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Re: on mathematical ghosts --- PLO

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  Re: on mathematical ghosts --- PLO polcott <polcott333@gmail.com> - 2025-12-08 22:00 -0600
    Re: on mathematical ghosts --- PLO Richard Damon <Richard@Damon-Family.org> - 2025-12-08 23:20 -0500
      Re: on mathematical ghosts --- PLO polcott <polcott333@gmail.com> - 2025-12-08 22:33 -0600
        Re: on mathematical ghosts --- PLO Richard Damon <Richard@Damon-Family.org> - 2025-12-09 07:42 -0500
          Re: on mathematical ghosts --- PLO polcott <polcott333@gmail.com> - 2025-12-09 09:53 -0600
            Re: on mathematical ghosts --- PLO Richard Damon <Richard@Damon-Family.org> - 2025-12-09 23:02 -0500
      Re: on mathematical ghosts --- PLO polcott <polcott333@gmail.com> - 2025-12-08 22:51 -0600
        Re: on mathematical ghosts --- PLO Richard Damon <Richard@Damon-Family.org> - 2025-12-09 07:42 -0500
          Re: on mathematical ghosts --- PLO polcott <polcott333@gmail.com> - 2025-12-09 09:39 -0600
            Re: on mathematical ghosts --- PLO Richard Damon <Richard@Damon-Family.org> - 2025-12-09 23:02 -0500
    Re: on mathematical ghosts --- PLO dart200 <user7160@newsgrouper.org.invalid> - 2025-12-08 20:54 -0800
      Re: on mathematical ghosts --- PLO polcott <polcott333@gmail.com> - 2025-12-08 23:02 -0600

#342988 — Re: on mathematical ghosts --- PLO

On 12/8/2025 9:38 PM, dart200 wrote:

*You have support for this in high places*

The Halting Paradox
Bill Stoddart

6 Conclusions
The idea of a universal halting test seems reasonable,
but cannot be formalised as a consistent specification.
It has no model and does not exist as a conceptual object.
Assuming its conceptual existence leads to a paradox.

https://arxiv.org/pdf/1906.05340

-- 
Copyright 2025 Olcott

My 28 year goal has been to make
"true on the basis of meaning" computable.

This required establishing a new foundation
for correct reasoning.

[toc] | [next] | [standalone]

#342990

On 12/8/25 11:00 PM, polcott wrote:
> On 12/8/2025 9:38 PM, dart200 wrote:
> 
> *You have support for this in high places*
> 
> The Halting Paradox
> Bill Stoddart
> 
> 6 Conclusions
> The idea of a universal halting test seems reasonable,
> but cannot be formalised as a consistent specification.
> It has no model and does not exist as a conceptual object.
> Assuming its conceptual existence leads to a paradox.
> 
> https://arxiv.org/pdf/1906.05340
> 

Which doesn't prove anything, as there IS a consistant specification for 
the test.

The problem is you (and Bill) just don't understand it.

Part of the problem is Bill doesn't understand the nature of Turing 
Complete systems. In particular, he assume there is a UNIQUE encoding 
for every program, which is a false assumption in Turing Complete systems.

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#342992

On 12/8/2025 10:20 PM, Richard Damon wrote:
> On 12/8/25 11:00 PM, polcott wrote:
>> On 12/8/2025 9:38 PM, dart200 wrote:
>>
>> *You have support for this in high places*
>>
>> The Halting Paradox
>> Bill Stoddart
>>
>> 6 Conclusions
>> The idea of a universal halting test seems reasonable,
>> but cannot be formalised as a consistent specification.
>> It has no model and does not exist as a conceptual object.
>> Assuming its conceptual existence leads to a paradox.
>>
>> https://arxiv.org/pdf/1906.05340
>>
> 
> Which doesn't prove anything, as there IS a consistant specification for 
> the test.
> 
> The problem is you (and Bill) just don't understand it.
> 

He and Eric have been PhD computer science professors
for decades. Of course that by itself means that
they must be woefully less than your own infallibility.

> Part of the problem is Bill doesn't understand the nature of Turing 
> Complete systems. In particular, he assume there is a UNIQUE encoding 
> for every program, which is a false assumption in Turing Complete systems.

