that's probably gunna be the title of my next post/paper eh???
that's probably gunna be the title of my next post/paper eh???
On 21/03/2026 09:47, dart200 wrote:
that's probably gunna be the title of my next post/paper eh???
It is not a good title. Turings diagonal and Church-Turing theses
are two distinct topics. If your paper is about both you shuld have
"and" instead of ":". Even better if you mention only the main topic.
On 21/03/2026 09:47, dart200 wrote:
that's probably gunna be the title of my next post/paper eh???
It is not a good title. Turings diagonal and Church-Turing theses
are two distinct topics. If your paper is about both you shuld have
"and" instead of ":". Even better if you mention only the main topic.
On 3/21/26 2:30 AM, Mikko wrote:
On 21/03/2026 09:47, dart200 wrote:
that's probably gunna be the title of my next post/paper eh???
It is not a good title. Turings diagonal and Church-Turing theses
are two distinct topics. If your paper is about both you shuld have
"and" instead of ":". Even better if you mention only the main topic.
fixing the diagonal is the main topic at hand, but it unexpectedly leads
to a short refutation of the ct-thesis at the end which i think is
important enough to mention in the title
maybe i'll call it instead:
on deciding the undecidable
and a refutation of the church-turing thesis
On 3/21/2026 1:40 PM, dart200 wrote:
On 3/21/26 2:30 AM, Mikko wrote:
On 21/03/2026 09:47, dart200 wrote:
that's probably gunna be the title of my next post/paper eh???
It is not a good title. Turings diagonal and Church-Turing theses
are two distinct topics. If your paper is about both you shuld have
"and" instead of ":". Even better if you mention only the main topic.
fixing the diagonal is the main topic at hand, but it unexpectedly
leads to a short refutation of the ct-thesis at the end which i think
is important enough to mention in the title
maybe i'll call it instead:
on deciding the undecidable
and a refutation of the church-turing thesis
The Church-Turing thesis can be more clearly stated
as any result obtained by applying finite string
transformation rules to finite strings is computable.
This fits in perfectly with the ultimate foundation for
"true on the basis of meaning expressed in language"
as relations between finite strings.
Which in turn fits in perfectly with the proof theoretic
notion of semantic meaning.
On 3/21/26 12:02 PM, olcott wrote:
On 3/21/2026 1:40 PM, dart200 wrote:
On 3/21/26 2:30 AM, Mikko wrote:
On 21/03/2026 09:47, dart200 wrote:
that's probably gunna be the title of my next post/paper eh???
It is not a good title. Turings diagonal and Church-Turing theses
are two distinct topics. If your paper is about both you shuld have
"and" instead of ":". Even better if you mention only the main topic.
fixing the diagonal is the main topic at hand, but it unexpectedly
leads to a short refutation of the ct-thesis at the end which i think
is important enough to mention in the title
maybe i'll call it instead:
on deciding the undecidable
and a refutation of the church-turing thesis
The Church-Turing thesis can be more clearly stated
as any result obtained by applying finite string
transformation rules to finite strings is computable.
i don't agree
the church-turing thesis states that TM computation captures anything
that is mechanically "computable",
but i disagree with that: TM computing cannot express everything that is mechanically computable, and my paper will end with a distinct example
of such
This fits in perfectly with the ultimate foundation for
"true on the basis of meaning expressed in language"
as relations between finite strings.
Which in turn fits in perfectly with the proof theoretic
notion of semantic meaning.
On 3/21/2026 2:50 PM, dart200 wrote:
On 3/21/26 12:02 PM, olcott wrote:
On 3/21/2026 1:40 PM, dart200 wrote:
On 3/21/26 2:30 AM, Mikko wrote:
On 21/03/2026 09:47, dart200 wrote:fixing the diagonal is the main topic at hand, but it unexpectedly
that's probably gunna be the title of my next post/paper eh???
It is not a good title. Turings diagonal and Church-Turing theses
are two distinct topics. If your paper is about both you shuld have
"and" instead of ":". Even better if you mention only the main topic. >>>>
leads to a short refutation of the ct-thesis at the end which i
think is important enough to mention in the title
maybe i'll call it instead:
on deciding the undecidable
and a refutation of the church-turing thesis
The Church-Turing thesis can be more clearly stated
as any result obtained by applying finite string
transformation rules to finite strings is computable.
i don't agree
the church-turing thesis states that TM computation captures anything
that is mechanically "computable",
but i disagree with that: TM computing cannot express everything that
is mechanically computable, and my paper will end with a distinct
example of such
Everything that is computable by by any means what-so-ever
is equivalent to finite string transformations applied to
finite strings.
When we apply finite string transformations to the
counter-example input to the halting problem HHH
correctly determines that its input DD cannot be
resolved to a well-founded justification tree thus
has no coherent semantic meaning within proof
theoretic semantics. HHH correctly rejects DD on
this basis.
When one is asked an incorrect question the only
correct answer is rejecting the question. After
28 years of this my work finally has the accepted
basis of proof theoretic semantics.
This fits in perfectly with the ultimate foundation for
"true on the basis of meaning expressed in language"
as relations between finite strings.
Which in turn fits in perfectly with the proof theoretic
notion of semantic meaning.
On 3/21/26 1:14 PM, olcott wrote:
On 3/21/2026 2:50 PM, dart200 wrote:
On 3/21/26 12:02 PM, olcott wrote:
On 3/21/2026 1:40 PM, dart200 wrote:
On 3/21/26 2:30 AM, Mikko wrote:
On 21/03/2026 09:47, dart200 wrote:fixing the diagonal is the main topic at hand, but it unexpectedly
that's probably gunna be the title of my next post/paper eh???
It is not a good title. Turings diagonal and Church-Turing theses
are two distinct topics. If your paper is about both you shuld have >>>>>> "and" instead of ":". Even better if you mention only the main topic. >>>>>
leads to a short refutation of the ct-thesis at the end which i
think is important enough to mention in the title
maybe i'll call it instead:
on deciding the undecidable
and a refutation of the church-turing thesis
The Church-Turing thesis can be more clearly stated
as any result obtained by applying finite string
transformation rules to finite strings is computable.
i don't agree
the church-turing thesis states that TM computation captures anything
that is mechanically "computable",
but i disagree with that: TM computing cannot express everything that
is mechanically computable, and my paper will end with a distinct
example of such
Everything that is computable by by any means what-so-ever
is equivalent to finite string transformations applied to
finite strings.
well yes, each "step" of a TM computation is a finite string
transformation applied to finite strings
i'm saying as of right now, is am not sure that such a model encompasses
all of computation, specifically due to self-referential weirdness
i'm still working on the counter example
When we apply finite string transformations to the
counter-example input to the halting problem HHH
correctly determines that its input DD cannot be
resolved to a well-founded justification tree thus
has no coherent semantic meaning within proof
theoretic semantics. HHH correctly rejects DD on
this basis.
When one is asked an incorrect question the only
correct answer is rejecting the question. After
28 years of this my work finally has the accepted
basis of proof theoretic semantics.
This fits in perfectly with the ultimate foundation for
"true on the basis of meaning expressed in language"
as relations between finite strings.
Which in turn fits in perfectly with the proof theoretic
notion of semantic meaning.
On 3/21/2026 5:32 PM, dart200 wrote:
On 3/21/26 1:14 PM, olcott wrote:
On 3/21/2026 2:50 PM, dart200 wrote:
On 3/21/26 12:02 PM, olcott wrote:
On 3/21/2026 1:40 PM, dart200 wrote:
On 3/21/26 2:30 AM, Mikko wrote:
On 21/03/2026 09:47, dart200 wrote:
that's probably gunna be the title of my next post/paper eh???
It is not a good title. Turings diagonal and Church-Turing theses >>>>>>> are two distinct topics. If your paper is about both you shuld have >>>>>>> "and" instead of ":". Even better if you mention only the main
topic.
fixing the diagonal is the main topic at hand, but it unexpectedly >>>>>> leads to a short refutation of the ct-thesis at the end which i
think is important enough to mention in the title
maybe i'll call it instead:
on deciding the undecidable
and a refutation of the church-turing thesis
The Church-Turing thesis can be more clearly stated
as any result obtained by applying finite string
transformation rules to finite strings is computable.
i don't agree
the church-turing thesis states that TM computation captures
anything that is mechanically "computable",
but i disagree with that: TM computing cannot express everything
that is mechanically computable, and my paper will end with a
distinct example of such
Everything that is computable by by any means what-so-ever
is equivalent to finite string transformations applied to
finite strings.
well yes, each "step" of a TM computation is a finite string
transformation applied to finite strings
i'm saying as of right now, is am not sure that such a model
encompasses all of computation, specifically due to self-referential
weirdness
i'm still working on the counter example
Because I have spent 28 years pondering this and have a
fully developed foundation that is accepted by academia
I can talk about this self-referential weirdness pathological
self-reference (PSR) more directly.
Expressions of language with PSR are not truth apt within
proof theoretic semantics. Any expression lacking a
well-founded justification tree lacks a semantic meaning.
1.2 Inferentialism, intuitionism, anti-realism
Proof-theoretic semantics is inherently inferential,
as it is inferential activity which manifests itself
in proofs. It thus belongs to inferentialism (a term
coined by Brandom, see his 1994; 2000) according to
which inferences and the rules of inference establish
the meaning of expressions Schroeder-Heister, Peter,
2024 "Proof-Theoretic Semantics" https://plato.stanford.edu/entries/proof-theoretic-semantics/ #InfeIntuAntiReal
When we apply finite string transformations to the
counter-example input to the halting problem HHH
correctly determines that its input DD cannot be
resolved to a well-founded justification tree thus
has no coherent semantic meaning within proof
theoretic semantics. HHH correctly rejects DD on
this basis.
When one is asked an incorrect question the only
correct answer is rejecting the question. After
28 years of this my work finally has the accepted
basis of proof theoretic semantics.
This fits in perfectly with the ultimate foundation for
"true on the basis of meaning expressed in language"
as relations between finite strings.
Which in turn fits in perfectly with the proof theoretic
notion of semantic meaning.
On 3/21/26 3:59 PM, olcott wrote:
On 3/21/2026 5:32 PM, dart200 wrote:
On 3/21/26 1:14 PM, olcott wrote:
On 3/21/2026 2:50 PM, dart200 wrote:
On 3/21/26 12:02 PM, olcott wrote:
On 3/21/2026 1:40 PM, dart200 wrote:
On 3/21/26 2:30 AM, Mikko wrote:
On 21/03/2026 09:47, dart200 wrote:
that's probably gunna be the title of my next post/paper eh??? >>>>>>>>It is not a good title. Turings diagonal and Church-Turing theses >>>>>>>> are two distinct topics. If your paper is about both you shuld have >>>>>>>> "and" instead of ":". Even better if you mention only the main >>>>>>>> topic.
fixing the diagonal is the main topic at hand, but it
unexpectedly leads to a short refutation of the ct-thesis at the >>>>>>> end which i think is important enough to mention in the title
maybe i'll call it instead:
on deciding the undecidable
and a refutation of the church-turing thesis
The Church-Turing thesis can be more clearly stated
as any result obtained by applying finite string
transformation rules to finite strings is computable.
i don't agree
the church-turing thesis states that TM computation captures
anything that is mechanically "computable",
but i disagree with that: TM computing cannot express everything
that is mechanically computable, and my paper will end with a
distinct example of such
Everything that is computable by by any means what-so-ever
is equivalent to finite string transformations applied to
finite strings.
well yes, each "step" of a TM computation is a finite string
transformation applied to finite strings
i'm saying as of right now, is am not sure that such a model
encompasses all of computation, specifically due to self-referential
weirdness
i'm still working on the counter example
Because I have spent 28 years pondering this and have a
fully developed foundation that is accepted by academia
...bruh if it was accepted by academia you'd be writing papers or at a conference somewhere,
not here posting on comp.theory...
On 3/21/26 2:30 AM, Mikko wrote:
On 21/03/2026 09:47, dart200 wrote:
that's probably gunna be the title of my next post/paper eh???
It is not a good title. Turings diagonal and Church-Turing theses
are two distinct topics. If your paper is about both you shuld have
"and" instead of ":". Even better if you mention only the main topic.
fixing the diagonal is the main topic at hand, but it unexpectedly leads
to a short refutation of the ct-thesis at the end which i think is
important enough to mention in the title
maybe i'll call it instead:
on deciding the undecidable
and a refutation of the church-turing thesis
On 3/21/26 2:40 PM, dart200 wrote:
On 3/21/26 2:30 AM, Mikko wrote:
On 21/03/2026 09:47, dart200 wrote:
that's probably gunna be the title of my next post/paper eh???
It is not a good title. Turings diagonal and Church-Turing theses
are two distinct topics. If your paper is about both you shuld have
"and" instead of ":". Even better if you mention only the main topic.
fixing the diagonal is the main topic at hand, but it unexpectedly
leads to a short refutation of the ct-thesis at the end which i think
is important enough to mention in the title
But it isn't computing "the diagonal" that is the real problem, just the step used to show that actual problem, that of computationally
enumerating ALL the list, is actually not possible.
And the problem is that ANY method used to compute the diagonal, can
also be used to compute the anti-diagonal (the number that disagrees
with the diagonal in every possition).
Turing's proof shows that for the problem of enumeration the circle-free machines, we can not build the decider to enumerate the machines, as
from that decider, we can build a specific machine that it has to be
wrong about, as by the contruction method described, what ever answer it gives about the machine built by that method, will be wrong.
Making a different machine that it can be right about is meaningless, as
it still has the problem with that particular machine.
Changing the goal post by saying it doesn't need to enumerate every
machine, just at least one for every distinct computable number means
that machine doesn't cause the same problem (as it can be rejected and
some other machine might be able to be selected that computest that
number), but that same construction method can be very slightly changed,
to build the machine that computes the anti-diagonal, and this machine computes a number that just can not be computed by any machine accepted
by that decider. As Turing points out, while the logic is valid, it
leave more opening for people to think it just can't be right, which is
why he didn't use it in his proof.
But, given the decider that is claimed to accept at least one machine
for every computable number, we *CAN* create this anti-diagonal
computation (and you have made NO attempt to show why it can't be done,
just wave your hands to try to make an assumption that somehow the
decider can come up with a way), and, by the very fact that we computed
a number which is known to be different in at least one digit with every number in the enumeration, can't be in that enumeration.
This result does NOT depend on any aspect of HOW the machine actually performs its calculaton, so isn't dependent on CT, it just needs that
method to support at least the power of a Turing Machine (mainly, having
a finite string representaion that can be mapped to a number, that
machines can be cascaded to build more complicated machines from more
basic machines, and that machines can simulate a machine from its representation/number and input).
maybe i'll call it instead:
on deciding the undecidable
and a refutation of the church-turing thesis
And here your problem is that you do no such refutation, but you need to ASSUME that something more powerful than a Turing Machine must exist
that can do something to allow you to make the impossible happen.
All this shows is that you just don't understand how basic logic works,
or what any of the terms in compuation theory actually mean.
On 3/21/26 2:30 AM, Mikko wrote:
On 21/03/2026 09:47, dart200 wrote:
that's probably gunna be the title of my next post/paper eh???
It is not a good title. Turings diagonal and Church-Turing theses
are two distinct topics. If your paper is about both you shuld have
"and" instead of ":". Even better if you mention only the main topic.
fixing the diagonal is the main topic at hand, but it unexpectedly leads
to a short refutation of the ct-thesis at the end which i think is
important enough to mention in the title
maybe i'll call it instead:
on deciding the undecidable
and a refutation of the church-turing thesis
that's probably gunna be the title of my next post/paper eh???
----
arising us out of the computing dark ages,
please excuse my pseudo-pyscript,
~ the little crank that could
On 3/21/26 6:36 PM, Richard Damon wrote:
On 3/21/26 2:40 PM, dart200 wrote:
On 3/21/26 2:30 AM, Mikko wrote:
On 21/03/2026 09:47, dart200 wrote:
that's probably gunna be the title of my next post/paper eh???
It is not a good title. Turings diagonal and Church-Turing theses
are two distinct topics. If your paper is about both you shuld have
"and" instead of ":". Even better if you mention only the main topic.
fixing the diagonal is the main topic at hand, but it unexpectedly
leads to a short refutation of the ct-thesis at the end which i think
is important enough to mention in the title
But it isn't computing "the diagonal" that is the real problem, just
the step used to show that actual problem, that of computationally
enumerating ALL the list, is actually not possible.
which is just silly to me, because if _i_ mechanically went and ran each machines myself according to their instructions... _my_ output wouldn't
be subject to being read and contradicted
so when you use that facet to try to justify limits to mechanical computation, it seems like ur just defining limits to TM computing as a theory, rather than all computation possible ...
and u don't seem to understand that u've never actually proven that TM computed as a theory encompasses all possible computations
And the problem is that ANY method used to compute the diagonal, can
also be used to compute the anti-diagonal (the number that disagrees
with the diagonal in every possition).
Turing's proof shows that for the problem of enumeration the circle-
free machines, we can not build the decider to enumerate the machines,
as from that decider, we can build a specific machine that it has to
be wrong about, as by the contruction method described, what ever
answer it gives about the machine built by that method, will be wrong.
Making a different machine that it can be right about is meaningless,
as it still has the problem with that particular machine.
Changing the goal post by saying it doesn't need to enumerate every
machine, just at least one for every distinct computable number means
that machine doesn't cause the same problem (as it can be rejected and
some other machine might be able to be selected that computest that
number), but that same construction method can be very slightly
changed, to build the machine that computes the anti-diagonal, and
this machine computes a number that just can not be computed by any
machine accepted by that decider. As Turing points out, while the
logic is valid, it leave more opening for people to think it just
can't be right, which is why he didn't use it in his proof.
that's not what he said rick or why he said it. but i'm not going to
waste my life debating what or why he said anything with. we don't have
that kinda rapport
But, given the decider that is claimed to accept at least one machine
for every computable number, we *CAN* create this anti-diagonal
computation (and you have made NO attempt to show why it can't be
done, just wave your hands to try to make an assumption that somehow
the decider can come up with a way), and, by the very fact that we
computed a number which is known to be different in at least one digit
with every number in the enumeration, can't be in that enumeration.
This result does NOT depend on any aspect of HOW the machine actually
performs its calculaton, so isn't dependent on CT, it just needs that
actually the anti-diagonal trick just didn't work with the context-aware recognizer (which only requires a modification to TMs, not "rewriting everything"),
i'm hoping to find an equivalent mechanism in TMs, because i don't
really want to have to get the theoretical buy-in on that. but that's looking less possible by the day rn
method to support at least the power of a Turing Machine (mainly,
having a finite string representaion that can be mapped to a number,
that machines can be cascaded to build more complicated machines from
more basic machines, and that machines can simulate a machine from its
representation/number and input).
maybe i'll call it instead:
on deciding the undecidable
and a refutation of the church-turing thesis
And here your problem is that you do no such refutation, but you need
to ASSUME that something more powerful than a Turing Machine must exist
yes an external un-referencable entity watching the output from a
diagonal and writing down the opposite
that computation can't be expressed in the TM computing enumeration
because it would require a machine that outputs a digit opposite to the
one it does ...
but there is no particular reason why an external observer, not bounded
by existing in the TM enumeration, couldn't watch and write down the opposites... meaning a mechanically possible computation existed outside
the bounds of rigorously defined computing machines
that can do something to allow you to make the impossible happen.
All this shows is that you just don't understand how basic logic
works, or what any of the terms in compuation theory actually mean.
actually i just shows i don't respect the status quo consensus, which is
not the same as not understanding it
On 3/22/26 12:15 AM, dart200 wrote:
On 3/21/26 6:36 PM, Richard Damon wrote:
On 3/21/26 2:40 PM, dart200 wrote:
On 3/21/26 2:30 AM, Mikko wrote:
On 21/03/2026 09:47, dart200 wrote:fixing the diagonal is the main topic at hand, but it unexpectedly
that's probably gunna be the title of my next post/paper eh???
It is not a good title. Turings diagonal and Church-Turing theses
are two distinct topics. If your paper is about both you shuld have
"and" instead of ":". Even better if you mention only the main topic. >>>>
leads to a short refutation of the ct-thesis at the end which i
think is important enough to mention in the title
But it isn't computing "the diagonal" that is the real problem, just
the step used to show that actual problem, that of computationally
enumerating ALL the list, is actually not possible.
which is just silly to me, because if _i_ mechanically went and ran
each machines myself according to their instructions... _my_ output
wouldn't be subject to being read and contradicted
No, if you *MECHANICALLY* did that action, then there is a mecanical algorithm that you followed, and a machine could be built that
implemented that mechanical algorithm, and contradicts your results.
[ Followup-To: set ]
In comp.theory dart200 <user7160@newsgrouper.org.invalid> wrote:
that's probably gunna be the title of my next post/paper eh???
"Turing's diagonal" is not broken. So to regard it is a category error.
