It is self-evident that a subset of Turing machines
can be Turing complete entirely on the basis of the
meaning of the words.
Every machine that performs the same set of
finite string transformations on the same inputs
and produces the same finite string outputs from
these inputs is equivalent by definition and thus
redundant in the set of Turing complete computations.
Can we change the subject now?
On 1/22/26 3:58 PM, olcott wrote:
It is self-evident that a subset of Turing machines
can be Turing complete entirely on the basis of the
meaning of the words.
Every machine that performs the same set of
finite string transformations on the same inputs
and produces the same finite string outputs from
these inputs is equivalent by definition and thus
redundant in the set of Turing complete computations.
Can we change the subject now?
no because perhaps isolating out non-paradoxical machine may prove a turing-complete subset of machines with no decision paradoxes, removing
a core pillar in the undecidability arguments.
sure maybe that's not the only pillar ... but it's the pillar that was
known about and used the most, so if it was invalid that should indeed
be very exciting
On 1/22/2026 11:21 PM, dart200 wrote:
On 1/22/26 3:58 PM, olcott wrote:
It is self-evident that a subset of Turing machines
can be Turing complete entirely on the basis of the
meaning of the words.
Every machine that performs the same set of
finite string transformations on the same inputs
and produces the same finite string outputs from
these inputs is equivalent by definition and thus
redundant in the set of Turing complete computations.
Can we change the subject now?
no because perhaps isolating out non-paradoxical machine may prove a
turing-complete subset of machines with no decision paradoxes,
removing a core pillar in the undecidability arguments.
FYI, five LLMs have all agreed that I have conquered that.
sure maybe that's not the only pillar ... but it's the pillar that was
known about and used the most, so if it was invalid that should indeed
be very exciting
On 1/23/26 2:19 AM, olcott wrote:
On 1/22/2026 11:21 PM, dart200 wrote:
On 1/22/26 3:58 PM, olcott wrote:
It is self-evident that a subset of Turing machines
can be Turing complete entirely on the basis of the
meaning of the words.
Every machine that performs the same set of
finite string transformations on the same inputs
and produces the same finite string outputs from
these inputs is equivalent by definition and thus
redundant in the set of Turing complete computations.
Can we change the subject now?
no because perhaps isolating out non-paradoxical machine may prove a
turing-complete subset of machines with no decision paradoxes,
removing a core pillar in the undecidability arguments.
FYI, five LLMs have all agreed that I have conquered that.
but no humans have and that's what actually counts
sure maybe that's not the only pillar ... but it's the pillar that
was known about and used the most, so if it was invalid that should
indeed be very exciting
On 1/23/26 2:19 AM, olcott wrote:
On 1/22/2026 11:21 PM, dart200 wrote:
On 1/22/26 3:58 PM, olcott wrote:
It is self-evident that a subset of Turing machines
can be Turing complete entirely on the basis of the
meaning of the words.
Every machine that performs the same set of
finite string transformations on the same inputs
and produces the same finite string outputs from
these inputs is equivalent by definition and thus
redundant in the set of Turing complete computations.
Can we change the subject now?
no because perhaps isolating out non-paradoxical machine may prove a
turing-complete subset of machines with no decision paradoxes,
removing a core pillar in the undecidability arguments.
FYI, five LLMs have all agreed that I have conquered that.
but no humans have and that's what actually counts
sure maybe that's not the only pillar ... but it's the pillar that
was known about and used the most, so if it was invalid that should
indeed be very exciting
On 1/23/2026 10:29 AM, dart200 wrote:
On 1/23/26 2:19 AM, olcott wrote:
On 1/22/2026 11:21 PM, dart200 wrote:
On 1/22/26 3:58 PM, olcott wrote:
It is self-evident that a subset of Turing machines
can be Turing complete entirely on the basis of the
meaning of the words.
Every machine that performs the same set of
finite string transformations on the same inputs
and produces the same finite string outputs from
these inputs is equivalent by definition and thus
redundant in the set of Turing complete computations.
Can we change the subject now?
no because perhaps isolating out non-paradoxical machine may prove a
turing-complete subset of machines with no decision paradoxes,
removing a core pillar in the undecidability arguments.
FYI, five LLMs have all agreed that I have conquered that.
but no humans have and that's what actually counts
*It really does seem to me that I am a human*
Also HHH(DD) Really does correctly detect the
non-well-founded cyclic dependency in the
evaluation graph.
https://github.com/plolcott/x86utm/blob/master/Halt7.c
It has done this for three years now. The only thing
that has changed is the words I use to describe what
it does. This anchors my ideas in the well established
ideas of others. Here are the exactly correct terms:
Within well-founded proof theoretic semantics
anchored in the operational semantics of the
c programming language HHH(DD) is correct to
reject its input as non-wellfounded.
sure maybe that's not the only pillar ... but it's the pillar that
was known about and used the most, so if it was invalid that should
indeed be very exciting
On 1/23/26 12:24 PM, olcott wrote:
On 1/23/2026 10:29 AM, dart200 wrote:
On 1/23/26 2:19 AM, olcott wrote:
On 1/22/2026 11:21 PM, dart200 wrote:
On 1/22/26 3:58 PM, olcott wrote:
It is self-evident that a subset of Turing machines
can be Turing complete entirely on the basis of the
meaning of the words.
Every machine that performs the same set of
finite string transformations on the same inputs
and produces the same finite string outputs from
these inputs is equivalent by definition and thus
redundant in the set of Turing complete computations.
Can we change the subject now?
no because perhaps isolating out non-paradoxical machine may prove
a turing-complete subset of machines with no decision paradoxes,
removing a core pillar in the undecidability arguments.