That has nothing to do with foundations.

-- 
Copyright 2025 Olcott

My 28 year goal has been to make
"true on the basis of meaning" computable.

This required establishing a new foundation
for correct reasoning.

[toc] | [prev] | [next] | [standalone]

#342997

On 12/8/25 11:33 PM, polcott wrote:
> On 12/8/2025 10:20 PM, Richard Damon wrote:
>> On 12/8/25 11:00 PM, polcott wrote:
>>> On 12/8/2025 9:38 PM, dart200 wrote:
>>>
>>> *You have support for this in high places*
>>>
>>> The Halting Paradox
>>> Bill Stoddart
>>>
>>> 6 Conclusions
>>> The idea of a universal halting test seems reasonable,
>>> but cannot be formalised as a consistent specification.
>>> It has no model and does not exist as a conceptual object.
>>> Assuming its conceptual existence leads to a paradox.
>>>
>>> https://arxiv.org/pdf/1906.05340
>>>
>>
>> Which doesn't prove anything, as there IS a consistant specification 
>> for the test.
>>
>> The problem is you (and Bill) just don't understand it.
>>
> 
> He and Eric have been PhD computer science professors
> for decades. Of course that by itself means that
> they must be woefully less than your own infallibility.

So?

Appeal to Authority is just a FALICY.

The fact this is you full arguement just show the error in your logic.

> 
>> Part of the problem is Bill doesn't understand the nature of Turing 
>> Complete systems. In particular, he assume there is a UNIQUE encoding 
>> for every program, which is a false assumption in Turing Complete 
>> systems.
> 
> That has nothing to do with foundations.
> 

Sure it does.

His decider check if the input uses it. That is based on the decider 
being able to detect that usage. Since there is no unique value to test, 
the test can't be done.

Your logic is based on assuming you can make assumptions about things 
that are not true, and thus your logic is based on falsehoods being 
true, and thus shows it is just unsound, as are you.

Sorry, all you are doing is showing how bad your logic abilities.

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#343001

On 12/9/2025 6:42 AM, Richard Damon wrote:
> On 12/8/25 11:33 PM, polcott wrote:
>> On 12/8/2025 10:20 PM, Richard Damon wrote:
>>> On 12/8/25 11:00 PM, polcott wrote:
>>>> On 12/8/2025 9:38 PM, dart200 wrote:
>>>>
>>>> *You have support for this in high places*
>>>>
>>>> The Halting Paradox
>>>> Bill Stoddart
>>>>
>>>> 6 Conclusions
>>>> The idea of a universal halting test seems reasonable,
>>>> but cannot be formalised as a consistent specification.
>>>> It has no model and does not exist as a conceptual object.
>>>> Assuming its conceptual existence leads to a paradox.
>>>>
>>>> https://arxiv.org/pdf/1906.05340
>>>>
>>>
>>> Which doesn't prove anything, as there IS a consistant specification 
>>> for the test.
>>>
>>> The problem is you (and Bill) just don't understand it.
>>>
>>
>> He and Eric have been PhD computer science professors
>> for decades. Of course that by itself means that
>> they must be woefully less than your own infallibility.
> 
> So?
> 
> Appeal to Authority is just a FALICY.
> 
> The fact this is you full arguement just show the error in your logic.
> 

He and Eric just understand these things better
than you and you lack of understanding is not
a rebuttal. I honestly believe that you are
capable of understanding these very difficult
things if you merely give up your insistence
on remaining in rebuttal mode.

It has take me more than 21 years to finally get
clear and correct words that are consistent with
standard definitions. For my first fifteen years
I only had strongly held intuitions and had to
overload terms of the art with different meanings
because there were no exiting terms that conveyed
the meanings that I needed to convey.

>>
>>> Part of the problem is Bill doesn't understand the nature of Turing 
>>> Complete systems. In particular, he assume there is a UNIQUE encoding 
>>> for every program, which is a false assumption in Turing Complete 
>>> systems.
>>
>> That has nothing to do with foundations.
>>
> 
> Sure it does.
> 
> His decider check if the input uses it. That is based on the decider 
> being able to detect that usage. Since there is no unique value to test, 
> the test can't be done.
> 

For the conventional halting problem proof there
is a unique value. That the proof can be adapted
is off-topic. We must make one point at a time
with no leaping to conclusions.