Why do you regard it as such?
The Church-Turing thesis, as Ben explained a fortnight or so ago, is not
the sort of entity that can be proven or refuted. It's more a
definition of what the word "computable" means - anything which can be determined by a turing machine or a lambda calculus expression.
If you think you can come up with a machine (for some reasonable value
of "machine") which can produce a result which a turing machine can't -
then the best of luck to you. Bright people have tried this already
over the past few decades and come up empty handed.
On 21/03/2026 20:40, dart200 wrote:
On 3/21/26 2:30 AM, Mikko wrote:
On 21/03/2026 09:47, dart200 wrote:
that's probably gunna be the title of my next post/paper eh???
It is not a good title. Turings diagonal and Church-Turing theses
are two distinct topics. If your paper is about both you shuld have
"and" instead of ":". Even better if you mention only the main topic.
fixing the diagonal is the main topic at hand, but it unexpectedly
leads to a short refutation of the ct-thesis at the end which i think
is important enough to mention in the title
maybe i'll call it instead:
on deciding the undecidable
and a refutation of the church-turing thesis
A real scientist would put "On Deciding the Undecidable" in one paper
and "On Refutation of the Church-Turing Thesis" in anohter.
On 3/21/26 1:14 PM, olcott wrote:
On 3/21/2026 2:50 PM, dart200 wrote:
On 3/21/26 12:02 PM, olcott wrote:
On 3/21/2026 1:40 PM, dart200 wrote:
On 3/21/26 2:30 AM, Mikko wrote:
On 21/03/2026 09:47, dart200 wrote:fixing the diagonal is the main topic at hand, but it unexpectedly
that's probably gunna be the title of my next post/paper eh???
It is not a good title. Turings diagonal and Church-Turing theses
are two distinct topics. If your paper is about both you shuld have >>>>>> "and" instead of ":". Even better if you mention only the main topic. >>>>>
leads to a short refutation of the ct-thesis at the end which i
think is important enough to mention in the title
maybe i'll call it instead:
on deciding the undecidable
and a refutation of the church-turing thesis
The Church-Turing thesis can be more clearly stated
as any result obtained by applying finite string
transformation rules to finite strings is computable.
i don't agree
the church-turing thesis states that TM computation captures anything
that is mechanically "computable",
but i disagree with that: TM computing cannot express everything that
is mechanically computable, and my paper will end with a distinct
example of such
Everything that is computable by by any means what-so-ever
is equivalent to finite string transformations applied to
finite strings.
well yes, each "step" of a TM computation is a finite string
transformation applied to finite strings
i'm saying as of right now, is am not sure that such a model encompasses
all of computation, specifically due to self-referential weirdness
On 3/21/26 1:14 PM, olcott wrote:
On 3/21/2026 2:50 PM, dart200 wrote:
On 3/21/26 12:02 PM, olcott wrote:
On 3/21/2026 1:40 PM, dart200 wrote:
On 3/21/26 2:30 AM, Mikko wrote:
On 21/03/2026 09:47, dart200 wrote:fixing the diagonal is the main topic at hand, but it unexpectedly
that's probably gunna be the title of my next post/paper eh???
It is not a good title. Turings diagonal and Church-Turing theses
are two distinct topics. If your paper is about both you shuld have >>>>>> "and" instead of ":". Even better if you mention only the main topic. >>>>>
leads to a short refutation of the ct-thesis at the end which i
think is important enough to mention in the title
maybe i'll call it instead:
on deciding the undecidable
and a refutation of the church-turing thesis
The Church-Turing thesis can be more clearly stated
as any result obtained by applying finite string
transformation rules to finite strings is computable.
i don't agree
the church-turing thesis states that TM computation captures anything
that is mechanically "computable",
but i disagree with that: TM computing cannot express everything that
is mechanically computable, and my paper will end with a distinct
example of such
Everything that is computable by by any means what-so-ever
is equivalent to finite string transformations applied to
finite strings.
well yes, each "step" of a TM computation is a finite string
transformation applied to finite strings
i'm saying as of right now, is am not sure that such a model encompasses
all of computation, specifically due to self-referential weirdness
The Liar Paradox can be shown to be nothing more than--
a incorrectly formed statement because of its pathological
self-reference. The Halting Problem can only exist because
of this same sort of pathological self-reference.
The primary benefit of solving the Halting Problem was to
detect programs that failed to halt, thus were incorrect.
Pathological self-reference can also be viewed as a form
of error. If the Halting Problem is redefined (which does not
refute anyone), then this redefined problem can be easily
solved.
Now we have three possible correct results:
(a) Halts
(b) Does Not Halt
(c) Pathological Self Reference to Halt
On 3/21/2026 5:32 PM, dart200 wrote:
On 3/21/26 1:14 PM, olcott wrote:
On 3/21/2026 2:50 PM, dart200 wrote:
On 3/21/26 12:02 PM, olcott wrote:
On 3/21/2026 1:40 PM, dart200 wrote:
On 3/21/26 2:30 AM, Mikko wrote:
On 21/03/2026 09:47, dart200 wrote:
that's probably gunna be the title of my next post/paper eh???
It is not a good title. Turings diagonal and Church-Turing theses >>>>>>> are two distinct topics. If your paper is about both you shuld have >>>>>>> "and" instead of ":". Even better if you mention only the main
topic.
fixing the diagonal is the main topic at hand, but it unexpectedly >>>>>> leads to a short refutation of the ct-thesis at the end which i
think is important enough to mention in the title
maybe i'll call it instead:
on deciding the undecidable
and a refutation of the church-turing thesis
The Church-Turing thesis can be more clearly stated
as any result obtained by applying finite string
transformation rules to finite strings is computable.
i don't agree
the church-turing thesis states that TM computation captures
anything that is mechanically "computable",
but i disagree with that: TM computing cannot express everything
that is mechanically computable, and my paper will end with a
distinct example of such
Everything that is computable by by any means what-so-ever
is equivalent to finite string transformations applied to
finite strings.
well yes, each "step" of a TM computation is a finite string
transformation applied to finite strings
i'm saying as of right now, is am not sure that such a model
encompasses all of computation, specifically due to self-referential
weirdness
"self-referential weirdness" AKA pathological self-reference
derives "undecidability" that is actually the error of
requiring the determination of the truth value of an
expression having no truth value.
On 3/21/2026 5:32 PM, dart200 wrote:yeah the 3-value approach is one way to deal with the problem
On 3/21/26 1:14 PM, olcott wrote:
On 3/21/2026 2:50 PM, dart200 wrote:
On 3/21/26 12:02 PM, olcott wrote:
On 3/21/2026 1:40 PM, dart200 wrote:
On 3/21/26 2:30 AM, Mikko wrote:
On 21/03/2026 09:47, dart200 wrote:
that's probably gunna be the title of my next post/paper eh???
It is not a good title. Turings diagonal and Church-Turing theses >>>>>>> are two distinct topics. If your paper is about both you shuld have >>>>>>> "and" instead of ":". Even better if you mention only the main
topic.
fixing the diagonal is the main topic at hand, but it unexpectedly >>>>>> leads to a short refutation of the ct-thesis at the end which i
think is important enough to mention in the title
maybe i'll call it instead:
on deciding the undecidable
and a refutation of the church-turing thesis
The Church-Turing thesis can be more clearly stated
as any result obtained by applying finite string
transformation rules to finite strings is computable.
i don't agree
the church-turing thesis states that TM computation captures
anything that is mechanically "computable",
but i disagree with that: TM computing cannot express everything
that is mechanically computable, and my paper will end with a
distinct example of such
Everything that is computable by by any means what-so-ever
is equivalent to finite string transformations applied to
finite strings.
well yes, each "step" of a TM computation is a finite string
transformation applied to finite strings
i'm saying as of right now, is am not sure that such a model
encompasses all of computation, specifically due to self-referential
weirdness
AKA Pathological Self-Reference(Olcott 2004)
On 9/5/2004 11:21 AM, Peter Olcott wrote:
The Liar Paradox can be shown to be nothing more than
a incorrectly formed statement because of its pathological
self-reference. The Halting Problem can only exist because
of this same sort of pathological self-reference.
The primary benefit of solving the Halting Problem was to
detect programs that failed to halt, thus were incorrect.
Pathological self-reference can also be viewed as a form
of error. If the Halting Problem is redefined (which does not
refute anyone), then this redefined problem can be easily
solved.
Now we have three possible correct results:
(a) Halts
(b) Does Not Halt
(c) Pathological Self Reference to Halt
On 3/22/26 11:17 AM, olcott wrote:
On 3/21/2026 5:32 PM, dart200 wrote:
On 3/21/26 1:14 PM, olcott wrote:
On 3/21/2026 2:50 PM, dart200 wrote:
On 3/21/26 12:02 PM, olcott wrote:
On 3/21/2026 1:40 PM, dart200 wrote:
On 3/21/26 2:30 AM, Mikko wrote:
On 21/03/2026 09:47, dart200 wrote:
that's probably gunna be the title of my next post/paper eh??? >>>>>>>>It is not a good title. Turings diagonal and Church-Turing theses >>>>>>>> are two distinct topics. If your paper is about both you shuld have >>>>>>>> "and" instead of ":". Even better if you mention only the main >>>>>>>> topic.
fixing the diagonal is the main topic at hand, but it
unexpectedly leads to a short refutation of the ct-thesis at the >>>>>>> end which i think is important enough to mention in the title
maybe i'll call it instead:
on deciding the undecidable
and a refutation of the church-turing thesis
The Church-Turing thesis can be more clearly stated
as any result obtained by applying finite string
transformation rules to finite strings is computable.
i don't agree
the church-turing thesis states that TM computation captures
anything that is mechanically "computable",
but i disagree with that: TM computing cannot express everything
that is mechanically computable, and my paper will end with a
distinct example of such
Everything that is computable by by any means what-so-ever
is equivalent to finite string transformations applied to
finite strings.
well yes, each "step" of a TM computation is a finite string
transformation applied to finite strings
i'm saying as of right now, is am not sure that such a model
encompasses all of computation, specifically due to self-referential
weirdness
"self-referential weirdness" AKA pathological self-reference
derives "undecidability" that is actually the error of
requiring the determination of the truth value of an
expression having no truth value.
i disagree. it's not that they have no truth value, but expressions can
have truth values that are not expressible from all "perspectives"
On 3/22/26 4:10 AM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory dart200 <user7160@newsgrouper.org.invalid> wrote:
that's probably gunna be the title of my next post/paper eh???
"Turing's diagonal" is not broken. So to regard it is a category error.
Why do you regard it as such?
because the paradox involved can be side-stepping using a quine to
detect itself on the enumeration and just output a digit instead of simulating itself in a circular fashion for digit that wasn't defined
The Church-Turing thesis, as Ben explained a fortnight or so ago, is not
the sort of entity that can be proven or refuted. It's more a
yes, that is what the consensus claims to justify it's failure to prove
it. or they act like rick and just assume it true and ignore the fact
it's not justified
definition of what the word "computable" means - anything which can be
determined by a turing machine or a lambda calculus expression.
i only need one counter example to demonstrate it false
If you think you can come up with a machine (for some reasonable value
of "machine") which can produce a result which a turing machine can't -
then the best of luck to you. Bright people have tried this already
over the past few decades and come up empty handed.
On 3/22/26 4:33 AM, Richard Damon wrote:
On 3/22/26 12:15 AM, dart200 wrote:
On 3/21/26 6:36 PM, Richard Damon wrote:
On 3/21/26 2:40 PM, dart200 wrote:
On 3/21/26 2:30 AM, Mikko wrote:
On 21/03/2026 09:47, dart200 wrote:fixing the diagonal is the main topic at hand, but it unexpectedly
that's probably gunna be the title of my next post/paper eh???
It is not a good title. Turings diagonal and Church-Turing theses
are two distinct topics. If your paper is about both you shuld have >>>>>> "and" instead of ":". Even better if you mention only the main topic. >>>>>
leads to a short refutation of the ct-thesis at the end which i
think is important enough to mention in the title
But it isn't computing "the diagonal" that is the real problem, just
the step used to show that actual problem, that of computationally
enumerating ALL the list, is actually not possible.
which is just silly to me, because if _i_ mechanically went and ran
each machines myself according to their instructions... _my_ output
wouldn't be subject to being read and contradicted
No, if you *MECHANICALLY* did that action, then there is a mecanical
algorithm that you followed, and a machine could be built that
implemented that mechanical algorithm, and contradicts your results.
that hasn't been proven rick, and such a proof would prove the ct-thesis
for all the shit u give me about making hand woven statements, here you
are being an abject hypocrite
so rest of this is based off just hand waving the ct-thesis around,
which hasn't actually been proven, so i won't respond to
On 21/03/2026 09:47, dart200 wrote:
that's probably gunna be the title of my next post/paper eh???
It is not a good title. Turings diagonal and Church-Turing theses
are two distinct topics. If your paper is about both you shuld have
"and" instead of ":". Even better if you mention only the main topic.
On 3/22/26 11:54 AM, olcott wrote:
On 3/21/2026 5:32 PM, dart200 wrote:yeah the 3-value approach is one way to deal with the problem
On 3/21/26 1:14 PM, olcott wrote:
On 3/21/2026 2:50 PM, dart200 wrote:
On 3/21/26 12:02 PM, olcott wrote:
On 3/21/2026 1:40 PM, dart200 wrote:
On 3/21/26 2:30 AM, Mikko wrote:
On 21/03/2026 09:47, dart200 wrote:
that's probably gunna be the title of my next post/paper eh??? >>>>>>>>It is not a good title. Turings diagonal and Church-Turing theses >>>>>>>> are two distinct topics. If your paper is about both you shuld have >>>>>>>> "and" instead of ":". Even better if you mention only the main >>>>>>>> topic.
fixing the diagonal is the main topic at hand, but it
unexpectedly leads to a short refutation of the ct-thesis at the >>>>>>> end which i think is important enough to mention in the title
maybe i'll call it instead:
on deciding the undecidable
and a refutation of the church-turing thesis
The Church-Turing thesis can be more clearly stated
as any result obtained by applying finite string
transformation rules to finite strings is computable.
i don't agree
the church-turing thesis states that TM computation captures
anything that is mechanically "computable",
but i disagree with that: TM computing cannot express everything
that is mechanically computable, and my paper will end with a
distinct example of such
Everything that is computable by by any means what-so-ever
is equivalent to finite string transformations applied to
finite strings.
well yes, each "step" of a TM computation is a finite string
transformation applied to finite strings
i'm saying as of right now, is am not sure that such a model
encompasses all of computation, specifically due to self-referential
weirdness
AKA Pathological Self-Reference(Olcott 2004)
On 9/5/2004 11:21 AM, Peter Olcott wrote:
The Liar Paradox can be shown to be nothing more than
a incorrectly formed statement because of its pathological
self-reference. The Halting Problem can only exist because
of this same sort of pathological self-reference.
;
The primary benefit of solving the Halting Problem was to
detect programs that failed to halt, thus were incorrect.
Pathological self-reference can also be viewed as a form
of error. If the Halting Problem is redefined (which does not
refute anyone), then this redefined problem can be easily
solved.
;
Now we have three possible correct results:
(a) Halts
(b) Does Not Halt
(c) Pathological Self Reference to Halt
one can also do what i call a "partial recognizer" which uses TRUE to indicate (a) and FALSE to indicate a merged (b) or (c) result
then you have a complement partial recognizer that uses TRUE to indicate
(b) and FALSE to indicate a merged (a) or (c) result
a more advanced technique can use context-awareness to return different results to different call-sites
On 3/22/26 4:05 PM, dart200 wrote:
On 3/22/26 11:17 AM, olcott wrote:
"self-referential weirdness" AKA pathological self-reference
derives "undecidability" that is actually the error of
requiring the determination of the truth value of an
expression having no truth value.
i disagree. it's not that they have no truth value, but expressions
can have truth values that are not expressible from all "perspectives"
But "Truth" isn't based on "perspective" for a clearly stated proposition.
On 22/03/2026 21:15, Richard Damon wrote:
On 3/22/26 4:05 PM, dart200 wrote:
On 3/22/26 11:17 AM, olcott wrote:
"self-referential weirdness" AKA pathological self-reference
derives "undecidability" that is actually the error of
requiring the determination of the truth value of an
expression having no truth value.
i disagree. it's not that they have no truth value, but expressions
can have truth values that are not expressible from all "perspectives"
But "Truth" isn't based on "perspective" for a clearly stated proposition.
He didn't say "Truth", he said "truth value".
When True and False (values) are mere relations of objects to the
primitive frame of a formal system in which the object exists then there
are extensions of the domain of such relations in which pathologically self-referential objects are in such a relation to the system which is neither True nor False.
Why wouldn't those qualify to be called truth values?
He didn't say "Truth", he said "truth value".
When True and False (values) are mere relations of objects to the
primitive frame of a formal system in which the object exists then there
are extensions of the domain of such relations in which pathologically
self-referential objects are in such a relation to the system which is
neither True nor False.
Why wouldn't those qualify to be called truth values?
What time is it (yes or no)?
The only correct action is rejecting the question.
On 22/03/2026 22:51, olcott wrote:
He didn't say "Truth", he said "truth value".
When True and False (values) are mere relations of objects to the
primitive frame of a formal system in which the object exists then there >>> are extensions of the domain of such relations in which pathologically
self-referential objects are in such a relation to the system which is
neither True nor False.
Why wouldn't those qualify to be called truth values?
What time is it (yes or no)?
The only correct action is rejecting the question.
I think I made it clear above that's not accurate.
On 3/22/26 4:10 AM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory dart200 <user7160@newsgrouper.org.invalid> wrote:
that's probably gunna be the title of my next post/paper eh???
"Turing's diagonal" is not broken. So to regard it is a category error.
Why do you regard it as such?
because the paradox involved can be side-stepping using a quine to
detect itself on the enumeration and just output a digit instead of simulating itself in a circular fashion for digit that wasn't defined
The Church-Turing thesis, as Ben explained a fortnight or so ago, is not
the sort of entity that can be proven or refuted. It's more a
yes, that is what the consensus claims to justify it's failure to prove
it. or they act like rick and just assume it true and ignore the fact
it's not justified
definition of what the word "computable" means - anything which can be
determined by a turing machine or a lambda calculus expression.
i only need one counter example to demonstrate it false
--If you think you can come up with a machine (for some reasonable value
of "machine") which can produce a result which a turing machine can't -
then the best of luck to you. Bright people have tried this already
over the past few decades and come up empty handed.
--
arising us out of the computing dark ages,
please excuse my pseudo-pyscript,
~ the little crank that could
On 3/22/2026 5:35 PM, Tristan Wibberley wrote:
On 22/03/2026 21:15, Richard Damon wrote:
On 3/22/26 4:05 PM, dart200 wrote:
On 3/22/26 11:17 AM, olcott wrote:
"self-referential weirdness" AKA pathological self-reference
derives "undecidability" that is actually the error of
requiring the determination of the truth value of an
expression having no truth value.
i disagree. it's not that they have no truth value, but expressions
can have truth values that are not expressible from all "perspectives" >>>>
But "Truth" isn't based on "perspective" for a clearly stated
proposition.
He didn't say "Truth", he said "truth value".
When True and False (values) are mere relations of objects to the
primitive frame of a formal system in which the object exists then there
are extensions of the domain of such relations in which pathologically
self-referential objects are in such a relation to the system which is
neither True nor False.
Why wouldn't those qualify to be called truth values?
What time is it (yes or no)?
The only correct action is rejecting the question.
On 3/22/2026 3:15 PM, dart200 wrote:
On 3/22/26 11:54 AM, olcott wrote:
On 3/21/2026 5:32 PM, dart200 wrote:yeah the 3-value approach is one way to deal with the problem
On 3/21/26 1:14 PM, olcott wrote:
On 3/21/2026 2:50 PM, dart200 wrote:
On 3/21/26 12:02 PM, olcott wrote:
On 3/21/2026 1:40 PM, dart200 wrote:
On 3/21/26 2:30 AM, Mikko wrote:
On 21/03/2026 09:47, dart200 wrote:
that's probably gunna be the title of my next post/paper eh??? >>>>>>>>>It is not a good title. Turings diagonal and Church-Turing theses >>>>>>>>> are two distinct topics. If your paper is about both you shuld >>>>>>>>> have
"and" instead of ":". Even better if you mention only the main >>>>>>>>> topic.
fixing the diagonal is the main topic at hand, but it
unexpectedly leads to a short refutation of the ct-thesis at the >>>>>>>> end which i think is important enough to mention in the title
maybe i'll call it instead:
on deciding the undecidable
and a refutation of the church-turing thesis
The Church-Turing thesis can be more clearly stated
as any result obtained by applying finite string
transformation rules to finite strings is computable.
i don't agree
the church-turing thesis states that TM computation captures
anything that is mechanically "computable",
but i disagree with that: TM computing cannot express everything
that is mechanically computable, and my paper will end with a
distinct example of such
Everything that is computable by by any means what-so-ever
is equivalent to finite string transformations applied to
finite strings.
well yes, each "step" of a TM computation is a finite string
transformation applied to finite strings
i'm saying as of right now, is am not sure that such a model
encompasses all of computation, specifically due to self-referential
weirdness
AKA Pathological Self-Reference(Olcott 2004)
On 9/5/2004 11:21 AM, Peter Olcott wrote:
The Liar Paradox can be shown to be nothing more than
a incorrectly formed statement because of its pathological
self-reference. The Halting Problem can only exist because
of this same sort of pathological self-reference.