FYI, five LLMs have all agreed that I have conquered that.
but no humans have and that's what actually counts
*It really does seem to me that I am a human*
Also HHH(DD) Really does correctly detect the
non-well-founded cyclic dependency in the
evaluation graph.
Since DD isn't doing a proof or making a declariation of truth, "non- well-founded" is a meaningless term in this context.
On 1/23/2026 5:01 PM, Richard Damon wrote:
On 1/23/26 12:24 PM, olcott wrote:
On 1/23/2026 10:29 AM, dart200 wrote:
On 1/23/26 2:19 AM, olcott wrote:
On 1/22/2026 11:21 PM, dart200 wrote:
On 1/22/26 3:58 PM, olcott wrote:
It is self-evident that a subset of Turing machines
can be Turing complete entirely on the basis of the
meaning of the words.
Every machine that performs the same set of
finite string transformations on the same inputs
and produces the same finite string outputs from
these inputs is equivalent by definition and thus
redundant in the set of Turing complete computations.
Can we change the subject now?
no because perhaps isolating out non-paradoxical machine may prove >>>>>> a turing-complete subset of machines with no decision paradoxes,
removing a core pillar in the undecidability arguments.
FYI, five LLMs have all agreed that I have conquered that.
but no humans have and that's what actually counts
*It really does seem to me that I am a human*
Also HHH(DD) Really does correctly detect the
non-well-founded cyclic dependency in the
evaluation graph.
Since DD isn't doing a proof or making a declariation of truth, "non-
well-founded" is a meaningless term in this context.
Only while you make sure to have no idea what
this term means:
"non-well-founded in proof theoretic semantics"
On 1/23/26 6:50 PM, olcott wrote:
On 1/23/2026 5:01 PM, Richard Damon wrote:
On 1/23/26 12:24 PM, olcott wrote:
On 1/23/2026 10:29 AM, dart200 wrote:
On 1/23/26 2:19 AM, olcott wrote:
On 1/22/2026 11:21 PM, dart200 wrote:
On 1/22/26 3:58 PM, olcott wrote:
It is self-evident that a subset of Turing machines
can be Turing complete entirely on the basis of the
meaning of the words.
Every machine that performs the same set of
finite string transformations on the same inputs
and produces the same finite string outputs from
these inputs is equivalent by definition and thus
redundant in the set of Turing complete computations.
Can we change the subject now?
no because perhaps isolating out non-paradoxical machine may
prove a turing-complete subset of machines with no decision
paradoxes, removing a core pillar in the undecidability arguments. >>>>>>>
FYI, five LLMs have all agreed that I have conquered that.
but no humans have and that's what actually counts
*It really does seem to me that I am a human*
Also HHH(DD) Really does correctly detect the
non-well-founded cyclic dependency in the
evaluation graph.
Since DD isn't doing a proof or making a declariation of truth, "non-
well-founded" is a meaningless term in this context.
Only while you make sure to have no idea what
this term means:
"non-well-founded in proof theoretic semantics"
Since proof theoretic semantics insists that only things that can be
proven can be asserted, it needs to be able to PROVE that the statement
is not provable or refutable for it to assert that the input is non- well-founded.
Or, are you admitting that you proof theoretics semantics are really
just truth-conditional semantics with a downgrading of Truth to being probvabilility? (Which isn't what others consider it to be).
On 1/23/2026 7:30 PM, Richard Damon wrote:
On 1/23/26 6:50 PM, olcott wrote:
On 1/23/2026 5:01 PM, Richard Damon wrote:
On 1/23/26 12:24 PM, olcott wrote:
On 1/23/2026 10:29 AM, dart200 wrote:
On 1/23/26 2:19 AM, olcott wrote:
On 1/22/2026 11:21 PM, dart200 wrote:
On 1/22/26 3:58 PM, olcott wrote:
It is self-evident that a subset of Turing machines
can be Turing complete entirely on the basis of the
meaning of the words.
Every machine that performs the same set of
finite string transformations on the same inputs
and produces the same finite string outputs from
these inputs is equivalent by definition and thus
redundant in the set of Turing complete computations.
Can we change the subject now?
no because perhaps isolating out non-paradoxical machine may
prove a turing-complete subset of machines with no decision
paradoxes, removing a core pillar in the undecidability arguments. >>>>>>>>
FYI, five LLMs have all agreed that I have conquered that.
but no humans have and that's what actually counts
*It really does seem to me that I am a human*
Also HHH(DD) Really does correctly detect the
non-well-founded cyclic dependency in the
evaluation graph.
Since DD isn't doing a proof or making a declariation of truth,
"non- well-founded" is a meaningless term in this context.
Only while you make sure to have no idea what
this term means:
"non-well-founded in proof theoretic semantics"
Since proof theoretic semantics insists that only things that can be
proven can be asserted, it needs to be able to PROVE that the
statement is not provable or refutable for it to assert that the input
is non- well-founded.
Or, are you admitting that you proof theoretics semantics are really
just truth-conditional semantics with a downgrading of Truth to being
probvabilility? (Which isn't what others consider it to be).
I didn't think this stuff up on my own. I had at
least 100 dialogues with five different LLM systems
and after much push-back they all agreed that I am
correct after 60 pages of dialogue each. I have
been working on this every waking moment for weeks.
It was Copilot that recognized that my system was
Proof Theoretic Semantics (PTS) that resolves to
provable / refutable / non-well-founded.
Every system also agrees that HHH(DD) does
correctly reject DD as non-well-founded.
I just can't get them to do that concisely yet.
Once I can get them to actually do the simulation
then they immediately see from their own simulation
trace that HHH correctly rejects DD as non-well-founded
within proof theoretic semantics.
non-well-founded literally means that the proof
itself is stuck in a loop.
