.... and he has no doubt that the Turing Machine halting problem is
unsolvable, which apparently contradicts what Olcott thinks he thinks.

His most relevant belief is that the halting problem is not proven
unsolvable in cases where the halting decider is written in a different
language from the language of the program it's supposed to be deciding.

On 2/25/2024 6:33 AM, immibis wrote:
> ... and he has no doubt that the Turing Machine halting problem is
> unsolvable, which apparently contradicts what Olcott thinks he thinks.
>

He and Professor Stoddart say that it is unsolvable because
there is something wrong with it thus affirming my 2004 statement.

Alan Turing's Halting Problem is incorrectly formed (PART-TWO) sci.logic
*On 6/20/2004 11:31 AM, Peter Olcott wrote*
> PREMISES:
> (1) The Halting Problem was specified in such a way that a solution
> was defined to be impossible.
>
> (2) The set of questions that are defined to not have any possible
> correct answer(s) forms a proper subset of all possible questions.
> …
> CONCLUSION:
> Therefore the Halting Problem is an ill-formed question.
>
USENET Message-ID:
<kZiBc.103407$Gx4.18142@bgtnsc04-news.ops.worldnet.att.net>

E C R Hehner. *Objective and Subjective Specifications*
WST Workshop on Termination, Oxford. 2018 July 18.
See https://www.cs.toronto.edu/~hehner/OSS.pdf

Bill Stoddart. *The Halting Paradox*
20 December 2017
https://arxiv.org/abs/1906.05340
arXiv:1906.05340 [cs.LO]

> His most relevant belief is that the halting problem is not proven
> unsolvable in cases where the halting decider is written in a different
> language from the language of the program it's supposed to be deciding.

--
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 2/25/24 7:33 AM, immibis wrote:
> ... and he has no doubt that the Turing Machine halting problem is
> unsolvable, which apparently contradicts what Olcott thinks he thinks.
>
> His most relevant belief is that the halting problem is not proven
> unsolvable in cases where the halting decider is written in a different
> language from the language of the program it's supposed to be deciding.

Which just shows he doesn't understand the actual problem, likely
because he has only heard it described by people who don't understand
that problem.

The key point is the actual Problem isn't described in terms of
"Programs", but Turing Machines (or Equivalents) so the "different
language" issue can't come up.

On 2/25/2024 12:27 PM, Richard Damon wrote:
> On 2/25/24 7:33 AM, immibis wrote:
>> ... and he has no doubt that the Turing Machine halting problem is
>> unsolvable, which apparently contradicts what Olcott thinks he thinks.
>>
>> His most relevant belief is that the halting problem is not proven
>> unsolvable in cases where the halting decider is written in a
>> different language from the language of the program it's supposed to
>> be deciding.
>
> Which just shows he doesn't understand the actual problem, likely
> because he has only heard it described by people who don't understand
> that problem.
>
> The key point is the actual Problem isn't described in terms of
> "Programs", but Turing Machines (or Equivalents) so the "different
> language" issue can't come up.
>
>

Hence my Turing Machine template adapted from Linz
proves that Stoddart and Hehner were right all along.

Ȟ.q0 ⟨Ȟ⟩ ⟨Ȟ⟩ ⊢* Ȟ.qy ∞ // Ȟ applied to ⟨Ȟ⟩ halts
Ȟ.q0 ⟨Ȟ⟩ ⟨Ȟ⟩ ⊢* Ȟ.qn // Ȟ applied to ⟨Ȟ⟩ does not halt

Ȟ cannot transition to a value corresponding to its own behavior
because Ȟ applied to ⟨Ȟ⟩ ⟨Ȟ⟩ was intentionally defined to contradict
every value that Ȟ returns.

Ȟ applied to ⟨Ȟ⟩ ⟨Ȟ⟩ is self-contradictory and those that disagree
have proven to be liars.

--
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 2/25/24 2:45 PM, olcott wrote:
> On 2/25/2024 12:27 PM, Richard Damon wrote:
>> On 2/25/24 7:33 AM, immibis wrote:
>>> ... and he has no doubt that the Turing Machine halting problem is
>>> unsolvable, which apparently contradicts what Olcott thinks he thinks.
>>>
>>> His most relevant belief is that the halting problem is not proven
>>> unsolvable in cases where the halting decider is written in a
>>> different language from the language of the program it's supposed to
>>> be deciding.
>>
>> Which just shows he doesn't understand the actual problem, likely
>> because he has only heard it described by people who don't understand
>> that problem.
>>
>> The key point is the actual Problem isn't described in terms of
>> "Programs", but Turing Machines (or Equivalents) so the "different
>> language" issue can't come up.
>>
>>
>
> Hence my Turing Machine template adapted from Linz
> proves that Stoddart and Hehner were right all along.

Except that Turing Machine TEMPLATES aren't valid input for the Halting
Question.

You are just proving your ignorance of the subject.

And just proving that the POOP question (which apparently can use
templates) in incorrect.

>
> Ȟ.q0 ⟨Ȟ⟩ ⟨Ȟ⟩ ⊢* Ȟ.qy ∞ // Ȟ applied to ⟨Ȟ⟩ halts
> Ȟ.q0 ⟨Ȟ⟩ ⟨Ȟ⟩ ⊢* Ȟ.qn // Ȟ applied to ⟨Ȟ⟩ does not halt
>
> Ȟ cannot transition to a value corresponding to its own behavior
> because Ȟ applied to ⟨Ȟ⟩ ⟨Ȟ⟩ was intentionally defined to contradict
> every value that Ȟ returns.
>
> Ȟ applied to ⟨Ȟ⟩ ⟨Ȟ⟩ is self-contradictory and those that disagree
> have proven to be liars.
>

Nope, YOU are proven to be a LIAR, and have confessed to it by refusing
to answer the refutations made against your "logic", thus abandoning it.

On 25/02/24 17:53, olcott wrote:
> On 2/25/2024 6:33 AM, immibis wrote:
>> ... and he has no doubt that the Turing Machine halting problem is
>> unsolvable, which apparently contradicts what Olcott thinks he thinks.
>>
>
> He and Professor Stoddart say that it is unsolvable because > there is something wrong with it thus affirming my 2004 statement.

No, I don't see where he's said there is something wrong with it. He
simply agrees that it is unsolvable.