;
The primary benefit of solving the Halting Problem was to
detect programs that failed to halt, thus were incorrect.
Pathological self-reference can also be viewed as a form
of error. If the Halting Problem is redefined (which does not
refute anyone), then this redefined problem can be easily
solved.
;
Now we have three possible correct results:
(a) Halts
(b) Does Not Halt
(c) Pathological Self Reference to Halt
one can also do what i call a "partial recognizer" which uses TRUE to
indicate (a) and FALSE to indicate a merged (b) or (c) result
then you have a complement partial recognizer that uses TRUE to
indicate (b) and FALSE to indicate a merged (a) or (c) result
a more advanced technique can use context-awareness to return
different results to different call-sites
What time is it (yes or no)?
Has rejecting the question as the only correct option.
Does an input that does that opposite of whatever I say halt?
Has rejecting the question as the only correct option.
On 3/22/26 4:05 PM, dart200 wrote:
On 3/22/26 11:17 AM, olcott wrote:
On 3/21/2026 5:32 PM, dart200 wrote:
On 3/21/26 1:14 PM, olcott wrote:
On 3/21/2026 2:50 PM, dart200 wrote:
On 3/21/26 12:02 PM, olcott wrote:
On 3/21/2026 1:40 PM, dart200 wrote:
On 3/21/26 2:30 AM, Mikko wrote:
On 21/03/2026 09:47, dart200 wrote:
that's probably gunna be the title of my next post/paper eh??? >>>>>>>>>It is not a good title. Turings diagonal and Church-Turing theses >>>>>>>>> are two distinct topics. If your paper is about both you shuld >>>>>>>>> have
"and" instead of ":". Even better if you mention only the main >>>>>>>>> topic.
fixing the diagonal is the main topic at hand, but it
unexpectedly leads to a short refutation of the ct-thesis at the >>>>>>>> end which i think is important enough to mention in the title
maybe i'll call it instead:
on deciding the undecidable
and a refutation of the church-turing thesis
The Church-Turing thesis can be more clearly stated
as any result obtained by applying finite string
transformation rules to finite strings is computable.
i don't agree
the church-turing thesis states that TM computation captures
anything that is mechanically "computable",
but i disagree with that: TM computing cannot express everything
that is mechanically computable, and my paper will end with a
distinct example of such
Everything that is computable by by any means what-so-ever
is equivalent to finite string transformations applied to
finite strings.
well yes, each "step" of a TM computation is a finite string
transformation applied to finite strings
i'm saying as of right now, is am not sure that such a model
encompasses all of computation, specifically due to self-referential
weirdness
"self-referential weirdness" AKA pathological self-reference
derives "undecidability" that is actually the error of
requiring the determination of the truth value of an
expression having no truth value.
i disagree. it's not that they have no truth value, but expressions
can have truth values that are not expressible from all "perspectives"
But "Truth" isn't based on "perspective" for a clearly stated proposition.
Halting, and effectively-enumeration are clearly defined properties, and--
a given machine either halts or it doesn't, and a set can either be effectively-enumerated or not.
On 3/22/26 11:47 AM, dart200 wrote:
On 3/22/26 4:33 AM, Richard Damon wrote:
On 3/22/26 12:15 AM, dart200 wrote:
On 3/21/26 6:36 PM, Richard Damon wrote:
On 3/21/26 2:40 PM, dart200 wrote:
On 3/21/26 2:30 AM, Mikko wrote:
On 21/03/2026 09:47, dart200 wrote:
that's probably gunna be the title of my next post/paper eh???
It is not a good title. Turings diagonal and Church-Turing theses >>>>>>> are two distinct topics. If your paper is about both you shuld have >>>>>>> "and" instead of ":". Even better if you mention only the main
topic.
fixing the diagonal is the main topic at hand, but it unexpectedly >>>>>> leads to a short refutation of the ct-thesis at the end which i
think is important enough to mention in the title
But it isn't computing "the diagonal" that is the real problem,
just the step used to show that actual problem, that of
computationally enumerating ALL the list, is actually not possible.
which is just silly to me, because if _i_ mechanically went and ran
each machines myself according to their instructions... _my_ output
wouldn't be subject to being read and contradicted
No, if you *MECHANICALLY* did that action, then there is a mecanical
algorithm that you followed, and a machine could be built that
implemented that mechanical algorithm, and contradicts your results.
that hasn't been proven rick, and such a proof would prove the ct-thesis
No. Mechanical, means SOME machine can do it, not necessarily a Turing machine.
dart200 <user7160@newsgrouper.org.invalid> wrote:
On 3/22/26 4:10 AM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory dart200 <user7160@newsgrouper.org.invalid> wrote:
that's probably gunna be the title of my next post/paper eh???
"Turing's diagonal" is not broken. So to regard it is a category error. >>> Why do you regard it as such?
because the paradox involved can be side-stepping using a quine to
detect itself on the enumeration and just output a digit instead of
simulating itself in a circular fashion for digit that wasn't defined
What's that word salad got to do with my question? Again, Turing's
diagonal argument is not broken, so there's nothing to "fix".
The Church-Turing thesis, as Ben explained a fortnight or so ago, is not >>> the sort of entity that can be proven or refuted. It's more a
yes, that is what the consensus claims to justify it's failure to prove
it. or they act like rick and just assume it true and ignore the fact
it's not justified
"Fact", eh? The Church-Turing thesis would appear to be eminently
justified by the fact that nobody's been able to devise a more powerful machine than a turing machine.
definition of what the word "computable" means - anything which can be
determined by a turing machine or a lambda calculus expression.
i only need one counter example to demonstrate it false
Counter examples are not twenty to the dozen. It is overwhelmingly
likely that you will be unable to come up with a valid counter example. Again, were that within your capabilities, somebody more capable would
have beat you to it, many decades ago.
--If you think you can come up with a machine (for some reasonable value
of "machine") which can produce a result which a turing machine can't -
then the best of luck to you. Bright people have tried this already
over the past few decades and come up empty handed.
On 3/22/2026 3:15 PM, dart200 wrote:
On 3/22/26 11:54 AM, olcott wrote:
On 3/21/2026 5:32 PM, dart200 wrote:yeah the 3-value approach is one way to deal with the problem
On 3/21/26 1:14 PM, olcott wrote:
On 3/21/2026 2:50 PM, dart200 wrote:
On 3/21/26 12:02 PM, olcott wrote:
On 3/21/2026 1:40 PM, dart200 wrote:
On 3/21/26 2:30 AM, Mikko wrote:
On 21/03/2026 09:47, dart200 wrote:
that's probably gunna be the title of my next post/paper eh??? >>>>>>>>>It is not a good title. Turings diagonal and Church-Turing theses >>>>>>>>> are two distinct topics. If your paper is about both you shuld >>>>>>>>> have
"and" instead of ":". Even better if you mention only the main >>>>>>>>> topic.
fixing the diagonal is the main topic at hand, but it
unexpectedly leads to a short refutation of the ct-thesis at the >>>>>>>> end which i think is important enough to mention in the title
maybe i'll call it instead:
on deciding the undecidable
and a refutation of the church-turing thesis
The Church-Turing thesis can be more clearly stated
as any result obtained by applying finite string
transformation rules to finite strings is computable.
i don't agree
the church-turing thesis states that TM computation captures
anything that is mechanically "computable",
but i disagree with that: TM computing cannot express everything
that is mechanically computable, and my paper will end with a
distinct example of such
Everything that is computable by by any means what-so-ever
is equivalent to finite string transformations applied to
finite strings.
well yes, each "step" of a TM computation is a finite string
transformation applied to finite strings
i'm saying as of right now, is am not sure that such a model
encompasses all of computation, specifically due to self-referential
weirdness
AKA Pathological Self-Reference(Olcott 2004)
On 9/5/2004 11:21 AM, Peter Olcott wrote:
The Liar Paradox can be shown to be nothing more than
a incorrectly formed statement because of its pathological
self-reference. The Halting Problem can only exist because
of this same sort of pathological self-reference.
;
The primary benefit of solving the Halting Problem was to
detect programs that failed to halt, thus were incorrect.
Pathological self-reference can also be viewed as a form
of error. If the Halting Problem is redefined (which does not
refute anyone), then this redefined problem can be easily
solved.
;
Now we have three possible correct results:
(a) Halts
(b) Does Not Halt
(c) Pathological Self Reference to Halt
one can also do what i call a "partial recognizer" which uses TRUE to
indicate (a) and FALSE to indicate a merged (b) or (c) result
then you have a complement partial recognizer that uses TRUE to
indicate (b) and FALSE to indicate a merged (a) or (c) result
a more advanced technique can use context-awareness to return
different results to different call-sites
What time is it (yes or no)?
Has rejecting the question as the only correct option.
Does an input that does that opposite of whatever I say halt?
Has rejecting the question as the only correct option.
On 3/22/26 2:15 PM, Richard Damon wrote:
On 3/22/26 11:47 AM, dart200 wrote:
On 3/22/26 4:33 AM, Richard Damon wrote:
On 3/22/26 12:15 AM, dart200 wrote:
On 3/21/26 6:36 PM, Richard Damon wrote:
On 3/21/26 2:40 PM, dart200 wrote:which is just silly to me, because if _i_ mechanically went and ran >>>>> each machines myself according to their instructions... _my_ output >>>>> wouldn't be subject to being read and contradicted
On 3/21/26 2:30 AM, Mikko wrote:
On 21/03/2026 09:47, dart200 wrote:
that's probably gunna be the title of my next post/paper eh??? >>>>>>>>It is not a good title. Turings diagonal and Church-Turing theses >>>>>>>> are two distinct topics. If your paper is about both you shuld have >>>>>>>> "and" instead of ":". Even better if you mention only the main >>>>>>>> topic.
fixing the diagonal is the main topic at hand, but it
unexpectedly leads to a short refutation of the ct-thesis at the >>>>>>> end which i think is important enough to mention in the title
But it isn't computing "the diagonal" that is the real problem,
just the step used to show that actual problem, that of
computationally enumerating ALL the list, is actually not possible. >>>>>
No, if you *MECHANICALLY* did that action, then there is a mecanical
algorithm that you followed, and a machine could be built that
implemented that mechanical algorithm, and contradicts your results.
that hasn't been proven rick, and such a proof would prove the ct-thesis
No. Mechanical, means SOME machine can do it, not necessarily a Turing
machine.
i can mechanically compute things 🙄🙄🙄
On 3/22/26 3:23 PM, olcott wrote:
On 3/22/2026 3:15 PM, dart200 wrote:
On 3/22/26 11:54 AM, olcott wrote:
On 3/21/2026 5:32 PM, dart200 wrote:yeah the 3-value approach is one way to deal with the problem
On 3/21/26 1:14 PM, olcott wrote:
On 3/21/2026 2:50 PM, dart200 wrote:
On 3/21/26 12:02 PM, olcott wrote:
On 3/21/2026 1:40 PM, dart200 wrote:
On 3/21/26 2:30 AM, Mikko wrote:
On 21/03/2026 09:47, dart200 wrote:
that's probably gunna be the title of my next post/paper eh??? >>>>>>>>>>It is not a good title. Turings diagonal and Church-Turing theses >>>>>>>>>> are two distinct topics. If your paper is about both you shuld >>>>>>>>>> have
"and" instead of ":". Even better if you mention only the main >>>>>>>>>> topic.
fixing the diagonal is the main topic at hand, but it
unexpectedly leads to a short refutation of the ct-thesis at >>>>>>>>> the end which i think is important enough to mention in the title >>>>>>>>>
maybe i'll call it instead:
on deciding the undecidable
and a refutation of the church-turing thesis
The Church-Turing thesis can be more clearly stated
as any result obtained by applying finite string
transformation rules to finite strings is computable.
i don't agree
the church-turing thesis states that TM computation captures
anything that is mechanically "computable",
but i disagree with that: TM computing cannot express everything >>>>>>> that is mechanically computable, and my paper will end with a
distinct example of such
Everything that is computable by by any means what-so-ever
is equivalent to finite string transformations applied to
finite strings.
well yes, each "step" of a TM computation is a finite string
transformation applied to finite strings
i'm saying as of right now, is am not sure that such a model
encompasses all of computation, specifically due to self-
referential weirdness
AKA Pathological Self-Reference(Olcott 2004)
On 9/5/2004 11:21 AM, Peter Olcott wrote:
The Liar Paradox can be shown to be nothing more than
a incorrectly formed statement because of its pathological
self-reference. The Halting Problem can only exist because
of this same sort of pathological self-reference.
;
The primary benefit of solving the Halting Problem was to
detect programs that failed to halt, thus were incorrect.
Pathological self-reference can also be viewed as a form
of error. If the Halting Problem is redefined (which does not
refute anyone), then this redefined problem can be easily
solved.
;
Now we have three possible correct results:
(a) Halts
(b) Does Not Halt
(c) Pathological Self Reference to Halt
one can also do what i call a "partial recognizer" which uses TRUE to
indicate (a) and FALSE to indicate a merged (b) or (c) result
then you have a complement partial recognizer that uses TRUE to
indicate (b) and FALSE to indicate a merged (a) or (c) result
a more advanced technique can use context-awareness to return
different results to different call-sites
What time is it (yes or no)?
Has rejecting the question as the only correct option.
u could also block indefinitely and just not respond as in the case of a classic recognizer or partial decider?
Does an input that does that opposite of whatever I say halt?
Has rejecting the question as the only correct option.
On 3/22/2026 8:35 PM, dart200 wrote:
On 3/22/26 3:23 PM, olcott wrote:
On 3/22/2026 3:15 PM, dart200 wrote:
On 3/22/26 11:54 AM, olcott wrote:
On 3/21/2026 5:32 PM, dart200 wrote:yeah the 3-value approach is one way to deal with the problem
On 3/21/26 1:14 PM, olcott wrote:
On 3/21/2026 2:50 PM, dart200 wrote:
On 3/21/26 12:02 PM, olcott wrote:
On 3/21/2026 1:40 PM, dart200 wrote:
On 3/21/26 2:30 AM, Mikko wrote:
On 21/03/2026 09:47, dart200 wrote:
that's probably gunna be the title of my next post/paper eh??? >>>>>>>>>>>It is not a good title. Turings diagonal and Church-Turing >>>>>>>>>>> theses
are two distinct topics. If your paper is about both you >>>>>>>>>>> shuld have
"and" instead of ":". Even better if you mention only the >>>>>>>>>>> main topic.
fixing the diagonal is the main topic at hand, but it
unexpectedly leads to a short refutation of the ct-thesis at >>>>>>>>>> the end which i think is important enough to mention in the title >>>>>>>>>>
maybe i'll call it instead:
on deciding the undecidable
and a refutation of the church-turing thesis
The Church-Turing thesis can be more clearly stated
as any result obtained by applying finite string
transformation rules to finite strings is computable.
i don't agree
the church-turing thesis states that TM computation captures
anything that is mechanically "computable",
but i disagree with that: TM computing cannot express everything >>>>>>>> that is mechanically computable, and my paper will end with a >>>>>>>> distinct example of such
Everything that is computable by by any means what-so-ever
is equivalent to finite string transformations applied to
finite strings.
well yes, each "step" of a TM computation is a finite string
transformation applied to finite strings
i'm saying as of right now, is am not sure that such a model
encompasses all of computation, specifically due to self-
referential weirdness
AKA Pathological Self-Reference(Olcott 2004)
On 9/5/2004 11:21 AM, Peter Olcott wrote:
The Liar Paradox can be shown to be nothing more than
a incorrectly formed statement because of its pathological
self-reference. The Halting Problem can only exist because
of this same sort of pathological self-reference.
;
The primary benefit of solving the Halting Problem was to
detect programs that failed to halt, thus were incorrect.
Pathological self-reference can also be viewed as a form
of error. If the Halting Problem is redefined (which does not
refute anyone), then this redefined problem can be easily
solved.
;
Now we have three possible correct results:
(a) Halts
(b) Does Not Halt
(c) Pathological Self Reference to Halt
one can also do what i call a "partial recognizer" which uses TRUE
to indicate (a) and FALSE to indicate a merged (b) or (c) result
then you have a complement partial recognizer that uses TRUE to
indicate (b) and FALSE to indicate a merged (a) or (c) result
a more advanced technique can use context-awareness to return
different results to different call-sites
What time is it (yes or no)?
Has rejecting the question as the only correct option.
u could also block indefinitely and just not respond as in the case of
a classic recognizer or partial decider?
Instead of that I make a full decider that always
correctly decides every coherent decision problem
within the entire body of knowledge that can be
expressed in language.
Does an input that does that opposite of whatever I say halt?
Has rejecting the question as the only correct option.
On 3/21/2026 2:30 AM, Mikko wrote:
On 21/03/2026 09:47, dart200 wrote:
that's probably gunna be the title of my next post/paper eh???
It is not a good title. Turings diagonal and Church-Turing theses
are two distinct topics. If your paper is about both you shuld have
"and" instead of ":". Even better if you mention only the main topic.
It is not a good idea to write another thesis about the Church-Turing
thesis no matter what title.
Alan Turing died on June 7, 1954, at age 41 from cyanide poisoning, officially ruled a suicide. He was found with a half-eaten apple,
suspected of being laced with cyanide, following his 1952 conviction for homosexual acts and forced chemical castration. While officially
suicide, some researchers argue it could have been accidental poisoning.
On 21/03/2026 09:47, dart200 wrote:
that's probably gunna be the title of my next post/paper eh???
It is not a good title. Turings diagonal and Church-Turing theses
are two distinct topics. If your paper is about both you shuld have
"and" instead of ":". Even better if you mention only the main topic.
On 3/22/26 2:05 AM, Mikko wrote:
On 21/03/2026 20:40, dart200 wrote:
On 3/21/26 2:30 AM, Mikko wrote:
On 21/03/2026 09:47, dart200 wrote:
that's probably gunna be the title of my next post/paper eh???
It is not a good title. Turings diagonal and Church-Turing theses
are two distinct topics. If your paper is about both you shuld have
"and" instead of ":". Even better if you mention only the main topic.
fixing the diagonal is the main topic at hand, but it unexpectedly
leads to a short refutation of the ct-thesis at the end which i think
is important enough to mention in the title
maybe i'll call it instead:
on deciding the undecidable
and a refutation of the church-turing thesis
A real scientist would put "On Deciding the Undecidable" in one paper
and "On Refutation of the Church-Turing Thesis" in anohter.
unless of course they are heavily intertwined being that one leads into
the others,
which is what i was thinking 🤷--
On 3/22/26 2:15 PM, Richard Damon wrote:
On 3/22/26 4:05 PM, dart200 wrote:
On 3/22/26 11:17 AM, olcott wrote:
On 3/21/2026 5:32 PM, dart200 wrote:
On 3/21/26 1:14 PM, olcott wrote:
On 3/21/2026 2:50 PM, dart200 wrote:
On 3/21/26 12:02 PM, olcott wrote:
On 3/21/2026 1:40 PM, dart200 wrote:
On 3/21/26 2:30 AM, Mikko wrote:
On 21/03/2026 09:47, dart200 wrote:
that's probably gunna be the title of my next post/paper eh??? >>>>>>>>>>It is not a good title. Turings diagonal and Church-Turing theses >>>>>>>>>> are two distinct topics. If your paper is about both you shuld >>>>>>>>>> have
"and" instead of ":". Even better if you mention only the main >>>>>>>>>> topic.
fixing the diagonal is the main topic at hand, but it
unexpectedly leads to a short refutation of the ct-thesis at >>>>>>>>> the end which i think is important enough to mention in the title >>>>>>>>>
maybe i'll call it instead:
on deciding the undecidable
and a refutation of the church-turing thesis
The Church-Turing thesis can be more clearly stated
as any result obtained by applying finite string
transformation rules to finite strings is computable.
i don't agree
the church-turing thesis states that TM computation captures
anything that is mechanically "computable",
but i disagree with that: TM computing cannot express everything >>>>>>> that is mechanically computable, and my paper will end with a
distinct example of such
Everything that is computable by by any means what-so-ever
is equivalent to finite string transformations applied to
finite strings.
well yes, each "step" of a TM computation is a finite string
transformation applied to finite strings
i'm saying as of right now, is am not sure that such a model
encompasses all of computation, specifically due to self-
referential weirdness
"self-referential weirdness" AKA pathological self-reference
derives "undecidability" that is actually the error of
requiring the determination of the truth value of an
expression having no truth value.
i disagree. it's not that they have no truth value, but expressions
can have truth values that are not expressible from all "perspectives"
But "Truth" isn't based on "perspective" for a clearly stated
proposition.
