17:00, Richard Damon wrote:
>>>> On 5/14/22 6:21 PM, olcott wrote:
>>>
>>>>> Wittgenstein, Ludwig 1983. Remarks on the Foundations of
>>>>> Mathematics (Appendix III), 118-119.Cambridge, Massachusetts and
>>>>> London, England: The MIT Press
>>>>>
>>>> And, my understanding is that Wittgestein hadn't read Godel's paper
>>>> at this point either, so he makes the same error you do of know
>>>> knowing what he is talking about.
>>>
>>> There is one crucial difference -- Wittgenstein recorded his initial
>>> reactions to first hearing of Gödel's proof in a private journal
>>> which was never intended for publication (which explains why he never
>>> bothered to retract this remark once the error became clear to him).
>>>
>>> Olcott, on the other hand, is intent on broadcasting his
>>> misunderstanding to the world even after his errors have been pointed
>>> out to him repeatedly.
>>>
>>> André
>>>
>>
>> Unprovable(F, G) merely means Untrue(F, G) and not Incomplete(F).
>
> That's an assertion, not an argument.

And an UNPROVEN assertion, so by its own meaning, self-contradictory.

olcott

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May 14, 2022, 11:02:41 PMMay 14
to
On 5/14/2022 6:32 PM, André G. Isaak wrote:
> On 2022-05-14 17:27, olcott wrote:
>> On 5/14/2022 6:21 PM, André G. Isaak wrote:
>>> On 2022-05-14 17:00, Richard Damon wrote:
>>>> On 5/14/22 6:21 PM, olcott wrote:
>>>
>>>>> Wittgenstein, Ludwig 1983. Remarks on the Foundations of
>>>>> Mathematics (Appendix III), 118-119.Cambridge, Massachusetts and
>>>>> London, England: The MIT Press
>>>>>
>>>> And, my understanding is that Wittgestein hadn't read Godel's paper
>>>> at this point either, so he makes the same error you do of know
>>>> knowing what he is talking about.
>>>
>>> There is one crucial difference -- Wittgenstein recorded his initial
>>> reactions to first hearing of Gödel's proof in a private journal
>>> which was never intended for publication (which explains why he never
>>> bothered to retract this remark once the error became clear to him).
>>>
>>> Olcott, on the other hand, is intent on broadcasting his
>>> misunderstanding to the world even after his errors have been pointed
>>> out to him repeatedly.
>>>
>>> André
>>>
>>
>> Unprovable(F, G) merely means Untrue(F, G) and not Incomplete(F).
>
> That's an assertion, not an argument.
>


Some of these terms are from standard analytic philosophy.

Proofs over infinite sets can be tricky.

KEY_INSIGHT:
(a) The proof is that the entire body of analytic knowledge (including
all math, logic, et cetera) is structured as semantic connections
between elements of this same body.

(b) All analytic expressions of language only obtain their meaning
through semantic connections.

*The proof of these two is that no counter-examples can be found*

STANDARD_MEANING:
(c) Analytic expressions of language are only true on the basis of their
meaning.

∴ True(x) only exists on the basis of the semantic connections that x
has or fails to have. This is another way of saying the True(x) is based
on Provable(x) as these semantic connections are verified or fail
verification.

>> (Untrue(F, G) and Untrue(F, ~G)) means ~Truth_Bearer(G).
>
> That's an assertion, not an argument.
>
> And the logics which Gödel is considering all include the law of the
> excluded middle. There is no 'untrue' in these systems; only true and
> false.
>
> André
>


--

olcott

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May 14, 2022, 11:04:14 PMMay 14
to
On 5/14/2022 6:39 PM, André G. Isaak wrote:
> On 2022-05-14 17:35, olcott wrote:
>> On 5/14/2022 6:00 PM, Richard Damon wrote:
>
>>> The PRESUMES that True -> Provable, which has NOT been proven (so
>>> isnt' True by its own words), and only applies in a system that
>>> accepts it as a basis, so it can be true.
>>>
>>
>> This is simply the way that correct reasoning works and when logic
>> diverges from this it becomes incorrect.
>
> Where exactly can one read up on this 'correct reasoning'? Can you point
> us to a source where its axioms and rules of inference are collected?
>
> Or is this just some vague concept that exists only in your head?
>
> André
>

Its in my head, I have begun to elborate it in my other reply to you.

André G. Isaak

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May 15, 2022, 12:06:09 AMMay 15
to
Yet people make proofs over infinite sets all the time.

> KEY_INSIGHT:
> (a) The proof is that the entire body of analytic knowledge (including
> all math, logic, et cetera) is structured as semantic connections
> between elements of this same body.

Again, this is simply a baseless assertion, not an argument.

> (b) All analytic expressions of language only obtain their meaning
> through semantic connections.

Again, this is simply a baseless assertion, not an argument. And your
use of the term 'analytic' doesn't seem to correspond to the standard
usage. The analytic/synthetic distinction is one that normally arises
when talking about the philosophy of language, not logic.

> *The proof of these two is that no counter-examples can be found*

That is not how proofs work. You're the one making a claim. The burden
of proof lies with you.

And your specific claims are far too vaguely defined for anyone to track
down counterexamples. For example, I have absolutely no idea what you
mean by 'semantic connection'.

> STANDARD_MEANING:
> (c) Analytic expressions of language are only true on the basis of their
> meaning.

That's not the standard meaning of 'analytic'.

