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Groups > comp.software-eng > #3751 > unrolled thread
| Started by | olcott <polcott333@gmail.com> |
|---|---|
| First post | 2026-01-06 22:44 -0600 |
| Last post | 2026-01-09 09:47 -0600 |
| Articles | 20 on this page of 50 — 4 participants |
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The Halting Problem asks for too much olcott <polcott333@gmail.com> - 2026-01-06 22:44 -0600
Re: The Halting Problem asks for too much Mikko <mikko.levanto@iki.fi> - 2026-01-07 13:49 +0200
Re: The Halting Problem asks for too much olcott <polcott333@gmail.com> - 2026-01-07 05:54 -0600
Re: The Halting Problem asks for too much Mikko <mikko.levanto@iki.fi> - 2026-01-08 12:22 +0200
Re: The Halting Problem asks for too much olcott <polcott333@gmail.com> - 2026-01-08 08:22 -0600
Re: The Halting Problem asks for too much Mikko <mikko.levanto@iki.fi> - 2026-01-09 11:59 +0200
Re: The Halting Problem asks for too much olcott <polcott333@gmail.com> - 2026-01-09 09:52 -0600
Re: The Halting Problem asks for too much Mikko <mikko.levanto@iki.fi> - 2026-01-10 10:23 +0200
Re: The Halting Problem asks for too much olcott <polcott333@gmail.com> - 2026-01-10 09:47 -0600
Re: The Halting Problem asks for too much Richard Damon <news.x.richarddamon@xoxy.net> - 2026-01-10 18:19 -0500
Re: The Halting Problem asks for too much olcott <polcott333@gmail.com> - 2026-01-10 18:13 -0600
Re: The Halting Problem asks for too much Richard Damon <news.x.richarddamon@xoxy.net> - 2026-01-10 19:35 -0500
Re: The Halting Problem asks for too much olcott <polcott333@gmail.com> - 2026-01-10 18:52 -0600
Re: The Halting Problem asks for too much Richard Damon <news.x.richarddamon@xoxy.net> - 2026-01-10 21:03 -0500
Re: The Halting Problem asks for too much olcott <polcott333@gmail.com> - 2026-01-10 20:22 -0600
Re: The Halting Problem asks for too much Richard Damon <news.x.richarddamon@xoxy.net> - 2026-01-10 21:34 -0500
Computation and Undecidability olcott <polcott333@gmail.com> - 2026-01-10 21:24 -0600
Re: Computation and Undecidability Richard Damon <news.x.richarddamon@xoxy.net> - 2026-01-10 22:32 -0500
Re: The Halting Problem asks for too much Mikko <mikko.levanto@iki.fi> - 2026-01-11 12:13 +0200
Re: The Halting Problem asks for too much olcott <polcott333@gmail.com> - 2026-01-11 08:18 -0600
Re: The Halting Problem asks for too much Mikko <mikko.levanto@iki.fi> - 2026-01-12 12:44 +0200
Re: The Halting Problem asks for too much Mikko <mikko.levanto@iki.fi> - 2026-01-11 12:22 +0200
Re: The Halting Problem asks for too much olcott <polcott333@gmail.com> - 2026-01-11 08:23 -0600
Re: The Halting Problem asks for too much Mikko <mikko.levanto@iki.fi> - 2026-01-12 12:51 +0200
Re: The Halting Problem asks for too much olcott <polcott333@gmail.com> - 2026-01-12 08:43 -0600
Re: The Halting Problem asks for too much Richard Damon <Richard@Damon-Family.org> - 2026-01-12 22:22 -0500
Re: The Halting Problem asks for too much Mikko <mikko.levanto@iki.fi> - 2026-01-13 10:46 +0200
Re: The Halting Problem asks for too much olcott <polcott333@gmail.com> - 2026-01-13 08:17 -0600
Re: The Halting Problem asks for too much Mikko <mikko.levanto@iki.fi> - 2026-01-14 09:58 +0200
Re: The Halting Problem asks for too much Mikko <mikko.levanto@iki.fi> - 2026-01-14 11:04 +0200
Re: The Halting Problem asks for too much olcott <polcott333@gmail.com> - 2026-01-14 13:35 -0600
Re: The Halting Problem asks for too much Mikko <mikko.levanto@iki.fi> - 2026-01-15 11:21 +0200
Computation and Undecidability olcott <polcott333@gmail.com> - 2026-01-10 17:19 -0600
Re: Computation and Undecidability Richard Damon <news.x.richarddamon@xoxy.net> - 2026-01-10 19:35 -0500
Re: Computation and Undecidability olcott <polcott333@gmail.com> - 2026-01-10 19:03 -0600
Re: Computation and Undecidability Richard Damon <news.x.richarddamon@xoxy.net> - 2026-01-10 21:03 -0500
Re: Computation and Undecidability olcott <polcott333@gmail.com> - 2026-01-10 20:20 -0600
Re: Computation and Undecidability Richard Damon <news.x.richarddamon@xoxy.net> - 2026-01-10 21:33 -0500
Re: Computation and Undecidability olcott <polcott333@gmail.com> - 2026-01-10 21:18 -0600
Re: Computation and Undecidability Richard Damon <news.x.richarddamon@xoxy.net> - 2026-01-10 22:30 -0500
Re: Computation and Undecidability olcott <polcott333@gmail.com> - 2026-01-10 19:05 -0600
Re: Computation and Undecidability Richard Damon <news.x.richarddamon@xoxy.net> - 2026-01-10 21:03 -0500
Re: Computation and Undecidability olcott <polcott333@gmail.com> - 2026-01-10 20:09 -0600
Re: Computation and Undecidability Richard Damon <news.x.richarddamon@xoxy.net> - 2026-01-10 21:33 -0500
Re: Computation and Undecidability olcott <polcott333@gmail.com> - 2026-01-10 21:16 -0600
Re: Computation and Undecidability Richard Damon <news.x.richarddamon@xoxy.net> - 2026-01-10 22:28 -0500
Re: Computation and Undecidability olcott <polcott333@gmail.com> - 2026-01-10 21:34 -0600
Re: Computation and Undecidability Richard Damon <news.x.richarddamon@xoxy.net> - 2026-01-11 06:31 -0500
Re: Computation and Undecidability olcott <polcott333@gmail.com> - 2026-01-11 08:03 -0600
Haskell Curry Foundations of Mathematical Logic sense of true in the system olcott <polcott333@gmail.com> - 2026-01-09 09:47 -0600
Page 2 of 3 — ← Prev page 1 [2] 3 Next page →
| From | Mikko <mikko.levanto@iki.fi> |
|---|---|
| Date | 2026-01-12 12:44 +0200 |
| Message-ID | <10k2jb6$29881$1@dont-email.me> |
| In reply to | #3799 |
On 11/01/2026 16:18, olcott wrote:
> On 1/11/2026 4:13 AM, Mikko wrote:
>> On 10/01/2026 17:47, olcott wrote:
>>> On 1/10/2026 2:23 AM, Mikko wrote:
>>>> On 09/01/2026 17:52, olcott wrote:
>>>>> On 1/9/2026 3:59 AM, Mikko wrote:
>>>>>> On 08/01/2026 16:22, olcott wrote:
>>>>>>> On 1/8/2026 4:22 AM, Mikko wrote:
>>>>>>>> On 07/01/2026 13:54, olcott wrote:
>>>>>>>>> On 1/7/2026 5:49 AM, Mikko wrote:
>>>>>>>>>> On 07/01/2026 06:44, olcott wrote:
>>>>>>>>>>> All deciders essentially: Transform finite string
>>>>>>>>>>> inputs by finite string transformation rules into
>>>>>>>>>>> {Accept, Reject} values.
>>>>>>>>>>>
>>>>>>>>>>> The counter-example input to requires more than
>>>>>>>>>>> can be derived from finite string transformation
>>>>>>>>>>> rules applied to this specific input thus the
>>>>>>>>>>> Halting Problem requires too much.
>>>>>>>>>
>>>>>>>>>> In a sense the halting problem asks too much: the problem is
>>>>>>>>>> proven to
>>>>>>>>>> be unsolvable. In another sense it asks too little: usually we
>>>>>>>>>> want to
>>>>>>>>>> know whether a method halts on every input, not just one.
>>>>>>>>>>
>>>>>>>>>> Although the halting problem is unsolvable, there are partial
>>>>>>>>>> solutions
>>>>>>>>>> to the halting problem. In particular, every counter-example
>>>>>>>>>> to the
>>>>>>>>>> full solution is correctly solved by some partial deciders.
>>>>>>>>>
>>>>>>>>> *if undecidability is correct then truth itself is broken*
>>>>>>>>
>>>>>>>> Depends on whether the word "truth" is interpeted in the standard
>>>>>>>> sense or in Olcott's sense.
>>>>>>>
>>>>>>> Undecidability is misconception. Self-contradictory
>>>>>>> expressions are correctly rejected as semantically
>>>>>>> incoherent thus form no undecidability or incompleteness.
>>>>>>
>>>>>> The misconception is yours. No expression in the language of the
>>>>>> first
>>>>>> order group theory is self-contradictory. But the first order goupr
>>>>>> theory is incomplete: it is impossible to prove that AB = BA is true
>>>>>> for every A and every B but it is also impossible to prove that AB
>>>>>> = BA
>>>>>> is false for some A and some B.
>>>>>>
>>>>>
>>>>> All deciders essentially: Transform finite string
>>>>> inputs by finite string transformation rules into
>>>>> {Accept, Reject} values.
>>>>>
>>>>> When a required result cannot be derived by applying
>>>>> finite string transformation rules to actual finite
>>>>> string inputs, then the required result exceeds the
>>>>> scope of computation and must be rejected as an
>>>>> incorrect requirement.
>>>>
>>>> No, that does not follow. If a required result cannot be derived by
>>>> appying a finite string transformation then the it it is uncomputable.
>>>
>>> Right. Outside the scope of computation. Requiring anything
>>> outside the scope of computation is an incorrect requirement.
>>
>> You can't determine whether the required result is computable before
>> you have the requirement.
>
> *Computation and Undecidability*
> https://philpapers.org/go.pl?aid=OLCCAU
>
> We know that there does not exist any finite
> string transformations that H can apply to its
> input P to derive the halt status of any P
> that does the opposite of whatever H returns.
Which only nmakes sense when the requirement that H must determine
whether the computation presented by its input halts has already
been presented.
> *ChatGPT explains how and why I am correct*
>
> *Reinterpretation of undecidability*
> The example of P and H demonstrates that what is
> often called “undecidable” is better understood as
> ill-posed with respect to computable semantics.
> When the specification is constrained to properties
> detectable via finite simulation and finite pattern
> recognition, computation proceeds normally and
> correctly. Undecidability only appears when the
> specification overreaches that boundary.
It tries to explain but it does not prove.
--
Mikko
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| From | Mikko <mikko.levanto@iki.fi> |
|---|---|
| Date | 2026-01-11 12:22 +0200 |
| Message-ID | <10jvtkc$3qq6h$1@dont-email.me> |
| In reply to | #3770 |
On 10/01/2026 17:47, olcott wrote:
> On 1/10/2026 2:23 AM, Mikko wrote:
>> On 09/01/2026 17:52, olcott wrote:
>>> On 1/9/2026 3:59 AM, Mikko wrote:
>>>> On 08/01/2026 16:22, olcott wrote:
>>>>> On 1/8/2026 4:22 AM, Mikko wrote:
>>>>>> On 07/01/2026 13:54, olcott wrote:
>>>>>>> On 1/7/2026 5:49 AM, Mikko wrote:
>>>>>>>> On 07/01/2026 06:44, olcott wrote:
>>>>>>>>> All deciders essentially: Transform finite string
>>>>>>>>> inputs by finite string transformation rules into
>>>>>>>>> {Accept, Reject} values.
>>>>>>>>>
>>>>>>>>> The counter-example input to requires more than
>>>>>>>>> can be derived from finite string transformation
>>>>>>>>> rules applied to this specific input thus the
>>>>>>>>> Halting Problem requires too much.
>>>>>>>
>>>>>>>> In a sense the halting problem asks too much: the problem is
>>>>>>>> proven to
>>>>>>>> be unsolvable. In another sense it asks too little: usually we
>>>>>>>> want to
>>>>>>>> know whether a method halts on every input, not just one.
>>>>>>>>
>>>>>>>> Although the halting problem is unsolvable, there are partial
>>>>>>>> solutions
>>>>>>>> to the halting problem. In particular, every counter-example to the
>>>>>>>> full solution is correctly solved by some partial deciders.
>>>>>>>
>>>>>>> *if undecidability is correct then truth itself is broken*
>>>>>>
>>>>>> Depends on whether the word "truth" is interpeted in the standard
>>>>>> sense or in Olcott's sense.
>>>>>
>>>>> Undecidability is misconception. Self-contradictory
>>>>> expressions are correctly rejected as semantically
>>>>> incoherent thus form no undecidability or incompleteness.
>>>>
>>>> The misconception is yours. No expression in the language of the first
>>>> order group theory is self-contradictory. But the first order goupr
>>>> theory is incomplete: it is impossible to prove that AB = BA is true
>>>> for every A and every B but it is also impossible to prove that AB = BA
>>>> is false for some A and some B.
>>>>
>>>
>>> All deciders essentially: Transform finite string
>>> inputs by finite string transformation rules into
>>> {Accept, Reject} values.
>>>
>>> When a required result cannot be derived by applying
>>> finite string transformation rules to actual finite
>>> string inputs, then the required result exceeds the
>>> scope of computation and must be rejected as an
>>> incorrect requirement.
>>
>> No, that does not follow. If a required result cannot be derived by
>> appying a finite string transformation then the it it is uncomputable.
>
> Right. Outside the scope of computation. Requiring anything
> outside the scope of computation is an incorrect requirement.
>
>> Of course, it one can prove that the required result is not computable
>> then that helps to avoid wasting effort to try the impossible. The
>> situation is worse if it is not known that the required result is not
>> computable.
>>
>> That something is not computable does not mean that there is anyting
>> "incorrect" in the requirement.
>
> Yes it certainly does. Requiring the impossible is always an error.
It is a perfectly valid question to ask whther a particular reuqirement
is satisfiable.
--
Mikko
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| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2026-01-11 08:23 -0600 |
| Message-ID | <10k0bo6$3uvrl$1@dont-email.me> |
| In reply to | #3796 |
On 1/11/2026 4:22 AM, Mikko wrote:
> On 10/01/2026 17:47, olcott wrote:
>> On 1/10/2026 2:23 AM, Mikko wrote:
>>> On 09/01/2026 17:52, olcott wrote:
>>>> On 1/9/2026 3:59 AM, Mikko wrote:
>>>>> On 08/01/2026 16:22, olcott wrote:
>>>>>> On 1/8/2026 4:22 AM, Mikko wrote:
>>>>>>> On 07/01/2026 13:54, olcott wrote:
>>>>>>>> On 1/7/2026 5:49 AM, Mikko wrote:
>>>>>>>>> On 07/01/2026 06:44, olcott wrote:
>>>>>>>>>> All deciders essentially: Transform finite string
>>>>>>>>>> inputs by finite string transformation rules into
>>>>>>>>>> {Accept, Reject} values.