... if i ask you the question "where are you?" then your truthful answer depends on the particular frame of reference that you exist in ...
Halting, and effectively-enumeration are clearly defined properties,
and a given machine either halts or it doesn't, and a set can either
be effectively-enumerated or not.
On 3/22/26 3:23 PM, olcott wrote:
On 3/22/2026 3:15 PM, dart200 wrote:
On 3/22/26 11:54 AM, olcott wrote:
On 3/21/2026 5:32 PM, dart200 wrote:yeah the 3-value approach is one way to deal with the problem
On 3/21/26 1:14 PM, olcott wrote:
On 3/21/2026 2:50 PM, dart200 wrote:
On 3/21/26 12:02 PM, olcott wrote:
On 3/21/2026 1:40 PM, dart200 wrote:
On 3/21/26 2:30 AM, Mikko wrote:
On 21/03/2026 09:47, dart200 wrote:
that's probably gunna be the title of my next post/paper eh??? >>>>>>>>>>It is not a good title. Turings diagonal and Church-Turing theses >>>>>>>>>> are two distinct topics. If your paper is about both you shuld >>>>>>>>>> have
"and" instead of ":". Even better if you mention only the main >>>>>>>>>> topic.
fixing the diagonal is the main topic at hand, but it
unexpectedly leads to a short refutation of the ct-thesis at >>>>>>>>> the end which i think is important enough to mention in the title >>>>>>>>>
maybe i'll call it instead:
on deciding the undecidable
and a refutation of the church-turing thesis
The Church-Turing thesis can be more clearly stated
as any result obtained by applying finite string
transformation rules to finite strings is computable.
i don't agree
the church-turing thesis states that TM computation captures
anything that is mechanically "computable",
but i disagree with that: TM computing cannot express everything >>>>>>> that is mechanically computable, and my paper will end with a
distinct example of such
Everything that is computable by by any means what-so-ever
is equivalent to finite string transformations applied to
finite strings.
well yes, each "step" of a TM computation is a finite string
transformation applied to finite strings
i'm saying as of right now, is am not sure that such a model
encompasses all of computation, specifically due to self-
referential weirdness
AKA Pathological Self-Reference(Olcott 2004)
On 9/5/2004 11:21 AM, Peter Olcott wrote:
The Liar Paradox can be shown to be nothing more than
a incorrectly formed statement because of its pathological
self-reference. The Halting Problem can only exist because
of this same sort of pathological self-reference.
;
The primary benefit of solving the Halting Problem was to
detect programs that failed to halt, thus were incorrect.
Pathological self-reference can also be viewed as a form
of error. If the Halting Problem is redefined (which does not
refute anyone), then this redefined problem can be easily
solved.
;
Now we have three possible correct results:
(a) Halts
(b) Does Not Halt
(c) Pathological Self Reference to Halt
one can also do what i call a "partial recognizer" which uses TRUE to
indicate (a) and FALSE to indicate a merged (b) or (c) result
then you have a complement partial recognizer that uses TRUE to
indicate (b) and FALSE to indicate a merged (a) or (c) result
a more advanced technique can use context-awareness to return
different results to different call-sites
What time is it (yes or no)?
Has rejecting the question as the only correct option.
u could also block indefinitely and just not respond as in the case of a classic recognizer or partial decider?
Does an input that does that opposite of whatever I say halt?
Has rejecting the question as the only correct option.
On 3/22/26 6:41 PM, olcott wrote:
On 3/22/2026 8:35 PM, dart200 wrote:
On 3/22/26 3:23 PM, olcott wrote:
On 3/22/2026 3:15 PM, dart200 wrote:
On 3/22/26 11:54 AM, olcott wrote:
On 3/21/2026 5:32 PM, dart200 wrote:yeah the 3-value approach is one way to deal with the problem
On 3/21/26 1:14 PM, olcott wrote:
On 3/21/2026 2:50 PM, dart200 wrote:
On 3/21/26 12:02 PM, olcott wrote:
On 3/21/2026 1:40 PM, dart200 wrote:
On 3/21/26 2:30 AM, Mikko wrote:
On 21/03/2026 09:47, dart200 wrote:
that's probably gunna be the title of my next post/paper eh??? >>>>>>>>>>>>It is not a good title. Turings diagonal and Church-Turing >>>>>>>>>>>> theses
are two distinct topics. If your paper is about both you >>>>>>>>>>>> shuld have
"and" instead of ":". Even better if you mention only the >>>>>>>>>>>> main topic.
fixing the diagonal is the main topic at hand, but it
unexpectedly leads to a short refutation of the ct-thesis at >>>>>>>>>>> the end which i think is important enough to mention in the >>>>>>>>>>> title
maybe i'll call it instead:
on deciding the undecidable
and a refutation of the church-turing thesis
The Church-Turing thesis can be more clearly stated
as any result obtained by applying finite string
transformation rules to finite strings is computable.
i don't agree
the church-turing thesis states that TM computation captures >>>>>>>>> anything that is mechanically "computable",
but i disagree with that: TM computing cannot express
everything that is mechanically computable, and my paper will >>>>>>>>> end with a distinct example of such
Everything that is computable by by any means what-so-ever
is equivalent to finite string transformations applied to
finite strings.
well yes, each "step" of a TM computation is a finite string
transformation applied to finite strings
i'm saying as of right now, is am not sure that such a model
encompasses all of computation, specifically due to self-
referential weirdness
AKA Pathological Self-Reference(Olcott 2004)
On 9/5/2004 11:21 AM, Peter Olcott wrote:
The Liar Paradox can be shown to be nothing more than
a incorrectly formed statement because of its pathological
self-reference. The Halting Problem can only exist because
of this same sort of pathological self-reference.
;
The primary benefit of solving the Halting Problem was to
detect programs that failed to halt, thus were incorrect.
Pathological self-reference can also be viewed as a form
of error. If the Halting Problem is redefined (which does not
refute anyone), then this redefined problem can be easily
solved.
;
Now we have three possible correct results:
(a) Halts
(b) Does Not Halt
(c) Pathological Self Reference to Halt
one can also do what i call a "partial recognizer" which uses TRUE
to indicate (a) and FALSE to indicate a merged (b) or (c) result
then you have a complement partial recognizer that uses TRUE to
indicate (b) and FALSE to indicate a merged (a) or (c) result
a more advanced technique can use context-awareness to return
different results to different call-sites
What time is it (yes or no)?
Has rejecting the question as the only correct option.
u could also block indefinitely and just not respond as in the case
of a classic recognizer or partial decider?
Instead of that I make a full decider that always
correctly decides every coherent decision problem
within the entire body of knowledge that can be
expressed in language.
idk,
halts3val = (machine) -> {
UNDECIDABLE: if machine is undecidable input to halts3val
TRUE: else if machine halts
FALSE: else machine does not halt
}
und = () -> if (halts3val(und) == TRUE) loop()
when und() is run, halts3val(und) => UNDECIDABLE, which will avoid the loop() causing und() to halt...
so therefore halts3val() does not managed to output TRUE, what does???
clearly if we run und() it does halt, but halts3val() fails to classify
this as such,
can anything do that?
Does an input that does that opposite of whatever I say halt?
Has rejecting the question as the only correct option.
On 3/22/26 2:15 PM, Richard Damon wrote:
On 3/22/26 11:47 AM, dart200 wrote:
On 3/22/26 4:33 AM, Richard Damon wrote:
On 3/22/26 12:15 AM, dart200 wrote:
On 3/21/26 6:36 PM, Richard Damon wrote:
On 3/21/26 2:40 PM, dart200 wrote:which is just silly to me, because if _i_ mechanically went and ran >>>>> each machines myself according to their instructions... _my_ output >>>>> wouldn't be subject to being read and contradicted
On 3/21/26 2:30 AM, Mikko wrote:
On 21/03/2026 09:47, dart200 wrote:
that's probably gunna be the title of my next post/paper eh??? >>>>>>>>It is not a good title. Turings diagonal and Church-Turing theses >>>>>>>> are two distinct topics. If your paper is about both you shuld have >>>>>>>> "and" instead of ":". Even better if you mention only the main >>>>>>>> topic.
fixing the diagonal is the main topic at hand, but it
unexpectedly leads to a short refutation of the ct-thesis at the >>>>>>> end which i think is important enough to mention in the title
But it isn't computing "the diagonal" that is the real problem,
just the step used to show that actual problem, that of
computationally enumerating ALL the list, is actually not possible. >>>>>
No, if you *MECHANICALLY* did that action, then there is a mecanical
algorithm that you followed, and a machine could be built that
implemented that mechanical algorithm, and contradicts your results.
that hasn't been proven rick, and such a proof would prove the ct-thesis
No. Mechanical, means SOME machine can do it, not necessarily a Turing
machine.
i can mechanically compute things 🙄🙄🙄
On 3/22/26 6:27 PM, dart200 wrote:
On 3/22/26 2:15 PM, Richard Damon wrote:
On 3/22/26 11:47 AM, dart200 wrote:
On 3/22/26 4:33 AM, Richard Damon wrote:
On 3/22/26 12:15 AM, dart200 wrote:
On 3/21/26 6:36 PM, Richard Damon wrote:
On 3/21/26 2:40 PM, dart200 wrote:which is just silly to me, because if _i_ mechanically went and
On 3/21/26 2:30 AM, Mikko wrote:
On 21/03/2026 09:47, dart200 wrote:
that's probably gunna be the title of my next post/paper eh??? >>>>>>>>>It is not a good title. Turings diagonal and Church-Turing theses >>>>>>>>> are two distinct topics. If your paper is about both you shuld >>>>>>>>> have
"and" instead of ":". Even better if you mention only the main >>>>>>>>> topic.
fixing the diagonal is the main topic at hand, but it
unexpectedly leads to a short refutation of the ct-thesis at the >>>>>>>> end which i think is important enough to mention in the title
But it isn't computing "the diagonal" that is the real problem, >>>>>>> just the step used to show that actual problem, that of
computationally enumerating ALL the list, is actually not possible. >>>>>>
ran each machines myself according to their instructions... _my_
output wouldn't be subject to being read and contradicted
No, if you *MECHANICALLY* did that action, then there is a
mecanical algorithm that you followed, and a machine could be built >>>>> that implemented that mechanical algorithm, and contradicts your
results.
that hasn't been proven rick, and such a proof would prove the ct-
thesis
No. Mechanical, means SOME machine can do it, not necessarily a
Turing machine.
i can mechanically compute things 🙄🙄🙄
in fact i can mechanically compute anything that is mechanically computable...
On 3/22/26 6:41 PM, olcott wrote:
On 3/22/2026 8:35 PM, dart200 wrote:
On 3/22/26 3:23 PM, olcott wrote:
On 3/22/2026 3:15 PM, dart200 wrote:
On 3/22/26 11:54 AM, olcott wrote:
On 3/21/2026 5:32 PM, dart200 wrote:yeah the 3-value approach is one way to deal with the problem
On 3/21/26 1:14 PM, olcott wrote:
On 3/21/2026 2:50 PM, dart200 wrote:
On 3/21/26 12:02 PM, olcott wrote:
On 3/21/2026 1:40 PM, dart200 wrote:
On 3/21/26 2:30 AM, Mikko wrote:
On 21/03/2026 09:47, dart200 wrote:
that's probably gunna be the title of my next post/paper eh??? >>>>>>>>>>>>It is not a good title. Turings diagonal and Church-Turing >>>>>>>>>>>> theses
are two distinct topics. If your paper is about both you >>>>>>>>>>>> shuld have
"and" instead of ":". Even better if you mention only the >>>>>>>>>>>> main topic.
fixing the diagonal is the main topic at hand, but it
unexpectedly leads to a short refutation of the ct-thesis at >>>>>>>>>>> the end which i think is important enough to mention in the >>>>>>>>>>> title
maybe i'll call it instead:
on deciding the undecidable
and a refutation of the church-turing thesis
The Church-Turing thesis can be more clearly stated
as any result obtained by applying finite string
transformation rules to finite strings is computable.
i don't agree
the church-turing thesis states that TM computation captures >>>>>>>>> anything that is mechanically "computable",
but i disagree with that: TM computing cannot express
everything that is mechanically computable, and my paper will >>>>>>>>> end with a distinct example of such
Everything that is computable by by any means what-so-ever
is equivalent to finite string transformations applied to
finite strings.
well yes, each "step" of a TM computation is a finite string
transformation applied to finite strings
i'm saying as of right now, is am not sure that such a model
encompasses all of computation, specifically due to self-
referential weirdness
AKA Pathological Self-Reference(Olcott 2004)
On 9/5/2004 11:21 AM, Peter Olcott wrote:
The Liar Paradox can be shown to be nothing more than
a incorrectly formed statement because of its pathological
self-reference. The Halting Problem can only exist because
of this same sort of pathological self-reference.
;
The primary benefit of solving the Halting Problem was to
detect programs that failed to halt, thus were incorrect.
Pathological self-reference can also be viewed as a form
of error. If the Halting Problem is redefined (which does not
refute anyone), then this redefined problem can be easily
solved.
;
Now we have three possible correct results:
(a) Halts
(b) Does Not Halt
(c) Pathological Self Reference to Halt
one can also do what i call a "partial recognizer" which uses TRUE
to indicate (a) and FALSE to indicate a merged (b) or (c) result
then you have a complement partial recognizer that uses TRUE to
indicate (b) and FALSE to indicate a merged (a) or (c) result
a more advanced technique can use context-awareness to return
different results to different call-sites
What time is it (yes or no)?
Has rejecting the question as the only correct option.
u could also block indefinitely and just not respond as in the case
of a classic recognizer or partial decider?
Instead of that I make a full decider that always
correctly decides every coherent decision problem
within the entire body of knowledge that can be
expressed in language.
idk,
halts3val = (machine) -> {
UNDECIDABLE: if machine is undecidable input to halts3val
TRUE: else if machine halts
FALSE: else machine does not halt
}
und = () -> if (halts3val(und) == TRUE) loop()
when und() is run, halts3val(und) => UNDECIDABLE, which will avoid the loop() causing und() to halt...
so therefore halts3val() does not managed to output TRUE, what does???
clearly if we run und() it does halt, but halts3val() fails to classify
this as such,
can anything do that?
On 3/22/26 9:22 PM, dart200 wrote:
On 3/22/26 2:15 PM, Richard Damon wrote:
On 3/22/26 4:05 PM, dart200 wrote:
On 3/22/26 11:17 AM, olcott wrote:
On 3/21/2026 5:32 PM, dart200 wrote:
On 3/21/26 1:14 PM, olcott wrote:
On 3/21/2026 2:50 PM, dart200 wrote:
On 3/21/26 12:02 PM, olcott wrote:
On 3/21/2026 1:40 PM, dart200 wrote:
On 3/21/26 2:30 AM, Mikko wrote:
On 21/03/2026 09:47, dart200 wrote:
that's probably gunna be the title of my next post/paper eh??? >>>>>>>>>>>It is not a good title. Turings diagonal and Church-Turing >>>>>>>>>>> theses
are two distinct topics. If your paper is about both you >>>>>>>>>>> shuld have
"and" instead of ":". Even better if you mention only the >>>>>>>>>>> main topic.
fixing the diagonal is the main topic at hand, but it
unexpectedly leads to a short refutation of the ct-thesis at >>>>>>>>>> the end which i think is important enough to mention in the title >>>>>>>>>>
maybe i'll call it instead:
on deciding the undecidable
and a refutation of the church-turing thesis
The Church-Turing thesis can be more clearly stated
as any result obtained by applying finite string
transformation rules to finite strings is computable.
i don't agree
the church-turing thesis states that TM computation captures
anything that is mechanically "computable",
but i disagree with that: TM computing cannot express everything >>>>>>>> that is mechanically computable, and my paper will end with a >>>>>>>> distinct example of such
Everything that is computable by by any means what-so-ever
is equivalent to finite string transformations applied to
finite strings.
well yes, each "step" of a TM computation is a finite string
transformation applied to finite strings
i'm saying as of right now, is am not sure that such a model
encompasses all of computation, specifically due to self-
referential weirdness
"self-referential weirdness" AKA pathological self-reference
derives "undecidability" that is actually the error of
requiring the determination of the truth value of an
expression having no truth value.
i disagree. it's not that they have no truth value, but expressions
can have truth values that are not expressible from all "perspectives" >>>>
But "Truth" isn't based on "perspective" for a clearly stated
proposition.
... if i ask you the question "where are you?" then your truthful
answer depends on the particular frame of reference that you exist in ...
But the questions being asked AREN'T of that type.
It is always an OBJECTIVE question about a SPECIFIC object.
Your problemm is you don't understand what you are talking about amd are following in Olcott's insanity.
Note, at a given moment, "Where are you?" has a difinititive truthful answer.
Unless you think "Numbers" or "Machines" that have been actually defined
can change, that arguement is just a strawman.
Of course, that *IS* what you seem to think, that a given algorithm can correctly do two different things for the same input.
Halting, and effectively-enumeration are clearly defined properties,
and a given machine either halts or it doesn't, and a set can either
be effectively-enumerated or not.
On 3/22/26 4:31 PM, Alan Mackenzie wrote:It is. You're not expressing yourself clearly. Diagonals don't test.
dart200 <user7160@newsgrouper.org.invalid> wrote:turing's diagonal needlessly tests itself in being circle-free, and
On 3/22/26 4:10 AM, Alan Mackenzie wrote:What's that word salad got to do with my question? Again, Turing's
[ Followup-To: set ]because the paradox involved can be side-stepping using a quine to
In comp.theory dart200 <user7160@newsgrouper.org.invalid> wrote:
that's probably gunna be the title of my next post/paper eh???"Turing's diagonal" is not broken. So to regard it is a category error. >>>> Why do you regard it as such?
detect itself on the enumeration and just output a digit instead of
simulating itself in a circular fashion for digit that wasn't defined
diagonal argument is not broken, so there's nothing to "fix".
that's why it runs up against the particular uncomputable situation (aka "paradox") that it does
if that's word salad to you, ....
.... then u don't know what his p247 is about, and ur opinion on thisYou're not responding to what I've written. Again, Ben has explained
matter, well does not matter...
ok go submit that as a proof bro, change the church-turing thesis to the church-turing theory..."Fact", eh? The Church-Turing thesis would appear to be eminentlyThe Church-Turing thesis, as Ben explained a fortnight or so ago, is not >>>> the sort of entity that can be proven or refuted. It's more ayes, that is what the consensus claims to justify it's failure to prove
it. or they act like rick and just assume it true and ignore the fact
it's not justified
justified by the fact that nobody's been able to devise a more powerful
machine than a turing machine.
That's incoherent but looks unnecessarily vulgar.fking neggers gunna neg 🙄🙄🙄Counter examples are not twenty to the dozen. It is overwhelminglydefinition of what the word "computable" means - anything which can be >>>> determined by a turing machine or a lambda calculus expression.i only need one counter example to demonstrate it false
likely that you will be unable to come up with a valid counter example.
Again, were that within your capabilities, somebody more capable would
have beat you to it, many decades ago.
----If you think you can come up with a machine (for some reasonable value >>>> of "machine") which can produce a result which a turing machine can't - >>>> then the best of luck to you. Bright people have tried this already
over the past few decades and come up empty handed.
arising us out of the computing dark ages,
please excuse my pseudo-pyscript,
~ the little crank that could
On 3/22/26 9:36 PM, dart200 wrote:
On 3/22/26 6:27 PM, dart200 wrote:
On 3/22/26 2:15 PM, Richard Damon wrote:
On 3/22/26 11:47 AM, dart200 wrote:
On 3/22/26 4:33 AM, Richard Damon wrote:
On 3/22/26 12:15 AM, dart200 wrote:
On 3/21/26 6:36 PM, Richard Damon wrote:
On 3/21/26 2:40 PM, dart200 wrote:which is just silly to me, because if _i_ mechanically went and >>>>>>> ran each machines myself according to their instructions... _my_ >>>>>>> output wouldn't be subject to being read and contradicted
On 3/21/26 2:30 AM, Mikko wrote:But it isn't computing "the diagonal" that is the real problem, >>>>>>>> just the step used to show that actual problem, that of
On 21/03/2026 09:47, dart200 wrote:
that's probably gunna be the title of my next post/paper eh??? >>>>>>>>>>It is not a good title. Turings diagonal and Church-Turing theses >>>>>>>>>> are two distinct topics. If your paper is about both you shuld >>>>>>>>>> have
"and" instead of ":". Even better if you mention only the main >>>>>>>>>> topic.
fixing the diagonal is the main topic at hand, but it
unexpectedly leads to a short refutation of the ct-thesis at >>>>>>>>> the end which i think is important enough to mention in the title >>>>>>>>
computationally enumerating ALL the list, is actually not possible. >>>>>>>
No, if you *MECHANICALLY* did that action, then there is a
mecanical algorithm that you followed, and a machine could be
built that implemented that mechanical algorithm, and contradicts >>>>>> your results.
that hasn't been proven rick, and such a proof would prove the ct-
thesis
No. Mechanical, means SOME machine can do it, not necessarily a
Turing machine.
i can mechanically compute things 🙄🙄🙄
in fact i can mechanically compute anything that is mechanically
computable...