> ∴ True(x) only exists on the basis of the semantic connections that x
> has or fails to have. This is another way of saying the True(x) is based
> on Provable(x) as these semantic connections are verified or fail
> verification.

Again, that's just a baseless assertion, not an argument.

André G. Isaak

unread,
May 15, 2022, 12:07:29 AMMay 15
to
On 2022-05-14 21:04, olcott wrote:
> On 5/14/2022 6:39 PM, André G. Isaak wrote:
>> On 2022-05-14 17:35, olcott wrote:
>>> On 5/14/2022 6:00 PM, Richard Damon wrote:
>>
>>>> The PRESUMES that True -> Provable, which has NOT been proven (so
>>>> isnt' True by its own words), and only applies in a system that
>>>> accepts it as a basis, so it can be true.
>>>>
>>>
>>> This is simply the way that correct reasoning works and when logic
>>> diverges from this it becomes incorrect.
>>
>> Where exactly can one read up on this 'correct reasoning'? Can you
>> point us to a source where its axioms and rules of inference are
>> collected?
>>
>> Or is this just some vague concept that exists only in your head?
>>
>> André
>>
>
> Its in my head, I have begun to elborate it in my other reply to you.

Given your dismally poor track record where even basic reasoning is
concerned, why should anyone be interested in your particular view of
what constitutes 'correct reasoning'?

olcott

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May 15, 2022, 12:13:35 AMMay 15
to
I will make that one concrete.
Try to provide a sentence that is true that is not connected to anything
else that shows that it is true.

olcott

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May 15, 2022, 12:14:34 AMMay 15
to
I can define it so that it can be seen to be self-evidently correct.

André G. Isaak

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May 15, 2022, 12:28:12 AMMay 15
to
On 2022-05-14 22:14, olcott wrote:
> On 5/14/2022 11:07 PM, André G. Isaak wrote:
>> On 2022-05-14 21:04, olcott wrote:
>>> On 5/14/2022 6:39 PM, André G. Isaak wrote:
>>>> On 2022-05-14 17:35, olcott wrote:
>>>>> On 5/14/2022 6:00 PM, Richard Damon wrote:
>>>>
>>>>>> The PRESUMES that True -> Provable, which has NOT been proven (so
>>>>>> isnt' True by its own words), and only applies in a system that
>>>>>> accepts it as a basis, so it can be true.
>>>>>>
>>>>>
>>>>> This is simply the way that correct reasoning works and when logic
>>>>> diverges from this it becomes incorrect.
>>>>
>>>> Where exactly can one read up on this 'correct reasoning'? Can you
>>>> point us to a source where its axioms and rules of inference are
>>>> collected?
>>>>
>>>> Or is this just some vague concept that exists only in your head?
>>>>
>>>> André
>>>>
>>>
>>> Its in my head, I have begun to elborate it in my other reply to you.
>>
>> Given your dismally poor track record where even basic reasoning is
>> concerned, why should anyone be interested in your particular view of
>> what constitutes 'correct reasoning'?
>>
>> André
>>
>
> I can define it so that it can be seen to be self-evidently correct.

You certainly have not done this so far. And you have a bad habit of
referring to statements which are clearly false as 'self-evidently correct'.

olcott

unread,
May 15, 2022, 12:31:12 AMMay 15
to
Self evidently correct means that there are connected ideas that prove
it is correct.

André G. Isaak

unread,
May 15, 2022, 12:31:20 AMMay 15
to
How does that make anything more concrete? If I don't know what you mean
by 'semantic connection' why do you think I will know what you mean by
'connected'?

And this is besides the point since you have the burden of proof
backwards. It's not incumbent on anyone to find counterexamples to every
random 'theory' that someone on usenet puts forward. Its incumbent on
the person putting forth the theory to provide proof.

olcott

unread,
May 15, 2022, 12:39:02 AMMay 15
to
This is great we are trying to attain mutulual understanding now.

When you look to see how you know anything about anything it is all
connections between meanings.

This is a connected set of meanings:
"I am going to go to the store to buy some eggs."

> And this is besides the point since you have the burden of proof
> backwards. It's not incumbent on anyone to find counterexamples to every
> random 'theory' that someone on usenet puts forward. Its incumbent on
> the person putting forth the theory to provide proof.
>
> André
>


--

Mikko

unread,
May 15, 2022, 5:14:01 AMMay 15
to
On 2022-05-14 16:05:55 +0000, Mr Flibble said:

> The other day I claimed there was a category error in the halting
> theorem proof but I was mistaken: the category error actually exists in
> Pete Olcott's understanding of the proof which manifests as an infinite
> recursion in his simulation; his simulation is thus invalid and doesn't
> refute anything of substance.

Olcott's error contains an indirect recursion that is or is not infinite
depending on details of his H. It is not possible to point a single
statement of the program and say that the error is there, as there are
other points that could be changed so that the infinite recursion
disappears.

A category error is different: it is contained in a single sentence
where one word or phase is incompatible with the place where it is put.

Mikko

Richard Damon

unread,
May 15, 2022, 7:29:12 AMMay 15
to
Which PROVES that you don't know the meaning of the word PROOF.

By that standard, Collatz, and the Twin Primes, amoung many others, are
PROVED.


>
> STANDARD_MEANING:
> (c) Analytic expressions of language are only true on the basis of their
> meaning.

Source? That actually mean True, as opossed to just "Known True".

