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.
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.
Requiring an answer to a yes/no question that has no correct yes/no
answer is an incorrect question that must be rejected.
In order to claim that a requirement
is incorrect one must at least prove that the requirement does not
serve its intended purpose.
Requiring the impossible cannot possibly serve any purpose
except perhaps to exemplify one's own ignorance.
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.
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.
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:*if undecidability is correct then truth itself is broken*
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. >>>>>>>>>
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.
*ChatGPT explains how and why I am correct*
-a *Reinterpretation of undecidability*
-a The example of P and H demonstrates that what is
-a often called rCLundecidablerCY is better understood as
-a ill-posed with respect to computable semantics.
-a When the specification is constrained to properties
-a detectable via finite simulation and finite pattern
-a recognition, computation proceeds normally and
-a correctly. Undecidability only appears when the
-a specification overreaches that boundary.
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:*if undecidability is correct then truth itself is broken*
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. >>>>>>>>>
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.
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:Right. Outside the scope of computation. Requiring anything
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:*if undecidability is correct then truth itself is broken*
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. >>>>>>>>>>
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. >>>>
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*
-a-a *Reinterpretation of undecidability*
-a-a The example of P and H demonstrates that what is
-a-a often called rCLundecidablerCY is better understood as
-a-a ill-posed with respect to computable semantics.
-a-a When the specification is constrained to properties
-a-a detectable via finite simulation and finite pattern
-a-a recognition, computation proceeds normally and
-a-a correctly. Undecidability only appears when the
-a-a specification overreaches that boundary.
It tries to explain but it does not prove.
On 11/01/2026 16:24, Tristan Wibberley wrote:
On 11/01/2026 10:13, Mikko wrote:
On 10/01/2026 17:47, olcott wrote:
On 1/10/2026 2:23 AM, Mikko wrote:
No, that does not follow. If a required result cannot be derived byRight. Outside the scope of computation. Requiring anything
appying a finite string transformation then the it it is uncomputable. >>>>
outside the scope of computation is an incorrect requirement.
You can't determine whether the required result is computable before
you have the requirement.
Right, it is /in/ scope for computer science... for the /ology/. Olcott
here uses "computation" to refer to the practice. You give the
requirement to the /ologist/ who correctly decides that it is not for
computation because it is not computable.
You two so often violently agree; I find it warming to the heart.
For pracitcal programming it is useful to know what is known to be uncomputable in order to avoid wasting time in attemlpts to do the impossible.
On 1/12/2026 4:44 AM, Mikko wrote:
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:Depends on whether the word "truth" is interpeted in the standard >>>>>>>>>> sense or in Olcott's sense.
On 07/01/2026 06:44, olcott wrote:*if undecidability is correct then truth itself is broken* >>>>>>>>>>
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. >>>>>>>>>>>
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*
-a-a *Reinterpretation of undecidability*
-a-a The example of P and H demonstrates that what is
-a-a often called rCLundecidablerCY is better understood as
-a-a ill-posed with respect to computable semantics.
-a-a When the specification is constrained to properties
-a-a detectable via finite simulation and finite pattern
-a-a recognition, computation proceeds normally and
-a-a correctly. Undecidability only appears when the
-a-a specification overreaches that boundary.
It tries to explain but it does not prove.
Its the same thing that I have been saying for years.
It is not that a universal halt decider cannot exist.
It is that an input that does the opposite of whatever
value the halt decider returns is non-well-founded
within proof-theoretic semantics.
On 1/12/2026 4:47 AM, Mikko wrote:
On 11/01/2026 16:24, Tristan Wibberley wrote:
On 11/01/2026 10:13, Mikko wrote:
On 10/01/2026 17:47, olcott wrote:
On 1/10/2026 2:23 AM, Mikko wrote:
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.
Right, it is /in/ scope for computer science... for the /ology/. Olcott
here uses "computation" to refer to the practice. You give the
requirement to the /ologist/ who correctly decides that it is not for
computation because it is not computable.
You two so often violently agree; I find it warming to the heart.
For pracitcal programming it is useful to know what is known to be
uncomputable in order to avoid wasting time in attemlpts to do the
impossible.
It f-cking nuts that after more than 2000 years
people still don't understand that self-contradictory
expressions: "This sentence is not true" have no
truth value. A smart high school student should have
figured this out 2000 years ago.
On 1/12/2026 4:44 AM, Mikko wrote:
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:Depends on whether the word "truth" is interpeted in the standard >>>>>>>>>> sense or in Olcott's sense.
On 07/01/2026 06:44, olcott wrote:*if undecidability is correct then truth itself is broken* >>>>>>>>>>
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. >>>>>>>>>>>
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*
-a-a *Reinterpretation of undecidability*
-a-a The example of P and H demonstrates that what is
-a-a often called rCLundecidablerCY is better understood as
-a-a ill-posed with respect to computable semantics.
-a-a When the specification is constrained to properties
-a-a detectable via finite simulation and finite pattern
-a-a recognition, computation proceeds normally and
-a-a correctly. Undecidability only appears when the
-a-a specification overreaches that boundary.
It tries to explain but it does not prove.
Its the same thing that I have been saying for years.
It is not that a universal halt decider cannot exist.
It is that an input that does the opposite of whatever
value the halt decider returns is non-well-founded
within proof-theoretic semantics.