>>>>>>>>>>
>>>>>>>>>> The counter-example input to requires more than
>>>>>>>>>> can be derived from finite string transformation
>>>>>>>>>> rules applied to this specific input thus the
>>>>>>>>>> Halting Problem requires too much.
>>>>>>>>
>>>>>>>>> In a sense the halting problem asks too much: the problem is
>>>>>>>>> proven to
>>>>>>>>> be unsolvable. In another sense it asks too little: usually we
>>>>>>>>> want to
>>>>>>>>> know whether a method halts on every input, not just one.
>>>>>>>>>
>>>>>>>>> Although the halting problem is unsolvable, there are partial
>>>>>>>>> solutions
>>>>>>>>> to the halting problem. In particular, every counter-example to
>>>>>>>>> the
>>>>>>>>> full solution is correctly solved by some partial deciders.
>>>>>>>>
>>>>>>>> *if undecidability is correct then truth itself is broken*
>>>>>>>
>>>>>>> Depends on whether the word "truth" is interpeted in the standard
>>>>>>> sense or in Olcott's sense.
>>>>>>
>>>>>> Undecidability is misconception. Self-contradictory
>>>>>> expressions are correctly rejected as semantically
>>>>>> incoherent thus form no undecidability or incompleteness.
>>>>>
>>>>> The misconception is yours. No expression in the language of the first
>>>>> order group theory is self-contradictory. But the first order goupr
>>>>> theory is incomplete: it is impossible to prove that AB = BA is true
>>>>> for every A and every B but it is also impossible to prove that AB
>>>>> = BA
>>>>> is false for some A and some B.
>>>>>
>>>>
>>>> All deciders essentially: Transform finite string
>>>> inputs by finite string transformation rules into
>>>> {Accept, Reject} values.
>>>>
>>>> When a required result cannot be derived by applying
>>>> finite string transformation rules to actual finite
>>>> string inputs, then the required result exceeds the
>>>> scope of computation and must be rejected as an
>>>> incorrect requirement.
>>>
>>> No, that does not follow. If a required result cannot be derived by
>>> appying a finite string transformation then the it it is uncomputable.
>>
>> Right. Outside the scope of computation. Requiring anything
>> outside the scope of computation is an incorrect requirement.
>>
>>> Of course, it one can prove that the required result is not computable
>>> then that helps to avoid wasting effort to try the impossible. The
>>> situation is worse if it is not known that the required result is not
>>> computable.
>>>
>>> That something is not computable does not mean that there is anyting
>>> "incorrect" in the requirement.
>>
>> Yes it certainly does. Requiring the impossible is always an error.
>
> It is a perfectly valid question to ask whther a particular reuqirement
> is satisfiable.
>
Any yes/no question lacking a correct yes/no answer
is an incorrect question that must be rejected on
that basis.
The whole rest of the world is too stupid to even
reject self-contradictory expressions such as the
Liar Paradox: "This sentence is not true".
*Computation and Undecidability*
https://philpapers.org/go.pl?aid=OLCCAU
*ChatGPT explains how and why I am correct*
*Reinterpretation of undecidability*
The example of P and H demonstrates that what is
often called “undecidable” is better understood as
ill-posed with respect to computable semantics.
When the specification is constrained to properties
detectable via finite simulation and finite pattern
recognition, computation proceeds normally and
correctly. Undecidability only appears when the
specification overreaches that boundary.
--
Copyright 2026 Olcott<br><br>
My 28 year goal has been to make <br>
"true on the basis of meaning expressed in language"<br>
reliably computable.<br><br>
This required establishing a new foundation<br>
[toc] | [prev] | [next] | [standalone]
| From | Mikko <mikko.levanto@iki.fi> |
|---|---|
| Date | 2026-01-12 12:51 +0200 |
| Message-ID | <10k2jod$29c3h$1@dont-email.me> |
| In reply to | #3800 |
On 11/01/2026 16:23, olcott wrote:
> On 1/11/2026 4:22 AM, Mikko wrote:
>> On 10/01/2026 17:47, olcott wrote:
>>> On 1/10/2026 2:23 AM, Mikko wrote:
>>>> On 09/01/2026 17:52, olcott wrote:
>>>>> On 1/9/2026 3:59 AM, Mikko wrote:
>>>>>> On 08/01/2026 16:22, olcott wrote:
>>>>>>> On 1/8/2026 4:22 AM, Mikko wrote:
>>>>>>>> On 07/01/2026 13:54, olcott wrote:
>>>>>>>>> On 1/7/2026 5:49 AM, Mikko wrote:
>>>>>>>>>> On 07/01/2026 06:44, olcott wrote:
>>>>>>>>>>> All deciders essentially: Transform finite string
>>>>>>>>>>> inputs by finite string transformation rules into
>>>>>>>>>>> {Accept, Reject} values.
>>>>>>>>>>>
>>>>>>>>>>> The counter-example input to requires more than
>>>>>>>>>>> can be derived from finite string transformation
>>>>>>>>>>> rules applied to this specific input thus the
>>>>>>>>>>> Halting Problem requires too much.
>>>>>>>>>
>>>>>>>>>> In a sense the halting problem asks too much: the problem is
>>>>>>>>>> proven to
>>>>>>>>>> be unsolvable. In another sense it asks too little: usually we
>>>>>>>>>> want to
>>>>>>>>>> know whether a method halts on every input, not just one.
>>>>>>>>>>
>>>>>>>>>> Although the halting problem is unsolvable, there are partial
>>>>>>>>>> solutions
>>>>>>>>>> to the halting problem. In particular, every counter-example
>>>>>>>>>> to the
>>>>>>>>>> full solution is correctly solved by some partial deciders.
>>>>>>>>>
>>>>>>>>> *if undecidability is correct then truth itself is broken*
>>>>>>>>
>>>>>>>> Depends on whether the word "truth" is interpeted in the standard
>>>>>>>> sense or in Olcott's sense.
>>>>>>>
>>>>>>> Undecidability is misconception. Self-contradictory
>>>>>>> expressions are correctly rejected as semantically
>>>>>>> incoherent thus form no undecidability or incompleteness.
>>>>>>
>>>>>> The misconception is yours. No expression in the language of the
>>>>>> first
>>>>>> order group theory is self-contradictory. But the first order goupr
>>>>>> theory is incomplete: it is impossible to prove that AB = BA is true
>>>>>> for every A and every B but it is also impossible to prove that AB
>>>>>> = BA
>>>>>> is false for some A and some B.
>>>>>>
>>>>>
>>>>> All deciders essentially: Transform finite string
>>>>> inputs by finite string transformation rules into
>>>>> {Accept, Reject} values.
>>>>>
>>>>> When a required result cannot be derived by applying
>>>>> finite string transformation rules to actual finite
>>>>> string inputs, then the required result exceeds the
>>>>> scope of computation and must be rejected as an
>>>>> incorrect requirement.
>>>>
>>>> No, that does not follow. If a required result cannot be derived by
>>>> appying a finite string transformation then the it it is uncomputable.
>>>
>>> Right. Outside the scope of computation. Requiring anything
>>> outside the scope of computation is an incorrect requirement.
>>>
>>>> Of course, it one can prove that the required result is not computable
>>>> then that helps to avoid wasting effort to try the impossible. The
>>>> situation is worse if it is not known that the required result is not
>>>> computable.
>>>>
>>>> That something is not computable does not mean that there is anyting
>>>> "incorrect" in the requirement.
>>>
>>> Yes it certainly does. Requiring the impossible is always an error.
>>
>> It is a perfectly valid question to ask whther a particular reuqirement
>> is satisfiable.
>
> Any yes/no question lacking a correct yes/no answer
> is an incorrect question that must be rejected on
> that basis.
Irrelevant. The question whether a particular requirement is satisfiable
does have an answer that is either "yes" or "no". In some ases it is
not known whether it is "yes" or "no" and there may be no known way to
find out be even then either "yes" or "no" is the correct answer.
--
Mikko
[toc] | [prev] | [next] | [standalone]
| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2026-01-12 08:43 -0600 |
| Message-ID | <10k31b1$2dfd4$1@dont-email.me> |
| In reply to | #3805 |
On 1/12/2026 4:51 AM, Mikko wrote:
> On 11/01/2026 16:23, olcott wrote:
>> On 1/11/2026 4:22 AM, Mikko wrote:
>>> On 10/01/2026 17:47, olcott wrote:
>>>> On 1/10/2026 2:23 AM, Mikko wrote:
>>>>> On 09/01/2026 17:52, olcott wrote:
>>>>>> On 1/9/2026 3:59 AM, Mikko wrote:
>>>>>>> On 08/01/2026 16:22, olcott wrote:
>>>>>>>> On 1/8/2026 4:22 AM, Mikko wrote:
>>>>>>>>> On 07/01/2026 13:54, olcott wrote:
>>>>>>>>>> On 1/7/2026 5:49 AM, Mikko wrote:
>>>>>>>>>>> On 07/01/2026 06:44, olcott wrote:
>>>>>>>>>>>> All deciders essentially: Transform finite string
>>>>>>>>>>>> inputs by finite string transformation rules into
>>>>>>>>>>>> {Accept, Reject} values.
>>>>>>>>>>>>
>>>>>>>>>>>> The counter-example input to requires more than
>>>>>>>>>>>> can be derived from finite string transformation
>>>>>>>>>>>> rules applied to this specific input thus the
>>>>>>>>>>>> Halting Problem requires too much.
>>>>>>>>>>
>>>>>>>>>>> In a sense the halting problem asks too much: the problem is
>>>>>>>>>>> proven to
>>>>>>>>>>> be unsolvable. In another sense it asks too little: usually
>>>>>>>>>>> we want to
>>>>>>>>>>> know whether a method halts on every input, not just one.
>>>>>>>>>>>
>>>>>>>>>>> Although the halting problem is unsolvable, there are partial
>>>>>>>>>>> solutions
>>>>>>>>>>> to the halting problem. In particular, every counter-example
>>>>>>>>>>> to the
>>>>>>>>>>> full solution is correctly solved by some partial deciders.
>>>>>>>>>>
>>>>>>>>>> *if undecidability is correct then truth itself is broken*
>>>>>>>>>
>>>>>>>>> Depends on whether the word "truth" is interpeted in the standard
>>>>>>>>> sense or in Olcott's sense.
>>>>>>>>
>>>>>>>> Undecidability is misconception. Self-contradictory
>>>>>>>> expressions are correctly rejected as semantically
>>>>>>>> incoherent thus form no undecidability or incompleteness.
>>>>>>>
>>>>>>> The misconception is yours. No expression in the language of the
>>>>>>> first
>>>>>>> order group theory is self-contradictory. But the first order goupr
>>>>>>> theory is incomplete: it is impossible to prove that AB = BA is true
>>>>>>> for every A and every B but it is also impossible to prove that
>>>>>>> AB = BA
>>>>>>> is false for some A and some B.
>>>>>>>
>>>>>>
>>>>>> All deciders essentially: Transform finite string
>>>>>> inputs by finite string transformation rules into
>>>>>> {Accept, Reject} values.
>>>>>>
>>>>>> When a required result cannot be derived by applying
>>>>>> finite string transformation rules to actual finite
>>>>>> string inputs, then the required result exceeds the
>>>>>> scope of computation and must be rejected as an
>>>>>> incorrect requirement.
>>>>>
>>>>> No, that does not follow. If a required result cannot be derived by
>>>>> appying a finite string transformation then the it it is uncomputable.
>>>>
>>>> Right. Outside the scope of computation. Requiring anything
>>>> outside the scope of computation is an incorrect requirement.
>>>>
>>>>> Of course, it one can prove that the required result is not computable
>>>>> then that helps to avoid wasting effort to try the impossible. The
>>>>> situation is worse if it is not known that the required result is not
>>>>> computable.
>>>>>
>>>>> That something is not computable does not mean that there is anyting
>>>>> "incorrect" in the requirement.
>>>>
>>>> Yes it certainly does. Requiring the impossible is always an error.
>>>
>>> It is a perfectly valid question to ask whther a particular reuqirement
>>> is satisfiable.
>>
>> Any yes/no question lacking a correct yes/no answer
>> is an incorrect question that must be rejected on
>> that basis.
>
> Irrelevant. The question whether a particular requirement is satisfiable
> does have an answer that is either "yes" or "no". In some ases it is
> not known whether it is "yes" or "no" and there may be no known way to
> find out be even then either "yes" or "no" is the correct answer.
>
Now that I finally have the standard terminology:
Proof-theoretic semantics has always been the correct
formal system to handle decision problems.
When it is asked a yes/no question lacking a correct
yes/no answer it correctly determines non-well-founded.
I have been correct all along and merely lacked the
standard terminology.
--
Copyright 2026 Olcott<br><br>
My 28 year goal has been to make <br>
"true on the basis of meaning expressed in language"<br>
reliably computable.<br><br>
This required establishing a new foundation<br>
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| From | Richard Damon <Richard@Damon-Family.org> |
|---|---|
| Date | 2026-01-12 22:22 -0500 |
| Message-ID | <TTi9R.203780$Zqk9.97731@fx08.iad> |
| In reply to | #3809 |
On 1/12/26 9:43 AM, olcott wrote:
> On 1/12/2026 4:51 AM, Mikko wrote:
>> On 11/01/2026 16:23, olcott wrote:
>>> On 1/11/2026 4:22 AM, Mikko wrote:
>>>> On 10/01/2026 17:47, olcott wrote:
>>>>> On 1/10/2026 2:23 AM, Mikko wrote:
>>>>>> On 09/01/2026 17:52, olcott wrote:
>>>>>>> On 1/9/2026 3:59 AM, Mikko wrote:
>>>>>>>> On 08/01/2026 16:22, olcott wrote:
>>>>>>>>> On 1/8/2026 4:22 AM, Mikko wrote:
>>>>>>>>>> On 07/01/2026 13:54, olcott wrote:
>>>>>>>>>>> On 1/7/2026 5:49 AM, Mikko wrote:
>>>>>>>>>>>> On 07/01/2026 06:44, olcott wrote:
>>>>>>>>>>>>> All deciders essentially: Transform finite string
>>>>>>>>>>>>> inputs by finite string transformation rules into
>>>>>>>>>>>>> {Accept, Reject} values.
>>>>>>>>>>>>>
>>>>>>>>>>>>> The counter-example input to requires more than
>>>>>>>>>>>>> can be derived from finite string transformation
>>>>>>>>>>>>> rules applied to this specific input thus the
>>>>>>>>>>>>> Halting Problem requires too much.
>>>>>>>>>>>
>>>>>>>>>>>> In a sense the halting problem asks too much: the problem is
>>>>>>>>>>>> proven to
>>>>>>>>>>>> be unsolvable. In another sense it asks too little: usually
>>>>>>>>>>>> we want to
>>>>>>>>>>>> know whether a method halts on every input, not just one.
>>>>>>>>>>>>
>>>>>>>>>>>> Although the halting problem is unsolvable, there are
>>>>>>>>>>>> partial solutions
>>>>>>>>>>>> to the halting problem. In particular, every counter-example
>>>>>>>>>>>> to the
>>>>>>>>>>>> full solution is correctly solved by some partial deciders.
>>>>>>>>>>>
>>>>>>>>>>> *if undecidability is correct then truth itself is broken*
>>>>>>>>>>
>>>>>>>>>> Depends on whether the word "truth" is interpeted in the standard
>>>>>>>>>> sense or in Olcott's sense.