>
> ∴ True(x) only exists on the basis of the semantic connections that x
> has or fails to have. This is another way of saying the True(x) is based
> on Provable(x) as these semantic connections are verified or fail
> verification.
>

Unproven, and thus by its own definition, not True, and ANY arguement
based on it becomes UNSOND.

Richard Damon

unread,
May 15, 2022, 7:31:51 AMMay 15
to
One of:

The Collbatz conjecture is True.

The Collbatz conjecture is False.

Richard Damon

unread,
May 15, 2022, 7:39:03 AMMay 15
to

On 5/15/22 12:14 AM, olcott wrote:
> On 5/14/2022 11:07 PM, André G. Isaak wrote:
>> On 2022-05-14 21:04, olcott wrote:
>>> On 5/14/2022 6:39 PM, André G. Isaak wrote:
>>>> On 2022-05-14 17:35, olcott wrote:
>>>>> On 5/14/2022 6:00 PM, Richard Damon wrote:
>>>>
>>>>>> The PRESUMES that True -> Provable, which has NOT been proven (so
>>>>>> isnt' True by its own words), and only applies in a system that
>>>>>> accepts it as a basis, so it can be true.
>>>>>>
>>>>>
>>>>> This is simply the way that correct reasoning works and when logic
>>>>> diverges from this it becomes incorrect.
>>>>
>>>> Where exactly can one read up on this 'correct reasoning'? Can you
>>>> point us to a source where its axioms and rules of inference are
>>>> collected?
>>>>
>>>> Or is this just some vague concept that exists only in your head?
>>>>
>>>> André
>>>>
>>>
>>> Its in my head, I have begun to elborate it in my other reply to you.
>>
>> Given your dismally poor track record where even basic reasoning is
>> concerned, why should anyone be interested in your particular view of
>> what constitutes 'correct reasoning'?
>>
>> André
>>
>
> I can define it so that it can be seen to be self-evidently correct.
>

Given your track record, that makes it almost certainly wrong.

Self-Evident, for logic, is a GROUP decision, that the group accepts it
as self-evident and usable as a basis for common understanding.

YOU fail with that definition.

Also "can be Seen to be self-evidently correct" is a good description of
most of the fallicies, and many of the errors, they might APPEAR to be
self-evident, but on closer examination prove to be wrong.

André G. Isaak

unread,
May 15, 2022, 2:46:17 PMMay 15
to
I thought the issue being discussed was truth. How we know things is an
entirely separate issue.

> This is a connected set of meanings:
> "I am going to go to the store to buy some eggs."

No amount of examples is a substitute for a definition (especially
examples like the above which have absolutely no explanation given along
with them).

A definition should take the following form:

Two items, A and B, are semantically connected iff ...

olcott

unread,
May 17, 2022, 10:59:10 PMMay 17
to
On 5/15/2022 4:13 AM, Mikko wrote:
> On 2022-05-14 16:05:55 +0000, Mr Flibble said:
>
>> The other day I claimed there was a category error in the halting
>> theorem proof but I was mistaken: the category error actually exists in
>> Pete Olcott's understanding of the proof which manifests as an infinite
>> recursion in his simulation; his simulation is thus invalid and doesn't
>> refute anything of substance.
>
> Olcott's error contains an indirect recursion that is or is not infinite
> depending on details of his H.

The key point is that the correct simulation of the input to H(P,P)
never reaches its own final state thus never halts.

> It is not possible to point a single
> statement of the program and say that the error is there, as there are
> other points that could be changed so that the infinite recursion
> disappears.

Begin Local Halt Decider Simulation Execution Trace Stored at:212352
...[00001352][0021233e][00212342] 55 push ebp // enter P
...[00001353][0021233e][00212342] 8bec mov ebp,esp
...[00001355][0021233e][00212342] 8b4508 mov eax,[ebp+08]
...[00001358][0021233a][00001352] 50 push eax // push P
...[00001359][0021233a][00001352] 8b4d08 mov ecx,[ebp+08]
...[0000135c][00212336][00001352] 51 push ecx // push P
...[0000135d][00212332][00001362] e840feffff call 000011a2 // call H
...[00001352][0025cd66][0025cd6a] 55 push ebp // enter P
...[00001353][0025cd66][0025cd6a] 8bec mov ebp,esp
...[00001355][0025cd66][0025cd6a] 8b4508 mov eax,[ebp+08]
...[00001358][0025cd62][00001352] 50 push eax // push P
...[00001359][0025cd62][00001352] 8b4d08 mov ecx,[ebp+08]
...[0000135c][0025cd5e][00001352] 51 push ecx // push P
...[0000135d][0025cd5a][00001362] e840feffff call 000011a2 // call H
Local Halt Decider: Infinite Recursion Detected Simulation Stopped

H sees that P is calling the same function from the same machine address
with identical parameters, twice in sequence. This is the infinite
recursion (infinitely nested simulation) non-halting behavior pattern.

>
> A category error is different: it is contained in a single sentence
> where one word or phase is incompatible with the place where it is put.
>
> Mikko
>


olcott

unread,
May 17, 2022, 11:07:15 PMMay 17
to
The elements of the body of conceptual truth are connected together
semantically mutually defining the semantic meaning of each other.

Mostly this is done in an inheritance hierarchy such that specific
concepts are defined in terms of broader ones.

olcott

unread,
May 17, 2022, 11:15:39 PMMay 17
to
Proof generically means that an expression of language has been
definitely established as true by some means.