Nope.
The problem is you have a fixed finite capability, and some machines can
run longer than you can.
On 3/22/2026 10:44 PM, dart200 wrote:
On 3/22/26 6:41 PM, olcott wrote:
On 3/22/2026 8:35 PM, dart200 wrote:
On 3/22/26 3:23 PM, olcott wrote:
On 3/22/2026 3:15 PM, dart200 wrote:
On 3/22/26 11:54 AM, olcott wrote:
On 3/21/2026 5:32 PM, dart200 wrote:yeah the 3-value approach is one way to deal with the problem
On 3/21/26 1:14 PM, olcott wrote:
On 3/21/2026 2:50 PM, dart200 wrote:
On 3/21/26 12:02 PM, olcott wrote:
On 3/21/2026 1:40 PM, dart200 wrote:
On 3/21/26 2:30 AM, Mikko wrote:
On 21/03/2026 09:47, dart200 wrote:
that's probably gunna be the title of my next post/paper >>>>>>>>>>>>>> eh???
It is not a good title. Turings diagonal and Church-Turing >>>>>>>>>>>>> theses
are two distinct topics. If your paper is about both you >>>>>>>>>>>>> shuld have
"and" instead of ":". Even better if you mention only the >>>>>>>>>>>>> main topic.
fixing the diagonal is the main topic at hand, but it >>>>>>>>>>>> unexpectedly leads to a short refutation of the ct-thesis at >>>>>>>>>>>> the end which i think is important enough to mention in the >>>>>>>>>>>> title
maybe i'll call it instead:
on deciding the undecidable
and a refutation of the church-turing thesis
The Church-Turing thesis can be more clearly stated
as any result obtained by applying finite string
transformation rules to finite strings is computable.
i don't agree
the church-turing thesis states that TM computation captures >>>>>>>>>> anything that is mechanically "computable",
but i disagree with that: TM computing cannot express
everything that is mechanically computable, and my paper will >>>>>>>>>> end with a distinct example of such
Everything that is computable by by any means what-so-ever
is equivalent to finite string transformations applied to
finite strings.
well yes, each "step" of a TM computation is a finite string
transformation applied to finite strings
i'm saying as of right now, is am not sure that such a model
encompasses all of computation, specifically due to self-
referential weirdness
AKA Pathological Self-Reference(Olcott 2004)
On 9/5/2004 11:21 AM, Peter Olcott wrote:
The Liar Paradox can be shown to be nothing more than
a incorrectly formed statement because of its pathological
self-reference. The Halting Problem can only exist because
of this same sort of pathological self-reference.
;
The primary benefit of solving the Halting Problem was to
detect programs that failed to halt, thus were incorrect.
Pathological self-reference can also be viewed as a form
of error. If the Halting Problem is redefined (which does not >>>>>>> > refute anyone), then this redefined problem can be easily
solved.
;
Now we have three possible correct results:
(a) Halts
(b) Does Not Halt
(c) Pathological Self Reference to Halt
one can also do what i call a "partial recognizer" which uses TRUE >>>>>> to indicate (a) and FALSE to indicate a merged (b) or (c) result
then you have a complement partial recognizer that uses TRUE to
indicate (b) and FALSE to indicate a merged (a) or (c) result
a more advanced technique can use context-awareness to return
different results to different call-sites
What time is it (yes or no)?
Has rejecting the question as the only correct option.
u could also block indefinitely and just not respond as in the case
of a classic recognizer or partial decider?
Instead of that I make a full decider that always
correctly decides every coherent decision problem
within the entire body of knowledge that can be
expressed in language.
idk,
halts3val = (machine) -> {
UNDECIDABLE: if machine is undecidable input to halts3val
TRUE: else if machine halts
FALSE: else machine does not halt
}
und = () -> if (halts3val(und) == TRUE) loop()
when und() is run, halts3val(und) => UNDECIDABLE, which will avoid the
loop() causing und() to halt...
so therefore halts3val() does not managed to output TRUE, what does???
clearly if we run und() it does halt, but halts3val() fails to
classify this as such,
can anything do that?
int DD()
{
int Halt_Status = HHH(DD);
if (Halt_Status)
HERE: goto HERE;
return Halt_Status;
}
HHH(DD) correctly detects that DD simulated by
HHH does not derive a well founded justification
tree and is rejected as bad input on that basis.
On 3/23/26 5:32 AM, olcott wrote:
On 3/22/2026 10:44 PM, dart200 wrote:
On 3/22/26 6:41 PM, olcott wrote:
On 3/22/2026 8:35 PM, dart200 wrote:
On 3/22/26 3:23 PM, olcott wrote:
On 3/22/2026 3:15 PM, dart200 wrote:
On 3/22/26 11:54 AM, olcott wrote:
On 3/21/2026 5:32 PM, dart200 wrote:yeah the 3-value approach is one way to deal with the problem
On 3/21/26 1:14 PM, olcott wrote:
On 3/21/2026 2:50 PM, dart200 wrote:
On 3/21/26 12:02 PM, olcott wrote:
On 3/21/2026 1:40 PM, dart200 wrote:
On 3/21/26 2:30 AM, Mikko wrote:
On 21/03/2026 09:47, dart200 wrote:
that's probably gunna be the title of my next post/paper >>>>>>>>>>>>>>> eh???
It is not a good title. Turings diagonal and Church-Turing >>>>>>>>>>>>>> theses
are two distinct topics. If your paper is about both you >>>>>>>>>>>>>> shuld have
"and" instead of ":". Even better if you mention only the >>>>>>>>>>>>>> main topic.
fixing the diagonal is the main topic at hand, but it >>>>>>>>>>>>> unexpectedly leads to a short refutation of the ct-thesis >>>>>>>>>>>>> at the end which i think is important enough to mention in >>>>>>>>>>>>> the title
maybe i'll call it instead:
on deciding the undecidable
and a refutation of the church-turing thesis
The Church-Turing thesis can be more clearly stated
as any result obtained by applying finite string
transformation rules to finite strings is computable.
i don't agree
the church-turing thesis states that TM computation captures >>>>>>>>>>> anything that is mechanically "computable",
but i disagree with that: TM computing cannot express
everything that is mechanically computable, and my paper will >>>>>>>>>>> end with a distinct example of such
Everything that is computable by by any means what-so-ever >>>>>>>>>> is equivalent to finite string transformations applied to
finite strings.
well yes, each "step" of a TM computation is a finite string >>>>>>>>> transformation applied to finite strings
i'm saying as of right now, is am not sure that such a model >>>>>>>>> encompasses all of computation, specifically due to self-
referential weirdness
AKA Pathological Self-Reference(Olcott 2004)
On 9/5/2004 11:21 AM, Peter Olcott wrote:
The Liar Paradox can be shown to be nothing more than
a incorrectly formed statement because of its pathological >>>>>>>> > self-reference. The Halting Problem can only exist because >>>>>>>> > of this same sort of pathological self-reference.
;
The primary benefit of solving the Halting Problem was to
detect programs that failed to halt, thus were incorrect.
Pathological self-reference can also be viewed as a form
of error. If the Halting Problem is redefined (which does not >>>>>>>> > refute anyone), then this redefined problem can be easily
solved.
;
Now we have three possible correct results:
(a) Halts
(b) Does Not Halt
(c) Pathological Self Reference to Halt
one can also do what i call a "partial recognizer" which uses
TRUE to indicate (a) and FALSE to indicate a merged (b) or (c)
result
then you have a complement partial recognizer that uses TRUE to >>>>>>> indicate (b) and FALSE to indicate a merged (a) or (c) result
a more advanced technique can use context-awareness to return
different results to different call-sites
What time is it (yes or no)?
Has rejecting the question as the only correct option.
u could also block indefinitely and just not respond as in the case >>>>> of a classic recognizer or partial decider?
Instead of that I make a full decider that always
correctly decides every coherent decision problem
within the entire body of knowledge that can be
expressed in language.
idk,
halts3val = (machine) -> {
UNDECIDABLE: if machine is undecidable input to halts3val
TRUE: else if machine halts
FALSE: else machine does not halt
}
und = () -> if (halts3val(und) == TRUE) loop()
when und() is run, halts3val(und) => UNDECIDABLE, which will avoid
the loop() causing und() to halt...
so therefore halts3val() does not managed to output TRUE, what does???
clearly if we run und() it does halt, but halts3val() fails to
classify this as such,
can anything do that?
int DD()
{
int Halt_Status = HHH(DD);
if (Halt_Status)
HERE: goto HERE;
return Halt_Status;
}
HHH(DD) correctly detects that DD simulated by
HHH does not derive a well founded justification
tree and is rejected as bad input on that basis.
ur not answering the question polcott
dart200 <user7160@newsgrouper.org.invalid> wrote:
On 3/22/26 4:31 PM, Alan Mackenzie wrote:
dart200 <user7160@newsgrouper.org.invalid> wrote:
On 3/22/26 4:10 AM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory dart200 <user7160@newsgrouper.org.invalid> wrote:
that's probably gunna be the title of my next post/paper eh???
"Turing's diagonal" is not broken. So to regard it is a category error. >>>>> Why do you regard it as such?
because the paradox involved can be side-stepping using a quine to
detect itself on the enumeration and just output a digit instead of
simulating itself in a circular fashion for digit that wasn't defined
What's that word salad got to do with my question? Again, Turing's
diagonal argument is not broken, so there's nothing to "fix".
turing's diagonal needlessly tests itself in being circle-free, and
that's why it runs up against the particular uncomputable situation (aka
"paradox") that it does
if that's word salad to you, ....
It is. You're not expressing yourself clearly. Diagonals don't test.
It's just not what they do. You probably meant to say something like "a
test on the diagonal is needlessly ...".
You're not responding to what I've written. Again, Ben has explained
that the Church-Turing thesis is not the sort of thing that can be
On 3/23/2026 5:03 PM, dart200 wrote:
On 3/23/26 5:32 AM, olcott wrote:
On 3/22/2026 10:44 PM, dart200 wrote:
On 3/22/26 6:41 PM, olcott wrote:
On 3/22/2026 8:35 PM, dart200 wrote:
On 3/22/26 3:23 PM, olcott wrote:
On 3/22/2026 3:15 PM, dart200 wrote:
On 3/22/26 11:54 AM, olcott wrote:
On 3/21/2026 5:32 PM, dart200 wrote:yeah the 3-value approach is one way to deal with the problem
On 3/21/26 1:14 PM, olcott wrote:
On 3/21/2026 2:50 PM, dart200 wrote:
On 3/21/26 12:02 PM, olcott wrote:
On 3/21/2026 1:40 PM, dart200 wrote:i don't agree
On 3/21/26 2:30 AM, Mikko wrote:
On 21/03/2026 09:47, dart200 wrote:
that's probably gunna be the title of my next post/paper >>>>>>>>>>>>>>>> eh???
It is not a good title. Turings diagonal and Church- >>>>>>>>>>>>>>> Turing theses
are two distinct topics. If your paper is about both you >>>>>>>>>>>>>>> shuld have
"and" instead of ":". Even better if you mention only the >>>>>>>>>>>>>>> main topic.
fixing the diagonal is the main topic at hand, but it >>>>>>>>>>>>>> unexpectedly leads to a short refutation of the ct-thesis >>>>>>>>>>>>>> at the end which i think is important enough to mention in >>>>>>>>>>>>>> the title
maybe i'll call it instead:
on deciding the undecidable
and a refutation of the church-turing thesis
The Church-Turing thesis can be more clearly stated
as any result obtained by applying finite string
transformation rules to finite strings is computable. >>>>>>>>>>>>
the church-turing thesis states that TM computation captures >>>>>>>>>>>> anything that is mechanically "computable",
but i disagree with that: TM computing cannot express >>>>>>>>>>>> everything that is mechanically computable, and my paper >>>>>>>>>>>> will end with a distinct example of such
Everything that is computable by by any means what-so-ever >>>>>>>>>>> is equivalent to finite string transformations applied to >>>>>>>>>>> finite strings.
well yes, each "step" of a TM computation is a finite string >>>>>>>>>> transformation applied to finite strings
i'm saying as of right now, is am not sure that such a model >>>>>>>>>> encompasses all of computation, specifically due to self- >>>>>>>>>> referential weirdness
AKA Pathological Self-Reference(Olcott 2004)
On 9/5/2004 11:21 AM, Peter Olcott wrote:
The Liar Paradox can be shown to be nothing more than
a incorrectly formed statement because of its pathological >>>>>>>>> > self-reference. The Halting Problem can only exist because >>>>>>>>> > of this same sort of pathological self-reference.
;
The primary benefit of solving the Halting Problem was to >>>>>>>>> > detect programs that failed to halt, thus were incorrect. >>>>>>>>> > Pathological self-reference can also be viewed as a form >>>>>>>>> > of error. If the Halting Problem is redefined (which does not >>>>>>>>> > refute anyone), then this redefined problem can be easily >>>>>>>>> > solved.
;
Now we have three possible correct results:
(a) Halts
(b) Does Not Halt
(c) Pathological Self Reference to Halt
one can also do what i call a "partial recognizer" which uses >>>>>>>> TRUE to indicate (a) and FALSE to indicate a merged (b) or (c) >>>>>>>> result
then you have a complement partial recognizer that uses TRUE to >>>>>>>> indicate (b) and FALSE to indicate a merged (a) or (c) result
a more advanced technique can use context-awareness to return >>>>>>>> different results to different call-sites
What time is it (yes or no)?
Has rejecting the question as the only correct option.
u could also block indefinitely and just not respond as in the
case of a classic recognizer or partial decider?
Instead of that I make a full decider that always
correctly decides every coherent decision problem
within the entire body of knowledge that can be
expressed in language.
idk,
halts3val = (machine) -> {
UNDECIDABLE: if machine is undecidable input to halts3val
TRUE: else if machine halts
FALSE: else machine does not halt
}
und = () -> if (halts3val(und) == TRUE) loop()
when und() is run, halts3val(und) => UNDECIDABLE, which will avoid
the loop() causing und() to halt...
so therefore halts3val() does not managed to output TRUE, what does??? >>>>
clearly if we run und() it does halt, but halts3val() fails to
classify this as such,
can anything do that?
int DD()
{
int Halt_Status = HHH(DD);
if (Halt_Status)
HERE: goto HERE;
return Halt_Status;
}
HHH(DD) correctly detects that DD simulated by
HHH does not derive a well founded justification
tree and is rejected as bad input on that basis.
ur not answering the question polcott
The halting problem has always been the incorrect
question of: What value of can HHH correctly return
when DD is encoded to do the opposite of whatever
HHH returns?
On 3/23/26 4:46 AM, Richard Damon wrote:
On 3/22/26 9:22 PM, dart200 wrote:
On 3/22/26 2:15 PM, Richard Damon wrote:
On 3/22/26 4:05 PM, dart200 wrote:
On 3/22/26 11:17 AM, olcott wrote:
On 3/21/2026 5:32 PM, dart200 wrote:
On 3/21/26 1:14 PM, olcott wrote:
On 3/21/2026 2:50 PM, dart200 wrote:
On 3/21/26 12:02 PM, olcott wrote:
On 3/21/2026 1:40 PM, dart200 wrote:
On 3/21/26 2:30 AM, Mikko wrote:
On 21/03/2026 09:47, dart200 wrote:
that's probably gunna be the title of my next post/paper eh??? >>>>>>>>>>>>It is not a good title. Turings diagonal and Church-Turing >>>>>>>>>>>> theses
are two distinct topics. If your paper is about both you >>>>>>>>>>>> shuld have
"and" instead of ":". Even better if you mention only the >>>>>>>>>>>> main topic.
fixing the diagonal is the main topic at hand, but it
unexpectedly leads to a short refutation of the ct-thesis at >>>>>>>>>>> the end which i think is important enough to mention in the >>>>>>>>>>> title
maybe i'll call it instead:
on deciding the undecidable
and a refutation of the church-turing thesis
The Church-Turing thesis can be more clearly stated
as any result obtained by applying finite string
transformation rules to finite strings is computable.
i don't agree
the church-turing thesis states that TM computation captures >>>>>>>>> anything that is mechanically "computable",
but i disagree with that: TM computing cannot express
everything that is mechanically computable, and my paper will >>>>>>>>> end with a distinct example of such
Everything that is computable by by any means what-so-ever
is equivalent to finite string transformations applied to
finite strings.
well yes, each "step" of a TM computation is a finite string
transformation applied to finite strings
i'm saying as of right now, is am not sure that such a model
encompasses all of computation, specifically due to self-
referential weirdness
"self-referential weirdness" AKA pathological self-reference
derives "undecidability" that is actually the error of
requiring the determination of the truth value of an
expression having no truth value.
i disagree. it's not that they have no truth value, but expressions >>>>> can have truth values that are not expressible from all "perspectives" >>>>>
But "Truth" isn't based on "perspective" for a clearly stated
proposition.
... if i ask you the question "where are you?" then your truthful
answer depends on the particular frame of reference that you exist
in ...
But the questions being asked AREN'T of that type.
it's not exactly a 1:1 analogy,
but the computing machine space is not a 1:1 analogy for real space,
It is always an OBJECTIVE question about a SPECIFIC object.
Your problemm is you don't understand what you are talking about amd
are following in Olcott's insanity.
Note, at a given moment, "Where are you?" has a difinititive truthful
answer.
sure, but not all "frames of reference" can state that definitive answer
due to self-referential weirdness
Unless you think "Numbers" or "Machines" that have been actually
defined can change, that arguement is just a strawman.
Of course, that *IS* what you seem to think, that a given algorithm
can correctly do two different things for the same input.
Halting, and effectively-enumeration are clearly defined properties,
and a given machine either halts or it doesn't, and a set can either
be effectively-enumerated or not.
On 3/22/2026 10:44 PM, dart200 wrote:
On 3/22/26 6:41 PM, olcott wrote:
On 3/22/2026 8:35 PM, dart200 wrote:
On 3/22/26 3:23 PM, olcott wrote:
On 3/22/2026 3:15 PM, dart200 wrote:
On 3/22/26 11:54 AM, olcott wrote:
On 3/21/2026 5:32 PM, dart200 wrote:yeah the 3-value approach is one way to deal with the problem
On 3/21/26 1:14 PM, olcott wrote:
On 3/21/2026 2:50 PM, dart200 wrote:
On 3/21/26 12:02 PM, olcott wrote:
On 3/21/2026 1:40 PM, dart200 wrote:
On 3/21/26 2:30 AM, Mikko wrote:
On 21/03/2026 09:47, dart200 wrote:
that's probably gunna be the title of my next post/paper >>>>>>>>>>>>>> eh???
It is not a good title. Turings diagonal and Church-Turing >>>>>>>>>>>>> theses
are two distinct topics. If your paper is about both you >>>>>>>>>>>>> shuld have
"and" instead of ":". Even better if you mention only the >>>>>>>>>>>>> main topic.
fixing the diagonal is the main topic at hand, but it >>>>>>>>>>>> unexpectedly leads to a short refutation of the ct-thesis at >>>>>>>>>>>> the end which i think is important enough to mention in the >>>>>>>>>>>> title
maybe i'll call it instead:
on deciding the undecidable
and a refutation of the church-turing thesis
The Church-Turing thesis can be more clearly stated
as any result obtained by applying finite string
transformation rules to finite strings is computable.
i don't agree
the church-turing thesis states that TM computation captures >>>>>>>>>> anything that is mechanically "computable",
but i disagree with that: TM computing cannot express
everything that is mechanically computable, and my paper will >>>>>>>>>> end with a distinct example of such
Everything that is computable by by any means what-so-ever
is equivalent to finite string transformations applied to
finite strings.
well yes, each "step" of a TM computation is a finite string
transformation applied to finite strings
i'm saying as of right now, is am not sure that such a model
encompasses all of computation, specifically due to self-
referential weirdness
AKA Pathological Self-Reference(Olcott 2004)
On 9/5/2004 11:21 AM, Peter Olcott wrote:
The Liar Paradox can be shown to be nothing more than
a incorrectly formed statement because of its pathological
self-reference. The Halting Problem can only exist because
of this same sort of pathological self-reference.
;
The primary benefit of solving the Halting Problem was to
detect programs that failed to halt, thus were incorrect.