>>>>>>>>>
>>>>>>>>> Undecidability is misconception. Self-contradictory
>>>>>>>>> expressions are correctly rejected as semantically
>>>>>>>>> incoherent thus form no undecidability or incompleteness.
>>>>>>>>
>>>>>>>> The misconception is yours. No expression in the language of the
>>>>>>>> first
>>>>>>>> order group theory is self-contradictory. But the first order goupr
>>>>>>>> theory is incomplete: it is impossible to prove that AB = BA is
>>>>>>>> true
>>>>>>>> for every A and every B but it is also impossible to prove that
>>>>>>>> AB = BA
>>>>>>>> is false for some A and some B.
>>>>>>>>
>>>>>>>
>>>>>>> All deciders essentially: Transform finite string
>>>>>>> inputs by finite string transformation rules into
>>>>>>> {Accept, Reject} values.
>>>>>>>
>>>>>>> When a required result cannot be derived by applying
>>>>>>> finite string transformation rules to actual finite
>>>>>>> string inputs, then the required result exceeds the
>>>>>>> scope of computation and must be rejected as an
>>>>>>> incorrect requirement.
>>>>>>
>>>>>> No, that does not follow. If a required result cannot be derived by
>>>>>> appying a finite string transformation then the it it is
>>>>>> uncomputable.
>>>>>
>>>>> Right. Outside the scope of computation. Requiring anything
>>>>> outside the scope of computation is an incorrect requirement.
>>>>>
>>>>>> Of course, it one can prove that the required result is not
>>>>>> computable
>>>>>> then that helps to avoid wasting effort to try the impossible. The
>>>>>> situation is worse if it is not known that the required result is not
>>>>>> computable.
>>>>>>
>>>>>> That something is not computable does not mean that there is anyting
>>>>>> "incorrect" in the requirement.
>>>>>
>>>>> Yes it certainly does. Requiring the impossible is always an error.
>>>>
>>>> It is a perfectly valid question to ask whther a particular reuqirement
>>>> is satisfiable.
>>>
>>> Any yes/no question lacking a correct yes/no answer
>>> is an incorrect question that must be rejected on
>>> that basis.
>>
>> Irrelevant. The question whether a particular requirement is satisfiable
>> does have an answer that is either "yes" or "no". In some ases it is
>> not known whether it is "yes" or "no" and there may be no known way to
>> find out be even then either "yes" or "no" is the correct answer.
>>
>
> Now that I finally have the standard terminology:
> Proof-theoretic semantics has always been the correct
> formal system to handle decision problems.
Nope, because not all systems meet the requirements.
>
> When it is asked a yes/no question lacking a correct
> yes/no answer it correctly determines non-well-founded.
> I have been correct all along and merely lacked the
> standard terminology.
>
But the halting problem HAS a correct answer for every input. It is just
that for every possible decider, we can make an input that it will get
wrong, thus no universal decider can exist.
Your problem is you just don't understand the nature or actual truth.
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| From | Mikko <mikko.levanto@iki.fi> |
|---|---|
| Date | 2026-01-13 10:46 +0200 |
| Message-ID | <10k50ph$30fch$1@dont-email.me> |
| In reply to | #3809 |
On 12/01/2026 16:43, olcott wrote:
> On 1/12/2026 4:51 AM, Mikko wrote:
>> On 11/01/2026 16:23, olcott wrote:
>>> On 1/11/2026 4:22 AM, Mikko wrote:
>>>> On 10/01/2026 17:47, olcott wrote:
>>>>> On 1/10/2026 2:23 AM, Mikko wrote:
>>>>>> On 09/01/2026 17:52, olcott wrote:
>>>>>>> On 1/9/2026 3:59 AM, Mikko wrote:
>>>>>>>> On 08/01/2026 16:22, olcott wrote:
>>>>>>>>> On 1/8/2026 4:22 AM, Mikko wrote:
>>>>>>>>>> On 07/01/2026 13:54, olcott wrote:
>>>>>>>>>>> On 1/7/2026 5:49 AM, Mikko wrote:
>>>>>>>>>>>> On 07/01/2026 06:44, olcott wrote:
>>>>>>>>>>>>> All deciders essentially: Transform finite string
>>>>>>>>>>>>> inputs by finite string transformation rules into
>>>>>>>>>>>>> {Accept, Reject} values.
>>>>>>>>>>>>>
>>>>>>>>>>>>> The counter-example input to requires more than
>>>>>>>>>>>>> can be derived from finite string transformation
>>>>>>>>>>>>> rules applied to this specific input thus the
>>>>>>>>>>>>> Halting Problem requires too much.
>>>>>>>>>>>
>>>>>>>>>>>> In a sense the halting problem asks too much: the problem is
>>>>>>>>>>>> proven to
>>>>>>>>>>>> be unsolvable. In another sense it asks too little: usually
>>>>>>>>>>>> we want to
>>>>>>>>>>>> know whether a method halts on every input, not just one.
>>>>>>>>>>>>
>>>>>>>>>>>> Although the halting problem is unsolvable, there are
>>>>>>>>>>>> partial solutions
>>>>>>>>>>>> to the halting problem. In particular, every counter-example
>>>>>>>>>>>> to the
>>>>>>>>>>>> full solution is correctly solved by some partial deciders.
>>>>>>>>>>>
>>>>>>>>>>> *if undecidability is correct then truth itself is broken*
>>>>>>>>>>
>>>>>>>>>> Depends on whether the word "truth" is interpeted in the standard
>>>>>>>>>> sense or in Olcott's sense.
>>>>>>>>>
>>>>>>>>> Undecidability is misconception. Self-contradictory
>>>>>>>>> expressions are correctly rejected as semantically
>>>>>>>>> incoherent thus form no undecidability or incompleteness.
>>>>>>>>
>>>>>>>> The misconception is yours. No expression in the language of the
>>>>>>>> first
>>>>>>>> order group theory is self-contradictory. But the first order goupr
>>>>>>>> theory is incomplete: it is impossible to prove that AB = BA is
>>>>>>>> true
>>>>>>>> for every A and every B but it is also impossible to prove that
>>>>>>>> AB = BA
>>>>>>>> is false for some A and some B.
>>>>>>>>
>>>>>>>
>>>>>>> All deciders essentially: Transform finite string
>>>>>>> inputs by finite string transformation rules into
>>>>>>> {Accept, Reject} values.
>>>>>>>
>>>>>>> When a required result cannot be derived by applying
>>>>>>> finite string transformation rules to actual finite
>>>>>>> string inputs, then the required result exceeds the
>>>>>>> scope of computation and must be rejected as an
>>>>>>> incorrect requirement.
>>>>>>
>>>>>> No, that does not follow. If a required result cannot be derived by
>>>>>> appying a finite string transformation then the it it is
>>>>>> uncomputable.
>>>>>
>>>>> Right. Outside the scope of computation. Requiring anything
>>>>> outside the scope of computation is an incorrect requirement.
>>>>>
>>>>>> Of course, it one can prove that the required result is not
>>>>>> computable
>>>>>> then that helps to avoid wasting effort to try the impossible. The
>>>>>> situation is worse if it is not known that the required result is not
>>>>>> computable.
>>>>>>
>>>>>> That something is not computable does not mean that there is anyting
>>>>>> "incorrect" in the requirement.
>>>>>
>>>>> Yes it certainly does. Requiring the impossible is always an error.
>>>>
>>>> It is a perfectly valid question to ask whther a particular reuqirement
>>>> is satisfiable.
>>>
>>> Any yes/no question lacking a correct yes/no answer
>>> is an incorrect question that must be rejected on
>>> that basis.
>>
>> Irrelevant. The question whether a particular requirement is satisfiable
>> does have an answer that is either "yes" or "no". In some ases it is
>> not known whether it is "yes" or "no" and there may be no known way to
>> find out be even then either "yes" or "no" is the correct answer.
>
> Now that I finally have the standard terminology:
> Proof-theoretic semantics has always been the correct
> formal system to handle decision problems.
>
> When it is asked a yes/no question lacking a correct
> yes/no answer it correctly determines non-well-founded.
> I have been correct all along and merely lacked the
> standard terminology.
Irrelevant, as already noted above.
--
Mikko
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| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2026-01-13 08:17 -0600 |
| Message-ID | <10k5k6i$36bf9$1@dont-email.me> |
| In reply to | #3817 |
On 1/13/2026 2:46 AM, Mikko wrote:
> On 12/01/2026 16:43, olcott wrote:
>> On 1/12/2026 4:51 AM, Mikko wrote:
>>> On 11/01/2026 16:23, olcott wrote:
>>>> On 1/11/2026 4:22 AM, Mikko wrote:
>>>>> On 10/01/2026 17:47, olcott wrote:
>>>>>> On 1/10/2026 2:23 AM, Mikko wrote:
>>>>>>> On 09/01/2026 17:52, olcott wrote:
>>>>>>>> On 1/9/2026 3:59 AM, Mikko wrote:
>>>>>>>>> On 08/01/2026 16:22, olcott wrote:
>>>>>>>>>> On 1/8/2026 4:22 AM, Mikko wrote:
>>>>>>>>>>> On 07/01/2026 13:54, olcott wrote:
>>>>>>>>>>>> On 1/7/2026 5:49 AM, Mikko wrote:
>>>>>>>>>>>>> On 07/01/2026 06:44, olcott wrote:
>>>>>>>>>>>>>> All deciders essentially: Transform finite string
>>>>>>>>>>>>>> inputs by finite string transformation rules into
>>>>>>>>>>>>>> {Accept, Reject} values.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> The counter-example input to requires more than
>>>>>>>>>>>>>> can be derived from finite string transformation
>>>>>>>>>>>>>> rules applied to this specific input thus the
>>>>>>>>>>>>>> Halting Problem requires too much.
>>>>>>>>>>>>
>>>>>>>>>>>>> In a sense the halting problem asks too much: the problem
>>>>>>>>>>>>> is proven to
>>>>>>>>>>>>> be unsolvable. In another sense it asks too little: usually
>>>>>>>>>>>>> we want to
>>>>>>>>>>>>> know whether a method halts on every input, not just one.
>>>>>>>>>>>>>
>>>>>>>>>>>>> Although the halting problem is unsolvable, there are
>>>>>>>>>>>>> partial solutions
>>>>>>>>>>>>> to the halting problem. In particular, every counter-
>>>>>>>>>>>>> example to the
>>>>>>>>>>>>> full solution is correctly solved by some partial deciders.
>>>>>>>>>>>>
>>>>>>>>>>>> *if undecidability is correct then truth itself is broken*
>>>>>>>>>>>
>>>>>>>>>>> Depends on whether the word "truth" is interpeted in the
>>>>>>>>>>> standard
>>>>>>>>>>> sense or in Olcott's sense.
>>>>>>>>>>
>>>>>>>>>> Undecidability is misconception. Self-contradictory
>>>>>>>>>> expressions are correctly rejected as semantically
>>>>>>>>>> incoherent thus form no undecidability or incompleteness.
>>>>>>>>>
>>>>>>>>> The misconception is yours. No expression in the language of
>>>>>>>>> the first
>>>>>>>>> order group theory is self-contradictory. But the first order
>>>>>>>>> goupr
>>>>>>>>> theory is incomplete: it is impossible to prove that AB = BA is
>>>>>>>>> true
>>>>>>>>> for every A and every B but it is also impossible to prove that
>>>>>>>>> AB = BA
>>>>>>>>> is false for some A and some B.
>>>>>>>>>
>>>>>>>>
>>>>>>>> All deciders essentially: Transform finite string
>>>>>>>> inputs by finite string transformation rules into
>>>>>>>> {Accept, Reject} values.
>>>>>>>>
>>>>>>>> When a required result cannot be derived by applying
>>>>>>>> finite string transformation rules to actual finite
>>>>>>>> string inputs, then the required result exceeds the
>>>>>>>> scope of computation and must be rejected as an
>>>>>>>> incorrect requirement.
>>>>>>>
>>>>>>> No, that does not follow. If a required result cannot be derived by
>>>>>>> appying a finite string transformation then the it it is
>>>>>>> uncomputable.
>>>>>>
>>>>>> Right. Outside the scope of computation. Requiring anything
>>>>>> outside the scope of computation is an incorrect requirement.
>>>>>>
>>>>>>> Of course, it one can prove that the required result is not
>>>>>>> computable
>>>>>>> then that helps to avoid wasting effort to try the impossible. The
>>>>>>> situation is worse if it is not known that the required result is
>>>>>>> not
>>>>>>> computable.
>>>>>>>
>>>>>>> That something is not computable does not mean that there is anyting
>>>>>>> "incorrect" in the requirement.
>>>>>>
>>>>>> Yes it certainly does. Requiring the impossible is always an error.
>>>>>
>>>>> It is a perfectly valid question to ask whther a particular
>>>>> reuqirement
>>>>> is satisfiable.
>>>>
>>>> Any yes/no question lacking a correct yes/no answer
>>>> is an incorrect question that must be rejected on
>>>> that basis.
>>>
>>> Irrelevant. The question whether a particular requirement is satisfiable
>>> does have an answer that is either "yes" or "no". In some ases it is
>>> not known whether it is "yes" or "no" and there may be no known way to
>>> find out be even then either "yes" or "no" is the correct answer.
>>
>> Now that I finally have the standard terminology:
>> Proof-theoretic semantics has always been the correct
>> formal system to handle decision problems.
>>
>> When it is asked a yes/no question lacking a correct
>> yes/no answer it correctly determines non-well-founded.
>> I have been correct all along and merely lacked the
>> standard terminology.
>
> Irrelevant, as already noted above.
>
It is not irrelevant at all. Most all of undecidability
cease to exist in this system:
“The system adopts Proof-Theoretic Semantics:
meaning is determined by inferential role,
and truth is internal to the theory. A theory
T is defined by a finite set of stipulated atomic
statements together with all expressions derivable
from them under the inference rules. The statements
belonging to T constitute its theorems, and these
are exactly the statements that are true-in-T.”
Is the foundation of the system that I have been
talking about all of these years making
∀x ∈ T ((True(T, x) ≡ (T ⊢ x))
and Gödel Incompleteness impossible.
The above system fulfills:
My 28 year goal has been to make
"true on the basis of meaning expressed in language"
reliably computable.
Formal systems with undecidability and incompleteness
merely had the wrong foundation.