On 1/23/26 8:51 PM, olcott wrote:
On 1/23/2026 7:30 PM, Richard Damon wrote:
On 1/23/26 6:50 PM, olcott wrote:
On 1/23/2026 5:01 PM, Richard Damon wrote:
On 1/23/26 12:24 PM, olcott wrote:
On 1/23/2026 10:29 AM, dart200 wrote:
On 1/23/26 2:19 AM, olcott wrote:
On 1/22/2026 11:21 PM, dart200 wrote:
On 1/22/26 3:58 PM, olcott wrote:
It is self-evident that a subset of Turing machines
can be Turing complete entirely on the basis of the
meaning of the words.
Every machine that performs the same set of
finite string transformations on the same inputs
and produces the same finite string outputs from
these inputs is equivalent by definition and thus
redundant in the set of Turing complete computations.
Can we change the subject now?
no because perhaps isolating out non-paradoxical machine may >>>>>>>>> prove a turing-complete subset of machines with no decision >>>>>>>>> paradoxes, removing a core pillar in the undecidability arguments. >>>>>>>>>
FYI, five LLMs have all agreed that I have conquered that.
but no humans have and that's what actually counts
*It really does seem to me that I am a human*
Also HHH(DD) Really does correctly detect the
non-well-founded cyclic dependency in the
evaluation graph.
Since DD isn't doing a proof or making a declariation of truth,
"non- well-founded" is a meaningless term in this context.
Only while you make sure to have no idea what
this term means:
"non-well-founded in proof theoretic semantics"
Since proof theoretic semantics insists that only things that can be
proven can be asserted, it needs to be able to PROVE that the
statement is not provable or refutable for it to assert that the
input is non- well-founded.
Or, are you admitting that you proof theoretics semantics are really
just truth-conditional semantics with a downgrading of Truth to being
probvabilility? (Which isn't what others consider it to be).
I didn't think this stuff up on my own. I had at
least 100 dialogues with five different LLM systems
and after much push-back they all agreed that I am
correct after 60 pages of dialogue each. I have
been working on this every waking moment for weeks.
In other words you are working with the counsel of admitted liars, whose terms of use include that you acknoldege their results may not be accurate.
It was Copilot that recognized that my system was
Proof Theoretic Semantics (PTS) that resolves to
provable / refutable / non-well-founded.
Every system also agrees that HHH(DD) does
correctly reject DD as non-well-founded.
I just can't get them to do that concisely yet.
Once I can get them to actually do the simulation
then they immediately see from their own simulation
trace that HHH correctly rejects DD as non-well-founded
within proof theoretic semantics.
non-well-founded literally means that the proof
itself is stuck in a loop.
Nope, non-well-founded means that there is no proof.
"Proofs" don't get stuck in a loop, as it isn't a proof until it is complete.
THe fact that ONE attempted method of proving doesn't result in getting--
to the answer doesn't mean that some other method doesn't work
All you are doing is showing that you are just ignorant of what you are talking about, and you admit that you are trusting programs known to lie
and give false results, and are even admittedly programmed to try to
give good sounding results over factually accurate results.
On 1/22/26 3:58 PM, olcott wrote:
It is self-evident that a subset of Turing machines
can be Turing complete entirely on the basis of the
meaning of the words.
Every machine that performs the same set of
finite string transformations on the same inputs
and produces the same finite string outputs from
these inputs is equivalent by definition and thus
redundant in the set of Turing complete computations.
Can we change the subject now?
no because perhaps isolating out non-paradoxical machine may prove a turing-complete subset of machines with no decision paradoxes, removing
a core pillar in the undecidability arguments.
On 23/01/2026 07:21, dart200 wrote:
On 1/22/26 3:58 PM, olcott wrote:
It is self-evident that a subset of Turing machines
can be Turing complete entirely on the basis of the
meaning of the words.
Every machine that performs the same set of
finite string transformations on the same inputs
and produces the same finite string outputs from
these inputs is equivalent by definition and thus
redundant in the set of Turing complete computations.
Can we change the subject now?
no because perhaps isolating out non-paradoxical machine may prove a
turing-complete subset of machines with no decision paradoxes,
removing a core pillar in the undecidability arguments.
The set of non-paradoxical Turing machines is indeed Truing complete
because there are no paradoxical Turing machines. Of course any Turing machine can be mentioned in a paradox.
On 1/23/2026 7:56 PM, Richard Damon wrote:
On 1/23/26 8:51 PM, olcott wrote:
On 1/23/2026 7:30 PM, Richard Damon wrote:
On 1/23/26 6:50 PM, olcott wrote:
On 1/23/2026 5:01 PM, Richard Damon wrote:
On 1/23/26 12:24 PM, olcott wrote:
On 1/23/2026 10:29 AM, dart200 wrote:
On 1/23/26 2:19 AM, olcott wrote:
On 1/22/2026 11:21 PM, dart200 wrote:
On 1/22/26 3:58 PM, olcott wrote:
It is self-evident that a subset of Turing machines
can be Turing complete entirely on the basis of the
meaning of the words.
Every machine that performs the same set of
finite string transformations on the same inputs
and produces the same finite string outputs from
these inputs is equivalent by definition and thus
redundant in the set of Turing complete computations.
Can we change the subject now?
no because perhaps isolating out non-paradoxical machine may >>>>>>>>>> prove a turing-complete subset of machines with no decision >>>>>>>>>> paradoxes, removing a core pillar in the undecidability
arguments.