> By that standard, Collatz, and the Twin Primes, amoung many others, are
> PROVED.
>
>
>>
>> STANDARD_MEANING:
>> (c) Analytic expressions of language are only true on the basis of
>> their meaning.
>
> Source? That actually mean True, as opossed to just "Known True".
>

That is the definition of analytic truth.

“Analytic” sentences, such as “Pediatricians are doctors,” have
historically been characterized as ones that are true by virtue of the
meanings of their words alone and/or can be known to be so solely by
knowing those meanings.
https://plato.stanford.edu/entries/analytic-synthetic/

>>
>> ∴ True(x) only exists on the basis of the semantic connections that x
>> has or fails to have. This is another way of saying the True(x) is
>> based on Provable(x) as these semantic connections are verified or
>> fail verification.
>>
>
> Unproven, and thus by its own definition, not True, and ANY arguement
> based on it becomes UNSOND.

I think that we agree on this.

>>>> (Untrue(F, G) and Untrue(F, ~G)) means ~Truth_Bearer(G).
>>>
>>> That's an assertion, not an argument.
>>>
>>> And the logics which Gödel is considering all include the law of the
>>> excluded middle. There is no 'untrue' in these systems; only true and
>>> false.
>>>
>>> André
>>>
>>
>>
>


olcott

unread,
May 17, 2022, 11:17:41 PMMay 17
to
That is connected to tautology.

olcott

unread,
May 17, 2022, 11:20:30 PMMay 17
to
A self-evident truth proves that it is completely true entirely on the
basis of its meaning. If everyone in the universe disagrees then
everyone in the universe is wrong.

> YOU fail with that definition.
>
> Also "can be Seen to be self-evidently correct" is a good description of
> most of the fallicies, and many of the errors, they might APPEAR to be
> self-evident, but on closer examination prove to be wrong.


“Analytic” sentences, such as “Pediatricians are doctors,” have
historically been characterized as ones that are true by virtue of the
meanings of their words alone and/or can be known to be so solely by
knowing those meanings.
https://plato.stanford.edu/entries/analytic-synthetic/

Richard Damon

unread,
May 18, 2022, 7:32:19 AMMay 18
to
Nope. We know that one of the sentences is true.

THAT sentence is not establisned by "Tautology"

That sentence being true disproves your statement.

Unless you are defining that "untrue or untrue" is True, you have a
problem (and if yoy do, you still have a proble).

Richard Damon

unread,
May 18, 2022, 7:49:20 AMMay 18
to
A self-evident truth requires ALL (or all reasonable) to aggree that it
is true. If someone sees something as true that no one else does, that
is not "self-evident truth", that is DELUSION.

>
>> YOU fail with that definition.
>>
>> Also "can be Seen to be self-evidently correct" is a good description
>> of most of the fallicies, and many of the errors, they might APPEAR to
>> be self-evident, but on closer examination prove to be wrong.
>
>
> “Analytic” sentences, such as “Pediatricians are doctors,” have
> historically been characterized as ones that are true by virtue of the
> meanings of their words alone and/or can be known to be so solely by
> knowing those meanings.
> https://plato.stanford.edu/entries/analytic-synthetic/
>

Analyses of philosophically important terms and concepts, such as
“material object,” “cause,” “freedom,” or “knowledge” turned out,
however, to be far more problematic than philosophers had anticipated, ...


I will note that if you read through that article (I will admit I just
scanned it) it talks a lot about how mathematics cause PROBLEMS for the
analytic philosophies, and how to try to handle it.

I note it largely is talking about KNOWLEDGE, not actual TRUTH. it also
talks about how to try to LIMIT the domain of the logic to that which
can be reasoned (i.e. proved).

Yes, this is a valid domain to work in, but it CAN'T handle
"Mathematics" in the full sense, so can't be used to "Disprove" things
like the Halting Problem or the Incomplentness Theorem, because the
logics that define those problems are outside the domain that such a
logic can handle.

You just don't understand that basic property of logic.

Richard Damon

unread,
May 18, 2022, 7:51:46 AMMay 18
to
No, it didn't, at least NOT with a "Correct Trace". It sees it a trace
of P where H has been replaced with just a call to its input.

Since that is NOT what H is, the logic is based on a false premise, an
is thus unsound.

If you are defining that to be correct, then your logic is incorrrect,
or at least NOT the "Halting Problem".

All you have done is maybe show that your H can decides your POOP
correctly, not Halting.

Richard Damon

unread,
May 18, 2022, 8:07:28 AMMay 18
to
Note "Historically", that was what was assumed to be a characteristic of
such statements, that they could be shown true or false by a manner of
proof.

Then, we got the proof that some statements, that might want to be
called analytic couldn't be proven or disproven.

As pointed out, in part, the question is "Is Mathematics Analytic", or
is it more emperical.

Can "The Square of the Hypotenuse is equal to the sum of the squares of
the other two sides", be actually thought of as a ANALYTIC proof,
doesn't it truth come out of the MEANING of the words, or is it an
emperical truth show to be true because it just works.

Once you do that, then all the pesky mathematical problems disapper to
analytics, because they have been moved outside the domain.

>
>>>
>>> ∴ True(x) only exists on the basis of the semantic connections that x
>>> has or fails to have. This is another way of saying the True(x) is
>>> based on Provable(x) as these semantic connections are verified or
>>> fail verification.
>>>
>>
>> Unproven, and thus by its own definition, not True, and ANY arguement
>> based on it becomes UNSOND.
>
> I think that we agree on this.