The question "What is the natural number x such that x=1-x?" is
unsolvable because there is no such natural number. It is just a fact.
There is no need to blame anyone, and there is nothing wrong with the
question except for the fact that it has no solution.

"What is the natural number x such that x=2-x?" DOES have a solution. We
can see that some questions in this format have solutions, and some
don't. Mathematicians can study why some of them have solutions and some
don't (it's only solvable for even numbers). It doesn't mean there is
anything wrong with any of them.

On 25/02/24 19:27, Richard Damon wrote:
> On 2/25/24 7:33 AM, immibis wrote:
>> ... and he has no doubt that the Turing Machine halting problem is
>> unsolvable, which apparently contradicts what Olcott thinks he thinks.
>>
>> His most relevant belief is that the halting problem is not proven
>> unsolvable in cases where the halting decider is written in a
>> different language from the language of the program it's supposed to
>> be deciding.
>
> Which just shows he doesn't understand the actual problem, likely
> because he has only heard it described by people who don't understand
> that problem.

Note that he doesn't seem to claim it is solvable, just that it hasn't
been unsolvable. I told him reasons why it is still unsolvable in this
case. Eventually we will find out what he thinks about them.

> The key point is the actual Problem isn't described in terms of
> "Programs", but Turing Machines (or Equivalents) so the "different
> language" issue can't come up.

He agrees the Turing Machine Halting Problem is unsolvable because of
the well-known proof, and turns his attention to more general halting
problems, such as the halting problems for other general-purpose
programming languages and tries to discover something there.

On 2024-02-25 12:33:19 +0000, immibis said:

> ... and he has no doubt that the Turing Machine halting problem is
> unsolvable, which apparently contradicts what Olcott thinks he thinks.
>
> His most relevant belief is that the halting problem is not proven
> unsolvable in cases where the halting decider is written in a different
> language from the language of the program it's supposed to be deciding.

That is partly true. If the latter language is not Turing complete
its halting problem may be Turing computable.

--
Mikko

On 2/26/2024 2:28 AM, Mikko wrote:
> On 2024-02-25 12:33:19 +0000, immibis said:
>
>> ... and he has no doubt that the Turing Machine halting problem is
>> unsolvable, which apparently contradicts what Olcott thinks he thinks.
>>
>> His most relevant belief is that the halting problem is not proven
>> unsolvable in cases where the halting decider is written in a
>> different language from the language of the program it's supposed to
>> be deciding.
>
> That is partly true. If the latter language is not Turing complete
> its halting problem may be Turing computable.
>

His most relevant belief (and professor Stoddart concurs) is
that the halting problem cannot be solved because there is
something wrong with it.

--
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 26/02/24 18:43, olcott wrote:
> On 2/26/2024 2:28 AM, Mikko wrote:
>> On 2024-02-25 12:33:19 +0000, immibis said:
>>
>>> ... and he has no doubt that the Turing Machine halting problem is
>>> unsolvable, which apparently contradicts what Olcott thinks he thinks.
>>>
>>> His most relevant belief is that the halting problem is not proven
>>> unsolvable in cases where the halting decider is written in a
>>> different language from the language of the program it's supposed to
>>> be deciding.
>>
>> That is partly true. If the latter language is not Turing complete
>> its halting problem may be Turing computable.
>>
>
> His most relevant belief (and professor Stoddart concurs) is
> that the halting problem cannot be solved because there is
> something wrong with it.
>

Professor Hehner does not believe there is anything "wrong with" the
Turing machine halting problem.

On 2/26/2024 12:08 PM, immibis wrote:
> On 26/02/24 18:43, olcott wrote:
>> On 2/26/2024 2:28 AM, Mikko wrote:
>>> On 2024-02-25 12:33:19 +0000, immibis said:
>>>
>>>> ... and he has no doubt that the Turing Machine halting problem is
>>>> unsolvable, which apparently contradicts what Olcott thinks he thinks.
>>>>
>>>> His most relevant belief is that the halting problem is not proven
>>>> unsolvable in cases where the halting decider is written in a
>>>> different language from the language of the program it's supposed to
>>>> be deciding.
>>>
>>> That is partly true. If the latter language is not Turing complete
>>> its halting problem may be Turing computable.
>>>
>>
>> His most relevant belief (and professor Stoddart concurs) is
>> that the halting problem cannot be solved because there is
>> something wrong with it.
>>
>
> Professor Hehner does not believe there is anything "wrong with" the
> Turing machine halting problem.
>

Professor Hehner:

This is my summation of your work and the work of professor
Stoddart:

His most relevant belief (and professor Stoddart concurs) is
that the halting problem cannot be solved because there is
something wrong with it.

Is this an accurate assessment?

Here is his reply: *Yes, I would sign that statement*

--
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 26/02/24 20:49, olcott wrote:
> On 2/26/2024 12:08 PM, immibis wrote:
>> On 26/02/24 18:43, olcott wrote:
>>> On 2/26/2024 2:28 AM, Mikko wrote:
>>>> On 2024-02-25 12:33:19 +0000, immibis said:
>>>>
>>>>> ... and he has no doubt that the Turing Machine halting problem is
>>>>> unsolvable, which apparently contradicts what Olcott thinks he thinks.
>>>>>
>>>>> His most relevant belief is that the halting problem is not proven
>>>>> unsolvable in cases where the halting decider is written in a
>>>>> different language from the language of the program it's supposed
>>>>> to be deciding.
>>>>
>>>> That is partly true. If the latter language is not Turing complete
>>>> its halting problem may be Turing computable.
>>>>
>>>
>>> His most relevant belief (and professor Stoddart concurs) is
>>> that the halting problem cannot be solved because there is
>>> something wrong with it.
>>>
>>
>> Professor Hehner does not believe there is anything "wrong with" the
>> Turing machine halting problem.
>>
>
> Professor Hehner:
>
> This is my summation of your work and the work of professor
> Stoddart:
>
> His most relevant belief (and professor Stoddart concurs) is
> that the halting problem cannot be solved because there is
> something wrong with it.
>
> Is this an accurate assessment?
>
> Here is his reply: *Yes, I would sign that statement*
>

I believe you disagree with me because there is something wrong with
you. I would sign that statement.