> Your logic is based on assuming you can make assumptions about things 
> that are not true, and thus your logic is based on falsehoods being 
> true, and thus shows it is just unsound, as are you.
> 
> Sorry, all you are doing is showing how bad your logic abilities.

That I understand these things at deeper philosophical
levels is not any lack of understanding on my part. I
am merely having the same problem as Ludwig Wittgenstein
in that mathematicians and logicians are rigid-minded
and utterly unwilling to reexamine philosophical foundations.

-- 
Copyright 2025 Olcott

My 28 year goal has been to make
"true on the basis of meaning" computable.

This required establishing a new foundation
for correct reasoning.

[toc] | [prev] | [next] | [standalone]

#343010

On 12/9/25 10:53 AM, polcott wrote:
> On 12/9/2025 6:42 AM, Richard Damon wrote:
>> On 12/8/25 11:33 PM, polcott wrote:
>>> On 12/8/2025 10:20 PM, Richard Damon wrote:
>>>> On 12/8/25 11:00 PM, polcott wrote:
>>>>> On 12/8/2025 9:38 PM, dart200 wrote:
>>>>>
>>>>> *You have support for this in high places*
>>>>>
>>>>> The Halting Paradox
>>>>> Bill Stoddart
>>>>>
>>>>> 6 Conclusions
>>>>> The idea of a universal halting test seems reasonable,
>>>>> but cannot be formalised as a consistent specification.
>>>>> It has no model and does not exist as a conceptual object.
>>>>> Assuming its conceptual existence leads to a paradox.
>>>>>
>>>>> https://arxiv.org/pdf/1906.05340
>>>>>
>>>>
>>>> Which doesn't prove anything, as there IS a consistant specification 
>>>> for the test.
>>>>
>>>> The problem is you (and Bill) just don't understand it.
>>>>
>>>
>>> He and Eric have been PhD computer science professors
>>> for decades. Of course that by itself means that
>>> they must be woefully less than your own infallibility.
>>
>> So?
>>
>> Appeal to Authority is just a FALICY.
>>
>> The fact this is you full arguement just show the error in your logic.
>>
> 
> He and Eric just understand these things better
> than you and you lack of understanding is not
> a rebuttal. I honestly believe that you are
> capable of understanding these very difficult
> things if you merely give up your insistence
> on remaining in rebuttal mode.

Nope, he just shows he has the same ignorance (that you have admitted 
to) about what Computation Theory is about.

> 
> It has take me more than 21 years to finally get
> clear and correct words that are consistent with
> standard definitions. For my first fifteen years
> I only had strongly held intuitions and had to
> overload terms of the art with different meanings
> because there were no exiting terms that conveyed
> the meanings that I needed to convey.

Nope, you have wasted 21 years to try to create a better sounding LIE.

The problem is you don't actually know what anything you say actually 
means in the theory you claim to be working on, because you have 
admitted you keep yourself ignorant of the actual facts.

> 
>>>
>>>> Part of the problem is Bill doesn't understand the nature of Turing 
>>>> Complete systems. In particular, he assume there is a UNIQUE 
>>>> encoding for every program, which is a false assumption in Turing 
>>>> Complete systems.
>>>
>>> That has nothing to do with foundations.
>>>
>>
>> Sure it does.
>>
>> His decider check if the input uses it. That is based on the decider 
>> being able to detect that usage. Since there is no unique value to 
>> test, the test can't be done.
>>
> 
> For the conventional halting problem proof there
> is a unique value. That the proof can be adapted
> is off-topic. We must make one point at a time
> with no leaping to conclusions.

Nope. Just shows your ignorance.

It is computationally IMPOSSIBLE for H to universally detect that the 
machine H^ that it has been give is using a copy of itself.

Your problem is that in your ignorance, you created a bad representation 
system that only handles less than Turing Complete systems, and even 
admit to a condition that proves this fact.