So, you agree that your statement is UNSOUND?

olcott

unread,
May 18, 2022, 11:06:20 AMMay 18
to
You did not provide an example of a sentence that is true that is not
connected to anything else that shows that it is true.

We know that logic sentences are true or false on the basis of the
definition of logic sentence.


> Unless you are defining that "untrue or untrue" is True, you have a
> problem (and if yoy do, you still have a proble).


olcott

unread,
May 18, 2022, 11:10:33 AMMay 18
to
Not at all. THAT IS NOT THE WAY IT IS DEFINED.

> If someone sees something as true that no one else does, that
> is not "self-evident truth", that is DELUSION.
>
>>
>>> YOU fail with that definition.
>>>
>>> Also "can be Seen to be self-evidently correct" is a good description
>>> of most of the fallicies, and many of the errors, they might APPEAR
>>> to be self-evident, but on closer examination prove to be wrong.
>>
>>
>> “Analytic” sentences, such as “Pediatricians are doctors,” have
>> historically been characterized as ones that are true by virtue of the
>> meanings of their words alone and/or can be known to be so solely by
>> knowing those meanings.
>> https://plato.stanford.edu/entries/analytic-synthetic/
>>
>
> Analyses of philosophically important terms and concepts, such as
> “material object,” “cause,” “freedom,” or “knowledge” turned out,
> however, to be far more problematic than philosophers had anticipated, ...
>

It was only the quoted paragraph that was significant.
Every expression of formal or natural language that can be determined to
be true entirely on the basis of its meaning is an analytic expression
language.

> I will note that if you read through that article (I will admit I just
> scanned it) it talks a lot about how mathematics cause PROBLEMS for the
> analytic philosophies, and how to try to handle it.
>
> I note it largely is talking about KNOWLEDGE, not actual TRUTH. it also
> talks about how to try to LIMIT the domain of the logic to that which
> can be reasoned (i.e. proved).
>
> Yes, this is a valid domain to work in, but it CAN'T handle
> "Mathematics" in the full sense, so can't be used to "Disprove" things
> like the Halting Problem or the Incomplentness Theorem, because the
> logics that define those problems are outside the domain that such a
> logic can handle.
>
> You just don't understand that basic property of logic.


olcott

unread,
May 18, 2022, 11:14:03 AMMay 18
to
When we know that H only performs a pure simulation of its input then we
don't need to see the hundreds of pages of execution trace of H.

SINCE I TOLD YOU THIS HUNDREDS OF TIMES YOU ARE BEING QUITE DESPICABLY
DISHONEST ABOUT THIS.

> Since that is NOT what H is, the logic is based on a false premise, an
> is thus unsound.
>
> If you are defining that to be correct, then your logic is incorrrect,
> or at least NOT the "Halting Problem".
>
> All you have done is maybe show that your H can decides your POOP
> correctly, not Halting.
>
>>
>>>
>>> A category error is different: it is contained in a single sentence
>>> where one word or phase is incompatible with the place where it is put.
>>>
>>> Mikko
>>>
>>
>>
>


Ben

unread,
May 18, 2022, 11:31:30 AMMay 18
to
olcott <No...@NoWhere.com> writes:

> Begin Local Halt Decider Simulation Execution Trace Stored at:212352
> ...[00001352][0021233e][00212342] 55 push ebp // enter P
> ...[00001353][0021233e][00212342] 8bec mov ebp,esp
> ...[00001355][0021233e][00212342] 8b4508 mov eax,[ebp+08]
> ...[00001358][0021233a][00001352] 50 push eax // push P
> ...[00001359][0021233a][00001352] 8b4d08 mov ecx,[ebp+08]
> ...[0000135c][00212336][00001352] 51 push ecx // push P
> ...[0000135d][00212332][00001362] e840feffff call 000011a2 // call H
> ...[00001352][0025cd66][0025cd6a] 55 push ebp // enter P

This can't be the trace of the function you have been talking about.
The H you claim to have simulates something (no one cares what, but it's
something) so the code at the start of H should be setting up and
entering a simulator.

You've admitted you edit some traces which is really not on. I think
you should stop posting them until you can be honest about them.

Mind you, my personally guess is that the trace is fundamentally honest
about you've been pulling our legs about what H really does. It's just
the top-level x86 emulator that does that does any "simulating" and H
really does call P which calls H which calls P...

--
Ben.
"le génie humain a des limites, quand la bêtise humaine n’en a pas"
Alexandre Dumas (fils)

olcott

unread,
May 18, 2022, 11:32:24 AMMay 18
to
There is no freaking "might want" there is only <is> and <not is>.
If you "might want the definitions of a term to be different than it is
then you are simply screwy.

> As pointed out, in part, the question is "Is Mathematics Analytic", or
> is it more emperical.
>

It is stipulated that math and logic are purely analytical.

> Can "The Square of the Hypotenuse is equal to the sum of the squares of
> the other two sides", be actually thought of as a ANALYTIC proof,
> doesn't it truth come out of the MEANING of the words, or is it an
> emperical truth show to be true because it just works.
>

Empirical means that you must be able to taste, touch, smell, or hear it.