--
Copyright 2026 Olcott<br><br>
My 28 year goal has been to make <br>
"true on the basis of meaning expressed in language"<br>
reliably computable.<br><br>
This required establishing a new foundation<br>
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| From | Mikko <mikko.levanto@iki.fi> |
|---|---|
| Date | 2026-01-14 09:58 +0200 |
| Message-ID | <10k7ib4$3pr4c$1@dont-email.me> |
| In reply to | #3820 |
On 13/01/2026 16:17, olcott wrote:
> On 1/13/2026 2:46 AM, Mikko wrote:
>> On 12/01/2026 16:43, olcott wrote:
>>> On 1/12/2026 4:51 AM, Mikko wrote:
>>>> On 11/01/2026 16:23, olcott wrote:
>>>>> On 1/11/2026 4:22 AM, Mikko wrote:
>>>>>> On 10/01/2026 17:47, olcott wrote:
>>>>>>> On 1/10/2026 2:23 AM, Mikko wrote:
>>>>>>>> On 09/01/2026 17:52, olcott wrote:
>>>>>>>>> On 1/9/2026 3:59 AM, Mikko wrote:
>>>>>>>>>> On 08/01/2026 16:22, olcott wrote:
>>>>>>>>>>> On 1/8/2026 4:22 AM, Mikko wrote:
>>>>>>>>>>>> On 07/01/2026 13:54, olcott wrote:
>>>>>>>>>>>>> On 1/7/2026 5:49 AM, Mikko wrote:
>>>>>>>>>>>>>> On 07/01/2026 06:44, olcott wrote:
>>>>>>>>>>>>>>> All deciders essentially: Transform finite string
>>>>>>>>>>>>>>> inputs by finite string transformation rules into
>>>>>>>>>>>>>>> {Accept, Reject} values.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> The counter-example input to requires more than
>>>>>>>>>>>>>>> can be derived from finite string transformation
>>>>>>>>>>>>>>> rules applied to this specific input thus the
>>>>>>>>>>>>>>> Halting Problem requires too much.
>>>>>>>>>>>>>
>>>>>>>>>>>>>> In a sense the halting problem asks too much: the problem
>>>>>>>>>>>>>> is proven to
>>>>>>>>>>>>>> be unsolvable. In another sense it asks too little:
>>>>>>>>>>>>>> usually we want to
>>>>>>>>>>>>>> know whether a method halts on every input, not just one.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Although the halting problem is unsolvable, there are
>>>>>>>>>>>>>> partial solutions
>>>>>>>>>>>>>> to the halting problem. In particular, every counter-
>>>>>>>>>>>>>> example to the
>>>>>>>>>>>>>> full solution is correctly solved by some partial deciders.
>>>>>>>>>>>>>
>>>>>>>>>>>>> *if undecidability is correct then truth itself is broken*
>>>>>>>>>>>>
>>>>>>>>>>>> Depends on whether the word "truth" is interpeted in the
>>>>>>>>>>>> standard
>>>>>>>>>>>> sense or in Olcott's sense.
>>>>>>>>>>>
>>>>>>>>>>> Undecidability is misconception. Self-contradictory
>>>>>>>>>>> expressions are correctly rejected as semantically
>>>>>>>>>>> incoherent thus form no undecidability or incompleteness.
>>>>>>>>>>
>>>>>>>>>> The misconception is yours. No expression in the language of
>>>>>>>>>> the first
>>>>>>>>>> order group theory is self-contradictory. But the first order
>>>>>>>>>> goupr
>>>>>>>>>> theory is incomplete: it is impossible to prove that AB = BA
>>>>>>>>>> is true
>>>>>>>>>> for every A and every B but it is also impossible to prove
>>>>>>>>>> that AB = BA
>>>>>>>>>> is false for some A and some B.
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> All deciders essentially: Transform finite string
>>>>>>>>> inputs by finite string transformation rules into
>>>>>>>>> {Accept, Reject} values.
>>>>>>>>>
>>>>>>>>> When a required result cannot be derived by applying
>>>>>>>>> finite string transformation rules to actual finite
>>>>>>>>> string inputs, then the required result exceeds the
>>>>>>>>> scope of computation and must be rejected as an
>>>>>>>>> incorrect requirement.
>>>>>>>>
>>>>>>>> No, that does not follow. If a required result cannot be derived by
>>>>>>>> appying a finite string transformation then the it it is
>>>>>>>> uncomputable.
>>>>>>>
>>>>>>> Right. Outside the scope of computation. Requiring anything
>>>>>>> outside the scope of computation is an incorrect requirement.
>>>>>>>
>>>>>>>> Of course, it one can prove that the required result is not
>>>>>>>> computable
>>>>>>>> then that helps to avoid wasting effort to try the impossible. The
>>>>>>>> situation is worse if it is not known that the required result
>>>>>>>> is not
>>>>>>>> computable.
>>>>>>>>
>>>>>>>> That something is not computable does not mean that there is
>>>>>>>> anyting
>>>>>>>> "incorrect" in the requirement.
>>>>>>>
>>>>>>> Yes it certainly does. Requiring the impossible is always an error.
>>>>>>
>>>>>> It is a perfectly valid question to ask whther a particular
>>>>>> reuqirement
>>>>>> is satisfiable.
>>>>>
>>>>> Any yes/no question lacking a correct yes/no answer
>>>>> is an incorrect question that must be rejected on
>>>>> that basis.
>>>>
>>>> Irrelevant. The question whether a particular requirement is
>>>> satisfiable
>>>> does have an answer that is either "yes" or "no". In some ases it is
>>>> not known whether it is "yes" or "no" and there may be no known way to
>>>> find out be even then either "yes" or "no" is the correct answer.
>>>
>>> Now that I finally have the standard terminology:
>>> Proof-theoretic semantics has always been the correct
>>> formal system to handle decision problems.
>>>
>>> When it is asked a yes/no question lacking a correct
>>> yes/no answer it correctly determines non-well-founded.
>>> I have been correct all along and merely lacked the
>>> standard terminology.
>>
>> Irrelevant, as already noted above.
Yes, it is. How to handle questions that lack a yes/no answer is
irrelevant when discussing questions that do have a yes/no asnwer.
Whether a particular requirement is satisriable always has a yes/no
answer, so it is irrelevat how to handle questions that don't.
--
Mikko
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| From | Mikko <mikko.levanto@iki.fi> |
|---|---|
| Date | 2026-01-14 11:04 +0200 |
| Message-ID | <10k7m6i$3r30e$2@dont-email.me> |
| In reply to | #3820 |
On 13/01/2026 16:17, olcott wrote:
> On 1/13/2026 2:46 AM, Mikko wrote:
>> On 12/01/2026 16:43, olcott wrote:
>>> On 1/12/2026 4:51 AM, Mikko wrote:
>>>> On 11/01/2026 16:23, olcott wrote:
>>>>> On 1/11/2026 4:22 AM, Mikko wrote:
>>>>>> On 10/01/2026 17:47, olcott wrote:
>>>>>>> On 1/10/2026 2:23 AM, Mikko wrote:
>>>>>>>> On 09/01/2026 17:52, olcott wrote:
>>>>>>>>> On 1/9/2026 3:59 AM, Mikko wrote:
>>>>>>>>>> On 08/01/2026 16:22, olcott wrote:
>>>>>>>>>>> On 1/8/2026 4:22 AM, Mikko wrote:
>>>>>>>>>>>> On 07/01/2026 13:54, olcott wrote:
>>>>>>>>>>>>> On 1/7/2026 5:49 AM, Mikko wrote:
>>>>>>>>>>>>>> On 07/01/2026 06:44, olcott wrote:
>>>>>>>>>>>>>>> All deciders essentially: Transform finite string
>>>>>>>>>>>>>>> inputs by finite string transformation rules into
>>>>>>>>>>>>>>> {Accept, Reject} values.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> The counter-example input to requires more than
>>>>>>>>>>>>>>> can be derived from finite string transformation
>>>>>>>>>>>>>>> rules applied to this specific input thus the
>>>>>>>>>>>>>>> Halting Problem requires too much.
>>>>>>>>>>>>>
>>>>>>>>>>>>>> In a sense the halting problem asks too much: the problem
>>>>>>>>>>>>>> is proven to
>>>>>>>>>>>>>> be unsolvable. In another sense it asks too little:
>>>>>>>>>>>>>> usually we want to
>>>>>>>>>>>>>> know whether a method halts on every input, not just one.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Although the halting problem is unsolvable, there are
>>>>>>>>>>>>>> partial solutions
>>>>>>>>>>>>>> to the halting problem. In particular, every counter-
>>>>>>>>>>>>>> example to the
>>>>>>>>>>>>>> full solution is correctly solved by some partial deciders.
>>>>>>>>>>>>>
>>>>>>>>>>>>> *if undecidability is correct then truth itself is broken*
>>>>>>>>>>>>
>>>>>>>>>>>> Depends on whether the word "truth" is interpeted in the
>>>>>>>>>>>> standard
>>>>>>>>>>>> sense or in Olcott's sense.
>>>>>>>>>>>
>>>>>>>>>>> Undecidability is misconception. Self-contradictory
>>>>>>>>>>> expressions are correctly rejected as semantically
>>>>>>>>>>> incoherent thus form no undecidability or incompleteness.
>>>>>>>>>>
>>>>>>>>>> The misconception is yours. No expression in the language of
>>>>>>>>>> the first
>>>>>>>>>> order group theory is self-contradictory. But the first order
>>>>>>>>>> goupr
>>>>>>>>>> theory is incomplete: it is impossible to prove that AB = BA
>>>>>>>>>> is true
>>>>>>>>>> for every A and every B but it is also impossible to prove
>>>>>>>>>> that AB = BA
>>>>>>>>>> is false for some A and some B.
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> All deciders essentially: Transform finite string
>>>>>>>>> inputs by finite string transformation rules into
>>>>>>>>> {Accept, Reject} values.
>>>>>>>>>
>>>>>>>>> When a required result cannot be derived by applying
>>>>>>>>> finite string transformation rules to actual finite
>>>>>>>>> string inputs, then the required result exceeds the
>>>>>>>>> scope of computation and must be rejected as an
>>>>>>>>> incorrect requirement.
>>>>>>>>
>>>>>>>> No, that does not follow. If a required result cannot be derived by
>>>>>>>> appying a finite string transformation then the it it is
>>>>>>>> uncomputable.
>>>>>>>
>>>>>>> Right. Outside the scope of computation. Requiring anything
>>>>>>> outside the scope of computation is an incorrect requirement.
>>>>>>>
>>>>>>>> Of course, it one can prove that the required result is not
>>>>>>>> computable
>>>>>>>> then that helps to avoid wasting effort to try the impossible. The
>>>>>>>> situation is worse if it is not known that the required result
>>>>>>>> is not
>>>>>>>> computable.
>>>>>>>>
>>>>>>>> That something is not computable does not mean that there is
>>>>>>>> anyting
>>>>>>>> "incorrect" in the requirement.
>>>>>>>
>>>>>>> Yes it certainly does. Requiring the impossible is always an error.
>>>>>>
>>>>>> It is a perfectly valid question to ask whther a particular
>>>>>> reuqirement
>>>>>> is satisfiable.
>>>>>
>>>>> Any yes/no question lacking a correct yes/no answer
>>>>> is an incorrect question that must be rejected on
>>>>> that basis.
>>>>
>>>> Irrelevant. The question whether a particular requirement is
>>>> satisfiable
>>>> does have an answer that is either "yes" or "no". In some ases it is
>>>> not known whether it is "yes" or "no" and there may be no known way to
>>>> find out be even then either "yes" or "no" is the correct answer.
>>>
>>> Now that I finally have the standard terminology:
>>> Proof-theoretic semantics has always been the correct
>>> formal system to handle decision problems.
>>>
>>> When it is asked a yes/no question lacking a correct
>>> yes/no answer it correctly determines non-well-founded.
>>> I have been correct all along and merely lacked the
>>> standard terminology.
>>
>> Irrelevant, as already noted above.
>
> It is not irrelevant at all. Most all of undecidability
> cease to exist in this system:
It does not help if the system is not sound. Or if the particuar
undecidability that one happens to care about does not cease to
exist.
--
Mikko
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| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2026-01-14 13:35 -0600 |
| Message-ID | <10k8r70$7i4u$1@dont-email.me> |
| In reply to | #3824 |
On 1/14/2026 3:04 AM, Mikko wrote:
> On 13/01/2026 16:17, olcott wrote:
>> On 1/13/2026 2:46 AM, Mikko wrote:
>>> On 12/01/2026 16:43, olcott wrote:
>>>> On 1/12/2026 4:51 AM, Mikko wrote:
>>>>> On 11/01/2026 16:23, olcott wrote:
>>>>>> On 1/11/2026 4:22 AM, Mikko wrote:
>>>>>>> On 10/01/2026 17:47, olcott wrote:
>>>>>>>> On 1/10/2026 2:23 AM, Mikko wrote:
>>>>>>>>> On 09/01/2026 17:52, olcott wrote:
>>>>>>>>>> On 1/9/2026 3:59 AM, Mikko wrote:
>>>>>>>>>>> On 08/01/2026 16:22, olcott wrote:
>>>>>>>>>>>> On 1/8/2026 4:22 AM, Mikko wrote:
>>>>>>>>>>>>> On 07/01/2026 13:54, olcott wrote:
>>>>>>>>>>>>>> On 1/7/2026 5:49 AM, Mikko wrote:
>>>>>>>>>>>>>>> On 07/01/2026 06:44, olcott wrote:
>>>>>>>>>>>>>>>> All deciders essentially: Transform finite string
>>>>>>>>>>>>>>>> inputs by finite string transformation rules into
>>>>>>>>>>>>>>>> {Accept, Reject} values.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> The counter-example input to requires more than
>>>>>>>>>>>>>>>> can be derived from finite string transformation
>>>>>>>>>>>>>>>> rules applied to this specific input thus the
>>>>>>>>>>>>>>>> Halting Problem requires too much.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> In a sense the halting problem asks too much: the problem
>>>>>>>>>>>>>>> is proven to
>>>>>>>>>>>>>>> be unsolvable. In another sense it asks too little:
>>>>>>>>>>>>>>> usually we want to
>>>>>>>>>>>>>>> know whether a method halts on every input, not just one.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> Although the halting problem is unsolvable, there are
>>>>>>>>>>>>>>> partial solutions
>>>>>>>>>>>>>>> to the halting problem. In particular, every counter-
>>>>>>>>>>>>>>> example to the
>>>>>>>>>>>>>>> full solution is correctly solved by some partial deciders.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> *if undecidability is correct then truth itself is broken*
>>>>>>>>>>>>>
>>>>>>>>>>>>> Depends on whether the word "truth" is interpeted in the
>>>>>>>>>>>>> standard
>>>>>>>>>>>>> sense or in Olcott's sense.
>>>>>>>>>>>>
>>>>>>>>>>>> Undecidability is misconception. Self-contradictory
>>>>>>>>>>>> expressions are correctly rejected as semantically
>>>>>>>>>>>> incoherent thus form no undecidability or incompleteness.
>>>>>>>>>>>
>>>>>>>>>>> The misconception is yours. No expression in the language of
>>>>>>>>>>> the first
>>>>>>>>>>> order group theory is self-contradictory. But the first order
>>>>>>>>>>> goupr
>>>>>>>>>>> theory is incomplete: it is impossible to prove that AB = BA
>>>>>>>>>>> is true
>>>>>>>>>>> for every A and every B but it is also impossible to prove
>>>>>>>>>>> that AB = BA
>>>>>>>>>>> is false for some A and some B.
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> All deciders essentially: Transform finite string
>>>>>>>>>> inputs by finite string transformation rules into
>>>>>>>>>> {Accept, Reject} values.
>>>>>>>>>>
>>>>>>>>>> When a required result cannot be derived by applying
>>>>>>>>>> finite string transformation rules to actual finite
>>>>>>>>>> string inputs, then the required result exceeds the
>>>>>>>>>> scope of computation and must be rejected as an
>>>>>>>>>> incorrect requirement.