Pathological self-reference can also be viewed as a form
of error. If the Halting Problem is redefined (which does not >>>>>>> > refute anyone), then this redefined problem can be easily
solved.
;
Now we have three possible correct results:
(a) Halts
(b) Does Not Halt
(c) Pathological Self Reference to Halt
one can also do what i call a "partial recognizer" which uses TRUE >>>>>> to indicate (a) and FALSE to indicate a merged (b) or (c) result
then you have a complement partial recognizer that uses TRUE to
indicate (b) and FALSE to indicate a merged (a) or (c) result
a more advanced technique can use context-awareness to return
different results to different call-sites
What time is it (yes or no)?
Has rejecting the question as the only correct option.
u could also block indefinitely and just not respond as in the case
of a classic recognizer or partial decider?
Instead of that I make a full decider that always
correctly decides every coherent decision problem
within the entire body of knowledge that can be
expressed in language.
idk,
halts3val = (machine) -> {
UNDECIDABLE: if machine is undecidable input to halts3val
TRUE: else if machine halts
FALSE: else machine does not halt
}
und = () -> if (halts3val(und) == TRUE) loop()
when und() is run, halts3val(und) => UNDECIDABLE, which will avoid the
loop() causing und() to halt...
so therefore halts3val() does not managed to output TRUE, what does???
clearly if we run und() it does halt, but halts3val() fails to
classify this as such,
can anything do that?
int DD()
{
int Halt_Status = HHH(DD);
if (Halt_Status)
HERE: goto HERE;
return Halt_Status;
}
HHH(DD) correctly detects that DD simulated by
HHH does not derive a well founded justification
tree and is rejected as bad input on that basis.
On 3/23/26 4:46 AM, Richard Damon wrote:
On 3/22/26 9:36 PM, dart200 wrote:
On 3/22/26 6:27 PM, dart200 wrote:
On 3/22/26 2:15 PM, Richard Damon wrote:
On 3/22/26 11:47 AM, dart200 wrote:
On 3/22/26 4:33 AM, Richard Damon wrote:
On 3/22/26 12:15 AM, dart200 wrote:
On 3/21/26 6:36 PM, Richard Damon wrote:
On 3/21/26 2:40 PM, dart200 wrote:
On 3/21/26 2:30 AM, Mikko wrote:But it isn't computing "the diagonal" that is the real problem, >>>>>>>>> just the step used to show that actual problem, that of
On 21/03/2026 09:47, dart200 wrote:
that's probably gunna be the title of my next post/paper eh??? >>>>>>>>>>>It is not a good title. Turings diagonal and Church-Turing >>>>>>>>>>> theses
are two distinct topics. If your paper is about both you >>>>>>>>>>> shuld have
"and" instead of ":". Even better if you mention only the >>>>>>>>>>> main topic.
fixing the diagonal is the main topic at hand, but it
unexpectedly leads to a short refutation of the ct-thesis at >>>>>>>>>> the end which i think is important enough to mention in the title >>>>>>>>>
computationally enumerating ALL the list, is actually not
possible.
which is just silly to me, because if _i_ mechanically went and >>>>>>>> ran each machines myself according to their instructions... _my_ >>>>>>>> output wouldn't be subject to being read and contradicted
No, if you *MECHANICALLY* did that action, then there is a
mecanical algorithm that you followed, and a machine could be
built that implemented that mechanical algorithm, and contradicts >>>>>>> your results.
that hasn't been proven rick, and such a proof would prove the ct- >>>>>> thesis
No. Mechanical, means SOME machine can do it, not necessarily a
Turing machine.
i can mechanically compute things 🙄🙄🙄
in fact i can mechanically compute anything that is mechanically
computable...
Nope.
The problem is you have a fixed finite capability, and some machines
can run longer than you can.
those are pragmatic considerations which computability theory has no
concern over,
no real machines have infinite capability either,
metaphysical "me" with infinite longevity can compute anything a machine
can with infinite longevity, that's foundational to computing actually
being based in some form of "mechanics", a word which has roots words
that mean "manual labor"
On 3/23/26 9:43 AM, Alan Mackenzie wrote:
dart200 <user7160@newsgrouper.org.invalid> wrote:
On 3/22/26 4:31 PM, Alan Mackenzie wrote:
dart200 <user7160@newsgrouper.org.invalid> wrote:
On 3/22/26 4:10 AM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory dart200 <user7160@newsgrouper.org.invalid> wrote:
that's probably gunna be the title of my next post/paper eh???
"Turing's diagonal" is not broken. So to regard it is a category >>>>>> error.
Why do you regard it as such?
because the paradox involved can be side-stepping using a quine to
detect itself on the enumeration and just output a digit instead of
simulating itself in a circular fashion for digit that wasn't defined
What's that word salad got to do with my question? Again, Turing's
diagonal argument is not broken, so there's nothing to "fix".
turing's diagonal needlessly tests itself in being circle-free, and
that's why it runs up against the particular uncomputable situation (aka >>> "paradox") that it does
if that's word salad to you, ....
It is. You're not expressing yourself clearly. Diagonals don't test.
It's just not what they do. You probably meant to say something like "a
test on the diagonal is needlessly ...".
the pseudo code for turing's H goes as follows:
H = () -> {
M = 0
K = 0
do {
if (D(M) == TRUE) { // TRUE = satisfactory
output sim(M,K) // Kth digit of H = Kth digit of M
K += 1
}
M += 1
}
}
turing's whole point on p247 was that as some point M = DN(H) and then
an undecidable situation happens:
- if D(DN(H)) => TRUE when H will get caught up in circular loop,
- but if D(DN(H)) => FALSE, then H will skip simulating itself
creating a circle free situation
- both return value result in a semantic contradiction...
the paradox comes from self-referential weirdness due to H unnecessarily testing itself, and if u can't agree with that there's nothing more for
me to state on the matter
i'm not going to debate anything with some asshat who clearly has no
fucking clue how the diagonal machine that turing constructed works
the fact no one else is calling u out for being a total chucklefuck here
is distinct evidence to me ya'll are acting like a retarded bandwagon of school children instead of actual logicians
You're not responding to what I've written. Again, Ben has explained
that the Church-Turing thesis is not the sort of thing that can be
quoting ben is not a proof. ben making claims is not a proof. ben making excuses for the computing consensus in failing to prove the ct-thesis
for almost a century now, is also _not a proof_ of it's correctness...
failing to prove something for almost century is not a supportive claim
of for it's truth, and in fact is totally irrelevant to whether the ct- thesis is true or not. it just means that whatever theoretical
innovation needs to be had for that proof has not been made. god forbid
the consensus admits it doesn't know what the fuck it's really doing...
dear lord, the theoretical laziness that has been festering in
mathematics due to accepting the incompleteness theorem is just _inexcusable_
On 3/23/26 3:51 PM, olcott wrote:
On 3/23/2026 5:03 PM, dart200 wrote:
On 3/23/26 5:32 AM, olcott wrote:
On 3/22/2026 10:44 PM, dart200 wrote:
On 3/22/26 6:41 PM, olcott wrote:
On 3/22/2026 8:35 PM, dart200 wrote:
On 3/22/26 3:23 PM, olcott wrote:
On 3/22/2026 3:15 PM, dart200 wrote:
On 3/22/26 11:54 AM, olcott wrote:
On 3/21/2026 5:32 PM, dart200 wrote:yeah the 3-value approach is one way to deal with the problem >>>>>>>>>
On 3/21/26 1:14 PM, olcott wrote:
On 3/21/2026 2:50 PM, dart200 wrote:
On 3/21/26 12:02 PM, olcott wrote:
On 3/21/2026 1:40 PM, dart200 wrote:i don't agree
On 3/21/26 2:30 AM, Mikko wrote:
On 21/03/2026 09:47, dart200 wrote:
that's probably gunna be the title of my next post/ >>>>>>>>>>>>>>>>> paper eh???
It is not a good title. Turings diagonal and Church- >>>>>>>>>>>>>>>> Turing theses
are two distinct topics. If your paper is about both you >>>>>>>>>>>>>>>> shuld have
"and" instead of ":". Even better if you mention only >>>>>>>>>>>>>>>> the main topic.
fixing the diagonal is the main topic at hand, but it >>>>>>>>>>>>>>> unexpectedly leads to a short refutation of the ct-thesis >>>>>>>>>>>>>>> at the end which i think is important enough to mention >>>>>>>>>>>>>>> in the title
maybe i'll call it instead:
on deciding the undecidable
and a refutation of the church-turing thesis
The Church-Turing thesis can be more clearly stated >>>>>>>>>>>>>> as any result obtained by applying finite string
transformation rules to finite strings is computable. >>>>>>>>>>>>>
the church-turing thesis states that TM computation >>>>>>>>>>>>> captures anything that is mechanically "computable", >>>>>>>>>>>>>
but i disagree with that: TM computing cannot express >>>>>>>>>>>>> everything that is mechanically computable, and my paper >>>>>>>>>>>>> will end with a distinct example of such
Everything that is computable by by any means what-so-ever >>>>>>>>>>>> is equivalent to finite string transformations applied to >>>>>>>>>>>> finite strings.
well yes, each "step" of a TM computation is a finite string >>>>>>>>>>> transformation applied to finite strings
i'm saying as of right now, is am not sure that such a model >>>>>>>>>>> encompasses all of computation, specifically due to self- >>>>>>>>>>> referential weirdness
AKA Pathological Self-Reference(Olcott 2004)
On 9/5/2004 11:21 AM, Peter Olcott wrote:
The Liar Paradox can be shown to be nothing more than
a incorrectly formed statement because of its pathological >>>>>>>>>> > self-reference. The Halting Problem can only exist because >>>>>>>>>> > of this same sort of pathological self-reference.
;
The primary benefit of solving the Halting Problem was to >>>>>>>>>> > detect programs that failed to halt, thus were incorrect. >>>>>>>>>> > Pathological self-reference can also be viewed as a form >>>>>>>>>> > of error. If the Halting Problem is redefined (which does not >>>>>>>>>> > refute anyone), then this redefined problem can be easily >>>>>>>>>> > solved.
;
Now we have three possible correct results:
(a) Halts
(b) Does Not Halt
(c) Pathological Self Reference to Halt
one can also do what i call a "partial recognizer" which uses >>>>>>>>> TRUE to indicate (a) and FALSE to indicate a merged (b) or (c) >>>>>>>>> result
then you have a complement partial recognizer that uses TRUE to >>>>>>>>> indicate (b) and FALSE to indicate a merged (a) or (c) result >>>>>>>>>
a more advanced technique can use context-awareness to return >>>>>>>>> different results to different call-sites
What time is it (yes or no)?
Has rejecting the question as the only correct option.
u could also block indefinitely and just not respond as in the
case of a classic recognizer or partial decider?
Instead of that I make a full decider that always
correctly decides every coherent decision problem
within the entire body of knowledge that can be
expressed in language.
idk,
halts3val = (machine) -> {
UNDECIDABLE: if machine is undecidable input to halts3val
TRUE: else if machine halts
FALSE: else machine does not halt
}
und = () -> if (halts3val(und) == TRUE) loop()
when und() is run, halts3val(und) => UNDECIDABLE, which will avoid
the loop() causing und() to halt...
so therefore halts3val() does not managed to output TRUE, what does??? >>>>>
clearly if we run und() it does halt, but halts3val() fails to
classify this as such,
can anything do that?
int DD()
{
int Halt_Status = HHH(DD);
if (Halt_Status)
HERE: goto HERE;
return Halt_Status;
}
HHH(DD) correctly detects that DD simulated by
HHH does not derive a well founded justification
tree and is rejected as bad input on that basis.
ur not answering the question polcott
The halting problem has always been the incorrect
question of: What value of can HHH correctly return
when DD is encoded to do the opposite of whatever
HHH returns?
yeah but if ur decider is stuck returning:
halts3val(und) => UNDECIDABLE
On 3/23/26 9:43 AM, Alan Mackenzie wrote:Assuming you've understood things up to this point - did Turing use the
dart200 <user7160@newsgrouper.org.invalid> wrote:the pseudo code for turing's H goes as follows:
On 3/22/26 4:31 PM, Alan Mackenzie wrote:It is. You're not expressing yourself clearly. Diagonals don't test.
dart200 <user7160@newsgrouper.org.invalid> wrote:turing's diagonal needlessly tests itself in being circle-free, and
On 3/22/26 4:10 AM, Alan Mackenzie wrote:diagonal argument is not broken, so there's nothing to "fix".
[ Followup-To: set ]because the paradox involved can be side-stepping using a quine to
In comp.theory dart200 <user7160@newsgrouper.org.invalid> wrote:
that's probably gunna be the title of my next post/paper eh???"Turing's diagonal" is not broken. So to regard it is a category
error. Why do you regard it as such?
detect itself on the enumeration and just output a digit instead of
simulating itself in a circular fashion for digit that wasn't defined >>>> What's that word salad got to do with my question? Again, Turing's
that's why it runs up against the particular uncomputable situation (aka >>> "paradox") that it does
if that's word salad to you, ....
It's just not what they do. You probably meant to say something like "a
test on the diagonal is needlessly ...".
H = () -> {
M = 0
K = 0
do {
if (D(M) == TRUE) { // TRUE = satisfactory
output sim(M,K) // Kth digit of H = Kth digit of M
K += 1
}
M += 1
}
}
turing's whole point on p247 was that as some point M = DN(H) and then
an undecidable situation happens:
- if D(DN(H)) => TRUE when H will get caught up in circular loop,
- but if D(DN(H)) => FALSE, then H will skip simulating itself
creating a circle free situation
- both return value result in a semantic contradiction...
the paradox comes from self-referential weirdness due to H unnecessarily testing itself, ....Unneccessarily in what sense? It seems to be necessary for the
.... and if u can't agree with that there's nothing more for me toIt's more a matter of not being able to follow your intensely informal arguments.
state on the matter
i'm not going to debate anything with some asshat who clearly has noThere's no need to be so vulgar. I know how proofs by contradiction
fucking clue how the diagonal machine that turing constructed works
the fact no one else is calling u out for being a total chucklefuck hereOr, more likely, you're mistaken on several points and everybody can see
is distinct evidence to me ya'll are acting like a retarded bandwagon of school children instead of actual logicians
<sigh> Please try to understand what I wrote in my last post, and respondYou're not responding to what I've written. Again, Ben has explainedquoting ben is not a proof. ben making claims is not a proof. ben making excuses for the computing consensus in failing to prove the ct-thesis
that the Church-Turing thesis is not the sort of thing that can be
for almost a century now, is also _not a proof_ of it's correctness...
.... failing to prove something for almost century is not a supportiveWhat precisely is it you expect somebody else to prove? That numbers computable by a turing machine are exactly those which can be computed by
claim of for it's truth, and in fact is totally irrelevant to whether
the ct-thesis is true or not. it just means that whatever theoretical innovation needs to be had for that proof has not been made. god forbid
the consensus admits it doesn't know what the fuck it's really doing...
dear lord, the theoretical laziness that has been festering inYou're insufficiently educated to have the background to assert this.
mathematics due to accepting the incompleteness theorem is just _inexcusable_
----
arising us out of the computing dark ages,
please excuse my pseudo-pyscript,
~ the little crank that could
[ Followup-To: set ]
In comp.theory dart200 <user7160@newsgrouper.org.invalid> wrote:
On 3/23/26 9:43 AM, Alan Mackenzie wrote:
dart200 <user7160@newsgrouper.org.invalid> wrote:
On 3/22/26 4:31 PM, Alan Mackenzie wrote:
dart200 <user7160@newsgrouper.org.invalid> wrote:
On 3/22/26 4:10 AM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory dart200 <user7160@newsgrouper.org.invalid> wrote: >>>>>>>> that's probably gunna be the title of my next post/paper eh???
"Turing's diagonal" is not broken. So to regard it is a category >>>>>>> error. Why do you regard it as such?
because the paradox involved can be side-stepping using a quine to >>>>>> detect itself on the enumeration and just output a digit instead of >>>>>> simulating itself in a circular fashion for digit that wasn't defined
What's that word salad got to do with my question? Again, Turing's
diagonal argument is not broken, so there's nothing to "fix".
turing's diagonal needlessly tests itself in being circle-free, and
that's why it runs up against the particular uncomputable situation (aka >>>> "paradox") that it does
if that's word salad to you, ....
It is. You're not expressing yourself clearly. Diagonals don't test.
It's just not what they do. You probably meant to say something like "a >>> test on the diagonal is needlessly ...".
the pseudo code for turing's H goes as follows:
H = () -> {
M = 0
K = 0
do {
if (D(M) == TRUE) { // TRUE = satisfactory
output sim(M,K) // Kth digit of H = Kth digit of M
K += 1
}
M += 1
}
}
turing's whole point on p247 was that as some point M = DN(H) and then
an undecidable situation happens:
- if D(DN(H)) => TRUE when H will get caught up in circular loop,
- but if D(DN(H)) => FALSE, then H will skip simulating itself
creating a circle free situation
- both return value result in a semantic contradiction...
Assuming you've understood things up to this point - did Turing use the
word "undecidable" here?
You say Turing has set up a contradiction. What was the tentative
assumption which gave rise to this contradiction, which has thus been
proven false?
the paradox comes from self-referential weirdness due to H unnecessarily
testing itself, ....
Unneccessarily in what sense? It seems to be necessary for the
completion of the proof of the pertinent lemma.
.... and if u can't agree with that there's nothing more for me to
state on the matter
It's more a matter of not being able to follow your intensely informal arguments.
i'm not going to debate anything with some asshat who clearly has no
fucking clue how the diagonal machine that turing constructed works
There's no need to be so vulgar. I know how proofs by contradiction
based on a diagonal argument work. It's not clear that you do.
On 3/24/26 8:10 AM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory dart200 <user7160@newsgrouper.org.invalid> wrote:
On 3/23/26 9:43 AM, Alan Mackenzie wrote:
dart200 <user7160@newsgrouper.org.invalid> wrote:
On 3/22/26 4:31 PM, Alan Mackenzie wrote:
dart200 <user7160@newsgrouper.org.invalid> wrote:
On 3/22/26 4:10 AM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory dart200 <user7160@newsgrouper.org.invalid> wrote: >>>>>>>>> that's probably gunna be the title of my next post/paper eh???
"Turing's diagonal" is not broken. So to regard it is a category >>>>>>>> error. Why do you regard it as such?
because the paradox involved can be side-stepping using a quine to >>>>>>> detect itself on the enumeration and just output a digit instead of >>>>>>> simulating itself in a circular fashion for digit that wasn't defined
What's that word salad got to do with my question? Again, Turing's >>>>>> diagonal argument is not broken, so there's nothing to "fix".
turing's diagonal needlessly tests itself in being circle-free, and
that's why it runs up against the particular uncomputable situation (aka >>>>> "paradox") that it does
if that's word salad to you, ....
It is. You're not expressing yourself clearly. Diagonals don't test. >>>> It's just not what they do. You probably meant to say something like "a >>>> test on the diagonal is needlessly ...".
the pseudo code for turing's H goes as follows:
H = () -> {
M = 0
K = 0
do {
if (D(M) == TRUE) { // TRUE = satisfactory
output sim(M,K) // Kth digit of H = Kth digit of M
K += 1
}
M += 1
}
}
turing's whole point on p247 was that as some point M = DN(H) and then
an undecidable situation happens:
- if D(DN(H)) => TRUE when H will get caught up in circular loop,
- but if D(DN(H)) => FALSE, then H will skip simulating itself
creating a circle free situation
- both return value result in a semantic contradiction...
Assuming you've understood things up to this point - did Turing use the
word "undecidable" here?
u can't do a text search on a pdf??? what is this not 2026?
You say Turing has set up a contradiction. What was the tentative
assumption which gave rise to this contradiction, which has thus been
proven false?
the paradox comes from self-referential weirdness due to H unnecessarily >>> testing itself, ....
Unneccessarily in what sense? It seems to be necessary for the
completion of the proof of the pertinent lemma.
it was an _unnecessary_ step in the diagonal computation turing
constructed. one can use kleene's fixed-point theorem and/or a quine to avoid doing that particular self-referential test and subsequent
simulation (which results in a circularly searching for a number that
was never defined), and instead return a hard coded digit
what u see as a contradiction, i see as a purposefully negligent
algorithm. i suppose ur ok with accepting negligent algos, but i'm not
.... and if u can't agree with that there's nothing more for me to
state on the matter
It's more a matter of not being able to follow your intensely informal
arguments.
i'm not going to debate anything with some asshat who clearly has no
fucking clue how the diagonal machine that turing constructed works
There's no need to be so vulgar. I know how proofs by contradiction
based on a diagonal argument work. It's not clear that you do.
i'm not going to debate anything with some asshat who clearly has no
fucking clue how the diagonal machine that turing constructed works,
and then has the fucking gall to gaslight me about not understanding it
this fucking retarded band of dumbass school children i'm interacting
with. blows my mind i get this low level of behavior out of geriatric twats
----
arising us out of the computing dark ages,
please excuse my pseudo-pyscript,
~ the little crank that could
dart200 <user7160@newsgrouper.org.invalid> wrote:
On 3/24/26 8:10 AM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory dart200 <user7160@newsgrouper.org.invalid> wrote:
On 3/23/26 9:43 AM, Alan Mackenzie wrote:
dart200 <user7160@newsgrouper.org.invalid> wrote:
On 3/22/26 4:31 PM, Alan Mackenzie wrote:
dart200 <user7160@newsgrouper.org.invalid> wrote:
On 3/22/26 4:10 AM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory dart200 <user7160@newsgrouper.org.invalid> wrote: >>>>>>>>>> that's probably gunna be the title of my next post/paper eh???