> Once you do that, then all the pesky mathematical problems disapper to
> analytics, because they have been moved outside the domain.
>
>>
>>>>
>>>> ∴ True(x) only exists on the basis of the semantic connections that
>>>> x has or fails to have. This is another way of saying the True(x) is
>>>> based on Provable(x) as these semantic connections are verified or
>>>> fail verification.
>>>>
>>>
>>> Unproven, and thus by its own definition, not True, and ANY arguement
>>> based on it becomes UNSOND.
>>
>> I think that we agree on this.
>
> So, you agree that your statement is UNSOUND?

Unproven means unsound. Sound requires proven.

>>
>>>>>> (Untrue(F, G) and Untrue(F, ~G)) means ~Truth_Bearer(G).
>>>>>
>>>>> That's an assertion, not an argument.
>>>>>
>>>>> And the logics which Gödel is considering all include the law of
>>>>> the excluded middle. There is no 'untrue' in these systems; only
>>>>> true and false.
>>>>>
>>>>> André
>>>>>
>>>>
>>>>
>>>
>>
>>
>


olcott

unread,
May 18, 2022, 11:41:11 AMMay 18
to
On 5/18/2022 10:31 AM, Ben wrote:
> olcott <No...@NoWhere.com> writes:
>
>> Begin Local Halt Decider Simulation Execution Trace Stored at:212352
>> ...[00001352][0021233e][00212342] 55 push ebp // enter P
>> ...[00001353][0021233e][00212342] 8bec mov ebp,esp
>> ...[00001355][0021233e][00212342] 8b4508 mov eax,[ebp+08]
>> ...[00001358][0021233a][00001352] 50 push eax // push P
>> ...[00001359][0021233a][00001352] 8b4d08 mov ecx,[ebp+08]
>> ...[0000135c][00212336][00001352] 51 push ecx // push P
>> ...[0000135d][00212332][00001362] e840feffff call 000011a2 // call H
>> ...[00001352][0025cd66][0025cd6a] 55 push ebp // enter P
>
> This can't be the trace of the function you have been talking about.
> The H you claim to have simulates something (no one cares what, but it's
> something) so the code at the start of H should be setting up and
> entering a simulator.
>

HOW MANY TIMES DO I HAVE TO TELL YOU THAT H PERFORMS A PURE SIMULATION
OF ITS INPUT THUS HAS NO BEHAVIOR THAT CAN HAVE ANY EFFECT ON THE
BEHAVIOR OF ITS INPUT THUS NO NEED TO SEE ITS HUNDREDS OF PAGES OF
EXECUTION TRACE ???

> You've admitted you edit some traces which is really not on. I think
> you should stop posting them until you can be honest about them.
>

YOU ARE SUCH A JACKASS. (and much better programmer than I knew).

> Mind you, my personally guess is that the trace is fundamentally honest
> about you've been pulling our legs about what H really does. It's just
> the top-level x86 emulator that does that does any "simulating" and H
> really does call P which calls H which calls P...
>


--

olcott

unread,
May 18, 2022, 12:49:51 PMMay 18
to
On 5/18/2022 10:31 AM, Ben wrote:
ON THE BASIS OF THE X86 MACHINE CODE PROVIDED FOR P AND THE
EXECUTION TRACE OF P PROVIDED BY H IT IS EASY TO SEE THAT
THE EXECUTION TRACE OF P IS THE EXECUTION TRACE OF P THAT
WOULD OCCUR IF H PERFORMED A PURE SIMULATION OF THE FIRST
13 INSTRUCTIONS OF P.

BECAUSE OF THIS THE INSISTENCE ON SEEING THE HUNDREDS OF
PAGES OF THE EXECUTION TRACE OF H OR THE SOURCE-CODE OF H
IS A JACKASS MOVE THAT IS ONLY PLAYING HEAD GAMES.

#include <stdint.h>
#define u32 uint32_t

void P(u32 x)
{
if (H(x, x))
HERE: goto HERE;
return;
}

int main()
{
Output("Input_Halts = ", H((u32)P, (u32)P));
}

_P()
[00001352](01) 55 push ebp
[00001353](02) 8bec mov ebp,esp
[00001355](03) 8b4508 mov eax,[ebp+08]
[00001358](01) 50 push eax
[00001359](03) 8b4d08 mov ecx,[ebp+08]
[0000135c](01) 51 push ecx
[0000135d](05) e840feffff call 000011a2 // call H
[00001362](03) 83c408 add esp,+08
[00001365](02) 85c0 test eax,eax
[00001367](02) 7402 jz 0000136b
[00001369](02) ebfe jmp 00001369
[0000136b](01) 5d pop ebp
[0000136c](01) c3 ret
Size in bytes:(0027) [0000136c]

_main()
[00001372](01) 55 push ebp
[00001373](02) 8bec mov ebp,esp
[00001375](05) 6852130000 push 00001352 // push P
[0000137a](05) 6852130000 push 00001352 // push P
[0000137f](05) e81efeffff call 000011a2 // call H
[00001384](03) 83c408 add esp,+08
[00001387](01) 50 push eax
[00001388](05) 6823040000 push 00000423 // "Input_Halts = "
[0000138d](05) e8e0f0ffff call 00000472 // call Output
[00001392](03) 83c408 add esp,+08
[00001395](02) 33c0 xor eax,eax
[00001397](01) 5d pop ebp
[00001398](01) c3 ret
Size in bytes:(0039) [00001398]

machine stack stack machine assembly
address address data code language
======== ======== ======== ========= =============
...[00001372][0010229e][00000000] 55 push ebp
...[00001373][0010229e][00000000] 8bec mov ebp,esp
...[00001375][0010229a][00001352] 6852130000 push 00001352 // push P
...[0000137a][00102296][00001352] 6852130000 push 00001352 // push P
...[0000137f][00102292][00001384] e81efeffff call 000011a2 // call H