>>>>>>>>>
>>>>>>>>> No, that does not follow. If a required result cannot be
>>>>>>>>> derived by
>>>>>>>>> appying a finite string transformation then the it it is
>>>>>>>>> uncomputable.
>>>>>>>>
>>>>>>>> Right. Outside the scope of computation. Requiring anything
>>>>>>>> outside the scope of computation is an incorrect requirement.
>>>>>>>>
>>>>>>>>> Of course, it one can prove that the required result is not
>>>>>>>>> computable
>>>>>>>>> then that helps to avoid wasting effort to try the impossible. The
>>>>>>>>> situation is worse if it is not known that the required result
>>>>>>>>> is not
>>>>>>>>> computable.
>>>>>>>>>
>>>>>>>>> That something is not computable does not mean that there is
>>>>>>>>> anyting
>>>>>>>>> "incorrect" in the requirement.
>>>>>>>>
>>>>>>>> Yes it certainly does. Requiring the impossible is always an error.
>>>>>>>
>>>>>>> It is a perfectly valid question to ask whther a particular
>>>>>>> reuqirement
>>>>>>> is satisfiable.
>>>>>>
>>>>>> Any yes/no question lacking a correct yes/no answer
>>>>>> is an incorrect question that must be rejected on
>>>>>> that basis.
>>>>>
>>>>> Irrelevant. The question whether a particular requirement is
>>>>> satisfiable
>>>>> does have an answer that is either "yes" or "no". In some ases it is
>>>>> not known whether it is "yes" or "no" and there may be no known way to
>>>>> find out be even then either "yes" or "no" is the correct answer.
>>>>
>>>> Now that I finally have the standard terminology:
>>>> Proof-theoretic semantics has always been the correct
>>>> formal system to handle decision problems.
>>>>
>>>> When it is asked a yes/no question lacking a correct
>>>> yes/no answer it correctly determines non-well-founded.
>>>> I have been correct all along and merely lacked the
>>>> standard terminology.
>>>
>>> Irrelevant, as already noted above.
>>
>> It is not irrelevant at all. Most all of undecidability
>> cease to exist in this system:
>
> It does not help if the system is not sound. Or if the particuar
> undecidability that one happens to care about does not cease to
> exist.
>
Soundness is exactly why proof‑theoretic semantics matters here.
When meaning is grounded in inferential structure and truth is anchored
in an axiomatic base, only well‑founded expressions are admissible. The
classical undecidability constructions (Halting, Gödel, Tarski, Curry)
all rely on expressions whose semantic dependency graphs contain cycles.
Those expressions are not well‑formed truthbearers in a sound, grounded
system, so the corresponding undecidability results do not arise.
--
Copyright 2026 Olcott<br><br>
My 28 year goal has been to make <br>
"true on the basis of meaning expressed in language"<br>
reliably computable.<br><br>
This required establishing a new foundation<br>
[toc] | [prev] | [next] | [standalone]
| From | Mikko <mikko.levanto@iki.fi> |
|---|---|
| Date | 2026-01-15 11:21 +0200 |
| Message-ID | <10kabip$ln0i$1@dont-email.me> |
| In reply to | #3825 |
On 14/01/2026 21:35, olcott wrote:
> On 1/14/2026 3:04 AM, Mikko wrote:
>> On 13/01/2026 16:17, olcott wrote:
>>> On 1/13/2026 2:46 AM, Mikko wrote:
>>>> On 12/01/2026 16:43, olcott wrote:
>>>>> On 1/12/2026 4:51 AM, Mikko wrote:
>>>>>> On 11/01/2026 16:23, olcott wrote:
>>>>>>> On 1/11/2026 4:22 AM, Mikko wrote:
>>>>>>>> On 10/01/2026 17:47, olcott wrote:
>>>>>>>>> On 1/10/2026 2:23 AM, Mikko wrote:
>>>>>>>>>> On 09/01/2026 17:52, olcott wrote:
>>>>>>>>>>> On 1/9/2026 3:59 AM, Mikko wrote:
>>>>>>>>>>>> On 08/01/2026 16:22, olcott wrote:
>>>>>>>>>>>>> On 1/8/2026 4:22 AM, Mikko wrote:
>>>>>>>>>>>>>> On 07/01/2026 13:54, olcott wrote:
>>>>>>>>>>>>>>> On 1/7/2026 5:49 AM, Mikko wrote:
>>>>>>>>>>>>>>>> On 07/01/2026 06:44, olcott wrote:
>>>>>>>>>>>>>>>>> All deciders essentially: Transform finite string
>>>>>>>>>>>>>>>>> inputs by finite string transformation rules into
>>>>>>>>>>>>>>>>> {Accept, Reject} values.
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> The counter-example input to requires more than
>>>>>>>>>>>>>>>>> can be derived from finite string transformation
>>>>>>>>>>>>>>>>> rules applied to this specific input thus the
>>>>>>>>>>>>>>>>> Halting Problem requires too much.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> In a sense the halting problem asks too much: the
>>>>>>>>>>>>>>>> problem is proven to
>>>>>>>>>>>>>>>> be unsolvable. In another sense it asks too little:
>>>>>>>>>>>>>>>> usually we want to
>>>>>>>>>>>>>>>> know whether a method halts on every input, not just one.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> Although the halting problem is unsolvable, there are
>>>>>>>>>>>>>>>> partial solutions
>>>>>>>>>>>>>>>> to the halting problem. In particular, every counter-
>>>>>>>>>>>>>>>> example to the
>>>>>>>>>>>>>>>> full solution is correctly solved by some partial deciders.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> *if undecidability is correct then truth itself is broken*
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Depends on whether the word "truth" is interpeted in the
>>>>>>>>>>>>>> standard
>>>>>>>>>>>>>> sense or in Olcott's sense.
>>>>>>>>>>>>>
>>>>>>>>>>>>> Undecidability is misconception. Self-contradictory
>>>>>>>>>>>>> expressions are correctly rejected as semantically
>>>>>>>>>>>>> incoherent thus form no undecidability or incompleteness.
>>>>>>>>>>>>
>>>>>>>>>>>> The misconception is yours. No expression in the language of
>>>>>>>>>>>> the first
>>>>>>>>>>>> order group theory is self-contradictory. But the first
>>>>>>>>>>>> order goupr
>>>>>>>>>>>> theory is incomplete: it is impossible to prove that AB = BA
>>>>>>>>>>>> is true
>>>>>>>>>>>> for every A and every B but it is also impossible to prove
>>>>>>>>>>>> that AB = BA
>>>>>>>>>>>> is false for some A and some B.
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> All deciders essentially: Transform finite string
>>>>>>>>>>> inputs by finite string transformation rules into
>>>>>>>>>>> {Accept, Reject} values.
>>>>>>>>>>>
>>>>>>>>>>> When a required result cannot be derived by applying
>>>>>>>>>>> finite string transformation rules to actual finite
>>>>>>>>>>> string inputs, then the required result exceeds the
>>>>>>>>>>> scope of computation and must be rejected as an
>>>>>>>>>>> incorrect requirement.
>>>>>>>>>>
>>>>>>>>>> No, that does not follow. If a required result cannot be
>>>>>>>>>> derived by
>>>>>>>>>> appying a finite string transformation then the it it is
>>>>>>>>>> uncomputable.
>>>>>>>>>
>>>>>>>>> Right. Outside the scope of computation. Requiring anything
>>>>>>>>> outside the scope of computation is an incorrect requirement.
>>>>>>>>>
>>>>>>>>>> Of course, it one can prove that the required result is not
>>>>>>>>>> computable
>>>>>>>>>> then that helps to avoid wasting effort to try the impossible.
>>>>>>>>>> The
>>>>>>>>>> situation is worse if it is not known that the required result
>>>>>>>>>> is not
>>>>>>>>>> computable.
>>>>>>>>>>
>>>>>>>>>> That something is not computable does not mean that there is
>>>>>>>>>> anyting
>>>>>>>>>> "incorrect" in the requirement.
>>>>>>>>>
>>>>>>>>> Yes it certainly does. Requiring the impossible is always an
>>>>>>>>> error.
>>>>>>>>
>>>>>>>> It is a perfectly valid question to ask whther a particular
>>>>>>>> reuqirement
>>>>>>>> is satisfiable.
>>>>>>>
>>>>>>> Any yes/no question lacking a correct yes/no answer
>>>>>>> is an incorrect question that must be rejected on
>>>>>>> that basis.
>>>>>>
>>>>>> Irrelevant. The question whether a particular requirement is
>>>>>> satisfiable
>>>>>> does have an answer that is either "yes" or "no". In some ases it is
>>>>>> not known whether it is "yes" or "no" and there may be no known
>>>>>> way to
>>>>>> find out be even then either "yes" or "no" is the correct answer.
>>>>>
>>>>> Now that I finally have the standard terminology:
>>>>> Proof-theoretic semantics has always been the correct
>>>>> formal system to handle decision problems.
>>>>>
>>>>> When it is asked a yes/no question lacking a correct
>>>>> yes/no answer it correctly determines non-well-founded.
>>>>> I have been correct all along and merely lacked the
>>>>> standard terminology.
>>>>
>>>> Irrelevant, as already noted above.
>>>
>>> It is not irrelevant at all. Most all of undecidability
>>> cease to exist in this system:
>>
>> It does not help if the system is not sound. Or if the particuar
>> undecidability that one happens to care about does not cease to
>> exist.
>
> Soundness is exactly why proof‑theoretic semantics matters here.
> When meaning is grounded in inferential structure and truth is anchored
> in an axiomatic base, only well‑founded expressions are admissible.
A system is useful only if admissibility is computable with a known
algorithm.
--
Mikko
[toc] | [prev] | [next] | [standalone]
| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2026-01-10 17:19 -0600 |
| Subject | Computation and Undecidability |
| Message-ID | <10jumqv$3haju$1@dont-email.me> |
| In reply to | #3768 |
On 1/10/2026 2:23 AM, Mikko wrote:
> On 09/01/2026 17:52, olcott wrote:
>> On 1/9/2026 3:59 AM, Mikko wrote:
>>> On 08/01/2026 16:22, olcott wrote:
>>>> On 1/8/2026 4:22 AM, Mikko wrote:
>>>>> On 07/01/2026 13:54, olcott wrote:
>>>>>> On 1/7/2026 5:49 AM, Mikko wrote:
>>>>>>> On 07/01/2026 06:44, olcott wrote:
>>>>>>>> All deciders essentially: Transform finite string
>>>>>>>> inputs by finite string transformation rules into
>>>>>>>> {Accept, Reject} values.
>>>>>>>>
>>>>>>>> The counter-example input to requires more than
>>>>>>>> can be derived from finite string transformation
>>>>>>>> rules applied to this specific input thus the
>>>>>>>> Halting Problem requires too much.
>>>>>>
>>>>>>> In a sense the halting problem asks too much: the problem is
>>>>>>> proven to
>>>>>>> be unsolvable. In another sense it asks too little: usually we
>>>>>>> want to
>>>>>>> know whether a method halts on every input, not just one.
>>>>>>>
>>>>>>> Although the halting problem is unsolvable, there are partial
>>>>>>> solutions
>>>>>>> to the halting problem. In particular, every counter-example to the
>>>>>>> full solution is correctly solved by some partial deciders.
>>>>>>
>>>>>> *if undecidability is correct then truth itself is broken*
>>>>>
>>>>> Depends on whether the word "truth" is interpeted in the standard
>>>>> sense or in Olcott's sense.
>>>>
>>>> Undecidability is misconception. Self-contradictory
>>>> expressions are correctly rejected as semantically
>>>> incoherent thus form no undecidability or incompleteness.
>>>
>>> The misconception is yours. No expression in the language of the first
>>> order group theory is self-contradictory. But the first order goupr
>>> theory is incomplete: it is impossible to prove that AB = BA is true
>>> for every A and every B but it is also impossible to prove that AB = BA
>>> is false for some A and some B.
>>>
>>
>> All deciders essentially: Transform finite string
>> inputs by finite string transformation rules into
>> {Accept, Reject} values.
>>
>> When a required result cannot be derived by applying
>> finite string transformation rules to actual finite
>> string inputs, then the required result exceeds the
>> scope of computation and must be rejected as an
>> incorrect requirement.
>
> No, that does not follow. If a required result cannot be derived by
> appying a finite string transformation then the it it is uncomputable.
> Of course, it one can prove that the required result is not computable
> then that helps to avoid wasting effort to try the impossible. The
> situation is worse if it is not known that the required result is not
> computable.
>
> That something is not computable does not mean that there is anyting
> "incorrect" in the requirement. In order to claim that a requirement
> is incorrect one must at least prove that the requirement does not
> serve its intended purpose. Even then it is possible that the
> requirement serves some other purpose. Even if a requirement serves
> no purpose that need not mean that it be "incorrect", only that it
> is useless.
>
*Computation and Undecidability*
Any result that cannot be derived as a pure function of
finite strings is outside the scope of computation. What
has been construed as decision problem undecidability
has always actually been requirements that are outside
of the scope of computation.
https://www.researchgate.net/publication/399111881_Computation_and_Undecidability
--
Copyright 2026 Olcott<br><br>
My 28 year goal has been to make <br>
"true on the basis of meaning expressed in language"<br>
reliably computable.<br><br>
This required establishing a new foundation<br>
[toc] | [prev] | [next] | [standalone]
| From | Richard Damon <news.x.richarddamon@xoxy.net> |
|---|---|
| Date | 2026-01-10 19:35 -0500 |
| Subject | Re: Computation and Undecidability |
| Message-ID | <10jur90$2erua$3@dont-email.me> |
| In reply to | #3772 |
On 1/10/26 6:19 PM, olcott wrote:
> On 1/10/2026 2:23 AM, Mikko wrote:
>> On 09/01/2026 17:52, olcott wrote:
>>> On 1/9/2026 3:59 AM, Mikko wrote:
>>>> On 08/01/2026 16:22, olcott wrote:
>>>>> On 1/8/2026 4:22 AM, Mikko wrote:
>>>>>> On 07/01/2026 13:54, olcott wrote:
>>>>>>> On 1/7/2026 5:49 AM, Mikko wrote:
>>>>>>>> On 07/01/2026 06:44, olcott wrote:
>>>>>>>>> All deciders essentially: Transform finite string
>>>>>>>>> inputs by finite string transformation rules into
>>>>>>>>> {Accept, Reject} values.
>>>>>>>>>
>>>>>>>>> The counter-example input to requires more than
>>>>>>>>> can be derived from finite string transformation
>>>>>>>>> rules applied to this specific input thus the
>>>>>>>>> Halting Problem requires too much.
>>>>>>>
>>>>>>>> In a sense the halting problem asks too much: the problem is
>>>>>>>> proven to
>>>>>>>> be unsolvable. In another sense it asks too little: usually we
>>>>>>>> want to
>>>>>>>> know whether a method halts on every input, not just one.
>>>>>>>>
>>>>>>>> Although the halting problem is unsolvable, there are partial
>>>>>>>> solutions
>>>>>>>> to the halting problem. In particular, every counter-example to the
>>>>>>>> full solution is correctly solved by some partial deciders.
>>>>>>>
>>>>>>> *if undecidability is correct then truth itself is broken*
>>>>>>
>>>>>> Depends on whether the word "truth" is interpeted in the standard
>>>>>> sense or in Olcott's sense.