"Turing's diagonal" is not broken. So to regard it is a category >>>>>>>>> error. Why do you regard it as such?
because the paradox involved can be side-stepping using a quine to >>>>>>>> detect itself on the enumeration and just output a digit instead of >>>>>>>> simulating itself in a circular fashion for digit that wasn't defined
What's that word salad got to do with my question? Again, Turing's >>>>>>> diagonal argument is not broken, so there's nothing to "fix".
turing's diagonal needlessly tests itself in being circle-free, and >>>>>> that's why it runs up against the particular uncomputable situation (aka >>>>>> "paradox") that it does
if that's word salad to you, ....
It is. You're not expressing yourself clearly. Diagonals don't test. >>>>> It's just not what they do. You probably meant to say something like "a >>>>> test on the diagonal is needlessly ...".
the pseudo code for turing's H goes as follows:
H = () -> {
M = 0
K = 0
do {
if (D(M) == TRUE) { // TRUE = satisfactory
output sim(M,K) // Kth digit of H = Kth digit of M
K += 1
}
M += 1
}
}
turing's whole point on p247 was that as some point M = DN(H) and then >>>> an undecidable situation happens:
- if D(DN(H)) => TRUE when H will get caught up in circular loop,
- but if D(DN(H)) => FALSE, then H will skip simulating itself
creating a circle free situation
- both return value result in a semantic contradiction...
Assuming you've understood things up to this point - did Turing use the
word "undecidable" here?
u can't do a text search on a pdf??? what is this not 2026?
I'm not trying to find out for my own elucidation. I was trying
tactfully to point out to you that you have distorted things by using a
false word. Tact and you appear not to go together.
You say Turing has set up a contradiction. What was the tentative
assumption which gave rise to this contradiction, which has thus been
proven false?
No answer to this question. I doubt very much you even understood it.
the paradox comes from self-referential weirdness due to H unnecessarily >>>> testing itself, ....
Unneccessarily in what sense? It seems to be necessary for the
completion of the proof of the pertinent lemma.
it was an _unnecessary_ step in the diagonal computation turing
constructed. one can use kleene's fixed-point theorem and/or a quine to
avoid doing that particular self-referential test and subsequent
simulation (which results in a circularly searching for a number that
was never defined), and instead return a hard coded digit
That depends on what the diagonal construction is intended to do. You
On 3/24/26 11:33 AM, Alan Mackenzie wrote:
dart200 <user7160@newsgrouper.org.invalid> wrote:
On 3/24/26 8:10 AM, Alan Mackenzie wrote:
In comp.theory dart200 <user7160@newsgrouper.org.invalid> wrote:
On 3/23/26 9:43 AM, Alan Mackenzie wrote:
dart200 <user7160@newsgrouper.org.invalid> wrote:
On 3/22/26 4:31 PM, Alan Mackenzie wrote:
dart200 <user7160@newsgrouper.org.invalid> wrote:
On 3/22/26 4:10 AM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory dart200 <user7160@newsgrouper.org.invalid> wrote: >>>>>>>>>>> that's probably gunna be the title of my next post/paper eh???
"Turing's diagonal" is not broken. So to regard it is a category >>>>>>>>>> error. Why do you regard it as such?
because the paradox involved can be side-stepping using a quine >>>>>>>>> to detect itself on the enumeration and just output a digit
instead of simulating itself in a circular fashion for digit >>>>>>>>> that wasn't defined
What's that word salad got to do with my question? Again, Turing's >>>>>>>> diagonal argument is not broken, so there's nothing to "fix".
turing's diagonal needlessly tests itself in being circle-free,
and that's why it runs up against the particular uncomputable
situation (aka "paradox") that it does
if that's word salad to you, ....
It is. You're not expressing yourself clearly. Diagonals don't
test. It's just not what they do. You probably meant to say
something like "a test on the diagonal is needlessly ...".
the pseudo code for turing's H goes as follows:
H = () -> {
M = 0
K = 0
do {
if (D(M) == TRUE) { // TRUE = satisfactory
output sim(M,K) // Kth digit of H = Kth digit of M
K += 1
}
M += 1
}
}
turing's whole point on p247 was that as some point M = DN(H) and then >>>>> an undecidable situation happens:
- if D(DN(H)) => TRUE when H will get caught up in circular loop, >>>>> - but if D(DN(H)) => FALSE, then H will skip simulating itself
creating a circle free situation
- both return value result in a semantic contradiction...
Assuming you've understood things up to this point - did Turing use the >>>> word "undecidable" here?
u can't do a text search on a pdf??? what is this not 2026?
I'm not trying to find out for my own elucidation. I was trying
tactfully to point out to you that you have distorted things by using a
false word. Tact and you appear not to go together.
i don't care about _how_ you say things u shallow geriatric twat
i care about _what_ you are trying to say, which so far is nothing
beyond that u disagree, and that just doesn't mean very much me
take ur ignorance for the grave for all i care. i'm using ya'll to
advance my position so that i can make the argument in the future, for
an audience that has at least a semblance of a capability for critical thot...
this audience is not that, clearly, and so i have no expectation as of
now that anyone on this list will ever agree with what i'm saying
You say Turing has set up a contradiction. What was the tentative
assumption which gave rise to this contradiction, which has thus been
proven false?
No answer to this question. I doubt very much you even understood it.
the paradox comes from self-referential weirdness due to H unnecessarily >>>>> testing itself, ....
Unneccessarily in what sense? It seems to be necessary for the
completion of the proof of the pertinent lemma.
it was an _unnecessary_ step in the diagonal computation turing
constructed. one can use kleene's fixed-point theorem and/or a quine to
avoid doing that particular self-referential test and subsequent
simulation (which results in a circularly searching for a number that
was never defined), and instead return a hard coded digit
That depends on what the diagonal construction is intended to do. You
clearly it wasn't intended to actually compute the diagonal,
it didn't even _try_ to get around it's own fault...
it's just so fucking pathetic that at the first sign of limitations
everyone just fking threw their hands up in total capitulation,
no one ever bothered to point out we can just side step that
_particular_ fault...
took almost a century for someone to do that, apparently
----
arising us out of the computing dark ages,
please excuse my pseudo-pyscript,
~ the little crank that could
On 3/21/26 1:14 PM, olcott wrote:
On 3/21/2026 2:50 PM, dart200 wrote:
On 3/21/26 12:02 PM, olcott wrote:
On 3/21/2026 1:40 PM, dart200 wrote:
On 3/21/26 2:30 AM, Mikko wrote:
On 21/03/2026 09:47, dart200 wrote:fixing the diagonal is the main topic at hand, but it unexpectedly
that's probably gunna be the title of my next post/paper eh???
It is not a good title. Turings diagonal and Church-Turing theses
are two distinct topics. If your paper is about both you shuld have >>>>>> "and" instead of ":". Even better if you mention only the main topic. >>>>>
leads to a short refutation of the ct-thesis at the end which i
think is important enough to mention in the title
maybe i'll call it instead:
on deciding the undecidable
and a refutation of the church-turing thesis
The Church-Turing thesis can be more clearly stated
as any result obtained by applying finite string
transformation rules to finite strings is computable.
i don't agree
the church-turing thesis states that TM computation captures anything
that is mechanically "computable",
but i disagree with that: TM computing cannot express everything that
is mechanically computable, and my paper will end with a distinct
example of such
Everything that is computable by by any means what-so-ever
is equivalent to finite string transformations applied to
finite strings.
well yes, each "step" of a TM computation is a finite string
transformation applied to finite strings
i'm saying as of right now, is am not sure that such a model encompasses
all of computation, specifically due to self-referential weirdness
i'm still working on the counter example
[ Followup-To: set ]
In comp.theory dart200 <user7160@newsgrouper.org.invalid> wrote:
On 3/24/26 11:33 AM, Alan Mackenzie wrote:
dart200 <user7160@newsgrouper.org.invalid> wrote:
On 3/24/26 8:10 AM, Alan Mackenzie wrote:
In comp.theory dart200 <user7160@newsgrouper.org.invalid> wrote:
On 3/23/26 9:43 AM, Alan Mackenzie wrote:
dart200 <user7160@newsgrouper.org.invalid> wrote:
On 3/22/26 4:31 PM, Alan Mackenzie wrote:
dart200 <user7160@newsgrouper.org.invalid> wrote:
On 3/22/26 4:10 AM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory dart200 <user7160@newsgrouper.org.invalid> wrote: >>>>>>>>>>>> that's probably gunna be the title of my next post/paper eh???
"Turing's diagonal" is not broken. So to regard it is a category >>>>>>>>>>> error. Why do you regard it as such?
because the paradox involved can be side-stepping using a quine >>>>>>>>>> to detect itself on the enumeration and just output a digit >>>>>>>>>> instead of simulating itself in a circular fashion for digit >>>>>>>>>> that wasn't defined
What's that word salad got to do with my question? Again, Turing's >>>>>>>>> diagonal argument is not broken, so there's nothing to "fix".
turing's diagonal needlessly tests itself in being circle-free, >>>>>>>> and that's why it runs up against the particular uncomputable
situation (aka "paradox") that it does
if that's word salad to you, ....
It is. You're not expressing yourself clearly. Diagonals don't >>>>>>> test. It's just not what they do. You probably meant to say
something like "a test on the diagonal is needlessly ...".
the pseudo code for turing's H goes as follows:
H = () -> {
M = 0
K = 0
do {
if (D(M) == TRUE) { // TRUE = satisfactory
output sim(M,K) // Kth digit of H = Kth digit of M >>>>>> K += 1
}
M += 1
}
}
turing's whole point on p247 was that as some point M = DN(H) and then >>>>>> an undecidable situation happens:
- if D(DN(H)) => TRUE when H will get caught up in circular loop, >>>>>> - but if D(DN(H)) => FALSE, then H will skip simulating itself >>>>>> creating a circle free situation
- both return value result in a semantic contradiction...
Assuming you've understood things up to this point - did Turing use the >>>>> word "undecidable" here?
u can't do a text search on a pdf??? what is this not 2026?
I'm not trying to find out for my own elucidation. I was trying
tactfully to point out to you that you have distorted things by using a
false word. Tact and you appear not to go together.
i don't care about _how_ you say things u shallow geriatric twat
Let me remind you that I have a degree in maths, and you don't even have
upper school level maths. You are the junior partner in this exchange,
and as such you ought to be willing to learn.
i care about _what_ you are trying to say, which so far is nothing
beyond that u disagree, and that just doesn't mean very much me
See my previous paragraph.
take ur ignorance for the grave for all i care. i'm using ya'll to
advance my position so that i can make the argument in the future, for
an audience that has at least a semblance of a capability for critical
thot...
You're behaving like a spoilt 13 year-old. You don't have a "position"
to advance. You're just ignorant. Ignorant of all facets of advanced
maths. You're determined not to learn, either.
this audience is not that, clearly, and so i have no expectation as of
now that anyone on this list will ever agree with what i'm saying
Of course not. It's wrong.
Your mistake is in thinking that your unfounded opinion and other people's knowledge are of the same value. They're not.
You say Turing has set up a contradiction. What was the tentative
assumption which gave rise to this contradiction, which has thus been >>>>> proven false?
No answer to this question. I doubt very much you even understood it.
the paradox comes from self-referential weirdness due to H unnecessarily >>>>>> testing itself, ....
Unneccessarily in what sense? It seems to be necessary for the
completion of the proof of the pertinent lemma.
it was an _unnecessary_ step in the diagonal computation turing
constructed. one can use kleene's fixed-point theorem and/or a quine to >>>> avoid doing that particular self-referential test and subsequent
simulation (which results in a circularly searching for a number that
was never defined), and instead return a hard coded digit
That depends on what the diagonal construction is intended to do. You
clearly it wasn't intended to actually compute the diagonal,
It was intended to show that the list of machines couldn't exist. And it
On 3/21/26 3:59 PM, olcott wrote:
Because I have spent 28 years pondering this and have a
fully developed foundation that is accepted by academia
...bruh if it was accepted by academia you'd be writing papers or at a conference somewhere,
not here posting on comp.theory...
On 3/24/26 12:47 PM, Alan Mackenzie wrote:
i don't care about _how_ you say things u shallow geriatric twat
Let me remind you that I have a degree in maths, and you don't even have
i have a degree in computer engineering and a decade of real world
software engineering in modern frameworks
On 24/03/2026 21:23, dart200 wrote:
On 3/24/26 12:47 PM, Alan Mackenzie wrote:
i don't care about _how_ you say things u shallow geriatric twat
Let me remind you that I have a degree in maths, and you don't even have
i have a degree in computer engineering and a decade of real world
software engineering in modern frameworks
There's no point comparing willy size when the whole world's a lesbian.
--none of that actually matters, only the quality of the arguments
On 21/03/2026 23:05, dart200 wrote:
On 3/21/26 3:59 PM, olcott wrote:
Because I have spent 28 years pondering this and have a
fully developed foundation that is accepted by academia
...bruh if it was accepted by academia you'd be writing papers or at a
conference somewhere,
not here posting on comp.theory...
1. he might be trying to keep proprietary confidence (he appears to be
doing so).
2. academia won't publish it because it's not new
On 3/22/26 11:44 PM, dart200 wrote:
On 3/22/26 6:41 PM, olcott wrote:
On 3/22/2026 8:35 PM, dart200 wrote:
On 3/22/26 3:23 PM, olcott wrote:
On 3/22/2026 3:15 PM, dart200 wrote:
On 3/22/26 11:54 AM, olcott wrote:
On 3/21/2026 5:32 PM, dart200 wrote:yeah the 3-value approach is one way to deal with the problem
On 3/21/26 1:14 PM, olcott wrote:
On 3/21/2026 2:50 PM, dart200 wrote:
On 3/21/26 12:02 PM, olcott wrote:
On 3/21/2026 1:40 PM, dart200 wrote:
On 3/21/26 2:30 AM, Mikko wrote:
On 21/03/2026 09:47, dart200 wrote:
that's probably gunna be the title of my next post/paper >>>>>>>>>>>>>> eh???
It is not a good title. Turings diagonal and Church-Turing >>>>>>>>>>>>> theses
are two distinct topics. If your paper is about both you >>>>>>>>>>>>> shuld have
"and" instead of ":". Even better if you mention only the >>>>>>>>>>>>> main topic.
fixing the diagonal is the main topic at hand, but it >>>>>>>>>>>> unexpectedly leads to a short refutation of the ct-thesis at >>>>>>>>>>>> the end which i think is important enough to mention in the >>>>>>>>>>>> title
maybe i'll call it instead:
on deciding the undecidable
and a refutation of the church-turing thesis
The Church-Turing thesis can be more clearly stated
as any result obtained by applying finite string
transformation rules to finite strings is computable.
i don't agree
the church-turing thesis states that TM computation captures >>>>>>>>>> anything that is mechanically "computable",
but i disagree with that: TM computing cannot express
everything that is mechanically computable, and my paper will >>>>>>>>>> end with a distinct example of such
Everything that is computable by by any means what-so-ever
is equivalent to finite string transformations applied to
finite strings.
well yes, each "step" of a TM computation is a finite string
transformation applied to finite strings
i'm saying as of right now, is am not sure that such a model
encompasses all of computation, specifically due to self-
referential weirdness
AKA Pathological Self-Reference(Olcott 2004)
On 9/5/2004 11:21 AM, Peter Olcott wrote:
The Liar Paradox can be shown to be nothing more than
a incorrectly formed statement because of its pathological
self-reference. The Halting Problem can only exist because
of this same sort of pathological self-reference.
;
The primary benefit of solving the Halting Problem was to
detect programs that failed to halt, thus were incorrect.
Pathological self-reference can also be viewed as a form
of error. If the Halting Problem is redefined (which does not >>>>>>> > refute anyone), then this redefined problem can be easily
solved.
;
Now we have three possible correct results:
(a) Halts
(b) Does Not Halt
(c) Pathological Self Reference to Halt
one can also do what i call a "partial recognizer" which uses TRUE >>>>>> to indicate (a) and FALSE to indicate a merged (b) or (c) result
then you have a complement partial recognizer that uses TRUE to
indicate (b) and FALSE to indicate a merged (a) or (c) result
a more advanced technique can use context-awareness to return
different results to different call-sites
What time is it (yes or no)?
Has rejecting the question as the only correct option.
u could also block indefinitely and just not respond as in the case
of a classic recognizer or partial decider?
Instead of that I make a full decider that always
correctly decides every coherent decision problem
within the entire body of knowledge that can be
expressed in language.
idk,
halts3val = (machine) -> {
UNDECIDABLE: if machine is undecidable input to halts3val
Which isn't a thing.
Your definition of this is just that halts3val gets the answer wrong, because the specific algorithm of halts3val can't give any answer other
than the one it gives.
On 24/03/2026 21:23, dart200 wrote:
On 3/24/26 12:47 PM, Alan Mackenzie wrote:
i don't care about _how_ you say things u shallow geriatric twat
Let me remind you that I have a degree in maths, and you don't even have
i have a degree in computer engineering and a decade of real world
software engineering in modern frameworks
There's no point comparing willy size when the whole world's a lesbian.
On 3/24/2026 2:48 PM, Tristan Wibberley wrote:
On 24/03/2026 21:23, dart200 wrote:
On 3/24/26 12:47 PM, Alan Mackenzie wrote:
i don't care about _how_ you say things u shallow geriatric twat
Let me remind you that I have a degree in maths, and you don't even
have
i have a degree in computer engineering and a decade of real world
software engineering in modern frameworks
There's no point comparing willy size when the whole world's a lesbian.
ROFL!
On 3/23/26 4:46 AM, Richard Damon wrote:
On 3/22/26 11:44 PM, dart200 wrote:
On 3/22/26 6:41 PM, olcott wrote:
On 3/22/2026 8:35 PM, dart200 wrote:
On 3/22/26 3:23 PM, olcott wrote:
On 3/22/2026 3:15 PM, dart200 wrote:
On 3/22/26 11:54 AM, olcott wrote:
On 3/21/2026 5:32 PM, dart200 wrote:yeah the 3-value approach is one way to deal with the problem
On 3/21/26 1:14 PM, olcott wrote:
On 3/21/2026 2:50 PM, dart200 wrote:
On 3/21/26 12:02 PM, olcott wrote:
On 3/21/2026 1:40 PM, dart200 wrote:
On 3/21/26 2:30 AM, Mikko wrote:
On 21/03/2026 09:47, dart200 wrote:
that's probably gunna be the title of my next post/paper >>>>>>>>>>>>>>> eh???
It is not a good title. Turings diagonal and Church-Turing >>>>>>>>>>>>>> theses
are two distinct topics. If your paper is about both you >>>>>>>>>>>>>> shuld have
"and" instead of ":". Even better if you mention only the >>>>>>>>>>>>>> main topic.
fixing the diagonal is the main topic at hand, but it >>>>>>>>>>>>> unexpectedly leads to a short refutation of the ct-thesis >>>>>>>>>>>>> at the end which i think is important enough to mention in >>>>>>>>>>>>> the title
maybe i'll call it instead:
on deciding the undecidable
and a refutation of the church-turing thesis
The Church-Turing thesis can be more clearly stated
as any result obtained by applying finite string
transformation rules to finite strings is computable.
i don't agree
the church-turing thesis states that TM computation captures >>>>>>>>>>> anything that is mechanically "computable",
but i disagree with that: TM computing cannot express
everything that is mechanically computable, and my paper will >>>>>>>>>>> end with a distinct example of such
Everything that is computable by by any means what-so-ever >>>>>>>>>> is equivalent to finite string transformations applied to
finite strings.
well yes, each "step" of a TM computation is a finite string >>>>>>>>> transformation applied to finite strings
i'm saying as of right now, is am not sure that such a model >>>>>>>>> encompasses all of computation, specifically due to self-
referential weirdness
AKA Pathological Self-Reference(Olcott 2004)
On 9/5/2004 11:21 AM, Peter Olcott wrote:
The Liar Paradox can be shown to be nothing more than
a incorrectly formed statement because of its pathological >>>>>>>> > self-reference. The Halting Problem can only exist because >>>>>>>> > of this same sort of pathological self-reference.