On 1/12/2026 4:47 AM, Mikko wrote:
On 11/01/2026 16:24, Tristan Wibberley wrote:
On 11/01/2026 10:13, Mikko wrote:
On 10/01/2026 17:47, olcott wrote:
On 1/10/2026 2:23 AM, Mikko wrote:
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.
Right, it is /in/ scope for computer science... for the /ology/. Olcott
here uses "computation" to refer to the practice. You give the
requirement to the /ologist/ who correctly decides that it is not for
computation because it is not computable.
You two so often violently agree; I find it warming to the heart.
For pracitcal programming it is useful to know what is known to be
uncomputable in order to avoid wasting time in attemlpts to do the
impossible.
It f-cking nuts that after more than 2000 years
people still don't understand that self-contradictory
expressions: "This sentence is not true" have no
truth value. A smart high school student should have
figured this out 2000 years ago.
On 12/01/2026 16:29, olcott wrote:
On 1/12/2026 4:44 AM, Mikko wrote:
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:Depends on whether the word "truth" is interpeted in the >>>>>>>>>>> standard
On 07/01/2026 06:44, olcott wrote:*if undecidability is correct then truth itself is broken* >>>>>>>>>>>
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. >>>>>>>>>>>>
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*
-a-a *Reinterpretation of undecidability*
-a-a The example of P and H demonstrates that what is
-a-a often called rCLundecidablerCY is better understood as
-a-a ill-posed with respect to computable semantics.
-a-a When the specification is constrained to properties
-a-a detectable via finite simulation and finite pattern
-a-a recognition, computation proceeds normally and
-a-a correctly. Undecidability only appears when the
-a-a specification overreaches that boundary.
It tries to explain but it does not prove.
Its the same thing that I have been saying for years.
It is not that a universal halt decider cannot exist.
It is proven that an universal halt decider does not exist.
A Turing
machine cannot determine the halting of all Turing machines and is
therefore not an universla halt decider.
An oracle machine may be
able to determine the haltinf of all Turing machines but not of all
oracle machines with the same oracle (or oracles) so it is not
universal.
It is that an input that does the opposite of whatever
value the halt decider returns is non-well-founded
within proof-theoretic semantics.
Yes, it is. What the "halt decider" returns is determinable: just run
it and see what it returns. From that the rest can be proven with a
well founded proof. In particular, there is a well-founded proof that
the "halt decider" is not a halt decider.
On 12/01/2026 16:32, olcott wrote:
On 1/12/2026 4:47 AM, Mikko wrote:
On 11/01/2026 16:24, Tristan Wibberley wrote:
On 11/01/2026 10:13, Mikko wrote:
On 10/01/2026 17:47, olcott wrote:
On 1/10/2026 2:23 AM, Mikko wrote:
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.
Right, it is /in/ scope for computer science... for the /ology/. Olcott >>>> here uses "computation" to refer to the practice. You give the
requirement to the /ologist/ who correctly decides that it is not for
computation because it is not computable.
You two so often violently agree; I find it warming to the heart.
For pracitcal programming it is useful to know what is known to be
uncomputable in order to avoid wasting time in attemlpts to do the
impossible.
It f-cking nuts that after more than 2000 years
people still don't understand that self-contradictory
expressions: "This sentence is not true" have no
truth value. A smart high school student should have
figured this out 2000 years ago.
Irrelevant. For practical programming that question needn't be answered.
On 13/01/2026 09:11, Mikko wrote:
An oracle machine may be
able to determine the haltinf of all Turing machines but not of all
oracle machines with the same oracle (or oracles) so it is not
universal.
What's the formal definition of "an oracle machine" ?
I would have thought an oracle always halts because it's an oracle it
answers every question that has an answer with either "HasAnswer answer"
or "HasNoAnswer".
On 1/13/2026 8:23 AM, Tristan Wibberley wrote:
On 13/01/2026 09:11, Mikko wrote:
An oracle machine may be
able to determine the haltinf of all Turing machines but not of all
oracle machines with the same oracle (or oracles) so it is not
universal.
What's the formal definition of "an oracle machine" ?
I would have thought an oracle always halts because it's an oracle it
answers every question that has an answer with either "HasAnswer answer"
or "HasNoAnswer".
It seems outside of computer science and into fantasy. https://en.wikipedia.org/wiki/Oracle_machine
On 13/01/2026 14:34, olcott wrote:
On 1/13/2026 8:23 AM, Tristan Wibberley wrote:
On 13/01/2026 09:11, Mikko wrote:
An oracle machine may be
able to determine the haltinf of all Turing machines but not of all
oracle machines with the same oracle (or oracles) so it is not
universal.
What's the formal definition of "an oracle machine" ?
I would have thought an oracle always halts because it's an oracle it
answers every question that has an answer with either "HasAnswer answer" >>> or "HasNoAnswer".
It seems outside of computer science and into fantasy.
https://en.wikipedia.org/wiki/Oracle_machine
Perhaps a halting oracle is real computer science, if it's own actions
are nondeterministic (ie, use bits of entropy from the environment via /dev/random to guide its search through confluent paths) then it could
always find whether a deterministic program halts because no
deterministic program has the oracle as a subprogram.
Then we have a new but different problem of making sure no two oracles receive the same sequence of entropy bits so an oracle can report on a program that contains it.
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