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*
*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.
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*
*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.
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*
*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.
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*
*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.
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*
*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.
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.
On 1/13/2026 3:11 AM, Mikko wrote:
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:The misconception is yours. No expression in the language of >>>>>>>>>> the first
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. >>>>>>>>>>
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.
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.
“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.”
Under a system like the above rough draft all inputs
having pathological self reference such as the halting
problem counter-example input are simply rejected as
non-well-founded. Tarski Undefinability, Gödel's
incompleteness and the halting problem cease to exist.
A Turing
machine cannot determine the halting of all Turing machines and is
therefore not an universla halt decider.
This is not true in Proof Theoretic Semantics. I
still have to refine my words. I may not have said
that exactly correctly. The result is that in Proof
Theoretic Semantics the counter-example is rejected
as non-well-founded.
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.
On 1/13/2026 3:13 AM, Mikko wrote:
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.
The halting problem counter-example input is anchored
in the Liar Paradox. Proof Theoretic Semantics rejects
those two and Gödel's incompleteness and a bunch more
as merely non-well-founded inputs.
Definition: An abstract machine with access to an "oracle"—a black box
that provides immediate answers to complex, even undecidable, problems
(like the Halting Problem). AKA a majick genie.
For a non-deterministic machine there are three possibilities: it may
halt always, sometimes, or never. THere is no oracle that can find the
right answer about every meachne that contains the same oracle.
On 13/01/2026 18:50, olcott wrote:
Definition: An abstract machine with access to an "oracle"—a black box
that provides immediate answers to complex, even undecidable, problems
(like the Halting Problem). AKA a majick genie.
What's it called when its almost an oracle but is arbitrarily slow?
On 13/01/2026 16:27, olcott wrote:
On 1/13/2026 3:11 AM, Mikko wrote:
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:The misconception is yours. No expression in the language of >>>>>>>>>>> the first
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. >>>>>>>>>>>
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.
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.
“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.”
Under a system like the above rough draft all inputs
having pathological self reference such as the halting
problem counter-example input are simply rejected as
non-well-founded. Tarski Undefinability, Gödel's
incompleteness and the halting problem cease to exist.
A Turing
machine cannot determine the halting of all Turing machines and is
therefore not an universla halt decider.
This is not true in Proof Theoretic Semantics. I
still have to refine my words. I may not have said
that exactly correctly. The result is that in Proof
Theoretic Semantics the counter-example is rejected
as non-well-founded.
That no Turing machine is a halt decider is a proven theorem and a
truth about Turing machines. If your "Proof Thoeretic Semnatics"
does not regard it as true then your "Proof Theoretic Semantics"
is incomplete.
On 13/01/2026 16:17, olcott wrote:
On 1/13/2026 2:46 AM, Mikko wrote:Yes, it is. How to handle questions that lack a yes/no answer is
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:It is a perfectly valid question to ask whther a particular
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:The misconception is yours. No expression in the language of >>>>>>>>>>> the first
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. >>>>>>>>>>>
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. >>>>>>>
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.
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.
On 13/01/2026 16:31, olcott wrote:
On 1/13/2026 3:13 AM, Mikko wrote:
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.
The halting problem counter-example input is anchored
in the Liar Paradox. Proof Theoretic Semantics rejects
those two and Gödel's incompleteness and a bunch more
as merely non-well-founded inputs.
For every Turing machine the halting problem counter-example provably
exists.
From the existence of the counter-example it is provable that
the first Turing machine is not a halting decider. With universal quationfication follows that no Turing machine is a halting decider.
Besides, there are other ways to prove that halting is not Turing
decidable.
On 1/12/26 9:29 AM, 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*
*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.
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.
But the problem is that Computation is not a proof-theoretic semantic system, and thus those rules don't apply.
On 1/12/2026 9:19 PM, Richard Damon wrote:
On 1/12/26 9:29 AM, 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:The misconception is yours. No expression in the language of >>>>>>>>>> the first
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. >>>>>>>>>>
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.
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.
But the problem is that Computation is not a proof-theoretic semantic
system, and thus those rules don't apply.