> 
>> Your logic is based on assuming you can make assumptions about things 
>> that are not true, and thus your logic is based on falsehoods being 
>> true, and thus shows it is just unsound, as are you.
>>
>> Sorry, all you are doing is showing how bad your logic abilities.
> 
> That I understand these things at deeper philosophical
> levels is not any lack of understanding on my part. I
> am merely having the same problem as Ludwig Wittgenstein
> in that mathematicians and logicians are rigid-minded
> and utterly unwilling to reexamine philosophical foundations.
> 

Nope, you just prove Dunning-Kruger because you THINK you understand 
something you are just totally ignorant of.

You have proved this many times, as your world is based on hopeful 
proclamations with no factual basis behind them, because you just don't 
understand what Truth actually is.

Mathematic and Logic *IS* "rigid-minded" as it has actual rules. A 
concept foreign to you, which is why you can't actually understand 
anything in them.

As has been pointed out many times, if you want create a totally new 
system, go ahead a do it, just be clear that is what you are doing, and 
thus nothing you say has any impact on the systems you left behind.

Your problem is, you refuse to leave the system behind, because you KNOW 
(maybe just subconsiously) that they usefully and validly point out 
things you don't want to admit.

Your problem is your mind can only handle trivially small logic system, 
so all you are trying to do is define "logic" to only handle those 
trivially small sets where incompleteness doesn't occur/

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#342993

On 12/8/2025 10:20 PM, Richard Damon wrote:
> On 12/8/25 11:00 PM, polcott wrote:
>> On 12/8/2025 9:38 PM, dart200 wrote:
>>
>> *You have support for this in high places*
>>
>> The Halting Paradox
>> Bill Stoddart
>>
>> 6 Conclusions
>> The idea of a universal halting test seems reasonable,
>> but cannot be formalised as a consistent specification.
>> It has no model and does not exist as a conceptual object.
>> Assuming its conceptual existence leads to a paradox.
>>
>> https://arxiv.org/pdf/1906.05340
>>
> 
> Which doesn't prove anything, as there IS a consistant specification for 
> the test.
> 
> The problem is you (and Bill) just don't understand it.
> 
> Part of the problem is Bill doesn't understand the nature of Turing 
> Complete systems. In particular, he assume there is a UNIQUE encoding 
> for every program, which is a false assumption in Turing Complete systems.

With the text of each program P we associate a
unique number ⌈P⌉, known as the program’s encoding,
which will stand for the program when we want to
use that program as data, e.g. when passing one
program to another as an argument.

You are just terribly inaccurate in paraphrasing.
Perhaps speaking to no one at all is better than
talking to you.

-- 
Copyright 2025 Olcott

My 28 year goal has been to make
"true on the basis of meaning" computable.

This required establishing a new foundation
for correct reasoning.

[toc] | [prev] | [next] | [standalone]

#342996

On 12/8/25 11:51 PM, polcott wrote:
> On 12/8/2025 10:20 PM, Richard Damon wrote:
>> On 12/8/25 11:00 PM, polcott wrote:
>>> On 12/8/2025 9:38 PM, dart200 wrote:
>>>
>>> *You have support for this in high places*
>>>
>>> The Halting Paradox
>>> Bill Stoddart
>>>
>>> 6 Conclusions
>>> The idea of a universal halting test seems reasonable,
>>> but cannot be formalised as a consistent specification.
>>> It has no model and does not exist as a conceptual object.
>>> Assuming its conceptual existence leads to a paradox.
>>>
>>> https://arxiv.org/pdf/1906.05340
>>>
>>
>> Which doesn't prove anything, as there IS a consistant specification 
>> for the test.
>>
>> The problem is you (and Bill) just don't understand it.
>>
>> Part of the problem is Bill doesn't understand the nature of Turing 
>> Complete systems. In particular, he assume there is a UNIQUE encoding 
>> for every program, which is a false assumption in Turing Complete 
>> systems.
> 
> With the text of each program P we associate a
> unique number ⌈P⌉, known as the program’s encoding,
> which will stand for the program when we want to
> use that program as data, e.g. when passing one
> program to another as an argument.
> 
> You are just terribly inaccurate in paraphrasing.
> Perhaps speaking to no one at all is better than
> talking to you.
> 

Except there are many texts that create the equivalent program, and thus 
many numbers for that program.