Begin Local Halt Decider Simulation Execution Trace Stored at:212352
...[00001352][0021233e][00212342] 55 push ebp // enter P
...[00001353][0021233e][00212342] 8bec mov ebp,esp
...[00001355][0021233e][00212342] 8b4508 mov eax,[ebp+08]
...[00001358][0021233a][00001352] 50 push eax // push P
...[00001359][0021233a][00001352] 8b4d08 mov ecx,[ebp+08]
...[0000135c][00212336][00001352] 51 push ecx // push P
...[0000135d][00212332][00001362] e840feffff call 000011a2 // call H
...[00001352][0025cd66][0025cd6a] 55 push ebp // enter P
...[00001353][0025cd66][0025cd6a] 8bec mov ebp,esp
...[00001355][0025cd66][0025cd6a] 8b4508 mov eax,[ebp+08]
...[00001358][0025cd62][00001352] 50 push eax // push P
...[00001359][0025cd62][00001352] 8b4d08 mov ecx,[ebp+08]
...[0000135c][0025cd5e][00001352] 51 push ecx // push P
...[0000135d][0025cd5a][00001362] e840feffff call 000011a2 // call H
Local Halt Decider: Infinite Recursion Detected Simulation Stopped

H sees that P is calling the same function from the same machine address
with identical parameters, twice in sequence. This is the infinite
recursion (infinitely nested simulation) non-halting behavior pattern.

...[00001384][0010229e][00000000] 83c408 add esp,+08
...[00001387][0010229a][00000000] 50 push eax
...[00001388][00102296][00000423] 6823040000 push 00000423 //
"Input_Halts = "
---[0000138d][00102296][00000423] e8e0f0ffff call 00000472 // call Output
Input_Halts = 0
...[00001392][0010229e][00000000] 83c408 add esp,+08
...[00001395][0010229e][00000000] 33c0 xor eax,eax
...[00001397][001022a2][00100000] 5d pop ebp
...[00001398][001022a6][00000004] c3 ret
Number_of_User_Instructions(1)
Number of Instructions Executed(15892)


Halting problem undecidability and infinitely nested simulation (V5)
https://www.researchgate.net/publication/359984584_Halting_problem_undecidability_and_infinitely_nested_simulation_V5

Richard Damon

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May 18, 2022, 7:30:08 PMMay 18
to
One of these sentences is such an example, I don't know which one:

The Collbatz conjecture is True.

The Collbatz conjecture is False.


The fact that I don't know which one doesn't make the arguement invalid,
it points out that there is a limit to knowledge.

A second example.

Godel sentence G is True.

You may not accept that it is True, but it is. To quote from one of your
favorite sources:

https://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems

The Gödel sentence is designed to refer, indirectly, to itself. The
sentence states that, when a particular sequence of steps is used to
construct another sentence, that constructed sentence will not be
provable in F. However, the sequence of steps is such that the
constructed sentence turns out to be GF itself. In this way, the Gödel
sentence GF indirectly states its own unprovability within F (Smith
2007, p. 135).

To prove the first incompleteness theorem, Gödel demonstrated that the
notion of provability within a system could be expressed purely in terms
of arithmetical functions that operate on Gödel numbers of sentences of
the system. Therefore, the system, which can prove certain facts about
numbers, can also indirectly prove facts about its own statements,
provided that it is effectively generated. Questions about the
provability of statements within the system are represented as questions
about the arithmetical properties of numbers themselves, which would be
decidable by the system if it were complete.

Thus, although the Gödel sentence refers indirectly to sentences of the
system F, when read as an arithmetical statement the Gödel sentence
directly refers only to natural numbers. It asserts that no natural
number has a particular property, where that property is given by a
primitive recursive relation (Smith 2007, p. 141). As such, the Gödel
sentence can be written in the language of arithmetic with a simple
syntactic form. In particular, it can be expressed as a formula in the
language of arithmetic consisting of a number of leading universal
quantifiers followed by a quantifier-free body (these formulas are at
level Π 1 0 {\displaystyle \Pi _{1}^{0}} \Pi _{1}^{0} of the
arithmetical hierarchy). Via the MRDP theorem, the Gödel sentence can be
re-written as a statement that a particular polynomial in many variables
with integer coefficients never takes the value zero when integers are
substituted for its variables (Franzén 2005, p. 71).


So the Godel sentence, being "Just" a mathematical sentence, if
definitionally a Truth Bearer, and either needs to be True, or it is False.



>
> We know that logic sentences are true or false on the basis of the
> definition of logic sentence.

Right, so G needs to be either True of False, and if it is False, then
we can prove it, making it True.

Richard Damon

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May 18, 2022, 7:40:47 PMMay 18
to
A century ago, Math was thought to be Analytical, and all Analytical
statements eventually provable or refutable. It was then discovered that
this can not be true.

You need to decide, either you remove Mathematics from Analytical or you
remove Provable from Analytically True.

>
>> As pointed out, in part, the question is "Is Mathematics Analytic", or
>> is it more emperical.
>>
>
> It is stipulated that math and logic are purely analytical.

Then there exists analytical statements that are True but not Provable.

That is PROVEN.