FYI, five LLMs have all agreed that I have conquered that.
but no humans have and that's what actually counts
*It really does seem to me that I am a human*
Also HHH(DD) Really does correctly detect the
non-well-founded cyclic dependency in the
evaluation graph.
Since DD isn't doing a proof or making a declariation of truth,
"non- well-founded" is a meaningless term in this context.
Only while you make sure to have no idea what
this term means:
"non-well-founded in proof theoretic semantics"
Since proof theoretic semantics insists that only things that can be
proven can be asserted, it needs to be able to PROVE that the
statement is not provable or refutable for it to assert that the
input is non- well-founded.
Or, are you admitting that you proof theoretics semantics are really
just truth-conditional semantics with a downgrading of Truth to
being probvabilility? (Which isn't what others consider it to be).
I didn't think this stuff up on my own. I had at
least 100 dialogues with five different LLM systems
and after much push-back they all agreed that I am
correct after 60 pages of dialogue each. I have
been working on this every waking moment for weeks.
In other words you are working with the counsel of admitted liars,
whose terms of use include that you acknoldege their results may not
be accurate.
It was Copilot that recognized that my system was
Proof Theoretic Semantics (PTS) that resolves to
provable / refutable / non-well-founded.
Every system also agrees that HHH(DD) does
correctly reject DD as non-well-founded.
I just can't get them to do that concisely yet.
Once I can get them to actually do the simulation
then they immediately see from their own simulation
trace that HHH correctly rejects DD as non-well-founded
within proof theoretic semantics.
non-well-founded literally means that the proof
itself is stuck in a loop.
Nope, non-well-founded means that there is no proof.
"Proofs" don't get stuck in a loop, as it isn't a proof until it is
complete.
You simply don't know enough about logic programming.
Logic programming routinely proves that an input does
not have a well-founded proof.
When I explain the details in terms of cycles in
directed graphs you don't have a clue. This has
always been anchored in well-founded proof theoretic
semantics.
Get AI to explain well-founded proof theoretic
semantics to you and ask it for references that
you can verify.
THe fact that ONE attempted method of proving doesn't result in
getting to the answer doesn't mean that some other method doesn't work
All you are doing is showing that you are just ignorant of what you
are talking about, and you admit that you are trusting programs known
to lie and give false results, and are even admittedly programmed to
try to give good sounding results over factually accurate results.
On 1/24/26 12:42 AM, Mikko wrote:
On 23/01/2026 07:21, dart200 wrote:
On 1/22/26 3:58 PM, olcott wrote:
It is self-evident that a subset of Turing machines
can be Turing complete entirely on the basis of the
meaning of the words.
Every machine that performs the same set of
finite string transformations on the same inputs
and produces the same finite string outputs from
these inputs is equivalent by definition and thus
redundant in the set of Turing complete computations.
Can we change the subject now?
no because perhaps isolating out non-paradoxical machine may prove a
turing-complete subset of machines with no decision paradoxes,
removing a core pillar in the undecidability arguments.
The set of non-paradoxical Turing machines is indeed Truing complete
because there are no paradoxical Turing machines. Of course any Turing
machine can be mentioned in a paradox.
i don't see how the lack of paradoxes ensures all possible computations
are represented (therefore being turing complete).
paradoxical machines are still produce computations ... just not computations that are unique in their functional result compared to non- paradoxical ones.
On 1/23/26 10:05 PM, olcott wrote:
On 1/23/2026 7:56 PM, Richard Damon wrote:
On 1/23/26 8:51 PM, olcott wrote:
On 1/23/2026 7:30 PM, Richard Damon wrote:
On 1/23/26 6:50 PM, olcott wrote:I didn't think this stuff up on my own. I had at
On 1/23/2026 5:01 PM, Richard Damon wrote:
On 1/23/26 12:24 PM, olcott wrote:
On 1/23/2026 10:29 AM, dart200 wrote:
On 1/23/26 2:19 AM, olcott wrote:
On 1/22/2026 11:21 PM, dart200 wrote:
On 1/22/26 3:58 PM, olcott wrote:
It is self-evident that a subset of Turing machines
can be Turing complete entirely on the basis of the
meaning of the words.
Every machine that performs the same set of
finite string transformations on the same inputs
and produces the same finite string outputs from
these inputs is equivalent by definition and thus
redundant in the set of Turing complete computations.
Can we change the subject now?
no because perhaps isolating out non-paradoxical machine may >>>>>>>>>>> prove a turing-complete subset of machines with no decision >>>>>>>>>>> paradoxes, removing a core pillar in the undecidability >>>>>>>>>>> arguments.
FYI, five LLMs have all agreed that I have conquered that.
but no humans have and that's what actually counts
*It really does seem to me that I am a human*
Also HHH(DD) Really does correctly detect the
non-well-founded cyclic dependency in the
evaluation graph.
Since DD isn't doing a proof or making a declariation of truth, >>>>>>> "non- well-founded" is a meaningless term in this context.
Only while you make sure to have no idea what
this term means:
"non-well-founded in proof theoretic semantics"
Since proof theoretic semantics insists that only things that can
be proven can be asserted, it needs to be able to PROVE that the
statement is not provable or refutable for it to assert that the
input is non- well-founded.
Or, are you admitting that you proof theoretics semantics are
really just truth-conditional semantics with a downgrading of Truth >>>>> to being probvabilility? (Which isn't what others consider it to be). >>>>
least 100 dialogues with five different LLM systems
and after much push-back they all agreed that I am
correct after 60 pages of dialogue each. I have
been working on this every waking moment for weeks.
In other words you are working with the counsel of admitted liars,
whose terms of use include that you acknoldege their results may not
be accurate.
It was Copilot that recognized that my system was
Proof Theoretic Semantics (PTS) that resolves to
provable / refutable / non-well-founded.