The dumbed down version is that the halting problem asks
a question outside of the scope of finite string transformations.
The halting problem proof does not fail because finite computation
is too weak. It fails because it asks finite computation to
decide a judgment that is not finitely grounded under operational
semantics.
By operational semantics I mean the standard proof‑theoretic
account of program meaning, where execution judgments are
given by inference rules and termination corresponds to the
existence of a finite derivation.
By proof‑theoretic semantics I mean the approach in which the
meaning of a statement is determined by its rules of proof
rather than by truth conditions in an external model.
Operational semantics fits this pattern: programs have meaning
through their execution rules, not through abstract denotations.
By denotational semantics I mean any semantics that assigns
mathematical objects—functions, truth values, domains-to programs independently of how they are executed or proved. This contrasts
with operational or proof‑theoretic semantics, where meaning is
grounded in the structure of derivations rather than in an abstract mathematical object.
I use “denotational semantics” simply to refer to any framework
that assigns meanings independently of operational behavior.
On 14/01/2026 08:53, Mikko wrote:
For a non-deterministic machine there are three possibilities: it may
halt always, sometimes, or never. THere is no oracle that can find the
right answer about every meachne that contains the same oracle.
We well into Turing c-machine territory here aren't we?
On 1/14/2026 3:01 AM, Mikko wrote:
On 13/01/2026 16:31, olcott wrote:
On 1/13/2026 3:13 AM, Mikko wrote:
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: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 10/01/2026 17:47, olcott wrote:
On 1/10/2026 2:23 AM, Mikko wrote:
You can't determine whether the required result is computable >>>>>>>> beforeNo, 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 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. >>>>>>
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.
The halting problem counter-example input is anchored
in the Liar Paradox. Proof Theoretic Semantics rejects
those two and Gödel's incompleteness and a bunch more
as merely non-well-founded inputs.
For every Turing machine the halting problem counter-example provably
exists.
Not when using Proof Theoretic Semantics grounded
in the specification language. In this case the
pathological input is simply rejected as ungrounded.
On 1/14/2026 1:58 AM, Mikko wrote:
On 13/01/2026 16:17, olcott wrote:
On 1/13/2026 2:46 AM, Mikko wrote:Yes, it is. How to handle questions that lack a yes/no answer is
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:The misconception is yours. No expression in the language of >>>>>>>>>>>> the first
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. >>>>>>>>>>>>
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.
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.
The classical diagonal argument for the Halting Problem asks a halt
decider H to evaluate a program D whose behavior depends on H’s own output.
On 1/14/2026 1:40 AM, Mikko wrote:
On 13/01/2026 16:27, olcott wrote:
On 1/13/2026 3:11 AM, Mikko wrote:
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:You can't determine whether the required result is computable >>>>>>>> before
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:The misconception is yours. No expression in the language of >>>>>>>>>>>> the first
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. >>>>>>>>>>>>
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 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.
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.
“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.”
Under a system like the above rough draft all inputs
having pathological self reference such as the halting
problem counter-example input are simply rejected as
non-well-founded. Tarski Undefinability, Gödel's
incompleteness and the halting problem cease to exist.
A Turing
machine cannot determine the halting of all Turing machines and is
therefore not an universla halt decider.
This is not true in Proof Theoretic Semantics. I
still have to refine my words. I may not have said
that exactly correctly. The result is that in Proof
Theoretic Semantics the counter-example is rejected
as non-well-founded.
That no Turing machine is a halt decider is a proven theorem and a
truth about Turing machines. If your "Proof Thoeretic Semnatics"
does not regard it as true then your "Proof Theoretic Semantics"
is incomplete.
My long‑term goal is to make ‘true on the basis of meaning’ computable.
On 1/14/26 8:25 PM, olcott wrote:
By operational semantics I mean the standard proof‑theoretic
account of program meaning, where execution judgments are
given by inference rules and termination corresponds to the
existence of a finite derivation.
Which is just incorrect. Since infinite derivation has meaning in the
field.