>>>>>
>>>>> Undecidability is misconception. Self-contradictory
>>>>> expressions are correctly rejected as semantically
>>>>> incoherent thus form no undecidability or incompleteness.
>>>>
>>>> The misconception is yours. No expression in the language of the first
>>>> order group theory is self-contradictory. But the first order goupr
>>>> theory is incomplete: it is impossible to prove that AB = BA is true
>>>> for every A and every B but it is also impossible to prove that AB = BA
>>>> is false for some A and some B.
>>>>
>>>
>>> All deciders essentially: Transform finite string
>>> inputs by finite string transformation rules into
>>> {Accept, Reject} values.
>>>
>>> When a required result cannot be derived by applying
>>> finite string transformation rules to actual finite
>>> string inputs, then the required result exceeds the
>>> scope of computation and must be rejected as an
>>> incorrect requirement.
>>
>> No, that does not follow. If a required result cannot be derived by
>> appying a finite string transformation then the it it is uncomputable.
>> Of course, it one can prove that the required result is not computable
>> then that helps to avoid wasting effort to try the impossible. The
>> situation is worse if it is not known that the required result is not
>> computable.
>>
>> That something is not computable does not mean that there is anyting
>> "incorrect" in the requirement. In order to claim that a requirement
>> is incorrect one must at least prove that the requirement does not
>> serve its intended purpose. Even then it is possible that the
>> requirement serves some other purpose. Even if a requirement serves
>> no purpose that need not mean that it be "incorrect", only that it
>> is useless.
>>
>
> *Computation and Undecidability*
>
> Any result that cannot be derived as a pure function of
> finite strings is outside the scope of computation. What
> has been construed as decision problem undecidability
> has always actually been requirements that are outside
> of the scope of computation.
>
> https://www.researchgate.net/
> publication/399111881_Computation_and_Undecidability
>
So why isn't DD() -> Halts (since your HHH(DD) returns 0) not a pure
function of the input.
Now, if your DD doesn't include the code for HHH, then you show your
problem, your input isn't that of a program, and thus out of sco[e.
The Halting Problem only talks about the behavior of PROGRAMS, which
requires that the input specify ALL of the algorith/code used by it. so
your "C function" DD isn't a valid input without also specifying the
SPECIFIC HHH that it calls.
[toc] | [prev] | [next] | [standalone]
| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2026-01-10 19:03 -0600 |
| Subject | Re: Computation and Undecidability |
| Message-ID | <10jussi$3j0bu$1@dont-email.me> |
| In reply to | #3775 |
On 1/10/2026 6:35 PM, Richard Damon wrote:
> On 1/10/26 6:19 PM, olcott wrote:
>> On 1/10/2026 2:23 AM, Mikko wrote:
>>> On 09/01/2026 17:52, olcott wrote:
>>>> On 1/9/2026 3:59 AM, Mikko wrote:
>>>>> On 08/01/2026 16:22, olcott wrote:
>>>>>> On 1/8/2026 4:22 AM, Mikko wrote:
>>>>>>> On 07/01/2026 13:54, olcott wrote:
>>>>>>>> On 1/7/2026 5:49 AM, Mikko wrote:
>>>>>>>>> On 07/01/2026 06:44, olcott wrote:
>>>>>>>>>> All deciders essentially: Transform finite string
>>>>>>>>>> inputs by finite string transformation rules into
>>>>>>>>>> {Accept, Reject} values.
>>>>>>>>>>
>>>>>>>>>> The counter-example input to requires more than
>>>>>>>>>> can be derived from finite string transformation
>>>>>>>>>> rules applied to this specific input thus the
>>>>>>>>>> Halting Problem requires too much.
>>>>>>>>
>>>>>>>>> In a sense the halting problem asks too much: the problem is
>>>>>>>>> proven to
>>>>>>>>> be unsolvable. In another sense it asks too little: usually we
>>>>>>>>> want to
>>>>>>>>> know whether a method halts on every input, not just one.
>>>>>>>>>
>>>>>>>>> Although the halting problem is unsolvable, there are partial
>>>>>>>>> solutions
>>>>>>>>> to the halting problem. In particular, every counter-example to
>>>>>>>>> the
>>>>>>>>> full solution is correctly solved by some partial deciders.
>>>>>>>>
>>>>>>>> *if undecidability is correct then truth itself is broken*
>>>>>>>
>>>>>>> Depends on whether the word "truth" is interpeted in the standard
>>>>>>> sense or in Olcott's sense.
>>>>>>
>>>>>> Undecidability is misconception. Self-contradictory
>>>>>> expressions are correctly rejected as semantically
>>>>>> incoherent thus form no undecidability or incompleteness.
>>>>>
>>>>> The misconception is yours. No expression in the language of the first
>>>>> order group theory is self-contradictory. But the first order goupr
>>>>> theory is incomplete: it is impossible to prove that AB = BA is true
>>>>> for every A and every B but it is also impossible to prove that AB
>>>>> = BA
>>>>> is false for some A and some B.
>>>>>
>>>>
>>>> All deciders essentially: Transform finite string
>>>> inputs by finite string transformation rules into
>>>> {Accept, Reject} values.
>>>>
>>>> When a required result cannot be derived by applying
>>>> finite string transformation rules to actual finite
>>>> string inputs, then the required result exceeds the
>>>> scope of computation and must be rejected as an
>>>> incorrect requirement.
>>>
>>> No, that does not follow. If a required result cannot be derived by
>>> appying a finite string transformation then the it it is uncomputable.
>>> Of course, it one can prove that the required result is not computable
>>> then that helps to avoid wasting effort to try the impossible. The
>>> situation is worse if it is not known that the required result is not
>>> computable.
>>>
>>> That something is not computable does not mean that there is anyting
>>> "incorrect" in the requirement. In order to claim that a requirement
>>> is incorrect one must at least prove that the requirement does not
>>> serve its intended purpose. Even then it is possible that the
>>> requirement serves some other purpose. Even if a requirement serves
>>> no purpose that need not mean that it be "incorrect", only that it
>>> is useless.
>>>
>>
>> *Computation and Undecidability*
>>
>> Any result that cannot be derived as a pure function of
>> finite strings is outside the scope of computation. What
>> has been construed as decision problem undecidability
>> has always actually been requirements that are outside
>> of the scope of computation.
>>
>> https://www.researchgate.net/
>> publication/399111881_Computation_and_Undecidability
>>
*Computation and Undecidability*
https://philpapers.org/go.pl?aid=OLCCAU
>
> So why isn't DD() -> Halts (since your HHH(DD) returns 0) not a pure
> function of the input.
>
> Now, if your DD doesn't include the code for HHH, then you show your
> problem, your input isn't that of a program, and thus out of sco[e.
>
> The Halting Problem only talks about the behavior of PROGRAMS, which
> requires that the input specify ALL of the algorith/code used by it. so
> your "C function" DD isn't a valid input without also specifying the
> SPECIFIC HHH that it calls.
*ChatGPT explains how and why I am correct*
*Reinterpretation of undecidability*
The example of P and H demonstrates that what is
often called “undecidable” is better understood as
ill-posed with respect to computable semantics.
When the specification is constrained to properties
detectable via finite simulation and finite pattern
recognition, computation proceeds normally and
correctly. Undecidability only appears when the
specification overreaches that boundary.
--
Copyright 2026 Olcott<br><br>
My 28 year goal has been to make <br>
"true on the basis of meaning expressed in language"<br>
reliably computable.<br><br>
This required establishing a new foundation<br>
[toc] | [prev] | [next] | [standalone]
| From | Richard Damon <news.x.richarddamon@xoxy.net> |
|---|---|
| Date | 2026-01-10 21:03 -0500 |
| Subject | Re: Computation and Undecidability |
| Message-ID | <10jv0dr$2eruc$4@dont-email.me> |
| In reply to | #3777 |
On 1/10/26 8:03 PM, olcott wrote:
> On 1/10/2026 6:35 PM, Richard Damon wrote:
>> On 1/10/26 6:19 PM, olcott wrote:
>>> On 1/10/2026 2:23 AM, Mikko wrote:
>>>> On 09/01/2026 17:52, olcott wrote:
>>>>> On 1/9/2026 3:59 AM, Mikko wrote:
>>>>>> On 08/01/2026 16:22, olcott wrote:
>>>>>>> On 1/8/2026 4:22 AM, Mikko wrote:
>>>>>>>> On 07/01/2026 13:54, olcott wrote:
>>>>>>>>> On 1/7/2026 5:49 AM, Mikko wrote:
>>>>>>>>>> On 07/01/2026 06:44, olcott wrote:
>>>>>>>>>>> All deciders essentially: Transform finite string
>>>>>>>>>>> inputs by finite string transformation rules into
>>>>>>>>>>> {Accept, Reject} values.
>>>>>>>>>>>
>>>>>>>>>>> The counter-example input to requires more than
>>>>>>>>>>> can be derived from finite string transformation
>>>>>>>>>>> rules applied to this specific input thus the
>>>>>>>>>>> Halting Problem requires too much.
>>>>>>>>>
>>>>>>>>>> In a sense the halting problem asks too much: the problem is
>>>>>>>>>> proven to
>>>>>>>>>> be unsolvable. In another sense it asks too little: usually we
>>>>>>>>>> want to
>>>>>>>>>> know whether a method halts on every input, not just one.
>>>>>>>>>>
>>>>>>>>>> Although the halting problem is unsolvable, there are partial
>>>>>>>>>> solutions
>>>>>>>>>> to the halting problem. In particular, every counter-example
>>>>>>>>>> to the
>>>>>>>>>> full solution is correctly solved by some partial deciders.
>>>>>>>>>
>>>>>>>>> *if undecidability is correct then truth itself is broken*
>>>>>>>>
>>>>>>>> Depends on whether the word "truth" is interpeted in the standard
>>>>>>>> sense or in Olcott's sense.
>>>>>>>
>>>>>>> Undecidability is misconception. Self-contradictory
>>>>>>> expressions are correctly rejected as semantically
>>>>>>> incoherent thus form no undecidability or incompleteness.
>>>>>>
>>>>>> The misconception is yours. No expression in the language of the
>>>>>> first
>>>>>> order group theory is self-contradictory. But the first order goupr
>>>>>> theory is incomplete: it is impossible to prove that AB = BA is true
>>>>>> for every A and every B but it is also impossible to prove that AB
>>>>>> = BA
>>>>>> is false for some A and some B.
>>>>>>
>>>>>
>>>>> All deciders essentially: Transform finite string
>>>>> inputs by finite string transformation rules into
>>>>> {Accept, Reject} values.
>>>>>
>>>>> When a required result cannot be derived by applying
>>>>> finite string transformation rules to actual finite
>>>>> string inputs, then the required result exceeds the
>>>>> scope of computation and must be rejected as an
>>>>> incorrect requirement.
>>>>
>>>> No, that does not follow. If a required result cannot be derived by
>>>> appying a finite string transformation then the it it is uncomputable.
>>>> Of course, it one can prove that the required result is not computable
>>>> then that helps to avoid wasting effort to try the impossible. The
>>>> situation is worse if it is not known that the required result is not
>>>> computable.
>>>>
>>>> That something is not computable does not mean that there is anyting
>>>> "incorrect" in the requirement. In order to claim that a requirement
>>>> is incorrect one must at least prove that the requirement does not
>>>> serve its intended purpose. Even then it is possible that the
>>>> requirement serves some other purpose. Even if a requirement serves
>>>> no purpose that need not mean that it be "incorrect", only that it
>>>> is useless.
>>>>
>>>
>>> *Computation and Undecidability*
>>>
>>> Any result that cannot be derived as a pure function of
>>> finite strings is outside the scope of computation. What
>>> has been construed as decision problem undecidability
>>> has always actually been requirements that are outside
>>> of the scope of computation.
>>>
>>> https://www.researchgate.net/
>>> publication/399111881_Computation_and_Undecidability
>>>
>
> *Computation and Undecidability*
> https://philpapers.org/go.pl?aid=OLCCAU
Which just shows you don't know what you are talking about.
You said:
Any result that cannot be derived as a pure function of finite strings
is outside the scope of computation. What has been construed as decision
problem undecidability has always actually been requirements that are
outside of the scope of computation.
Which is just a LIE, based on not knowing what you are talking about.
The "Scope of Computation", as in what scope of problems that Compuation
Theory looks at, are the mappings of one domain (often limited to a
countably infinite domain so it is representable as a finte string) to
another domain.
The primary question of that domain, is which mapping can be computed by
a finite machine using a specific fully defined algorithm.
What you can your "Scope of Computation" is the range of what is
computable. In other words, the "Scope" of what we want to be able to
do, and thus the set of problems that ARE computable.
You don't seem to understand the differnce between the problem of
determining Computability and what is actually computable, just like you
don't understand the difference between Truth and Knowledge.
>
>>
>> So why isn't DD() -> Halts (since your HHH(DD) returns 0) not a pure
>> function of the input.
>>
>> Now, if your DD doesn't include the code for HHH, then you show your
>> problem, your input isn't that of a program, and thus out of sco[e.
>>
>> The Halting Problem only talks about the behavior of PROGRAMS, which
>> requires that the input specify ALL of the algorith/code used by it.
>> so your "C function" DD isn't a valid input without also specifying
>> the SPECIFIC HHH that it calls.
>
> *ChatGPT explains how and why I am correct*
>
> *Reinterpretation of undecidability*
> The example of P and H demonstrates that what is
> often called “undecidable” is better understood as
> ill-posed with respect to computable semantics.
> When the specification is constrained to properties
> detectable via finite simulation and finite pattern
> recognition, computation proceeds normally and
> correctly. Undecidability only appears when the
> specification overreaches that boundary.
>
But "Finite Simulation and finite pattern recognition" is NOT "Finiite
String Transformation".
So, you are just showing you don't understand what you are talking about.
[toc] | [prev] | [next] | [standalone]
| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2026-01-10 20:20 -0600 |
| Subject | Re: Computation and Undecidability |
| Message-ID | <10jv1ck$3k39b$1@dont-email.me> |
| In reply to | #3780 |
On 1/10/2026 8:03 PM, Richard Damon wrote:
> On 1/10/26 8:03 PM, olcott wrote:
>> On 1/10/2026 6:35 PM, Richard Damon wrote:
>>> On 1/10/26 6:19 PM, olcott wrote:
>>>> On 1/10/2026 2:23 AM, Mikko wrote:
>>>>> On 09/01/2026 17:52, olcott wrote:
>>>>>> On 1/9/2026 3:59 AM, Mikko wrote:
>>>>>>> On 08/01/2026 16:22, olcott wrote:
>>>>>>>> On 1/8/2026 4:22 AM, Mikko wrote:
>>>>>>>>> On 07/01/2026 13:54, olcott wrote:
>>>>>>>>>> On 1/7/2026 5:49 AM, Mikko wrote:
>>>>>>>>>>> On 07/01/2026 06:44, olcott wrote:
>>>>>>>>>>>> All deciders essentially: Transform finite string
>>>>>>>>>>>> inputs by finite string transformation rules into
>>>>>>>>>>>> {Accept, Reject} values.
>>>>>>>>>>>>
>>>>>>>>>>>> The counter-example input to requires more than
>>>>>>>>>>>> can be derived from finite string transformation
>>>>>>>>>>>> rules applied to this specific input thus the
>>>>>>>>>>>> Halting Problem requires too much.