On 2/26/2024 2:07 PM, immibis wrote:
> On 26/02/24 20:49, olcott wrote:
>> On 2/26/2024 12:08 PM, immibis wrote:
>>> On 26/02/24 18:43, olcott wrote:
>>>> On 2/26/2024 2:28 AM, Mikko wrote:
>>>>> On 2024-02-25 12:33:19 +0000, immibis said:
>>>>>
>>>>>> ... and he has no doubt that the Turing Machine halting problem is
>>>>>> unsolvable, which apparently contradicts what Olcott thinks he
>>>>>> thinks.
>>>>>>
>>>>>> His most relevant belief is that the halting problem is not proven
>>>>>> unsolvable in cases where the halting decider is written in a
>>>>>> different language from the language of the program it's supposed
>>>>>> to be deciding.
>>>>>
>>>>> That is partly true. If the latter language is not Turing complete
>>>>> its halting problem may be Turing computable.
>>>>>
>>>>
>>>> His most relevant belief (and professor Stoddart concurs) is
>>>> that the halting problem cannot be solved because there is
>>>> something wrong with it.
>>>>
>>>
>>> Professor Hehner does not believe there is anything "wrong with" the
>>> Turing machine halting problem.
>>>
>>
>> Professor Hehner:
>>
>> This is my summation of your work and the work of professor
>> Stoddart:
>>
>> His most relevant belief (and professor Stoddart concurs) is
>> that the halting problem cannot be solved because there is
>> something wrong with it.
>>
>> Is this an accurate assessment?
>>
>> Here is his reply: *Yes, I would sign that statement*
>>
>
> I believe you disagree with me because there is something wrong with
> you. I would sign that statement.

Things a jackass would say...

--
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 2/26/24 3:07 PM, immibis wrote:
> On 26/02/24 20:49, olcott wrote:
>> On 2/26/2024 12:08 PM, immibis wrote:
>>> On 26/02/24 18:43, olcott wrote:
>>>> On 2/26/2024 2:28 AM, Mikko wrote:
>>>>> On 2024-02-25 12:33:19 +0000, immibis said:
>>>>>
>>>>>> ... and he has no doubt that the Turing Machine halting problem is
>>>>>> unsolvable, which apparently contradicts what Olcott thinks he
>>>>>> thinks.
>>>>>>
>>>>>> His most relevant belief is that the halting problem is not proven
>>>>>> unsolvable in cases where the halting decider is written in a
>>>>>> different language from the language of the program it's supposed
>>>>>> to be deciding.
>>>>>
>>>>> That is partly true. If the latter language is not Turing complete
>>>>> its halting problem may be Turing computable.
>>>>>
>>>>
>>>> His most relevant belief (and professor Stoddart concurs) is
>>>> that the halting problem cannot be solved because there is
>>>> something wrong with it.
>>>>
>>>
>>> Professor Hehner does not believe there is anything "wrong with" the
>>> Turing machine halting problem.
>>>
>>
>> Professor Hehner:
>>
>> This is my summation of your work and the work of professor
>> Stoddart:
>>
>> His most relevant belief (and professor Stoddart concurs) is
>> that the halting problem cannot be solved because there is
>> something wrong with it.
>>
>> Is this an accurate assessment?
>>
>> Here is his reply: *Yes, I would sign that statement*
>>
>
> I believe you disagree with me because there is something wrong with
> you. I would sign that statement.

+1

On 2/26/24 12:43 PM, olcott wrote:
> On 2/26/2024 2:28 AM, Mikko wrote:
>> On 2024-02-25 12:33:19 +0000, immibis said:
>>
>>> ... and he has no doubt that the Turing Machine halting problem is
>>> unsolvable, which apparently contradicts what Olcott thinks he thinks.
>>>
>>> His most relevant belief is that the halting problem is not proven
>>> unsolvable in cases where the halting decider is written in a
>>> different language from the language of the program it's supposed to
>>> be deciding.
>>
>> That is partly true. If the latter language is not Turing complete
>> its halting problem may be Turing computable.
>>
>
> His most relevant belief (and professor Stoddart concurs) is
> that the halting problem cannot be solved because there is
> something wrong with it.
>
>

But that is meaningless, unless they can state WHAT is wrong with it.

The fact that they have shown mis-understandings about what a
"Computation" is, doesn't make them a good source of "feelings" about
the topic.

On 2/26/2024 7:02 PM, Richard Damon wrote:
> On 2/26/24 12:43 PM, olcott wrote:
>> On 2/26/2024 2:28 AM, Mikko wrote:
>>> On 2024-02-25 12:33:19 +0000, immibis said:
>>>
>>>> ... and he has no doubt that the Turing Machine halting problem is
>>>> unsolvable, which apparently contradicts what Olcott thinks he thinks.
>>>>
>>>> His most relevant belief is that the halting problem is not proven
>>>> unsolvable in cases where the halting decider is written in a
>>>> different language from the language of the program it's supposed to
>>>> be deciding.
>>>
>>> That is partly true. If the latter language is not Turing complete
>>> its halting problem may be Turing computable.
>>>
>>
>> His most relevant belief (and professor Stoddart concurs) is
>> that the halting problem cannot be solved because there is
>> something wrong with it.
>>
>>
>
> But that is meaningless, unless they can state WHAT is wrong with it.
>

When speaking with people one must frame the ideas in a hierarchy
of the gist of the idea first and then the details that support
this gist progressively.

immibis could not understand that professor Hehner's essential
claim that he espoused in many papers
https://www.cs.toronto.edu/~hehner/halting.html
was that there is something wrong with the halting problem.

> The fact that they have shown mis-understandings about what a
> "Computation" is, doesn't make them a good source of "feelings" about
> the topic.

The point is that there really is something wrong with the halting problem.