Every system also agrees that HHH(DD) does
correctly reject DD as non-well-founded.
I just can't get them to do that concisely yet.
Once I can get them to actually do the simulation
then they immediately see from their own simulation
trace that HHH correctly rejects DD as non-well-founded
within proof theoretic semantics.
non-well-founded literally means that the proof
itself is stuck in a loop.
Nope, non-well-founded means that there is no proof.
"Proofs" don't get stuck in a loop, as it isn't a proof until it is
complete.
You simply don't know enough about logic programming.
Logic programming routinely proves that an input does
not have a well-founded proof.
Just because you can handle SOME problems, doesn't mean you can find an answer for ALL problems.
When I explain the details in terms of cycles in
directed graphs you don't have a clue. This has
always been anchored in well-founded proof theoretic
semantics.
But there isn't always a cycle in the graph, sometimes the graph is just infinitely deep.
But, I guess thinking about infinity is something your brain can't handle.
Get AI to explain well-founded proof theoretic
semantics to you and ask it for references that
you can verify.
Why should I ask an AI liar, when I can get it from a lying human.
THe fact that ONE attempted method of proving doesn't result in
getting to the answer doesn't mean that some other method doesn't work
All you are doing is showing that you are just ignorant of what you
are talking about, and you admit that you are trusting programs known
to lie and give false results, and are even admittedly programmed to
try to give good sounding results over factually accurate results.
We will not be able to have a productive
conversation until you learn more about
proof theory. I will look for some good
references.
On 1/24/26 9:21 AM, olcott wrote:
We will not be able to have a productive
conversation until you learn more about
proof theory. I will look for some good
references.
Yes, do so, and note that the concept of "Not Well Founded" isn't talked about as a "Truth Value", because it will not be actually determinable
(in general) by Proof Theoretic Semantics since it is often not actually provable in the system.
You will find that it (Proof Theory) just finds some statements outside--
its ability to interpret a semantics for them. This happens for a number
of mathematical statements, where assuming a proof of them not being
well founded ends up proving them to be well founded and provides the
truth value for them.
On 1/24/26 4:21 AM, dart200 wrote:
On 1/24/26 12:42 AM, Mikko wrote:
On 23/01/2026 07:21, dart200 wrote:
On 1/22/26 3:58 PM, olcott wrote:
It is self-evident that a subset of Turing machines
can be Turing complete entirely on the basis of the
meaning of the words.
Every machine that performs the same set of
finite string transformations on the same inputs
and produces the same finite string outputs from
these inputs is equivalent by definition and thus
redundant in the set of Turing complete computations.
Can we change the subject now?
no because perhaps isolating out non-paradoxical machine may prove a
turing-complete subset of machines with no decision paradoxes,
removing a core pillar in the undecidability arguments.
The set of non-paradoxical Turing machines is indeed Truing complete
because there are no paradoxical Turing machines. Of course any Turing
machine can be mentioned in a paradox.
i don't see how the lack of paradoxes ensures all possible
computations are represented (therefore being turing complete).
In other words, you disagree with you own claim.
paradoxical machines are still produce computations ... just not
computations that are unique in their functional result compared to
non- paradoxical ones.
The problem is no machine is generically a "paradox". In the proof, it
is only a paradox to a particular machine that it refutes.
The construction template (which isn't a machine, but a formula to build
a machine) is paradoxical to the Halt Decider API (which again isn't a machine but a definition of the mapping for a machine to generate).
You (like Peter) just confuse classes of machines with machines
themselves, which is just an error.
On 1/24/2026 8:39 AM, Richard Damon wrote:
On 1/24/26 9:21 AM, olcott wrote:
We will not be able to have a productive
conversation until you learn more about
proof theory. I will look for some good
references.
Yes, do so, and note that the concept of "Not Well Founded" isn't
talked about as a "Truth Value", because it will not be actually
determinable (in general) by Proof Theoretic Semantics since it is
often not actually provable in the system.
I am working on grounding my ideas in peer reviewed papers
on proof theoretic semantics. Most of the papers have lots
of irrelevant detail.
You will find that it (Proof Theory) just finds some statements
outside its ability to interpret a semantics for them. This happens
for a number of mathematical statements, where assuming a proof of
them not being well founded ends up proving them to be well founded
and provides the truth value for them.
On 1/24/26 4:24 AM, Richard Damon wrote:
On 1/24/26 4:21 AM, dart200 wrote:
On 1/24/26 12:42 AM, Mikko wrote:
On 23/01/2026 07:21, dart200 wrote:
On 1/22/26 3:58 PM, olcott wrote:
It is self-evident that a subset of Turing machines
can be Turing complete entirely on the basis of the
meaning of the words.
Every machine that performs the same set of
finite string transformations on the same inputs
and produces the same finite string outputs from
these inputs is equivalent by definition and thus
redundant in the set of Turing complete computations.
Can we change the subject now?
no because perhaps isolating out non-paradoxical machine may prove
a turing-complete subset of machines with no decision paradoxes,
removing a core pillar in the undecidability arguments.
The set of non-paradoxical Turing machines is indeed Truing complete
because there are no paradoxical Turing machines. Of course any Turing >>>> machine can be mentioned in a paradox.
i don't see how the lack of paradoxes ensures all possible
computations are represented (therefore being turing complete).
In other words, you disagree with you own claim.
may argument is that paradoxes are redundant, mikko did not add such a claim. so ur suggesting he was agreeing with my rational that they are redundant?
paradoxical machines are still produce computations ... just not
computations that are unique in their functional result compared to
non- paradoxical ones.
The problem is no machine is generically a "paradox". In the proof, it
is only a paradox to a particular machine that it refutes.