>>>>>>>>>>
>>>>>>>>>>> In a sense the halting problem asks too much: the problem is
>>>>>>>>>>> proven to
>>>>>>>>>>> be unsolvable. In another sense it asks too little: usually
>>>>>>>>>>> we want to
>>>>>>>>>>> know whether a method halts on every input, not just one.
>>>>>>>>>>>
>>>>>>>>>>> Although the halting problem is unsolvable, there are partial
>>>>>>>>>>> solutions
>>>>>>>>>>> to the halting problem. In particular, every counter-example
>>>>>>>>>>> to the
>>>>>>>>>>> full solution is correctly solved by some partial deciders.
>>>>>>>>>>
>>>>>>>>>> *if undecidability is correct then truth itself is broken*
>>>>>>>>>
>>>>>>>>> Depends on whether the word "truth" is interpeted in the standard
>>>>>>>>> sense or in Olcott's sense.
>>>>>>>>
>>>>>>>> Undecidability is misconception. Self-contradictory
>>>>>>>> expressions are correctly rejected as semantically
>>>>>>>> incoherent thus form no undecidability or incompleteness.
>>>>>>>
>>>>>>> The misconception is yours. No expression in the language of the
>>>>>>> first
>>>>>>> order group theory is self-contradictory. But the first order goupr
>>>>>>> theory is incomplete: it is impossible to prove that AB = BA is true
>>>>>>> for every A and every B but it is also impossible to prove that
>>>>>>> AB = BA
>>>>>>> is false for some A and some B.
>>>>>>>
>>>>>>
>>>>>> All deciders essentially: Transform finite string
>>>>>> inputs by finite string transformation rules into
>>>>>> {Accept, Reject} values.
>>>>>>
>>>>>> When a required result cannot be derived by applying
>>>>>> finite string transformation rules to actual finite
>>>>>> string inputs, then the required result exceeds the
>>>>>> scope of computation and must be rejected as an
>>>>>> incorrect requirement.
>>>>>
>>>>> No, that does not follow. If a required result cannot be derived by
>>>>> appying a finite string transformation then the it it is uncomputable.
>>>>> Of course, it one can prove that the required result is not computable
>>>>> then that helps to avoid wasting effort to try the impossible. The
>>>>> situation is worse if it is not known that the required result is not
>>>>> computable.
>>>>>
>>>>> That something is not computable does not mean that there is anyting
>>>>> "incorrect" in the requirement. In order to claim that a requirement
>>>>> is incorrect one must at least prove that the requirement does not
>>>>> serve its intended purpose. Even then it is possible that the
>>>>> requirement serves some other purpose. Even if a requirement serves
>>>>> no purpose that need not mean that it be "incorrect", only that it
>>>>> is useless.
>>>>>
>>>>
>>>> *Computation and Undecidability*
>>>>
>>>> Any result that cannot be derived as a pure function of
>>>> finite strings is outside the scope of computation. What
>>>> has been construed as decision problem undecidability
>>>> has always actually been requirements that are outside
>>>> of the scope of computation.
>>>>
>>>> https://www.researchgate.net/
>>>> publication/399111881_Computation_and_Undecidability
>>>>
>>
>> *Computation and Undecidability*
>> https://philpapers.org/go.pl?aid=OLCCAU
>
> Which just shows you don't know what you are talking about.
>
> You said:
> Any result that cannot be derived as a pure function of finite strings
> is outside the scope of computation. What has been construed as decision
> problem undecidability has always actually been requirements that are
> outside of the scope of computation.
>
> Which is just a LIE, based on not knowing what you are talking about.
>
> The "Scope of Computation", as in what scope of problems that Compuation
> Theory looks at, are the mappings of one domain (often limited to a
> countably infinite domain so it is representable as a finte string) to
> another domain.
>
You merely are not bothering to pay close enough
attention to the exact meaning of my words.
> The primary question of that domain, is which mapping can be computed by
> a finite machine using a specific fully defined algorithm.
>
Yes you are correct about this, yet that is a mere
paraphrase of my own words.
> What you can your "Scope of Computation" is the range of what is
> computable.
Yes that is still correct.
> In other words, the "Scope" of what we want to be able to
> do,
Not at all you are totally incorrect and the regulars
that know comp.theory will confirm this.
> and thus the set of problems that ARE computable.
>
> You don't seem to understand the differnce between the problem of
> determining Computability and what is actually computable, just like you
> don't understand the difference between Truth and Knowledge.
>
I proved that I do understand by creating my
own formal definition that is consistent with
standard definitions.
All deciders essentially: Transform finite string
inputs by finite string transformation rules into
{Accept, Reject} values.
>>
>>>
>>> So why isn't DD() -> Halts (since your HHH(DD) returns 0) not a pure
>>> function of the input.
>>>
>>> Now, if your DD doesn't include the code for HHH, then you show your
>>> problem, your input isn't that of a program, and thus out of sco[e.
>>>
>>> The Halting Problem only talks about the behavior of PROGRAMS, which
>>> requires that the input specify ALL of the algorith/code used by it.
>>> so your "C function" DD isn't a valid input without also specifying
>>> the SPECIFIC HHH that it calls.
>>
>> *ChatGPT explains how and why I am correct*
>>
>> *Reinterpretation of undecidability*
>> The example of P and H demonstrates that what is
>> often called “undecidable” is better understood as
>> ill-posed with respect to computable semantics.
>> When the specification is constrained to properties
>> detectable via finite simulation and finite pattern
>> recognition, computation proceeds normally and
>> correctly. Undecidability only appears when the
>> specification overreaches that boundary.
>>
>
> But "Finite Simulation and finite pattern recognition" is NOT "Finiite
> String Transformation".
>
> So, you are just showing you don't understand what you are talking about.
You are just showing you don't understand what you are talking about:
That you don't even know what elements are in the finite string
transformations prove this. *finite simulation* is the ultimate
measure of the behavior that an input finite string specifies.
--
Copyright 2026 Olcott<br><br>
My 28 year goal has been to make <br>
"true on the basis of meaning expressed in language"<br>
reliably computable.<br><br>
This required establishing a new foundation<br>
[toc] | [prev] | [next] | [standalone]
| From | Richard Damon <news.x.richarddamon@xoxy.net> |
|---|---|
| Date | 2026-01-10 21:33 -0500 |
| Subject | Re: Computation and Undecidability |
| Message-ID | <10jv264$2erua$5@dont-email.me> |
| In reply to | #3783 |
On 1/10/26 9:20 PM, olcott wrote:
> On 1/10/2026 8:03 PM, Richard Damon wrote:
>> On 1/10/26 8:03 PM, olcott wrote:
>>> On 1/10/2026 6:35 PM, Richard Damon wrote:
>>>> On 1/10/26 6:19 PM, olcott wrote:
>>>>> On 1/10/2026 2:23 AM, Mikko wrote:
>>>>>> On 09/01/2026 17:52, olcott wrote:
>>>>>>> On 1/9/2026 3:59 AM, Mikko wrote:
>>>>>>>> On 08/01/2026 16:22, olcott wrote:
>>>>>>>>> On 1/8/2026 4:22 AM, Mikko wrote:
>>>>>>>>>> On 07/01/2026 13:54, olcott wrote:
>>>>>>>>>>> On 1/7/2026 5:49 AM, Mikko wrote:
>>>>>>>>>>>> On 07/01/2026 06:44, olcott wrote:
>>>>>>>>>>>>> All deciders essentially: Transform finite string
>>>>>>>>>>>>> inputs by finite string transformation rules into
>>>>>>>>>>>>> {Accept, Reject} values.
>>>>>>>>>>>>>
>>>>>>>>>>>>> The counter-example input to requires more than
>>>>>>>>>>>>> can be derived from finite string transformation
>>>>>>>>>>>>> rules applied to this specific input thus the
>>>>>>>>>>>>> Halting Problem requires too much.
>>>>>>>>>>>
>>>>>>>>>>>> In a sense the halting problem asks too much: the problem is
>>>>>>>>>>>> proven to
>>>>>>>>>>>> be unsolvable. In another sense it asks too little: usually
>>>>>>>>>>>> we want to
>>>>>>>>>>>> know whether a method halts on every input, not just one.
>>>>>>>>>>>>
>>>>>>>>>>>> Although the halting problem is unsolvable, there are
>>>>>>>>>>>> partial solutions
>>>>>>>>>>>> to the halting problem. In particular, every counter-example
>>>>>>>>>>>> to the
>>>>>>>>>>>> full solution is correctly solved by some partial deciders.
>>>>>>>>>>>
>>>>>>>>>>> *if undecidability is correct then truth itself is broken*
>>>>>>>>>>
>>>>>>>>>> Depends on whether the word "truth" is interpeted in the standard
>>>>>>>>>> sense or in Olcott's sense.
>>>>>>>>>
>>>>>>>>> Undecidability is misconception. Self-contradictory
>>>>>>>>> expressions are correctly rejected as semantically
>>>>>>>>> incoherent thus form no undecidability or incompleteness.
>>>>>>>>
>>>>>>>> The misconception is yours. No expression in the language of the
>>>>>>>> first
>>>>>>>> order group theory is self-contradictory. But the first order goupr
>>>>>>>> theory is incomplete: it is impossible to prove that AB = BA is
>>>>>>>> true
>>>>>>>> for every A and every B but it is also impossible to prove that
>>>>>>>> AB = BA
>>>>>>>> is false for some A and some B.
>>>>>>>>
>>>>>>>
>>>>>>> All deciders essentially: Transform finite string
>>>>>>> inputs by finite string transformation rules into
>>>>>>> {Accept, Reject} values.
>>>>>>>
>>>>>>> When a required result cannot be derived by applying
>>>>>>> finite string transformation rules to actual finite
>>>>>>> string inputs, then the required result exceeds the
>>>>>>> scope of computation and must be rejected as an
>>>>>>> incorrect requirement.
>>>>>>
>>>>>> No, that does not follow. If a required result cannot be derived by
>>>>>> appying a finite string transformation then the it it is
>>>>>> uncomputable.
>>>>>> Of course, it one can prove that the required result is not
>>>>>> computable
>>>>>> then that helps to avoid wasting effort to try the impossible. The
>>>>>> situation is worse if it is not known that the required result is not
>>>>>> computable.
>>>>>>
>>>>>> That something is not computable does not mean that there is anyting
>>>>>> "incorrect" in the requirement. In order to claim that a requirement
>>>>>> is incorrect one must at least prove that the requirement does not
>>>>>> serve its intended purpose. Even then it is possible that the
>>>>>> requirement serves some other purpose. Even if a requirement serves
>>>>>> no purpose that need not mean that it be "incorrect", only that it
>>>>>> is useless.
>>>>>>
>>>>>
>>>>> *Computation and Undecidability*
>>>>>
>>>>> Any result that cannot be derived as a pure function of
>>>>> finite strings is outside the scope of computation. What
>>>>> has been construed as decision problem undecidability
>>>>> has always actually been requirements that are outside
>>>>> of the scope of computation.
>>>>>
>>>>> https://www.researchgate.net/
>>>>> publication/399111881_Computation_and_Undecidability
>>>>>
>>>
>>> *Computation and Undecidability*
>>> https://philpapers.org/go.pl?aid=OLCCAU
>>
>> Which just shows you don't know what you are talking about.
>>
>> You said:
>> Any result that cannot be derived as a pure function of finite strings
>> is outside the scope of computation. What has been construed as
>> decision problem undecidability has always actually been requirements
>> that are outside of the scope of computation.
>>
>> Which is just a LIE, based on not knowing what you are talking about.
>>
>> The "Scope of Computation", as in what scope of problems that
>> Compuation Theory looks at, are the mappings of one domain (often
>> limited to a countably infinite domain so it is representable as a
>> finte string) to another domain.
>>
>
> You merely are not bothering to pay close enough
> attention to the exact meaning of my words.
No, the problem is YOU don't know the actual meaning of your words.
>
>> The primary question of that domain, is which mapping can be computed
>> by a finite machine using a specific fully defined algorithm.
>>
>
> Yes you are correct about this, yet that is a mere
> paraphrase of my own words.
Which means YOUR WORDS are the incorrect paraphrase.
>
>> What you can your "Scope of Computation" is the range of what is
>> computable.
>
> Yes that is still correct.
Nops, which just shows you don't know the actual meaning of your words.
>
>> In other words, the "Scope" of what we want to be able to do,
>
> Not at all you are totally incorrect and the regulars
> that know comp.theory will confirm this.
We will see.
>
>> and thus the set of problems that ARE computable.
>>
>> You don't seem to understand the differnce between the problem of
>> determining Computability and what is actually computable, just like
>> you don't understand the difference between Truth and Knowledge.
>>
>
> I proved that I do understand by creating my
> own formal definition that is consistent with
> standard definitions.
Nope.
That you think it is, just shows youy are just a pathological liar.
>
> All deciders essentially: Transform finite string
> inputs by finite string transformation rules into
> {Accept, Reject} values.
Right, which is irrelevant for the scope of the field, it shows the
capabilities of the machines, which the field is trying to determine.
>
>
>>>
>>>>
>>>> So why isn't DD() -> Halts (since your HHH(DD) returns 0) not a pure
>>>> function of the input.
>>>>
>>>> Now, if your DD doesn't include the code for HHH, then you show your
>>>> problem, your input isn't that of a program, and thus out of sco[e.
>>>>
>>>> The Halting Problem only talks about the behavior of PROGRAMS, which
>>>> requires that the input specify ALL of the algorith/code used by it.
>>>> so your "C function" DD isn't a valid input without also specifying
>>>> the SPECIFIC HHH that it calls.
>>>
>>> *ChatGPT explains how and why I am correct*
>>>
>>> *Reinterpretation of undecidability*
>>> The example of P and H demonstrates that what is
>>> often called “undecidable” is better understood as
>>> ill-posed with respect to computable semantics.
>>> When the specification is constrained to properties
>>> detectable via finite simulation and finite pattern
>>> recognition, computation proceeds normally and
>>> correctly. Undecidability only appears when the
>>> specification overreaches that boundary.
>>>
>>
>> But "Finite Simulation and finite pattern recognition" is NOT "Finiite
>> String Transformation".
>>
>> So, you are just showing you don't understand what you are talking about.
>
> You are just showing you don't understand what you are talking about:
> That you don't even know what elements are in the finite string
> transformations prove this. *finite simulation* is the ultimate
> measure of the behavior that an input finite string specifies.
>
Really, what in the basic meaning of the words limits them to what you wnat.
Why isn't "(DD)" -> Halt a "Transformation" of a "Finite String"?
Your problem is you logic doesn't actually use semantics, so words don't
actually have meaning.