--
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 2/26/24 8:10 PM, olcott wrote:
> On 2/26/2024 7:02 PM, Richard Damon wrote:
>> On 2/26/24 12:43 PM, olcott wrote:
>>> On 2/26/2024 2:28 AM, Mikko wrote:
>>>> On 2024-02-25 12:33:19 +0000, immibis said:
>>>>
>>>>> ... and he has no doubt that the Turing Machine halting problem is
>>>>> unsolvable, which apparently contradicts what Olcott thinks he thinks.
>>>>>
>>>>> His most relevant belief is that the halting problem is not proven
>>>>> unsolvable in cases where the halting decider is written in a
>>>>> different language from the language of the program it's supposed
>>>>> to be deciding.
>>>>
>>>> That is partly true. If the latter language is not Turing complete
>>>> its halting problem may be Turing computable.
>>>>
>>>
>>> His most relevant belief (and professor Stoddart concurs) is
>>> that the halting problem cannot be solved because there is
>>> something wrong with it.
>>>
>>>
>>
>> But that is meaningless, unless they can state WHAT is wrong with it.
>>
>
> When speaking with people one must frame the ideas in a hierarchy
> of the gist of the idea first and then the details that support
> this gist progressively.
>
> immibis could not understand that professor Hehner's essential
> claim that he espoused in many papers
> https://www.cs.toronto.edu/~hehner/halting.html
> was that there is something wrong with the halting problem.
>
>> The fact that they have shown mis-understandings about what a
>> "Computation" is, doesn't make them a good source of "feelings" about
>> the topic.
>
> The point is that there really is something wrong with the halting problem.
>

Nope.

You may THINK so, because you have wrong presuppositions, but unless you
can actually PROVE it to be wrong, you just have NOTHING but lies.

On 2/26/2024 8:07 PM, Richard Damon wrote:
> On 2/26/24 8:10 PM, olcott wrote:
>> On 2/26/2024 7:02 PM, Richard Damon wrote:
>>> On 2/26/24 12:43 PM, olcott wrote:
>>>> On 2/26/2024 2:28 AM, Mikko wrote:
>>>>> On 2024-02-25 12:33:19 +0000, immibis said:
>>>>>
>>>>>> ... and he has no doubt that the Turing Machine halting problem is
>>>>>> unsolvable, which apparently contradicts what Olcott thinks he
>>>>>> thinks.
>>>>>>
>>>>>> His most relevant belief is that the halting problem is not proven
>>>>>> unsolvable in cases where the halting decider is written in a
>>>>>> different language from the language of the program it's supposed
>>>>>> to be deciding.
>>>>>
>>>>> That is partly true. If the latter language is not Turing complete
>>>>> its halting problem may be Turing computable.
>>>>>
>>>>
>>>> His most relevant belief (and professor Stoddart concurs) is
>>>> that the halting problem cannot be solved because there is
>>>> something wrong with it.
>>>>
>>>>
>>>
>>> But that is meaningless, unless they can state WHAT is wrong with it.
>>>
>>
>> When speaking with people one must frame the ideas in a hierarchy
>> of the gist of the idea first and then the details that support
>> this gist progressively.
>>
>> immibis could not understand that professor Hehner's essential
>> claim that he espoused in many papers
>> https://www.cs.toronto.edu/~hehner/halting.html
>> was that there is something wrong with the halting problem.
>>
>>> The fact that they have shown mis-understandings about what a
>>> "Computation" is, doesn't make them a good source of "feelings" about
>>> the topic.
>>
>> The point is that there really is something wrong with the halting
>> problem.
>>
>
> Nope.
>
> You may THINK so, because you have wrong presuppositions, but unless you
> can actually PROVE it to be wrong, you just have NOTHING but lies.

Ĥ.q0 ⟨Ĥ⟩ ⊢* H.q0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qy ∞ // Ĥ applied to ⟨Ĥ⟩ halts
Ĥ.q0 ⟨Ĥ⟩ ⊢* H.q0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qn // Ĥ applied to ⟨Ĥ⟩ does not halt

When a halt decider is assumed to be required to report on
the computation that its input represents that means that
Ĥ applied to ⟨Ĥ⟩ is reporting on itself.

*That means that Ĥ applied to ⟨Ĥ⟩ IS SELF-CONTRADICTORY*

--
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 2/26/24 9:32 PM, olcott wrote:
> On 2/26/2024 8:07 PM, Richard Damon wrote:
>> On 2/26/24 8:10 PM, olcott wrote:
>>> On 2/26/2024 7:02 PM, Richard Damon wrote:
>>>> On 2/26/24 12:43 PM, olcott wrote:
>>>>> On 2/26/2024 2:28 AM, Mikko wrote:
>>>>>> On 2024-02-25 12:33:19 +0000, immibis said:
>>>>>>
>>>>>>> ... and he has no doubt that the Turing Machine halting problem
>>>>>>> is unsolvable, which apparently contradicts what Olcott thinks he
>>>>>>> thinks.
>>>>>>>
>>>>>>> His most relevant belief is that the halting problem is not
>>>>>>> proven unsolvable in cases where the halting decider is written
>>>>>>> in a different language from the language of the program it's
>>>>>>> supposed to be deciding.
>>>>>>
>>>>>> That is partly true. If the latter language is not Turing complete
>>>>>> its halting problem may be Turing computable.
>>>>>>
>>>>>
>>>>> His most relevant belief (and professor Stoddart concurs) is
>>>>> that the halting problem cannot be solved because there is
>>>>> something wrong with it.
>>>>>
>>>>>
>>>>
>>>> But that is meaningless, unless they can state WHAT is wrong with it.
>>>>
>>>
>>> When speaking with people one must frame the ideas in a hierarchy
>>> of the gist of the idea first and then the details that support
>>> this gist progressively.
>>>
>>> immibis could not understand that professor Hehner's essential
>>> claim that he espoused in many papers
>>> https://www.cs.toronto.edu/~hehner/halting.html
>>> was that there is something wrong with the halting problem.
>>>
>>>> The fact that they have shown mis-understandings about what a
>>>> "Computation" is, doesn't make them a good source of "feelings"
>>>> about the topic.
>>>
>>> The point is that there really is something wrong with the halting
>>> problem.
>>>
>>
>> Nope.
>>
>> You may THINK so, because you have wrong presuppositions, but unless
>> you can actually PROVE it to be wrong, you just have NOTHING but lies.
>
> Ĥ.q0 ⟨Ĥ⟩ ⊢* H.q0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qy ∞ // Ĥ applied to ⟨Ĥ⟩ halts
> Ĥ.q0 ⟨Ĥ⟩ ⊢* H.q0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qn   // Ĥ applied to ⟨Ĥ⟩ does not halt
>
> When a halt decider is assumed to be required to report on
> the computation that its input represents that means that
> Ĥ applied to ⟨Ĥ⟩ is reporting on itself.
>
> *That means that Ĥ applied to ⟨Ĥ⟩ IS SELF-CONTRADICTORY*
>

If you ASSUME the existance of something, a contradiction doesn't mean
that something is self-contradictory, but that the thing never actually
existed.