Yes, we can convert a program into data, but there are many data values 
that all represent the same program.

This means that Program H can't use a "unique" value of its 
representation to detect the input using it, as the pathological program 
can just use an equivalent variation not in the finite list of values 
that H tests for.

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#343000

On 12/9/2025 6:42 AM, Richard Damon wrote:
> On 12/8/25 11:51 PM, polcott wrote:
>> On 12/8/2025 10:20 PM, Richard Damon wrote:
>>> On 12/8/25 11:00 PM, polcott wrote:
>>>> On 12/8/2025 9:38 PM, dart200 wrote:
>>>>
>>>> *You have support for this in high places*
>>>>
>>>> The Halting Paradox
>>>> Bill Stoddart
>>>>
>>>> 6 Conclusions
>>>> The idea of a universal halting test seems reasonable,
>>>> but cannot be formalised as a consistent specification.
>>>> It has no model and does not exist as a conceptual object.
>>>> Assuming its conceptual existence leads to a paradox.
>>>>
>>>> https://arxiv.org/pdf/1906.05340
>>>>
>>>
>>> Which doesn't prove anything, as there IS a consistant specification 
>>> for the test.
>>>
>>> The problem is you (and Bill) just don't understand it.
>>>
>>> Part of the problem is Bill doesn't understand the nature of Turing 
>>> Complete systems. In particular, he assume there is a UNIQUE encoding 
>>> for every program, which is a false assumption in Turing Complete 
>>> systems.
>>
>> With the text of each program P we associate a
>> unique number ⌈P⌉, known as the program’s encoding,
>> which will stand for the program when we want to
>> use that program as data, e.g. when passing one
>> program to another as an argument.
>>
>> You are just terribly inaccurate in paraphrasing.
>> Perhaps speaking to no one at all is better than
>> talking to you.
>>
> 
> Except there are many texts that create the equivalent program, and thus 
> many numbers for that program.
> 

He is doing this like Gödel numbers, thus a unique
identifier is needed. And again this is merely nit-picky
his point is that the foundations of computer science
are incorrect and I have shown that two different ways.

> Yes, we can convert a program into data, but there are many data values 
> that all represent the same program.
> 

No there are not you are just not being precise enough
in your choice of words. And yet again this is an
irrelevant nit-picky detail.

> This means that Program H can't use a "unique" value of its 
> representation to detect the input using it, as the pathological program 
> can just use an equivalent variation not in the finite list of values 
> that H tests for.

If the finite strings are not identical then the
inputs are not identical.

-- 
Copyright 2025 Olcott

My 28 year goal has been to make
"true on the basis of meaning" computable.

This required establishing a new foundation
for correct reasoning.

[toc] | [prev] | [next] | [standalone]

#343011

On 12/9/25 10:39 AM, polcott wrote:
> On 12/9/2025 6:42 AM, Richard Damon wrote:
>> On 12/8/25 11:51 PM, polcott wrote:
>>> On 12/8/2025 10:20 PM, Richard Damon wrote:
>>>> On 12/8/25 11:00 PM, polcott wrote:
>>>>> On 12/8/2025 9:38 PM, dart200 wrote:
>>>>>
>>>>> *You have support for this in high places*
>>>>>
>>>>> The Halting Paradox
>>>>> Bill Stoddart
>>>>>
>>>>> 6 Conclusions
>>>>> The idea of a universal halting test seems reasonable,
>>>>> but cannot be formalised as a consistent specification.
>>>>> It has no model and does not exist as a conceptual object.
>>>>> Assuming its conceptual existence leads to a paradox.
>>>>>
>>>>> https://arxiv.org/pdf/1906.05340
>>>>>
>>>>
>>>> Which doesn't prove anything, as there IS a consistant specification 
>>>> for the test.
>>>>
>>>> The problem is you (and Bill) just don't understand it.
>>>>
>>>> Part of the problem is Bill doesn't understand the nature of Turing 
>>>> Complete systems. In particular, he assume there is a UNIQUE 
>>>> encoding for every program, which is a false assumption in Turing 
>>>> Complete systems.
>>>
>>> With the text of each program P we associate a
>>> unique number ⌈P⌉, known as the program’s encoding,
>>> which will stand for the program when we want to
>>> use that program as data, e.g. when passing one
>>> program to another as an argument.
>>>
>>> You are just terribly inaccurate in paraphrasing.
>>> Perhaps speaking to no one at all is better than
>>> talking to you.
>>>
>>
>> Except there are many texts that create the equivalent program, and 
>> thus many numbers for that program.
>>
> 
> He is doing this like Gödel numbers, thus a unique
> identifier is needed. And again this is merely nit-picky
> his point is that the foundations of computer science
> are incorrect and I have shown that two different ways.