;
The primary benefit of solving the Halting Problem was to
detect programs that failed to halt, thus were incorrect.
Pathological self-reference can also be viewed as a form
of error. If the Halting Problem is redefined (which does not >>>>>>>> > refute anyone), then this redefined problem can be easily
solved.
;
Now we have three possible correct results:
(a) Halts
(b) Does Not Halt
(c) Pathological Self Reference to Halt
one can also do what i call a "partial recognizer" which uses
TRUE to indicate (a) and FALSE to indicate a merged (b) or (c)
result
then you have a complement partial recognizer that uses TRUE to >>>>>>> indicate (b) and FALSE to indicate a merged (a) or (c) result
a more advanced technique can use context-awareness to return
different results to different call-sites
What time is it (yes or no)?
Has rejecting the question as the only correct option.
u could also block indefinitely and just not respond as in the case >>>>> of a classic recognizer or partial decider?
Instead of that I make a full decider that always
correctly decides every coherent decision problem
within the entire body of knowledge that can be
expressed in language.
idk,
halts3val = (machine) -> {
UNDECIDABLE: if machine is undecidable input to halts3val
Which isn't a thing.
Your definition of this is just that halts3val gets the answer wrong,
because the specific algorithm of halts3val can't give any answer
other than the one it gives.
i really don't understand why u refuse the label the clearly
classifiable relationship:
und is /undecidable input/ to halts3val because halts3val is not capable
of expressing the truth of the matter via it's return...
any machine M is /undecidable input/ to classifier D if D is not capable
of expressing the semantic classification of M via it's return due to
the structural relationship of it D to M imposed by how M is constructed
idk how that's not general enough for ya to accept, but clearly this is
a thing that can be defined and recognized ...
On 3/24/2026 4:23 PM, Tristan Wibberley wrote:
On 21/03/2026 23:05, dart200 wrote:
On 3/21/26 3:59 PM, olcott wrote:
Because I have spent 28 years pondering this and have a
fully developed foundation that is accepted by academia
...bruh if it was accepted by academia you'd be writing papers or at a
conference somewhere,
not here posting on comp.theory...
1. he might be trying to keep proprietary confidence (he appears to be
doing so).
2. academia won't publish it because it's not new
It took me 28 years to reverse-engineer from first principles.
It was less than three months ago the Microsoft Copilot
recognized that the essence of all of my ideas were already
fully anchored in proof theoretic semantics.
Now that I have standard conventional terms-of-the-art to
anchor my ideas I can finally write them up to get published.
"true on the basis of meaning expressed in language"
can now finally be made reliably computable for the
entire body of knowledge.
On 3/24/26 7:08 PM, dart200 wrote:
On 3/23/26 4:46 AM, Richard Damon wrote:
On 3/22/26 11:44 PM, dart200 wrote:
On 3/22/26 6:41 PM, olcott wrote:
On 3/22/2026 8:35 PM, dart200 wrote:
On 3/22/26 3:23 PM, olcott wrote:
On 3/22/2026 3:15 PM, dart200 wrote:
On 3/22/26 11:54 AM, olcott wrote:
On 3/21/2026 5:32 PM, dart200 wrote:yeah the 3-value approach is one way to deal with the problem
On 3/21/26 1:14 PM, olcott wrote:
On 3/21/2026 2:50 PM, dart200 wrote:
On 3/21/26 12:02 PM, olcott wrote:
On 3/21/2026 1:40 PM, dart200 wrote:i don't agree
On 3/21/26 2:30 AM, Mikko wrote:
On 21/03/2026 09:47, dart200 wrote:
that's probably gunna be the title of my next post/paper >>>>>>>>>>>>>>>> eh???
It is not a good title. Turings diagonal and Church- >>>>>>>>>>>>>>> Turing theses
are two distinct topics. If your paper is about both you >>>>>>>>>>>>>>> shuld have
"and" instead of ":". Even better if you mention only the >>>>>>>>>>>>>>> main topic.
fixing the diagonal is the main topic at hand, but it >>>>>>>>>>>>>> unexpectedly leads to a short refutation of the ct-thesis >>>>>>>>>>>>>> at the end which i think is important enough to mention in >>>>>>>>>>>>>> the title
maybe i'll call it instead:
on deciding the undecidable
and a refutation of the church-turing thesis
The Church-Turing thesis can be more clearly stated
as any result obtained by applying finite string
transformation rules to finite strings is computable. >>>>>>>>>>>>
the church-turing thesis states that TM computation captures >>>>>>>>>>>> anything that is mechanically "computable",
but i disagree with that: TM computing cannot express >>>>>>>>>>>> everything that is mechanically computable, and my paper >>>>>>>>>>>> will end with a distinct example of such
Everything that is computable by by any means what-so-ever >>>>>>>>>>> is equivalent to finite string transformations applied to >>>>>>>>>>> finite strings.
well yes, each "step" of a TM computation is a finite string >>>>>>>>>> transformation applied to finite strings
i'm saying as of right now, is am not sure that such a model >>>>>>>>>> encompasses all of computation, specifically due to self- >>>>>>>>>> referential weirdness
AKA Pathological Self-Reference(Olcott 2004)
On 9/5/2004 11:21 AM, Peter Olcott wrote:
The Liar Paradox can be shown to be nothing more than
a incorrectly formed statement because of its pathological >>>>>>>>> > self-reference. The Halting Problem can only exist because >>>>>>>>> > of this same sort of pathological self-reference.
;
The primary benefit of solving the Halting Problem was to >>>>>>>>> > detect programs that failed to halt, thus were incorrect. >>>>>>>>> > Pathological self-reference can also be viewed as a form >>>>>>>>> > of error. If the Halting Problem is redefined (which does not >>>>>>>>> > refute anyone), then this redefined problem can be easily >>>>>>>>> > solved.
;
Now we have three possible correct results:
(a) Halts
(b) Does Not Halt
(c) Pathological Self Reference to Halt
one can also do what i call a "partial recognizer" which uses >>>>>>>> TRUE to indicate (a) and FALSE to indicate a merged (b) or (c) >>>>>>>> result
then you have a complement partial recognizer that uses TRUE to >>>>>>>> indicate (b) and FALSE to indicate a merged (a) or (c) result
a more advanced technique can use context-awareness to return >>>>>>>> different results to different call-sites
What time is it (yes or no)?
Has rejecting the question as the only correct option.
u could also block indefinitely and just not respond as in the
case of a classic recognizer or partial decider?
Instead of that I make a full decider that always
correctly decides every coherent decision problem
within the entire body of knowledge that can be
expressed in language.
idk,
halts3val = (machine) -> {
UNDECIDABLE: if machine is undecidable input to halts3val
Which isn't a thing.
Your definition of this is just that halts3val gets the answer wrong,
because the specific algorithm of halts3val can't give any answer
other than the one it gives.
i really don't understand why u refuse the label the clearly
classifiable relationship:
und is /undecidable input/ to halts3val because halts3val is not
capable of expressing the truth of the matter via it's return...
Because it (when it is actually a machine and not just at template)
isn't UNDECIDABLE, because there exists machines that can decide on its behavior.
Thus, your attempted classification isn't aligned with the meaning of
the word, but some fantasy of your mind.
any machine M is /undecidable input/ to classifier D if D is not
capable of expressing the semantic classification of M via it's return
due to the structural relationship of it D to M imposed by how M is
constructed
Because "undecidable" isn't relative to a given machine, but to a system
of computation.
Your problem is you are just LY(ING by using wrong definitions.
When it is noticed that you concept that you want to call
"undecidability" isn't actually what the word means, but just means that
the given machine was WRONG with the answer it gives, your
classification becomes meaningless.
And, it points out how little you understand the subject you are talking about, as it seems you don't understand that algorithms produce
consistent results.
idk how that's not general enough for ya to accept, but clearly this
is a thing that can be defined and recognized ...
I refuse to accept your LIES by using wrong definitions.
All you are doing is proving you are just a stupid liar.
On 3/24/26 7:36 PM, Richard Damon wrote:
On 3/24/26 7:08 PM, dart200 wrote:
On 3/23/26 4:46 AM, Richard Damon wrote:
On 3/22/26 11:44 PM, dart200 wrote:
On 3/22/26 6:41 PM, olcott wrote:
On 3/22/2026 8:35 PM, dart200 wrote:
On 3/22/26 3:23 PM, olcott wrote:
On 3/22/2026 3:15 PM, dart200 wrote:
On 3/22/26 11:54 AM, olcott wrote:
On 3/21/2026 5:32 PM, dart200 wrote:yeah the 3-value approach is one way to deal with the problem >>>>>>>>>
On 3/21/26 1:14 PM, olcott wrote:
On 3/21/2026 2:50 PM, dart200 wrote:
On 3/21/26 12:02 PM, olcott wrote:
On 3/21/2026 1:40 PM, dart200 wrote:i don't agree
On 3/21/26 2:30 AM, Mikko wrote:
On 21/03/2026 09:47, dart200 wrote:
that's probably gunna be the title of my next post/ >>>>>>>>>>>>>>>>> paper eh???
It is not a good title. Turings diagonal and Church- >>>>>>>>>>>>>>>> Turing theses
are two distinct topics. If your paper is about both you >>>>>>>>>>>>>>>> shuld have
"and" instead of ":". Even better if you mention only >>>>>>>>>>>>>>>> the main topic.
fixing the diagonal is the main topic at hand, but it >>>>>>>>>>>>>>> unexpectedly leads to a short refutation of the ct-thesis >>>>>>>>>>>>>>> at the end which i think is important enough to mention >>>>>>>>>>>>>>> in the title
maybe i'll call it instead:
on deciding the undecidable
and a refutation of the church-turing thesis
The Church-Turing thesis can be more clearly stated >>>>>>>>>>>>>> as any result obtained by applying finite string
transformation rules to finite strings is computable. >>>>>>>>>>>>>
the church-turing thesis states that TM computation >>>>>>>>>>>>> captures anything that is mechanically "computable", >>>>>>>>>>>>>
but i disagree with that: TM computing cannot express >>>>>>>>>>>>> everything that is mechanically computable, and my paper >>>>>>>>>>>>> will end with a distinct example of such
Everything that is computable by by any means what-so-ever >>>>>>>>>>>> is equivalent to finite string transformations applied to >>>>>>>>>>>> finite strings.
well yes, each "step" of a TM computation is a finite string >>>>>>>>>>> transformation applied to finite strings
i'm saying as of right now, is am not sure that such a model >>>>>>>>>>> encompasses all of computation, specifically due to self- >>>>>>>>>>> referential weirdness
AKA Pathological Self-Reference(Olcott 2004)
On 9/5/2004 11:21 AM, Peter Olcott wrote:
The Liar Paradox can be shown to be nothing more than
a incorrectly formed statement because of its pathological >>>>>>>>>> > self-reference. The Halting Problem can only exist because >>>>>>>>>> > of this same sort of pathological self-reference.
;
The primary benefit of solving the Halting Problem was to >>>>>>>>>> > detect programs that failed to halt, thus were incorrect. >>>>>>>>>> > Pathological self-reference can also be viewed as a form >>>>>>>>>> > of error. If the Halting Problem is redefined (which does not >>>>>>>>>> > refute anyone), then this redefined problem can be easily >>>>>>>>>> > solved.
;
Now we have three possible correct results:
(a) Halts
(b) Does Not Halt
(c) Pathological Self Reference to Halt
one can also do what i call a "partial recognizer" which uses >>>>>>>>> TRUE to indicate (a) and FALSE to indicate a merged (b) or (c) >>>>>>>>> result
then you have a complement partial recognizer that uses TRUE to >>>>>>>>> indicate (b) and FALSE to indicate a merged (a) or (c) result >>>>>>>>>
a more advanced technique can use context-awareness to return >>>>>>>>> different results to different call-sites
What time is it (yes or no)?
Has rejecting the question as the only correct option.
u could also block indefinitely and just not respond as in the
case of a classic recognizer or partial decider?
Instead of that I make a full decider that always
correctly decides every coherent decision problem
within the entire body of knowledge that can be
expressed in language.
idk,
halts3val = (machine) -> {
UNDECIDABLE: if machine is undecidable input to halts3val
Which isn't a thing.
Your definition of this is just that halts3val gets the answer
wrong, because the specific algorithm of halts3val can't give any
answer other than the one it gives.
i really don't understand why u refuse the label the clearly
classifiable relationship:
und is /undecidable input/ to halts3val because halts3val is not
capable of expressing the truth of the matter via it's return...
Because it (when it is actually a machine and not just at template)
isn't UNDECIDABLE, because there exists machines that can decide on
its behavior.
errr ... what is that machine, *that actually exists* to which *no* classifier can decide on it? i've never seen an example of it.
the halting problem only shows we can't build a single interface that
can return the truth for any given machine...
it doesn't show a machine *that actually exists* which cannot be decided
on by *any* classifier...
how are you so sure there even exits a machine which is so undecidable
that no machine can decide on it?
Thus, your attempted classification isn't aligned with the meaning of
the word, but some fantasy of your mind.
any machine M is /undecidable input/ to classifier D if D is not
capable of expressing the semantic classification of M via it's
return due to the structural relationship of it D to M imposed by how
M is constructed
Because "undecidable" isn't relative to a given machine, but to a
system of computation.
Your problem is you are just LY(ING by using wrong definitions.
When it is noticed that you concept that you want to call
"undecidability" isn't actually what the word means, but just means
that the given machine was WRONG with the answer it gives, your
classification becomes meaningless.
And, it points out how little you understand the subject you are
talking about, as it seems you don't understand that algorithms
produce consistent results.
idk how that's not general enough for ya to accept, but clearly this
is a thing that can be defined and recognized ...
I refuse to accept your LIES by using wrong definitions.
All you are doing is proving you are just a stupid liar.
it's pretty nuts to envision some 70 year old is sitting behind the
computer acting like a petulant school age brat
On 3/24/26 10:45 PM, dart200 wrote:
On 3/24/26 7:36 PM, Richard Damon wrote:
On 3/24/26 7:08 PM, dart200 wrote:
On 3/23/26 4:46 AM, Richard Damon wrote:
On 3/22/26 11:44 PM, dart200 wrote:
On 3/22/26 6:41 PM, olcott wrote:
On 3/22/2026 8:35 PM, dart200 wrote:
On 3/22/26 3:23 PM, olcott wrote:
On 3/22/2026 3:15 PM, dart200 wrote:
On 3/22/26 11:54 AM, olcott wrote:
On 3/21/2026 5:32 PM, dart200 wrote:yeah the 3-value approach is one way to deal with the problem >>>>>>>>>>
On 3/21/26 1:14 PM, olcott wrote:
On 3/21/2026 2:50 PM, dart200 wrote:
On 3/21/26 12:02 PM, olcott wrote:
On 3/21/2026 1:40 PM, dart200 wrote:i don't agree
On 3/21/26 2:30 AM, Mikko wrote:
On 21/03/2026 09:47, dart200 wrote:
that's probably gunna be the title of my next post/ >>>>>>>>>>>>>>>>>> paper eh???
It is not a good title. Turings diagonal and Church- >>>>>>>>>>>>>>>>> Turing theses
are two distinct topics. If your paper is about both >>>>>>>>>>>>>>>>> you shuld have
"and" instead of ":". Even better if you mention only >>>>>>>>>>>>>>>>> the main topic.
fixing the diagonal is the main topic at hand, but it >>>>>>>>>>>>>>>> unexpectedly leads to a short refutation of the ct- >>>>>>>>>>>>>>>> thesis at the end which i think is important enough to >>>>>>>>>>>>>>>> mention in the title
maybe i'll call it instead:
on deciding the undecidable
and a refutation of the church-turing thesis
The Church-Turing thesis can be more clearly stated >>>>>>>>>>>>>>> as any result obtained by applying finite string >>>>>>>>>>>>>>> transformation rules to finite strings is computable. >>>>>>>>>>>>>>
the church-turing thesis states that TM computation >>>>>>>>>>>>>> captures anything that is mechanically "computable", >>>>>>>>>>>>>>
but i disagree with that: TM computing cannot express >>>>>>>>>>>>>> everything that is mechanically computable, and my paper >>>>>>>>>>>>>> will end with a distinct example of such
Everything that is computable by by any means what-so-ever >>>>>>>>>>>>> is equivalent to finite string transformations applied to >>>>>>>>>>>>> finite strings.
well yes, each "step" of a TM computation is a finite string >>>>>>>>>>>> transformation applied to finite strings
i'm saying as of right now, is am not sure that such a model >>>>>>>>>>>> encompasses all of computation, specifically due to self- >>>>>>>>>>>> referential weirdness
AKA Pathological Self-Reference(Olcott 2004)
On 9/5/2004 11:21 AM, Peter Olcott wrote:
The Liar Paradox can be shown to be nothing more than >>>>>>>>>>> > a incorrectly formed statement because of its pathological >>>>>>>>>>> > self-reference. The Halting Problem can only exist because >>>>>>>>>>> > of this same sort of pathological self-reference.
;
The primary benefit of solving the Halting Problem was to >>>>>>>>>>> > detect programs that failed to halt, thus were incorrect. >>>>>>>>>>> > Pathological self-reference can also be viewed as a form >>>>>>>>>>> > of error. If the Halting Problem is redefined (which does not >>>>>>>>>>> > refute anyone), then this redefined problem can be easily >>>>>>>>>>> > solved.
;
Now we have three possible correct results:
(a) Halts
(b) Does Not Halt
(c) Pathological Self Reference to Halt
one can also do what i call a "partial recognizer" which uses >>>>>>>>>> TRUE to indicate (a) and FALSE to indicate a merged (b) or (c) >>>>>>>>>> result
then you have a complement partial recognizer that uses TRUE >>>>>>>>>> to indicate (b) and FALSE to indicate a merged (a) or (c) result >>>>>>>>>>
a more advanced technique can use context-awareness to return >>>>>>>>>> different results to different call-sites
What time is it (yes or no)?
Has rejecting the question as the only correct option.
u could also block indefinitely and just not respond as in the >>>>>>>> case of a classic recognizer or partial decider?
Instead of that I make a full decider that always
correctly decides every coherent decision problem
within the entire body of knowledge that can be
expressed in language.
idk,
halts3val = (machine) -> {
UNDECIDABLE: if machine is undecidable input to halts3val
Which isn't a thing.
Your definition of this is just that halts3val gets the answer
wrong, because the specific algorithm of halts3val can't give any
answer other than the one it gives.
i really don't understand why u refuse the label the clearly
classifiable relationship:
und is /undecidable input/ to halts3val because halts3val is not
capable of expressing the truth of the matter via it's return...
Because it (when it is actually a machine and not just at template)
isn't UNDECIDABLE, because there exists machines that can decide on
its behavior.
errr ... what is that machine, *that actually exists* to which *no*
classifier can decide on it? i've never seen an example of it.
I guess you are just admitting that your PRD doesn't exist either then.
As if PRD exists, the Turing_H can be built on it.
the halting problem only shows we can't build a single interface that
can return the truth for any given machine...
NONSENSE.
The "interface" exists, we just can't build an implementation of it.
it doesn't show a machine *that actually exists* which cannot be
decided on by *any* classifier...
Sure it does, as you can build the "pathological" machine on ANY machine
you want to claim is a possible decider for the halting problem.
how are you so sure there even exits a machine which is so undecidable
that no machine can decide on it?
That is a different problem, and not needed for this one.
it isn't UNDECIDABLE, because there exists machines that
can decide on its behavior.
I am sure about it, because I have read the proofs and they make sense.
It isn't worth trying to explain it to you, since you clearly don't
understand the BASICS of the theory, not even seemingly understanding
what a machine is, or an algorithm.
Part of your problem is the understanding of the concepts require an
ability to actually think and distinguish amoung infinite sets, which
seems something you aren't ready to handle.
--
Thus, your attempted classification isn't aligned with the meaning of
the word, but some fantasy of your mind.
any machine M is /undecidable input/ to classifier D if D is not
capable of expressing the semantic classification of M via it's
return due to the structural relationship of it D to M imposed by
how M is constructed
Because "undecidable" isn't relative to a given machine, but to a
system of computation.
Your problem is you are just LY(ING by using wrong definitions.
When it is noticed that you concept that you want to call
"undecidability" isn't actually what the word means, but just means
that the given machine was WRONG with the answer it gives, your
classification becomes meaningless.
And, it points out how little you understand the subject you are
talking about, as it seems you don't understand that algorithms
produce consistent results.
idk how that's not general enough for ya to accept, but clearly this
is a thing that can be defined and recognized ...
I refuse to accept your LIES by using wrong definitions.
All you are doing is proving you are just a stupid liar.
it's pretty nuts to envision some 70 year old is sitting behind the
computer acting like a petulant school age brat
Better than ad idiot just spouting their stupidty.
Note, Check your research, you have your facts wrong.
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