There IS NO H, and thus NO H^ to be "self-contradictory"

When you shift to your "infinite set" where you let H's exist that don't
meet the requirments, we see that H^ isn't SELF-Contradictory, but
H-Contradictory, which isn't an error, but makes the problem non-computable.

On 2/26/2024 9:10 PM, Richard Damon wrote:
> On 2/26/24 9:32 PM, olcott wrote:
>> On 2/26/2024 8:07 PM, Richard Damon wrote:
>>> On 2/26/24 8:10 PM, olcott wrote:
>>>> On 2/26/2024 7:02 PM, Richard Damon wrote:
>>>>> On 2/26/24 12:43 PM, olcott wrote:
>>>>>> On 2/26/2024 2:28 AM, Mikko wrote:
>>>>>>> On 2024-02-25 12:33:19 +0000, immibis said:
>>>>>>>
>>>>>>>> ... and he has no doubt that the Turing Machine halting problem
>>>>>>>> is unsolvable, which apparently contradicts what Olcott thinks
>>>>>>>> he thinks.
>>>>>>>>
>>>>>>>> His most relevant belief is that the halting problem is not
>>>>>>>> proven unsolvable in cases where the halting decider is written
>>>>>>>> in a different language from the language of the program it's
>>>>>>>> supposed to be deciding.
>>>>>>>
>>>>>>> That is partly true. If the latter language is not Turing complete
>>>>>>> its halting problem may be Turing computable.
>>>>>>>
>>>>>>
>>>>>> His most relevant belief (and professor Stoddart concurs) is
>>>>>> that the halting problem cannot be solved because there is
>>>>>> something wrong with it.
>>>>>>
>>>>>>
>>>>>
>>>>> But that is meaningless, unless they can state WHAT is wrong with it.
>>>>>
>>>>
>>>> When speaking with people one must frame the ideas in a hierarchy
>>>> of the gist of the idea first and then the details that support
>>>> this gist progressively.
>>>>
>>>> immibis could not understand that professor Hehner's essential
>>>> claim that he espoused in many papers
>>>> https://www.cs.toronto.edu/~hehner/halting.html
>>>> was that there is something wrong with the halting problem.
>>>>
>>>>> The fact that they have shown mis-understandings about what a
>>>>> "Computation" is, doesn't make them a good source of "feelings"
>>>>> about the topic.
>>>>
>>>> The point is that there really is something wrong with the halting
>>>> problem.
>>>>
>>>
>>> Nope.
>>>
>>> You may THINK so, because you have wrong presuppositions, but unless
>>> you can actually PROVE it to be wrong, you just have NOTHING but lies.
>>
>> Ĥ.q0 ⟨Ĥ⟩ ⊢* H.q0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qy ∞ // Ĥ applied to ⟨Ĥ⟩ halts
>> Ĥ.q0 ⟨Ĥ⟩ ⊢* H.q0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qn   // Ĥ applied to ⟨Ĥ⟩ does not halt
>>
>> When a halt decider is assumed to be required to report on
>> the computation that its input represents that means that
>> Ĥ applied to ⟨Ĥ⟩ is reporting on itself.
>>
>> *That means that Ĥ applied to ⟨Ĥ⟩ IS SELF-CONTRADICTORY*
>>
>
>
> If you ASSUME the existance of something, a contradiction doesn't mean
> that something is self-contradictory, but that the thing never actually
> existed.

By your reasoning the Liar Paradox does not exist.

When we have a set of hypothetical concepts that
specify incoherence these incoherent concepts do exist.

We can see this incoherence and can't just close our
eyes and pretend it does not exist.

> There IS NO H, and thus NO H^ to be "self-contradictory"
>

There is an H and an Ĥ as hypothetical concepts that
exist incoherently.

I am happy to say that it seems like you may have a
genuine misunderstanding.

> When you shift to your "infinite set" where you let H's exist that don't
> meet the requirments, we see that H^ isn't SELF-Contradictory, but
> H-Contradictory, which isn't an error, but makes the problem
> non-computable.
>

--
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 2/26/24 10:34 PM, olcott wrote:
> On 2/26/2024 9:10 PM, Richard Damon wrote:
>> On 2/26/24 9:32 PM, olcott wrote:
>>> On 2/26/2024 8:07 PM, Richard Damon wrote:
>>>> On 2/26/24 8:10 PM, olcott wrote:
>>>>> On 2/26/2024 7:02 PM, Richard Damon wrote:
>>>>>> On 2/26/24 12:43 PM, olcott wrote:
>>>>>>> On 2/26/2024 2:28 AM, Mikko wrote:
>>>>>>>> On 2024-02-25 12:33:19 +0000, immibis said:
>>>>>>>>
>>>>>>>>> ... and he has no doubt that the Turing Machine halting problem
>>>>>>>>> is unsolvable, which apparently contradicts what Olcott thinks
>>>>>>>>> he thinks.
>>>>>>>>>
>>>>>>>>> His most relevant belief is that the halting problem is not
>>>>>>>>> proven unsolvable in cases where the halting decider is written
>>>>>>>>> in a different language from the language of the program it's
>>>>>>>>> supposed to be deciding.
>>>>>>>>
>>>>>>>> That is partly true. If the latter language is not Turing complete
>>>>>>>> its halting problem may be Turing computable.
>>>>>>>>
>>>>>>>
>>>>>>> His most relevant belief (and professor Stoddart concurs) is
>>>>>>> that the halting problem cannot be solved because there is
>>>>>>> something wrong with it.
>>>>>>>
>>>>>>>
>>>>>>
>>>>>> But that is meaningless, unless they can state WHAT is wrong with it.
>>>>>>
>>>>>
>>>>> When speaking with people one must frame the ideas in a hierarchy
>>>>> of the gist of the idea first and then the details that support
>>>>> this gist progressively.
>>>>>
>>>>> immibis could not understand that professor Hehner's essential
>>>>> claim that he espoused in many papers
>>>>> https://www.cs.toronto.edu/~hehner/halting.html
>>>>> was that there is something wrong with the halting problem.
>>>>>
>>>>>> The fact that they have shown mis-understandings about what a
>>>>>> "Computation" is, doesn't make them a good source of "feelings"
>>>>>> about the topic.
>>>>>
>>>>> The point is that there really is something wrong with the halting
>>>>> problem.
>>>>>
>>>>
>>>> Nope.
>>>>
>>>> You may THINK so, because you have wrong presuppositions, but unless
>>>> you can actually PROVE it to be wrong, you just have NOTHING but lies.
>>>
>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* H.q0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qy ∞ // Ĥ applied to ⟨Ĥ⟩ halts
>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* H.q0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qn   // Ĥ applied to ⟨Ĥ⟩ does not halt
>>>
>>> When a halt decider is assumed to be required to report on
>>> the computation that its input represents that means that
>>> Ĥ applied to ⟨Ĥ⟩ is reporting on itself.
>>>
>>> *That means that Ĥ applied to ⟨Ĥ⟩ IS SELF-CONTRADICTORY*
>>>
>>
>>
>> If you ASSUME the existance of something, a contradiction doesn't mean
>> that something is self-contradictory, but that the thing never
>> actually existed.
>
> By your reasoning the Liar Paradox does not exist.