On 1/14/26 8:25 PM, olcott wrote:
On 1/12/2026 9:19 PM, Richard Damon wrote:
On 1/12/26 9:29 AM, 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:The misconception is yours. No expression in the language of >>>>>>>>>>> the first
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. >>>>>>>>>>>
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.
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.
But the problem is that Computation is not a proof-theoretic semantic
system, and thus those rules don't apply.
The dumbed down version is that the halting problem asks
a question outside of the scope of finite string transformations.
But it doesn't, not unless you think that programs can't be represented
as finite strings.
The halting problem proof does not fail because finite computation
is too weak. It fails because it asks finite computation to
decide a judgment that is not finitely grounded under operational
semantics.
But that is the issue, Operational Semantics for Programs are not
actually finitely based, since programs can be non-halting.
Just shows you don't know what your words actually mean.
By operational semantics I mean the standard proof‑theoretic
account of program meaning, where execution judgments are
given by inference rules and termination corresponds to the
existence of a finite derivation.
Which is just incorrect. Since infinite derivation has meaning in the
field.
On 1/14/26 8:25 PM, olcott wrote:
On 1/12/2026 9:19 PM, Richard Damon wrote:
On 1/12/26 9:29 AM, 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:The misconception is yours. No expression in the language of >>>>>>>>>>> the first
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. >>>>>>>>>>>
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.
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.
But the problem is that Computation is not a proof-theoretic semantic
system, and thus those rules don't apply.
The dumbed down version is that the halting problem asks
a question outside of the scope of finite string transformations.
But it doesn't, not unless you think that programs can't be represented
as finite strings.
The halting problem proof does not fail because finite computation
is too weak. It fails because it asks finite computation to
decide a judgment that is not finitely grounded under operational
semantics.
But that is the issue, Operational Semantics for Programs are not
actually finitely based, since programs can be non-halting.
Just shows you don't know what your words actually mean.
By operational semantics I mean the standard proof‑theoretic
account of program meaning, where execution judgments are
given by inference rules and termination corresponds to the
existence of a finite derivation.
Which is just incorrect. Since infinite derivation has meaning in the
field.
On 14/01/2026 21:32, olcott wrote:
On 1/14/2026 3:01 AM, Mikko wrote:
On 13/01/2026 16:31, olcott wrote:
On 1/13/2026 3:13 AM, Mikko wrote:
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: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 10/01/2026 17:47, olcott wrote:
On 1/10/2026 2:23 AM, Mikko wrote:
You can't determine whether the required result is computable >>>>>>>>> beforeNo, 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 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. >>>>>>>
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.
The halting problem counter-example input is anchored
in the Liar Paradox. Proof Theoretic Semantics rejects
those two and Gödel's incompleteness and a bunch more
as merely non-well-founded inputs.
For every Turing machine the halting problem counter-example provably
exists.
Not when using Proof Theoretic Semantics grounded
in the specification language. In this case the
pathological input is simply rejected as ungrounded.
Then your "Proof Theoretic Semantics" is not useful for discussion of
Turing machines. For every Turing machine a counter example exists.
And so exists a Turing machine that writes the counter example when
given a Turing machine as input.
On 14/01/2026 19:28, olcott wrote:
On 1/14/2026 1:40 AM, Mikko wrote:
On 13/01/2026 16:27, olcott wrote:
On 1/13/2026 3:11 AM, Mikko wrote:
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:You can't determine whether the required result is computable >>>>>>>>> before
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:The misconception is yours. No expression in the language >>>>>>>>>>>>> of the first
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:
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* >>>>>>>>>>>>>>>
sense or in Olcott's sense.
Undecidability is misconception. Self-contradictory >>>>>>>>>>>>>> expressions are correctly rejected as semantically >>>>>>>>>>>>>> incoherent thus form no undecidability or incompleteness. >>>>>>>>>>>>>
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 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.
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.
“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.”
Under a system like the above rough draft all inputs
having pathological self reference such as the halting
problem counter-example input are simply rejected as
non-well-founded. Tarski Undefinability, Gödel's
incompleteness and the halting problem cease to exist.
A Turing
machine cannot determine the halting of all Turing machines and is
therefore not an universla halt decider.