The construction template (which isn't a machine, but a formula to
build a machine) is paradoxical to the Halt Decider API (which again
isn't a machine but a definition of the mapping for a machine to
generate).
You (like Peter) just confuse classes of machines with machines
themselves, which is just an error.
any machine in that class is a paradox
On 1/24/26 11:49 AM, dart200 wrote:
On 1/24/26 4:24 AM, Richard Damon wrote:
On 1/24/26 4:21 AM, dart200 wrote:
On 1/24/26 12:42 AM, Mikko wrote:
On 23/01/2026 07:21, dart200 wrote:
On 1/22/26 3:58 PM, olcott wrote:
It is self-evident that a subset of Turing machines
can be Turing complete entirely on the basis of the
meaning of the words.
Every machine that performs the same set of
finite string transformations on the same inputs
and produces the same finite string outputs from
these inputs is equivalent by definition and thus
redundant in the set of Turing complete computations.
Can we change the subject now?
no because perhaps isolating out non-paradoxical machine may prove >>>>>> a turing-complete subset of machines with no decision paradoxes,
removing a core pillar in the undecidability arguments.
The set of non-paradoxical Turing machines is indeed Truing complete >>>>> because there are no paradoxical Turing machines. Of course any Turing >>>>> machine can be mentioned in a paradox.
i don't see how the lack of paradoxes ensures all possible
computations are represented (therefore being turing complete).
In other words, you disagree with you own claim.
may argument is that paradoxes are redundant, mikko did not add such a
claim. so ur suggesting he was agreeing with my rational that they are
redundant?
"Redundent" isn't really defined in Computation Theory.
ALL machines that compute the same answers are considered to be
semantically equivalent.
Part of your problem is you don't understand that trying to base you
idea on an uncomputable filter won't help you.
paradoxical machines are still produce computations ... just not
computations that are unique in their functional result compared to
non- paradoxical ones.
The problem is no machine is generically a "paradox". In the proof,
it is only a paradox to a particular machine that it refutes.
The construction template (which isn't a machine, but a formula to
build a machine) is paradoxical to the Halt Decider API (which again
isn't a machine but a definition of the mapping for a machine to
generate).
You (like Peter) just confuse classes of machines with machines
themselves, which is just an error.
any machine in that class is a paradox
Then you consider truth to be a paradox, and paradox to be an
uncomputeable property.
On 1/24/26 9:24 AM, Richard Damon wrote:
On 1/24/26 11:49 AM, dart200 wrote:
On 1/24/26 4:24 AM, Richard Damon wrote:
On 1/24/26 4:21 AM, dart200 wrote:
On 1/24/26 12:42 AM, Mikko wrote:
On 23/01/2026 07:21, dart200 wrote:
On 1/22/26 3:58 PM, olcott wrote:The set of non-paradoxical Turing machines is indeed Truing complete >>>>>> because there are no paradoxical Turing machines. Of course any
It is self-evident that a subset of Turing machines
can be Turing complete entirely on the basis of the
meaning of the words.
Every machine that performs the same set of
finite string transformations on the same inputs
and produces the same finite string outputs from
these inputs is equivalent by definition and thus
redundant in the set of Turing complete computations.
Can we change the subject now?
no because perhaps isolating out non-paradoxical machine may
prove a turing-complete subset of machines with no decision
paradoxes, removing a core pillar in the undecidability arguments. >>>>>>
Turing
machine can be mentioned in a paradox.
i don't see how the lack of paradoxes ensures all possible
computations are represented (therefore being turing complete).
In other words, you disagree with you own claim.
may argument is that paradoxes are redundant, mikko did not add such
a claim. so ur suggesting he was agreeing with my rational that they
are redundant?
"Redundent" isn't really defined in Computation Theory.
that's because i'm exploring it in ways that previous have gone unexplored
ALL machines that compute the same answers are considered to be
semantically equivalent.
and anything more than the first one which produces a particular result
is redundant in terms of a minimal turing complete subset of machines.
Part of your problem is you don't understand that trying to base you
idea on an uncomputable filter won't help you.
from the reference point of a partial recognizer for functional
equivalence, two machines can be one of three semantic classifications:
- decidable non-equivalent
- decidable equivalent
- undecidable
since a partial recognizer only has two output: true/false, we merge one
of the decidable results with undecidable for the false output, and we
are left with a partial recognizer for the other decidable result
there's no way to produce a contradiction with such a machine. from the reference of any given classifier an input can either be decidedly
decidable or not decidable. if it's decidedly decidable the we can
output the classification, if it's not decidable then we cannot. there's
no middle ground here to exploit for a contradiction
as we iterate down the full enumeration of machines to build a minimal turing complete subset, we can test each one for functional non-
equivalence against all previous found to be in that subset, with a non- equivalence partial recognizer that outputs true iff decidedly non- equivalent, or false iff decidedly equivalent OR not decidable. only if
a machine returns true when tested against all previous machines in the subset is it then added to the minimal turing complete subset. both
machines with any decidable equivalence or undecidability with respect
to machines already in the subset are therefore not put in the subset
paradoxical machines are still produce computations ... just not
computations that are unique in their functional result compared to >>>>> non- paradoxical ones.
The problem is no machine is generically a "paradox". In the proof,
it is only a paradox to a particular machine that it refutes.
The construction template (which isn't a machine, but a formula to
build a machine) is paradoxical to the Halt Decider API (which again
isn't a machine but a definition of the mapping for a machine to
generate).