Not what I said.

If a consistent system of logic, with an added hypothetical yields a
contradiction, that hypothetical is wrong.

I suppose you could say the Liar Paradox doesn't exist IN A CONSISTANT
SYSTEM, as it was defined out of it by consistancy.

>
> When we have a set of hypothetical concepts that
> specify incoherence these incoherent concepts do exist.ot

So If we assume that Purple Unicorns are yellow, we have shown that
Uncorns exist?

what I said.
>
> We can see this incoherence and can't just close our
> eyes and pretend it does not exist.

Except the problem is that your H and H^ don't exist, and thus can't be
in actual contradiction.

>
>> There IS NO H, and thus NO H^ to be "self-contradictory"
>>
>
> There is an H and an Ĥ as hypothetical concepts that
> exist incoherently.

Nope, it is the existance of an H that is correct that is incoherent. So
neither of them actually exist in a consistent logic system.

I guess that is the problem, you don't use Consistant Logic system, so
all your work has blown itself up in the internal contradicitions in
your system.

>
> I am happy to say that it seems like you may have a
> genuine misunderstanding.

Nope, you do.

>
>> When you shift to your "infinite set" where you let H's exist that
>> don't meet the requirments, we see that H^ isn't SELF-Contradictory,
>> but H-Contradictory, which isn't an error, but makes the problem
>> non-computable.
>>
>

On 2/26/2024 9:55 PM, Richard Damon wrote:
> On 2/26/24 10:34 PM, olcott wrote:
>> On 2/26/2024 9:10 PM, Richard Damon wrote:
>>> On 2/26/24 9:32 PM, olcott wrote:
>>>> On 2/26/2024 8:07 PM, Richard Damon wrote:
>>>>> On 2/26/24 8:10 PM, olcott wrote:
>>>>>> On 2/26/2024 7:02 PM, Richard Damon wrote:
>>>>>>> On 2/26/24 12:43 PM, olcott wrote:
>>>>>>>> On 2/26/2024 2:28 AM, Mikko wrote:
>>>>>>>>> On 2024-02-25 12:33:19 +0000, immibis said:
>>>>>>>>>
>>>>>>>>>> ... and he has no doubt that the Turing Machine halting
>>>>>>>>>> problem is unsolvable, which apparently contradicts what
>>>>>>>>>> Olcott thinks he thinks.
>>>>>>>>>>
>>>>>>>>>> His most relevant belief is that the halting problem is not
>>>>>>>>>> proven unsolvable in cases where the halting decider is
>>>>>>>>>> written in a different language from the language of the
>>>>>>>>>> program it's supposed to be deciding.
>>>>>>>>>
>>>>>>>>> That is partly true. If the latter language is not Turing complete
>>>>>>>>> its halting problem may be Turing computable.
>>>>>>>>>
>>>>>>>>
>>>>>>>> His most relevant belief (and professor Stoddart concurs) is
>>>>>>>> that the halting problem cannot be solved because there is
>>>>>>>> something wrong with it.
>>>>>>>>
>>>>>>>>
>>>>>>>
>>>>>>> But that is meaningless, unless they can state WHAT is wrong with
>>>>>>> it.
>>>>>>>
>>>>>>
>>>>>> When speaking with people one must frame the ideas in a hierarchy
>>>>>> of the gist of the idea first and then the details that support
>>>>>> this gist progressively.
>>>>>>
>>>>>> immibis could not understand that professor Hehner's essential
>>>>>> claim that he espoused in many papers
>>>>>> https://www.cs.toronto.edu/~hehner/halting.html
>>>>>> was that there is something wrong with the halting problem.
>>>>>>
>>>>>>> The fact that they have shown mis-understandings about what a
>>>>>>> "Computation" is, doesn't make them a good source of "feelings"
>>>>>>> about the topic.
>>>>>>
>>>>>> The point is that there really is something wrong with the halting
>>>>>> problem.
>>>>>>
>>>>>
>>>>> Nope.
>>>>>
>>>>> You may THINK so, because you have wrong presuppositions, but
>>>>> unless you can actually PROVE it to be wrong, you just have NOTHING
>>>>> but lies.
>>>>
>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* H.q0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qy ∞ // Ĥ applied to ⟨Ĥ⟩ halts
>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* H.q0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qn   // Ĥ applied to ⟨Ĥ⟩ does not halt
>>>>
>>>> When a halt decider is assumed to be required to report on
>>>> the computation that its input represents that means that
>>>> Ĥ applied to ⟨Ĥ⟩ is reporting on itself.
>>>>
>>>> *That means that Ĥ applied to ⟨Ĥ⟩ IS SELF-CONTRADICTORY*
>>>>
>>>
>>>
>>> If you ASSUME the existance of something, a contradiction doesn't
>>> mean that something is self-contradictory, but that the thing never
>>> actually existed.
>>
>> By your reasoning the Liar Paradox does not exist.
>
> Not what I said.
>
> If a consistent system of logic, with an added hypothetical yields a
> contradiction, that hypothetical is wrong.
>
> I suppose you could say the Liar Paradox doesn't exist IN A CONSISTANT
> SYSTEM, as it was defined out of it by consistancy.
>
>>
>> When we have a set of hypothetical concepts that
>> specify incoherence these incoherent concepts do exist.ot
>
> So If we assume that Purple Unicorns are yellow, we have shown that
> Uncorns exist?
>
>
> what I said.
>>
>> We can see this incoherence and can't just close our
>> eyes and pretend it does not exist.
>
> Except the problem is that your H and H^ don't exist, and thus can't be
> in actual contradiction.