This is not true in Proof Theoretic Semantics. I
still have to refine my words. I may not have said
that exactly correctly. The result is that in Proof
Theoretic Semantics the counter-example is rejected
as non-well-founded.
That no Turing machine is a halt decider is a proven theorem and a
truth about Turing machines. If your "Proof Thoeretic Semnatics"
does not regard it as true then your "Proof Theoretic Semantics"
is incomplete.
My long‑term goal is to make ‘true on the basis of meaning’ computable.
As meaning is not computable, how can "true on the balsis of meaning"
be commputable?
On 1/14/2026 9:51 PM, Richard Damon wrote:
On 1/14/26 8:25 PM, olcott wrote:
On 1/12/2026 9:19 PM, Richard Damon wrote:
On 1/12/26 9:29 AM, 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:You can't determine whether the required result is computable >>>>>>>> before
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:The misconception is yours. No expression in the language of >>>>>>>>>>>> the first
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. >>>>>>>>>>>>
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 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.
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.
But the problem is that Computation is not a proof-theoretic
semantic system, and thus those rules don't apply.
The dumbed down version is that the halting problem asks
a question outside of the scope of finite string transformations.
But it doesn't, not unless you think that programs can't be
represented as finite strings.
The halting problem proof does not fail because finite computation
is too weak. It fails because it asks finite computation to
decide a judgment that is not finitely grounded under operational
semantics.
But that is the issue, Operational Semantics for Programs are not
actually finitely based, since programs can be non-halting.
Just shows you don't know what your words actually mean.
By operational semantics I mean the standard proof‑theoretic
account of program meaning, where execution judgments are
given by inference rules and termination corresponds to the
existence of a finite derivation.
Which is just incorrect. Since infinite derivation has meaning in the
field.
The halting problem is not undecidable because computation is weak, but because the classical formulation uses a denotational semantics that is
too permissive.
In operational/proof‑theoretic semantics, where meaning is grounded in finite derivations, the halting predicate is not a well‑formed judgment — just as unrestricted comprehension was not a well‑formed judgment in naïve set theory.
On 1/15/26 12:34 PM, olcott wrote:
On 1/14/2026 9:51 PM, Richard Damon wrote:
On 1/14/26 8:25 PM, olcott wrote:
On 1/12/2026 9:19 PM, Richard Damon wrote:
On 1/12/26 9:29 AM, 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:You can't determine whether the required result is computable >>>>>>>>> before
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:The misconception is yours. No expression in the language >>>>>>>>>>>>> of the first
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:
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* >>>>>>>>>>>>>>>
sense or in Olcott's sense.
Undecidability is misconception. Self-contradictory >>>>>>>>>>>>>> expressions are correctly rejected as semantically >>>>>>>>>>>>>> incoherent thus form no undecidability or incompleteness. >>>>>>>>>>>>>
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 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.
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.
But the problem is that Computation is not a proof-theoretic
semantic system, and thus those rules don't apply.
The dumbed down version is that the halting problem asks
a question outside of the scope of finite string transformations.
But it doesn't, not unless you think that programs can't be
represented as finite strings.
The halting problem proof does not fail because finite computation
is too weak. It fails because it asks finite computation to
decide a judgment that is not finitely grounded under operational
semantics.
But that is the issue, Operational Semantics for Programs are not
actually finitely based, since programs can be non-halting.
Just shows you don't know what your words actually mean.
By operational semantics I mean the standard proof‑theoretic
account of program meaning, where execution judgments are
given by inference rules and termination corresponds to the
existence of a finite derivation.
Which is just incorrect. Since infinite derivation has meaning in the
field.
The halting problem is not undecidable because computation is weak,
but because the classical formulation uses a denotational semantics
that is too permissive.
Nope.
In operational/proof‑theoretic semantics, where meaning is grounded in
finite derivations, the halting predicate is not a well‑formed
judgment — just as unrestricted comprehension was not a well‑formed
judgment in naïve set theory.
In other words, by trying to enforce your interpreation, you system
becomes unworkable, as you can't tell if you can ask a question.