[toc] | [prev] | [next] | [standalone]
| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2026-01-10 21:18 -0600 |
| Subject | Re: Computation and Undecidability |
| Message-ID | <10jv4q4$3krd2$2@dont-email.me> |
| In reply to | #3786 |
On 1/10/2026 8:33 PM, Richard Damon wrote:
> On 1/10/26 9:20 PM, olcott wrote:
>> On 1/10/2026 8:03 PM, Richard Damon wrote:
>>> On 1/10/26 8:03 PM, olcott wrote:
>>>> On 1/10/2026 6:35 PM, Richard Damon wrote:
>>>>> On 1/10/26 6:19 PM, olcott wrote:
>>>>>> On 1/10/2026 2:23 AM, Mikko wrote:
>>>>>>> On 09/01/2026 17:52, olcott wrote:
>>>>>>>> On 1/9/2026 3:59 AM, Mikko wrote:
>>>>>>>>> On 08/01/2026 16:22, olcott wrote:
>>>>>>>>>> On 1/8/2026 4:22 AM, Mikko wrote:
>>>>>>>>>>> On 07/01/2026 13:54, olcott wrote:
>>>>>>>>>>>> On 1/7/2026 5:49 AM, Mikko wrote:
>>>>>>>>>>>>> On 07/01/2026 06:44, olcott wrote:
>>>>>>>>>>>>>> All deciders essentially: Transform finite string
>>>>>>>>>>>>>> inputs by finite string transformation rules into
>>>>>>>>>>>>>> {Accept, Reject} values.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> The counter-example input to requires more than
>>>>>>>>>>>>>> can be derived from finite string transformation
>>>>>>>>>>>>>> rules applied to this specific input thus the
>>>>>>>>>>>>>> Halting Problem requires too much.
>>>>>>>>>>>>
>>>>>>>>>>>>> In a sense the halting problem asks too much: the problem
>>>>>>>>>>>>> is proven to
>>>>>>>>>>>>> be unsolvable. In another sense it asks too little: usually
>>>>>>>>>>>>> we want to
>>>>>>>>>>>>> know whether a method halts on every input, not just one.
>>>>>>>>>>>>>
>>>>>>>>>>>>> Although the halting problem is unsolvable, there are
>>>>>>>>>>>>> partial solutions
>>>>>>>>>>>>> to the halting problem. In particular, every counter-
>>>>>>>>>>>>> example to the
>>>>>>>>>>>>> full solution is correctly solved by some partial deciders.
>>>>>>>>>>>>
>>>>>>>>>>>> *if undecidability is correct then truth itself is broken*
>>>>>>>>>>>
>>>>>>>>>>> Depends on whether the word "truth" is interpeted in the
>>>>>>>>>>> standard
>>>>>>>>>>> sense or in Olcott's sense.
>>>>>>>>>>
>>>>>>>>>> Undecidability is misconception. Self-contradictory
>>>>>>>>>> expressions are correctly rejected as semantically
>>>>>>>>>> incoherent thus form no undecidability or incompleteness.
>>>>>>>>>
>>>>>>>>> The misconception is yours. No expression in the language of
>>>>>>>>> the first
>>>>>>>>> order group theory is self-contradictory. But the first order
>>>>>>>>> goupr
>>>>>>>>> theory is incomplete: it is impossible to prove that AB = BA is
>>>>>>>>> true
>>>>>>>>> for every A and every B but it is also impossible to prove that
>>>>>>>>> AB = BA
>>>>>>>>> is false for some A and some B.
>>>>>>>>>
>>>>>>>>
>>>>>>>> All deciders essentially: Transform finite string
>>>>>>>> inputs by finite string transformation rules into
>>>>>>>> {Accept, Reject} values.
>>>>>>>>
>>>>>>>> When a required result cannot be derived by applying
>>>>>>>> finite string transformation rules to actual finite
>>>>>>>> string inputs, then the required result exceeds the
>>>>>>>> scope of computation and must be rejected as an
>>>>>>>> incorrect requirement.
>>>>>>>
>>>>>>> No, that does not follow. If a required result cannot be derived by
>>>>>>> appying a finite string transformation then the it it is
>>>>>>> uncomputable.
>>>>>>> Of course, it one can prove that the required result is not
>>>>>>> computable
>>>>>>> then that helps to avoid wasting effort to try the impossible. The
>>>>>>> situation is worse if it is not known that the required result is
>>>>>>> not
>>>>>>> computable.
>>>>>>>
>>>>>>> That something is not computable does not mean that there is anyting
>>>>>>> "incorrect" in the requirement. In order to claim that a requirement
>>>>>>> is incorrect one must at least prove that the requirement does not
>>>>>>> serve its intended purpose. Even then it is possible that the
>>>>>>> requirement serves some other purpose. Even if a requirement serves
>>>>>>> no purpose that need not mean that it be "incorrect", only that it
>>>>>>> is useless.
>>>>>>>
>>>>>>
>>>>>> *Computation and Undecidability*
>>>>>>
>>>>>> Any result that cannot be derived as a pure function of
>>>>>> finite strings is outside the scope of computation. What
>>>>>> has been construed as decision problem undecidability
>>>>>> has always actually been requirements that are outside
>>>>>> of the scope of computation.
>>>>>>
>>>>>> https://www.researchgate.net/
>>>>>> publication/399111881_Computation_and_Undecidability
>>>>>>
>>>>
>>>> *Computation and Undecidability*
>>>> https://philpapers.org/go.pl?aid=OLCCAU
>>>
>>> Which just shows you don't know what you are talking about.
>>>
>>> You said:
>>> Any result that cannot be derived as a pure function of finite
>>> strings is outside the scope of computation. What has been construed
>>> as decision problem undecidability has always actually been
>>> requirements that are outside of the scope of computation.
>>>
>>> Which is just a LIE, based on not knowing what you are talking about.
>>>
>>> The "Scope of Computation", as in what scope of problems that
>>> Compuation Theory looks at, are the mappings of one domain (often
>>> limited to a countably infinite domain so it is representable as a
>>> finte string) to another domain.
>>>
>>
>> You merely are not bothering to pay close enough
>> attention to the exact meaning of my words.
>
> No, the problem is YOU don't know the actual meaning of your words.
>
>
>>
>>> The primary question of that domain, is which mapping can be computed
>>> by a finite machine using a specific fully defined algorithm.
>>>
>>
>> Yes you are correct about this, yet that is a mere
>> paraphrase of my own words.
>
> Which means YOUR WORDS are the incorrect paraphrase.
>
>>
>>> What you can your "Scope of Computation" is the range of what is
>>> computable.
>>
>> Yes that is still correct.
>
> Nops, which just shows you don't know the actual meaning of your words.
>
>>
>>> In other words, the "Scope" of what we want to be able to do,
>>
>> Not at all you are totally incorrect and the regulars
>> that know comp.theory will confirm this.
>
> We will see.
>
>>
>>> and thus the set of problems that ARE computable.
>>>
>>> You don't seem to understand the differnce between the problem of
>>> determining Computability and what is actually computable, just like
>>> you don't understand the difference between Truth and Knowledge.
>>>
>>
>> I proved that I do understand by creating my
>> own formal definition that is consistent with
>> standard definitions.
>
> Nope.
>
> That you think it is, just shows youy are just a pathological liar.
>
>>
>> All deciders essentially: Transform finite string
>> inputs by finite string transformation rules into
>> {Accept, Reject} values.
>
> Right, which is irrelevant for the scope of the field, it shows the
> capabilities of the machines, which the field is trying to determine.
>
IT IS THE SCOPE OF THE FIELD
--
Copyright 2026 Olcott<br><br>
My 28 year goal has been to make <br>
"true on the basis of meaning expressed in language"<br>
reliably computable.<br><br>
This required establishing a new foundation<br>
[toc] | [prev] | [next] | [standalone]
| From | Richard Damon <news.x.richarddamon@xoxy.net> |
|---|---|
| Date | 2026-01-10 22:30 -0500 |
| Subject | Re: Computation and Undecidability |
| Message-ID | <10jv5g2$2erua$9@dont-email.me> |
| In reply to | #3789 |
On 1/10/26 10:18 PM, olcott wrote:
> On 1/10/2026 8:33 PM, Richard Damon wrote:
>> On 1/10/26 9:20 PM, olcott wrote:
>>> On 1/10/2026 8:03 PM, Richard Damon wrote:
>>>> On 1/10/26 8:03 PM, olcott wrote:
>>>>> On 1/10/2026 6:35 PM, Richard Damon wrote:
>>>>>> On 1/10/26 6:19 PM, olcott wrote:
>>>>>>> On 1/10/2026 2:23 AM, Mikko wrote:
>>>>>>>> On 09/01/2026 17:52, olcott wrote:
>>>>>>>>> On 1/9/2026 3:59 AM, Mikko wrote:
>>>>>>>>>> On 08/01/2026 16:22, olcott wrote:
>>>>>>>>>>> On 1/8/2026 4:22 AM, Mikko wrote:
>>>>>>>>>>>> On 07/01/2026 13:54, olcott wrote:
>>>>>>>>>>>>> On 1/7/2026 5:49 AM, Mikko wrote:
>>>>>>>>>>>>>> On 07/01/2026 06:44, olcott wrote:
>>>>>>>>>>>>>>> All deciders essentially: Transform finite string
>>>>>>>>>>>>>>> inputs by finite string transformation rules into
>>>>>>>>>>>>>>> {Accept, Reject} values.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> The counter-example input to requires more than
>>>>>>>>>>>>>>> can be derived from finite string transformation
>>>>>>>>>>>>>>> rules applied to this specific input thus the
>>>>>>>>>>>>>>> Halting Problem requires too much.
>>>>>>>>>>>>>
>>>>>>>>>>>>>> In a sense the halting problem asks too much: the problem
>>>>>>>>>>>>>> is proven to
>>>>>>>>>>>>>> be unsolvable. In another sense it asks too little:
>>>>>>>>>>>>>> usually we want to
>>>>>>>>>>>>>> know whether a method halts on every input, not just one.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Although the halting problem is unsolvable, there are
>>>>>>>>>>>>>> partial solutions
>>>>>>>>>>>>>> to the halting problem. In particular, every counter-
>>>>>>>>>>>>>> example to the
>>>>>>>>>>>>>> full solution is correctly solved by some partial deciders.
>>>>>>>>>>>>>
>>>>>>>>>>>>> *if undecidability is correct then truth itself is broken*
>>>>>>>>>>>>
>>>>>>>>>>>> Depends on whether the word "truth" is interpeted in the
>>>>>>>>>>>> standard
>>>>>>>>>>>> sense or in Olcott's sense.
>>>>>>>>>>>
>>>>>>>>>>> Undecidability is misconception. Self-contradictory
>>>>>>>>>>> expressions are correctly rejected as semantically
>>>>>>>>>>> incoherent thus form no undecidability or incompleteness.
>>>>>>>>>>
>>>>>>>>>> The misconception is yours. No expression in the language of
>>>>>>>>>> the first
>>>>>>>>>> order group theory is self-contradictory. But the first order
>>>>>>>>>> goupr
>>>>>>>>>> theory is incomplete: it is impossible to prove that AB = BA
>>>>>>>>>> is true
>>>>>>>>>> for every A and every B but it is also impossible to prove
>>>>>>>>>> that AB = BA
>>>>>>>>>> is false for some A and some B.
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> All deciders essentially: Transform finite string
>>>>>>>>> inputs by finite string transformation rules into
>>>>>>>>> {Accept, Reject} values.
>>>>>>>>>
>>>>>>>>> When a required result cannot be derived by applying
>>>>>>>>> finite string transformation rules to actual finite
>>>>>>>>> string inputs, then the required result exceeds the
>>>>>>>>> scope of computation and must be rejected as an
>>>>>>>>> incorrect requirement.
>>>>>>>>
>>>>>>>> No, that does not follow. If a required result cannot be derived by
>>>>>>>> appying a finite string transformation then the it it is
>>>>>>>> uncomputable.
>>>>>>>> Of course, it one can prove that the required result is not
>>>>>>>> computable
>>>>>>>> then that helps to avoid wasting effort to try the impossible. The
>>>>>>>> situation is worse if it is not known that the required result
>>>>>>>> is not
>>>>>>>> computable.
>>>>>>>>
>>>>>>>> That something is not computable does not mean that there is
>>>>>>>> anyting
>>>>>>>> "incorrect" in the requirement. In order to claim that a
>>>>>>>> requirement
>>>>>>>> is incorrect one must at least prove that the requirement does not
>>>>>>>> serve its intended purpose. Even then it is possible that the
>>>>>>>> requirement serves some other purpose. Even if a requirement serves
>>>>>>>> no purpose that need not mean that it be "incorrect", only that it
>>>>>>>> is useless.
>>>>>>>>
>>>>>>>
>>>>>>> *Computation and Undecidability*
>>>>>>>
>>>>>>> Any result that cannot be derived as a pure function of
>>>>>>> finite strings is outside the scope of computation. What
>>>>>>> has been construed as decision problem undecidability
>>>>>>> has always actually been requirements that are outside
>>>>>>> of the scope of computation.
>>>>>>>
>>>>>>> https://www.researchgate.net/
>>>>>>> publication/399111881_Computation_and_Undecidability
>>>>>>>
>>>>>
>>>>> *Computation and Undecidability*
>>>>> https://philpapers.org/go.pl?aid=OLCCAU
>>>>
>>>> Which just shows you don't know what you are talking about.
>>>>
>>>> You said:
>>>> Any result that cannot be derived as a pure function of finite
>>>> strings is outside the scope of computation. What has been construed
>>>> as decision problem undecidability has always actually been
>>>> requirements that are outside of the scope of computation.
>>>>
>>>> Which is just a LIE, based on not knowing what you are talking about.
>>>>
>>>> The "Scope of Computation", as in what scope of problems that
>>>> Compuation Theory looks at, are the mappings of one domain (often
>>>> limited to a countably infinite domain so it is representable as a
>>>> finte string) to another domain.
>>>>
>>>
>>> You merely are not bothering to pay close enough
>>> attention to the exact meaning of my words.
>>
>> No, the problem is YOU don't know the actual meaning of your words.
>>
>>
>>>
>>>> The primary question of that domain, is which mapping can be
>>>> computed by a finite machine using a specific fully defined algorithm.
>>>>
>>>
>>> Yes you are correct about this, yet that is a mere
>>> paraphrase of my own words.
>>
>> Which means YOUR WORDS are the incorrect paraphrase.
>>
>>>
>>>> What you can your "Scope of Computation" is the range of what is
>>>> computable.
>>>
>>> Yes that is still correct.
>>
>> Nops, which just shows you don't know the actual meaning of your words.
>>
>>>
>>>> In other words, the "Scope" of what we want to be able to do,
>>>
>>> Not at all you are totally incorrect and the regulars
>>> that know comp.theory will confirm this.
>>
>> We will see.
>>
>>>
>>>> and thus the set of problems that ARE computable.
>>>>
>>>> You don't seem to understand the differnce between the problem of
>>>> determining Computability and what is actually computable, just like
>>>> you don't understand the difference between Truth and Knowledge.
>>>>
>>>
>>> I proved that I do understand by creating my
>>> own formal definition that is consistent with
>>> standard definitions.
>>
>> Nope.
>>
>> That you think it is, just shows youy are just a pathological liar.
>>
>>>
>>> All deciders essentially: Transform finite string
>>> inputs by finite string transformation rules into
>>> {Accept, Reject} values.
>>
>> Right, which is irrelevant for the scope of the field, it shows the
>> capabilities of the machines, which the field is trying to determine.
>>
>
> IT IS THE SCOPE OF THE FIELD
>
>
Nope, Just of your stupidity.
How can its question be about what IS computable, if you try to restrict
the scope to what is.
It seems the only answer you allow is yes.
But then, in a logic system that is inconsistant, everything is true, so
I guess you are just being consistant in your error.
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