The incoherent notions of H and Ĥ do exist as incoherent
notions that can be verified to be incoherent.

You are trying to get away with claiming that incoherent
notions cannot be verified as incoherent because they
do not even exist as incoherent notions.

--
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 27/02/24 03:32, olcott wrote:
> On 2/26/2024 8:07 PM, Richard Damon wrote:
>> On 2/26/24 8:10 PM, olcott wrote:
>>> On 2/26/2024 7:02 PM, Richard Damon wrote:
>>>> On 2/26/24 12:43 PM, olcott wrote:
>>>>> On 2/26/2024 2:28 AM, Mikko wrote:
>>>>>> On 2024-02-25 12:33:19 +0000, immibis said:
>>>>>>
>>>>>>> ... and he has no doubt that the Turing Machine halting problem
>>>>>>> is unsolvable, which apparently contradicts what Olcott thinks he
>>>>>>> thinks.
>>>>>>>
>>>>>>> His most relevant belief is that the halting problem is not
>>>>>>> proven unsolvable in cases where the halting decider is written
>>>>>>> in a different language from the language of the program it's
>>>>>>> supposed to be deciding.
>>>>>>
>>>>>> That is partly true. If the latter language is not Turing complete
>>>>>> its halting problem may be Turing computable.
>>>>>>
>>>>>
>>>>> His most relevant belief (and professor Stoddart concurs) is
>>>>> that the halting problem cannot be solved because there is
>>>>> something wrong with it.
>>>>>
>>>>>
>>>>
>>>> But that is meaningless, unless they can state WHAT is wrong with it.
>>>>
>>>
>>> When speaking with people one must frame the ideas in a hierarchy
>>> of the gist of the idea first and then the details that support
>>> this gist progressively.
>>>
>>> immibis could not understand that professor Hehner's essential
>>> claim that he espoused in many papers
>>> https://www.cs.toronto.edu/~hehner/halting.html
>>> was that there is something wrong with the halting problem.
>>>
>>>> The fact that they have shown mis-understandings about what a
>>>> "Computation" is, doesn't make them a good source of "feelings"
>>>> about the topic.
>>>
>>> The point is that there really is something wrong with the halting
>>> problem.
>>>
>>
>> Nope.
>>
>> You may THINK so, because you have wrong presuppositions, but unless
>> you can actually PROVE it to be wrong, you just have NOTHING but lies.
>
> Ĥ.q0 ⟨Ĥ⟩ ⊢* H.q0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qy ∞ // Ĥ applied to ⟨Ĥ⟩ halts
> Ĥ.q0 ⟨Ĥ⟩ ⊢* H.q0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qn   // Ĥ applied to ⟨Ĥ⟩ does not halt
>
> When a halt decider is assumed to be required to report on
> the computation that its input represents that means that
> Ĥ applied to ⟨Ĥ⟩ is reporting on itself.
>
> *That means that Ĥ applied to ⟨Ĥ⟩ IS SELF-CONTRADICTORY*
>

An application of a Turing machine to input cannot be
self-contradictory. Do you know what self-contradictory means?

Self-contradictory means x=¬x

Applying Ĥ to ⟨Ĥ⟩ simply results in it halting or not halting. There's
no self-contradictory. Either Ĥ(⟨Ĥ⟩) halts or it doesn't halt.

On 27/02/24 04:34, olcott wrote:
> On 2/26/2024 9:10 PM, Richard Damon wrote:
>> On 2/26/24 9:32 PM, olcott wrote:
>>> On 2/26/2024 8:07 PM, Richard Damon wrote:
>>>> On 2/26/24 8:10 PM, olcott wrote:
>>>>> On 2/26/2024 7:02 PM, Richard Damon wrote:
>>>>>> On 2/26/24 12:43 PM, olcott wrote:
>>>>>>> On 2/26/2024 2:28 AM, Mikko wrote:
>>>>>>>> On 2024-02-25 12:33:19 +0000, immibis said:
>>>>>>>>
>>>>>>>>> ... and he has no doubt that the Turing Machine halting problem
>>>>>>>>> is unsolvable, which apparently contradicts what Olcott thinks
>>>>>>>>> he thinks.
>>>>>>>>>
>>>>>>>>> His most relevant belief is that the halting problem is not
>>>>>>>>> proven unsolvable in cases where the halting decider is written
>>>>>>>>> in a different language from the language of the program it's
>>>>>>>>> supposed to be deciding.
>>>>>>>>
>>>>>>>> That is partly true. If the latter language is not Turing complete
>>>>>>>> its halting problem may be Turing computable.
>>>>>>>>
>>>>>>>
>>>>>>> His most relevant belief (and professor Stoddart concurs) is
>>>>>>> that the halting problem cannot be solved because there is
>>>>>>> something wrong with it.
>>>>>>>
>>>>>>>
>>>>>>
>>>>>> But that is meaningless, unless they can state WHAT is wrong with it.
>>>>>>
>>>>>
>>>>> When speaking with people one must frame the ideas in a hierarchy
>>>>> of the gist of the idea first and then the details that support
>>>>> this gist progressively.
>>>>>
>>>>> immibis could not understand that professor Hehner's essential
>>>>> claim that he espoused in many papers
>>>>> https://www.cs.toronto.edu/~hehner/halting.html
>>>>> was that there is something wrong with the halting problem.
>>>>>
>>>>>> The fact that they have shown mis-understandings about what a
>>>>>> "Computation" is, doesn't make them a good source of "feelings"
>>>>>> about the topic.
>>>>>
>>>>> The point is that there really is something wrong with the halting
>>>>> problem.
>>>>>
>>>>
>>>> Nope.
>>>>
>>>> You may THINK so, because you have wrong presuppositions, but unless
>>>> you can actually PROVE it to be wrong, you just have NOTHING but lies.
>>>
>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* H.q0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qy ∞ // Ĥ applied to ⟨Ĥ⟩ halts
>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* H.q0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qn   // Ĥ applied to ⟨Ĥ⟩ does not halt
>>>
>>> When a halt decider is assumed to be required to report on
>>> the computation that its input represents that means that
>>> Ĥ applied to ⟨Ĥ⟩ is reporting on itself.
>>>
>>> *That means that Ĥ applied to ⟨Ĥ⟩ IS SELF-CONTRADICTORY*
>>>
>>
>>
>> If you ASSUME the existance of something, a contradiction doesn't mean
>> that something is self-contradictory, but that the thing never
>> actually existed.
>
> By your reasoning the Liar Paradox does not exist.