The problem is that systems like this grow faster in power to generate--
than your logic grow in power to decide, and either you accept that some truths are unprovable (and thus accept the truth-conditional view) or
you need to just abandon the ability to actually work in the system as
you can't tell what questions are reasonable.
All you are doing is proving that you are just too stupid to understand
the implications of what you are talking about, because you never really understood what the words actually mean.
On 1/15/2026 3:48 AM, Mikko wrote:
On 14/01/2026 19:28, olcott wrote:
On 1/14/2026 1:40 AM, Mikko wrote:
On 13/01/2026 16:27, olcott wrote:
On 1/13/2026 3:11 AM, Mikko wrote:
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:You can't determine whether the required result is computable >>>>>>>>>> before
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:The misconception is yours. No expression in the language >>>>>>>>>>>>>> of the first
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:
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* >>>>>>>>>>>>>>>>
sense or in Olcott's sense.
Undecidability is misconception. Self-contradictory >>>>>>>>>>>>>>> expressions are correctly rejected as semantically >>>>>>>>>>>>>>> incoherent thus form no undecidability or incompleteness. >>>>>>>>>>>>>>
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 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.
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.
“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.” >>>>>
Under a system like the above rough draft all inputs
having pathological self reference such as the halting
problem counter-example input are simply rejected as
non-well-founded. Tarski Undefinability, Gödel's
incompleteness and the halting problem cease to exist.
A Turing
machine cannot determine the halting of all Turing machines and is >>>>>> therefore not an universla halt decider.
This is not true in Proof Theoretic Semantics. I
still have to refine my words. I may not have said
that exactly correctly. The result is that in Proof
Theoretic Semantics the counter-example is rejected
as non-well-founded.
That no Turing machine is a halt decider is a proven theorem and a
truth about Turing machines. If your "Proof Thoeretic Semnatics"
does not regard it as true then your "Proof Theoretic Semantics"
is incomplete.
My long‑term goal is to make ‘true on the basis of meaning’ computable.
As meaning is not computable, how can "true on the balsis of meaning"
be commputable?
Under *proof‑theoretic semantics*
"true on the basis of meaning expressed in language"
has always been entirely computable.
On 1/15/2026 3:34 AM, Mikko wrote:
On 14/01/2026 21:32, olcott wrote:
On 1/14/2026 3:01 AM, Mikko wrote:
On 13/01/2026 16:31, olcott wrote:
On 1/13/2026 3:13 AM, Mikko wrote:
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: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 10/01/2026 17:47, olcott wrote:
On 1/10/2026 2:23 AM, Mikko wrote:
You can't determine whether the required result is computable >>>>>>>>>> beforeNo, 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 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. >>>>>>>>
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.
The halting problem counter-example input is anchored
in the Liar Paradox. Proof Theoretic Semantics rejects
those two and Gödel's incompleteness and a bunch more
as merely non-well-founded inputs.
For every Turing machine the halting problem counter-example provably
exists.
Not when using Proof Theoretic Semantics grounded
in the specification language. In this case the
pathological input is simply rejected as ungrounded.
Then your "Proof Theoretic Semantics" is not useful for discussion of
Turing machines. For every Turing machine a counter example exists.
And so exists a Turing machine that writes the counter example when
given a Turing machine as input.
It is "not useful" in the same way that ZFC was
"not useful" for addressing Russell's Paradox.
On 16/01/2026 01:38, olcott wrote:
On 1/15/2026 3:48 AM, Mikko wrote:
On 14/01/2026 19:28, olcott wrote:
On 1/14/2026 1:40 AM, Mikko wrote:
On 13/01/2026 16:27, olcott wrote:
On 1/13/2026 3:11 AM, Mikko wrote:
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:You can't determine whether the required result is computable >>>>>>>>>>> before
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:The misconception is yours. No expression in the language >>>>>>>>>>>>>>> of the first
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. >>>>>>>>>>>>>>>
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 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.
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.
“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.” >>>>>>
Under a system like the above rough draft all inputs
having pathological self reference such as the halting
problem counter-example input are simply rejected as
non-well-founded. Tarski Undefinability, Gödel's
incompleteness and the halting problem cease to exist.