Nope, doesn't work that way. A Godel number is just a way of converting 
a logical sentence into a number. Since there are many ways to say the 
same thing, and each variation would have a different Godel number, it 
isn't unique.

Even the same sentence, if it introduces new definitions, can have 
multiple Godel numbers, as every new definition creates an arbitraryness 
that gives you multiple values.

This just highlights that you don't understand what you are talking about.

> 
>> Yes, we can convert a program into data, but there are many data 
>> values that all represent the same program.
>>
> 
> No there are not you are just not being precise enough
> in your choice of words. And yet again this is an
> irrelevant nit-picky detail.

No, you ar just assuming the impossible. It isn't "picky", it is being 
accurate, a concept you don't understand.

How many computationally equivalent version of your HHH program do you 
think we can create?

> 
>> This means that Program H can't use a "unique" value of its 
>> representation to detect the input using it, as the pathological 
>> program can just use an equivalent variation not in the finite list of 
>> values that H tests for.
> 
> If the finite strings are not identical then the
> inputs are not identical.
> 

WHICH "finite string" of H are you lookiing at?

There is only one "input" in the problem, the representation of H^, 
which include a copy of the computational equivalent of H.

do you not agree that these two are identical programs:


int foo(int x) {
   return x+1;
}

and

int foo(int y) {
   int x = y + 1;
   return x;
}


Do they not compute the exact same value for all inputs?

Do the strings that represent the program exactly compate as equal?

How can you detect ALL possible variations of something like this.

Part of your problem is you don't understand that Compuations are based 
on actual algorithms being executed, and they don't have a native 
cononical representation.

Part of this is because you chose not to learn the details of what you 
talk about, and thus your reckless-disregard for the truth has turned 
you into a lying idiot.

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#342994

On 12/8/25 8:00 PM, polcott wrote:
> On 12/8/2025 9:38 PM, dart200 wrote:
> 
> *You have support for this in high places*
> 
> The Halting Paradox
> Bill Stoddart
> 
> 6 Conclusions
> The idea of a universal halting test seems reasonable,
> but cannot be formalised as a consistent specification.
> It has no model and does not exist as a conceptual object.
> Assuming its conceptual existence leads to a paradox.
> 
> https://arxiv.org/pdf/1906.05340
> 

stoddart didn't want to discuss anything and i've been pissing off eric 
u saw the emails

-- 
hi, i'm nick! let's end war 🙃

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#342995

On 12/8/2025 10:54 PM, dart200 wrote:
> On 12/8/25 8:00 PM, polcott wrote:
>> On 12/8/2025 9:38 PM, dart200 wrote:
>>
>> *You have support for this in high places*
>>
>> The Halting Paradox
>> Bill Stoddart
>>
>> 6 Conclusions
>> The idea of a universal halting test seems reasonable,
>> but cannot be formalised as a consistent specification.
>> It has no model and does not exist as a conceptual object.
>> Assuming its conceptual existence leads to a paradox.
>>
>> https://arxiv.org/pdf/1906.05340
>>
> 
> stoddart didn't want to discuss anything and i've been pissing off eric 
> u saw the emails
> 

None the less you can carefully examine
his work and see how and where he affirms
your position. Eric is happy with me.

-- 
Copyright 2025 Olcott

My 28 year goal has been to make
"true on the basis of meaning" computable.

This required establishing a new foundation
for correct reasoning.

[toc] | [prev] | [standalone]

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