>
>> Can "The Square of the Hypotenuse is equal to the sum of the squares
>> of the other two sides", be actually thought of as a ANALYTIC proof,
>> doesn't it truth come out of the MEANING of the words, or is it an
>> emperical truth show to be true because it just works.
>>
>
> Empirical means that you must be able to taste, touch, smell, or hear it.

Then read section 2.1, Mathematics, by "Thought" can "verify" concepts
in the domain that can not be "Proven" by mean analytic proof.

You either need to consider that "Thought" as a sense, or admit that not
all Analytic Statements are provable.

>
>> Once you do that, then all the pesky mathematical problems disapper to
>> analytics, because they have been moved outside the domain.
>>
>>>
>>>>>
>>>>> ∴ True(x) only exists on the basis of the semantic connections that
>>>>> x has or fails to have. This is another way of saying the True(x)
>>>>> is based on Provable(x) as these semantic connections are verified
>>>>> or fail verification.
>>>>>
>>>>
>>>> Unproven, and thus by its own definition, not True, and ANY
>>>> arguement based on it becomes UNSOND.
>>>
>>> I think that we agree on this.
>>
>> So, you agree that your statement is UNSOUND?
>
> Unproven means unsound. Sound requires proven.

You just showed that you don't know the meaning.

CLAIMING something to be True without proof is Unsound, but an Unproven
fact is mearly unknown.

The Collbatz conjuecture is Unknown as to its Truth, but we KNOW that it
must be either True of False.

The Collbatz Conjecture is NOT "Unsound", because it doesn't assert that
it IS true, just believed to be.

Richard Damon

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May 18, 2022, 7:42:57 PMMay 18
to
The PROVE that "The Square of the Hypotonuse of a Right Triangle is
equal to the Sum of the Squares of the other two sides" on the basis of
its meaning.

Or, is that NOT a analytic expression, and thus, most of mathematics is
not dispite your "stipuation".

Richard Damon

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May 18, 2022, 7:46:36 PMMay 18
to
And you keep lying about it.

Since P(P) NEVER calls another copy of P, the fact that the trace shows
this happening PROVES it is not a correct trace, unless you are going to
admit that H mearly calls its input (at least when called by P).

Once P calls H, the ONLY code that is executed (if H is a simulator) is
the code of H, NEVER do we get back to P.

Note, then you need to explain how it is still a actual computation when
the outer H behaves differently (since the behavior of a computaiton is
ONLY a function of its parameters, so is can't know that it is being
called by P).

Richard Damon

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May 18, 2022, 7:48:41 PMMay 18
to
On 5/18/22 11:41 AM, olcott wrote:
> On 5/18/2022 10:31 AM, Ben wrote:
>> olcott <No...@NoWhere.com> writes:
>>
>>> Begin Local Halt Decider Simulation   Execution Trace Stored at:212352
>>> ...[00001352][0021233e][00212342] 55         push ebp      // enter P
>>> ...[00001353][0021233e][00212342] 8bec       mov ebp,esp
>>> ...[00001355][0021233e][00212342] 8b4508     mov eax,[ebp+08]
>>> ...[00001358][0021233a][00001352] 50         push eax      // push P
>>> ...[00001359][0021233a][00001352] 8b4d08     mov ecx,[ebp+08]
>>> ...[0000135c][00212336][00001352] 51         push ecx      // push P
>>> ...[0000135d][00212332][00001362] e840feffff call 000011a2 // call H
>>> ...[00001352][0025cd66][0025cd6a] 55         push ebp      // enter P
>>
>> This can't be the trace of the function you have been talking about.
>> The H you claim to have simulates something (no one cares what, but it's
>> something) so the code at the start of H should be setting up and
>> entering a simulator.
>>
>
> HOW MANY TIMES DO I HAVE TO TELL YOU THAT H PERFORMS A PURE SIMULATION
> OF ITS INPUT THUS HAS NO BEHAVIOR THAT CAN HAVE ANY EFFECT ON THE
> BEHAVIOR OF ITS INPUT THUS NO NEED TO SEE ITS HUNDREDS OF PAGES OF
> EXECUTION TRACE ???

The the trace needs to just stop at the call to H, but then you don't
have anything to point at to "prove" your statement.

Richard Damon

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May 18, 2022, 7:50:50 PMMay 18
to
And the trace starts to LIE right here unless H actually calls P

> ...[00001352][0025cd66][0025cd6a] 55         push ebp      // enter P
> ...[00001353][0025cd66][0025cd6a] 8bec       mov ebp,esp
> ...[00001355][0025cd66][0025cd6a] 8b4508     mov eax,[ebp+08]
> ...[00001358][0025cd62][00001352] 50         push eax      // push P
> ...[00001359][0025cd62][00001352] 8b4d08     mov ecx,[ebp+08]
> ...[0000135c][0025cd5e][00001352] 51         push ecx      // push P
> ...[0000135d][0025cd5a][00001362] e840feffff call 000011a2 // call H
> Local Halt Decider: Infinite Recursion Detected Simulation Stopped
>
> H sees that P is calling the same function from the same machine address
> with identical parameters, twice in sequence. This is the infinite
> recursion (infinitely nested simulation) non-halting behavior pattern.

But H is seeing things, since it is looking at an incorrect trace,
unless the H that P called did just call P, then H is proven to NOT be a
computation as H(P,P) does different things at different times.

olcott

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May 18, 2022, 7:54:56 PMMay 18