You (like Peter) just confuse classes of machines with machines
themselves, which is just an error.
any machine in that class is a paradox
Then you consider truth to be a paradox, and paradox to be an
uncomputeable property.
no idea why u said that
On 1/24/26 5:28 PM, dart200 wrote:
On 1/24/26 9:24 AM, Richard Damon wrote:
On 1/24/26 11:49 AM, dart200 wrote:
On 1/24/26 4:24 AM, Richard Damon wrote:
On 1/24/26 4:21 AM, dart200 wrote:
On 1/24/26 12:42 AM, Mikko wrote:
On 23/01/2026 07:21, dart200 wrote:
On 1/22/26 3:58 PM, olcott wrote:The set of non-paradoxical Turing machines is indeed Truing complete >>>>>>> because there are no paradoxical Turing machines. Of course any >>>>>>> Turing
It is self-evident that a subset of Turing machines
can be Turing complete entirely on the basis of the
meaning of the words.
Every machine that performs the same set of
finite string transformations on the same inputs
and produces the same finite string outputs from
these inputs is equivalent by definition and thus
redundant in the set of Turing complete computations.
Can we change the subject now?
no because perhaps isolating out non-paradoxical machine may
prove a turing-complete subset of machines with no decision
paradoxes, removing a core pillar in the undecidability arguments. >>>>>>>
machine can be mentioned in a paradox.
i don't see how the lack of paradoxes ensures all possible
computations are represented (therefore being turing complete).
In other words, you disagree with you own claim.
may argument is that paradoxes are redundant, mikko did not add such
a claim. so ur suggesting he was agreeing with my rational that they
are redundant?
"Redundent" isn't really defined in Computation Theory.
that's because i'm exploring it in ways that previous have gone
unexplored
ALL machines that compute the same answers are considered to be
semantically equivalent.
and anything more than the first one which produces a particular
result is redundant in terms of a minimal turing complete subset of
machines.
Part of your problem is you don't understand that trying to base you
idea on an uncomputable filter won't help you.
from the reference point of a partial recognizer for functional
equivalence, two machines can be one of three semantic classifications:
- decidable non-equivalent
- decidable equivalent
- undecidable
since a partial recognizer only has two output: true/false, we merge
one of the decidable results with undecidable for the false output,
and we are left with a partial recognizer for the other decidable result
And "Partial Recognizers" are well known and nothing new,
there's no way to produce a contradiction with such a machine. from
the reference of any given classifier an input can either be decidedly
decidable or not decidable. if it's decidedly decidable the we can
output the classification, if it's not decidable then we cannot.
there's no middle ground here to exploit for a contradiction
And the "contradiction" input just makes sure that its recognizer can't decide on it, making sure it is just a partial recognizer.
as we iterate down the full enumeration of machines to build a minimal
turing complete subset, we can test each one for functional non-
equivalence against all previous found to be in that subset, with a
non- equivalence partial recognizer that outputs true iff decidedly
non- equivalent, or false iff decidedly equivalent OR not decidable.
only if a machine returns true when tested against all previous
machines in the subset is it then added to the minimal turing complete
subset. both machines with any decidable equivalence or undecidability
with respect to machines already in the subset are therefore not put
in the subset
And what good is this set. You don't know if it is even Turing Complete
Set (which it likely isn't).
paradoxical machines are still produce computations ... just not
computations that are unique in their functional result compared
to non- paradoxical ones.
The problem is no machine is generically a "paradox". In the proof, >>>>> it is only a paradox to a particular machine that it refutes.
The construction template (which isn't a machine, but a formula to
build a machine) is paradoxical to the Halt Decider API (which
again isn't a machine but a definition of the mapping for a machine >>>>> to generate).
You (like Peter) just confuse classes of machines with machines
themselves, which is just an error.
any machine in that class is a paradox
Then you consider truth to be a paradox, and paradox to be an
uncomputeable property.
no idea why u said that
Because the machine you just tried to classify, are really no different
if form than others you don't do so. Your criteria is based on
uncomputable values.
On 1/24/26 12:42 AM, Mikko wrote:
On 23/01/2026 07:21, dart200 wrote:
On 1/22/26 3:58 PM, olcott wrote:
It is self-evident that a subset of Turing machines
can be Turing complete entirely on the basis of the
meaning of the words.
Every machine that performs the same set of
finite string transformations on the same inputs
and produces the same finite string outputs from
these inputs is equivalent by definition and thus
redundant in the set of Turing complete computations.
Can we change the subject now?
no because perhaps isolating out non-paradoxical machine may prove a
turing-complete subset of machines with no decision paradoxes,
removing a core pillar in the undecidability arguments.
The set of non-paradoxical Turing machines is indeed Truing complete
because there are no paradoxical Turing machines. Of course any Turing
machine can be mentioned in a paradox.
i don't see how the lack of paradoxes ensures all possible computations
are represented (therefore being turing complete).
paradoxical machines are still produce computations ... just not computations that are unique in their functional result compared to non- paradoxical ones.
On 1/24/26 4:52 PM, Richard Damon wrote:
On 1/24/26 5:28 PM, dart200 wrote:
On 1/24/26 9:24 AM, Richard Damon wrote:
On 1/24/26 11:49 AM, dart200 wrote:
On 1/24/26 4:24 AM, Richard Damon wrote:
On 1/24/26 4:21 AM, dart200 wrote:
On 1/24/26 12:42 AM, Mikko wrote:
On 23/01/2026 07:21, dart200 wrote:
On 1/22/26 3:58 PM, olcott wrote:The set of non-paradoxical Turing machines is indeed Truing
It is self-evident that a subset of Turing machines
can be Turing complete entirely on the basis of the
meaning of the words.
Every machine that performs the same set of
finite string transformations on the same inputs
and produces the same finite string outputs from
these inputs is equivalent by definition and thus
redundant in the set of Turing complete computations.