A Turing
machine cannot determine the halting of all Turing machines and is >>>>>>> therefore not an universla halt decider.
This is not true in Proof Theoretic Semantics. I
still have to refine my words. I may not have said
that exactly correctly. The result is that in Proof
Theoretic Semantics the counter-example is rejected
as non-well-founded.
That no Turing machine is a halt decider is a proven theorem and a
truth about Turing machines. If your "Proof Thoeretic Semnatics"
does not regard it as true then your "Proof Theoretic Semantics"
is incomplete.
My long‑term goal is to make ‘true on the basis of meaning’ computable.
As meaning is not computable, how can "true on the balsis of meaning"
be commputable?
Under *proof‑theoretic semantics*
"true on the basis of meaning expressed in language"
has always been entirely computable.
Have you already put the algorithm to some web page?
On 16/01/2026 01:38, olcott wrote:
On 1/15/2026 3:48 AM, Mikko wrote:
On 14/01/2026 19:28, olcott wrote:
On 1/14/2026 1:40 AM, Mikko wrote:
On 13/01/2026 16:27, olcott wrote:
On 1/13/2026 3:11 AM, Mikko wrote:
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:You can't determine whether the required result is computable >>>>>>>>>>> before
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:The misconception is yours. No expression in the language >>>>>>>>>>>>>>> of the first
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. >>>>>>>>>>>>>>>
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 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.
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.
“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.” >>>>>>
Under a system like the above rough draft all inputs
having pathological self reference such as the halting
problem counter-example input are simply rejected as
non-well-founded. Tarski Undefinability, Gödel's
incompleteness and the halting problem cease to exist.
A Turing
machine cannot determine the halting of all Turing machines and is >>>>>>> therefore not an universla halt decider.
This is not true in Proof Theoretic Semantics. I
still have to refine my words. I may not have said
that exactly correctly. The result is that in Proof
Theoretic Semantics the counter-example is rejected
as non-well-founded.
That no Turing machine is a halt decider is a proven theorem and a
truth about Turing machines. If your "Proof Thoeretic Semnatics"
does not regard it as true then your "Proof Theoretic Semantics"
is incomplete.
My long‑term goal is to make ‘true on the basis of meaning’ computable.
As meaning is not computable, how can "true on the balsis of meaning"
be commputable?
Under *proof‑theoretic semantics*
"true on the basis of meaning expressed in language"
has always been entirely computable.
Have you already put the algorithm to some web page?
On 15/01/2026 22:30, olcott wrote:
On 1/15/2026 3:34 AM, Mikko wrote:
On 14/01/2026 21:32, olcott wrote:
On 1/14/2026 3:01 AM, Mikko wrote:
On 13/01/2026 16:31, olcott wrote:
On 1/13/2026 3:13 AM, Mikko wrote:
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: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 10/01/2026 17:47, olcott wrote:
On 1/10/2026 2:23 AM, Mikko wrote:
You can't determine whether the required result is computable >>>>>>>>>>> beforeNo, 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 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. >>>>>>>>>
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.
The halting problem counter-example input is anchored
in the Liar Paradox. Proof Theoretic Semantics rejects
those two and Gödel's incompleteness and a bunch more
as merely non-well-founded inputs.
For every Turing machine the halting problem counter-example provably >>>>> exists.
Not when using Proof Theoretic Semantics grounded
in the specification language. In this case the
pathological input is simply rejected as ungrounded.
Then your "Proof Theoretic Semantics" is not useful for discussion of
Turing machines. For every Turing machine a counter example exists.
And so exists a Turing machine that writes the counter example when
given a Turing machine as input.
It is "not useful" in the same way that ZFC was
"not useful" for addressing Russell's Paradox.
ZF or ZFC is to some extent useful for addressing Russell's paradox.
It is an example of a set theory where Russell's paradox is avoided.
If your "Proof Theretic Semantics" cannot handle the existence of
a counter example for every Turing decider then it is not usefule
for those who work on practical problems of program correctness.