That's correct. There is no Liar Paradox in mathematical logic because
it does not exist. Try to write the Liar Paradox as a well-formed
formula and you will see.

> When we have a set of hypothetical concepts that
> specify incoherence these incoherent concepts do exist.
>
> We can see this incoherence and can't just close our
> eyes and pretend it does not exist.
>
>> There IS NO H, and thus NO H^ to be "self-contradictory"
>>
>
> There is an H and an Ĥ as hypothetical concepts that
> exist incoherently.

Then you have to make them coherent.

On 27/02/24 05:01, olcott wrote:
> On 2/26/2024 9:55 PM, Richard Damon wrote:
>> On 2/26/24 10:34 PM, olcott wrote:
>>> On 2/26/2024 9:10 PM, Richard Damon wrote:
>>>> On 2/26/24 9:32 PM, olcott wrote:
>>>>> On 2/26/2024 8:07 PM, Richard Damon wrote:
>>>>>> On 2/26/24 8:10 PM, olcott wrote:
>>>>>>> On 2/26/2024 7:02 PM, Richard Damon wrote:
>>>>>>>> On 2/26/24 12:43 PM, olcott wrote:
>>>>>>>>> On 2/26/2024 2:28 AM, Mikko wrote:
>>>>>>>>>> On 2024-02-25 12:33:19 +0000, immibis said:
>>>>>>>>>>
>>>>>>>>>>> ... and he has no doubt that the Turing Machine halting
>>>>>>>>>>> problem is unsolvable, which apparently contradicts what
>>>>>>>>>>> Olcott thinks he thinks.
>>>>>>>>>>>
>>>>>>>>>>> His most relevant belief is that the halting problem is not
>>>>>>>>>>> proven unsolvable in cases where the halting decider is
>>>>>>>>>>> written in a different language from the language of the
>>>>>>>>>>> program it's supposed to be deciding.
>>>>>>>>>>
>>>>>>>>>> That is partly true. If the latter language is not Turing
>>>>>>>>>> complete
>>>>>>>>>> its halting problem may be Turing computable.
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> His most relevant belief (and professor Stoddart concurs) is
>>>>>>>>> that the halting problem cannot be solved because there is
>>>>>>>>> something wrong with it.
>>>>>>>>>
>>>>>>>>>
>>>>>>>>
>>>>>>>> But that is meaningless, unless they can state WHAT is wrong
>>>>>>>> with it.
>>>>>>>>
>>>>>>>
>>>>>>> When speaking with people one must frame the ideas in a hierarchy
>>>>>>> of the gist of the idea first and then the details that support
>>>>>>> this gist progressively.
>>>>>>>
>>>>>>> immibis could not understand that professor Hehner's essential
>>>>>>> claim that he espoused in many papers
>>>>>>> https://www.cs.toronto.edu/~hehner/halting.html
>>>>>>> was that there is something wrong with the halting problem.
>>>>>>>
>>>>>>>> The fact that they have shown mis-understandings about what a
>>>>>>>> "Computation" is, doesn't make them a good source of "feelings"
>>>>>>>> about the topic.
>>>>>>>
>>>>>>> The point is that there really is something wrong with the
>>>>>>> halting problem.
>>>>>>>
>>>>>>
>>>>>> Nope.
>>>>>>
>>>>>> You may THINK so, because you have wrong presuppositions, but
>>>>>> unless you can actually PROVE it to be wrong, you just have
>>>>>> NOTHING but lies.
>>>>>
>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* H.q0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qy ∞ // Ĥ applied to ⟨Ĥ⟩ halts
>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* H.q0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qn   // Ĥ applied to ⟨Ĥ⟩ does not halt
>>>>>
>>>>> When a halt decider is assumed to be required to report on
>>>>> the computation that its input represents that means that
>>>>> Ĥ applied to ⟨Ĥ⟩ is reporting on itself.
>>>>>
>>>>> *That means that Ĥ applied to ⟨Ĥ⟩ IS SELF-CONTRADICTORY*
>>>>>
>>>>
>>>>
>>>> If you ASSUME the existance of something, a contradiction doesn't
>>>> mean that something is self-contradictory, but that the thing never
>>>> actually existed.
>>>
>>> By your reasoning the Liar Paradox does not exist.
>>
>> Not what I said.
>>
>> If a consistent system of logic, with an added hypothetical yields a
>> contradiction, that hypothetical is wrong.
>>
>> I suppose you could say the Liar Paradox doesn't exist IN A CONSISTANT
>> SYSTEM, as it was defined out of it by consistancy.
>>
>>>
>>> When we have a set of hypothetical concepts that
>>> specify incoherence these incoherent concepts do exist.ot
>>
>> So If we assume that Purple Unicorns are yellow, we have shown that
>> Uncorns exist?
>>
>>
>> what I said.
>>>
>>> We can see this incoherence and can't just close our
>>> eyes and pretend it does not exist.
>>
>> Except the problem is that your H and H^ don't exist, and thus can't
>> be in actual contradiction.
>
> The incoherent notions of H and Ĥ do exist as incoherent
> notions that can be verified to be incoherent.

Incoherent notions have no place in mathematics.

> You are trying to get away with claiming that incoherent
> notions cannot be verified as incoherent because they
> do not even exist as incoherent notions.

You can assume wrong things for the purpose of proof by contradiction.