On 1/15/2026 9:27 PM, Richard Damon wrote:
On 1/15/26 12:34 PM, olcott wrote:
On 1/14/2026 9:51 PM, Richard Damon wrote:
On 1/14/26 8:25 PM, olcott wrote:
On 1/12/2026 9:19 PM, Richard Damon wrote:
On 1/12/26 9:29 AM, 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:You can't determine whether the required result is computable >>>>>>>>>> before
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:The misconception is yours. No expression in the language >>>>>>>>>>>>>> of the first
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:
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* >>>>>>>>>>>>>>>>
sense or in Olcott's sense.
Undecidability is misconception. Self-contradictory >>>>>>>>>>>>>>> expressions are correctly rejected as semantically >>>>>>>>>>>>>>> incoherent thus form no undecidability or incompleteness. >>>>>>>>>>>>>>
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 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.
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.
But the problem is that Computation is not a proof-theoretic
semantic system, and thus those rules don't apply.
The dumbed down version is that the halting problem asks
a question outside of the scope of finite string transformations.
But it doesn't, not unless you think that programs can't be
represented as finite strings.
The halting problem proof does not fail because finite computation
is too weak. It fails because it asks finite computation to
decide a judgment that is not finitely grounded under operational
semantics.
But that is the issue, Operational Semantics for Programs are not
actually finitely based, since programs can be non-halting.
Just shows you don't know what your words actually mean.
By operational semantics I mean the standard proof‑theoretic
account of program meaning, where execution judgments are
given by inference rules and termination corresponds to the
existence of a finite derivation.
Which is just incorrect. Since infinite derivation has meaning in
the field.
The halting problem is not undecidable because computation is weak,
but because the classical formulation uses a denotational semantics
that is too permissive.
Nope.
In operational/proof‑theoretic semantics, where meaning is grounded
in finite derivations, the halting predicate is not a well‑formed
judgment — just as unrestricted comprehension was not a well‑formed >>> judgment in naïve set theory.
In other words, by trying to enforce your interpreation, you system
becomes unworkable, as you can't tell if you can ask a question.
It is the same ∀x ∈ T ((True(T, x) ≡ (T ⊢ x))
that I have been talking about for years except that
it is now grounded in well-founded proof‑theoretic
semantics.
The problem is that systems like this grow faster in power to generate
than your logic grow in power to decide, and either you accept that
some truths are unprovable (and thus accept the truth-conditional
view) or you need to just abandon the ability to actually work in the
system as you can't tell what questions are reasonable.
All you are doing is proving that you are just too stupid to
understand the implications of what you are talking about, because you
never really understood what the words actually mean.
On 1/16/2026 3:17 AM, Mikko wrote:
On 16/01/2026 01:38, olcott wrote:
On 1/15/2026 3:48 AM, Mikko wrote:
On 14/01/2026 19:28, olcott wrote:
On 1/14/2026 1:40 AM, Mikko wrote:
On 13/01/2026 16:27, olcott wrote:
On 1/13/2026 3:11 AM, Mikko wrote:
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:You can't determine whether the required result is
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:The misconception is yours. No expression in the >>>>>>>>>>>>>>>> language of the first
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. >>>>>>>>>>>>>>>>
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. >>>>>>>>>>>>
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.
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.
“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.”
Under a system like the above rough draft all inputs
having pathological self reference such as the halting
problem counter-example input are simply rejected as
non-well-founded. Tarski Undefinability, Gödel's
incompleteness and the halting problem cease to exist.
A Turing
machine cannot determine the halting of all Turing machines and is >>>>>>>> therefore not an universla halt decider.
This is not true in Proof Theoretic Semantics. I
still have to refine my words. I may not have said
that exactly correctly. The result is that in Proof
Theoretic Semantics the counter-example is rejected
as non-well-founded.
That no Turing machine is a halt decider is a proven theorem and a >>>>>> truth about Turing machines. If your "Proof Thoeretic Semnatics"
does not regard it as true then your "Proof Theoretic Semantics"
is incomplete.
My long‑term goal is to make ‘true on the basis of meaning’
computable.
As meaning is not computable, how can "true on the balsis of meaning"
be commputable?
Under *proof‑theoretic semantics*
"true on the basis of meaning expressed in language"
has always been entirely computable.
Have you already put the algorithm to some web page?
I am still working on refining the presentation.
On 1/16/2026 3:17 AM, Mikko wrote:
On 16/01/2026 01:38, olcott wrote:
On 1/15/2026 3:48 AM, Mikko wrote:
On 14/01/2026 19:28, olcott wrote:
On 1/14/2026 1:40 AM, Mikko wrote:
On 13/01/2026 16:27, olcott wrote:
On 1/13/2026 3:11 AM, Mikko wrote:
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:You can't determine whether the required result is
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:The misconception is yours. No expression in the >>>>>>>>>>>>>>>> language of the first
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. >>>>>>>>>>>>>>>>
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. >>>>>>>>>>>>
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.
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.
“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.”
Under a system like the above rough draft all inputs
having pathological self reference such as the halting
problem counter-example input are simply rejected as
non-well-founded. Tarski Undefinability, Gödel's
incompleteness and the halting problem cease to exist.
A Turing
machine cannot determine the halting of all Turing machines and is >>>>>>>> therefore not an universla halt decider.
This is not true in Proof Theoretic Semantics. I
still have to refine my words. I may not have said
that exactly correctly. The result is that in Proof
Theoretic Semantics the counter-example is rejected
as non-well-founded.
That no Turing machine is a halt decider is a proven theorem and a >>>>>> truth about Turing machines. If your "Proof Thoeretic Semnatics"
does not regard it as true then your "Proof Theoretic Semantics"
is incomplete.
My long‑term goal is to make ‘true on the basis of meaning’
computable.
As meaning is not computable, how can "true on the balsis of meaning"
be commputable?
Under *proof‑theoretic semantics*
"true on the basis of meaning expressed in language"
has always been entirely computable.
Have you already put the algorithm to some web page?
Proof Theoretic Semantics Blocks Pathological Self-Reference https://philpapers.org/rec/OLCPTS
On 1/16/2026 3:17 AM, Mikko wrote:
On 16/01/2026 01:38, olcott wrote:
On 1/15/2026 3:48 AM, Mikko wrote:
On 14/01/2026 19:28, olcott wrote:
On 1/14/2026 1:40 AM, Mikko wrote:
On 13/01/2026 16:27, olcott wrote:
On 1/13/2026 3:11 AM, Mikko wrote:
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:You can't determine whether the required result is
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:The misconception is yours. No expression in the >>>>>>>>>>>>>>>> language of the first
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. >>>>>>>>>>>>>>>>
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. >>>>>>>>>>>>
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.
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.
“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.”
Under a system like the above rough draft all inputs
having pathological self reference such as the halting
problem counter-example input are simply rejected as
non-well-founded. Tarski Undefinability, Gödel's
incompleteness and the halting problem cease to exist.
A Turing
machine cannot determine the halting of all Turing machines and is >>>>>>>> therefore not an universla halt decider.
This is not true in Proof Theoretic Semantics. I
still have to refine my words. I may not have said
that exactly correctly. The result is that in Proof
Theoretic Semantics the counter-example is rejected
as non-well-founded.
That no Turing machine is a halt decider is a proven theorem and a >>>>>> truth about Turing machines. If your "Proof Thoeretic Semnatics"
does not regard it as true then your "Proof Theoretic Semantics"
is incomplete.
My long‑term goal is to make ‘true on the basis of meaning’
computable.
As meaning is not computable, how can "true on the balsis of meaning"
be commputable?
Under *proof‑theoretic semantics*
"true on the basis of meaning expressed in language"
has always been entirely computable.
Have you already put the algorithm to some web page?
Proof Theoretic Semantics Blocks Pathological Self-Reference https://philpapers.org/rec/OLCPTS
| Sysop: | datGSguy |
|---|---|
| Location: | Eugene, OR |
| Users: | 7 |
| Nodes: | 4 (0 / 4) |
| Uptime: | 219:17:17 |
| Calls: | 361 |
| Calls today: | 34 |
| Files: | 14 |
| D/L today: |
66 files (1,076K bytes) |
| Messages: | 5,751 |
| Posted today: | 1 |