Can we change the subject now?
no because perhaps isolating out non-paradoxical machine may >>>>>>>>> prove a turing-complete subset of machines with no decision >>>>>>>>> paradoxes, removing a core pillar in the undecidability arguments. >>>>>>>>
complete
because there are no paradoxical Turing machines. Of course any >>>>>>>> Turing
machine can be mentioned in a paradox.
i don't see how the lack of paradoxes ensures all possible
computations are represented (therefore being turing complete).
In other words, you disagree with you own claim.
may argument is that paradoxes are redundant, mikko did not add
such a claim. so ur suggesting he was agreeing with my rational
that they are redundant?
"Redundent" isn't really defined in Computation Theory.
that's because i'm exploring it in ways that previous have gone
unexplored
ALL machines that compute the same answers are considered to be
semantically equivalent.
and anything more than the first one which produces a particular
result is redundant in terms of a minimal turing complete subset of
machines.
Part of your problem is you don't understand that trying to base you
idea on an uncomputable filter won't help you.
from the reference point of a partial recognizer for functional
equivalence, two machines can be one of three semantic classifications:
- decidable non-equivalent
- decidable equivalent
- undecidable
since a partial recognizer only has two output: true/false, we merge
one of the decidable results with undecidable for the false output,
and we are left with a partial recognizer for the other decidable result >>>
And "Partial Recognizers" are well known and nothing new,
i suppose it's progress that we've gone from u repeatedly calling them "liars" because they merge results, to "well known and nothing new"...
there's no way to produce a contradiction with such a machine. from
the reference of any given classifier an input can either be
decidedly decidable or not decidable. if it's decidedly decidable the
we can output the classification, if it's not decidable then we
cannot. there's no middle ground here to exploit for a contradiction
And the "contradiction" input just makes sure that its recognizer
can't decide on it, making sure it is just a partial recognizer.
as we iterate down the full enumeration of machines to build a
minimal turing complete subset, we can test each one for functional
non- equivalence against all previous found to be in that subset,
with a non- equivalence partial recognizer that outputs true iff
decidedly non- equivalent, or false iff decidedly equivalent OR not
decidable. only if a machine returns true when tested against all
previous machines in the subset is it then added to the minimal
turing complete subset. both machines with any decidable equivalence
or undecidability with respect to machines already in the subset are
therefore not put in the subset
And what good is this set. You don't know if it is even Turing
Complete Set (which it likely isn't).
if it can be proven that no paradoxical machine is the simplest of all machines functionally equivalent to that paradoxical machine ...
then just excluding paradoxical machines does not reduce the
completeness of the minimal turing complete subset.
yes i get that i haven't proven that to u 🙄🙄🙄
paradoxical machines are still produce computations ... just not >>>>>>> computations that are unique in their functional result compared >>>>>>> to non- paradoxical ones.
The problem is no machine is generically a "paradox". In the
proof, it is only a paradox to a particular machine that it refutes. >>>>>>
The construction template (which isn't a machine, but a formula to >>>>>> build a machine) is paradoxical to the Halt Decider API (which
again isn't a machine but a definition of the mapping for a
machine to generate).
You (like Peter) just confuse classes of machines with machines
themselves, which is just an error.
any machine in that class is a paradox
Then you consider truth to be a paradox, and paradox to be an
uncomputeable property.
no idea why u said that
Because the machine you just tried to classify, are really no
different if form than others you don't do so. Your criteria is based
on uncomputable values.
i apologize, that did not clarify anything to me
On 1/24/26 10:03 PM, dart200 wrote:
On 1/24/26 4:52 PM, Richard Damon wrote:
On 1/24/26 5:28 PM, dart200 wrote:
On 1/24/26 9:24 AM, Richard Damon wrote:
On 1/24/26 11:49 AM, dart200 wrote:
On 1/24/26 4:24 AM, Richard Damon wrote:
On 1/24/26 4:21 AM, dart200 wrote:
On 1/24/26 12:42 AM, Mikko wrote:In other words, you disagree with you own claim.
On 23/01/2026 07:21, dart200 wrote:
On 1/22/26 3:58 PM, olcott wrote:
It is self-evident that a subset of Turing machines
can be Turing complete entirely on the basis of the
meaning of the words.
Every machine that performs the same set of
finite string transformations on the same inputs
and produces the same finite string outputs from
these inputs is equivalent by definition and thus
redundant in the set of Turing complete computations.
Can we change the subject now?
no because perhaps isolating out non-paradoxical machine may >>>>>>>>>> prove a turing-complete subset of machines with no decision >>>>>>>>>> paradoxes, removing a core pillar in the undecidability
arguments.
The set of non-paradoxical Turing machines is indeed Truing >>>>>>>>> complete
because there are no paradoxical Turing machines. Of course any >>>>>>>>> Turing
machine can be mentioned in a paradox.
i don't see how the lack of paradoxes ensures all possible
computations are represented (therefore being turing complete). >>>>>>>
may argument is that paradoxes are redundant, mikko did not add
such a claim. so ur suggesting he was agreeing with my rational
that they are redundant?
"Redundent" isn't really defined in Computation Theory.
that's because i'm exploring it in ways that previous have gone
unexplored
ALL machines that compute the same answers are considered to be
semantically equivalent.
and anything more than the first one which produces a particular
result is redundant in terms of a minimal turing complete subset of
machines.
Part of your problem is you don't understand that trying to base
you idea on an uncomputable filter won't help you.
from the reference point of a partial recognizer for functional
equivalence, two machines can be one of three semantic classifications: >>>>
- decidable non-equivalent
- decidable equivalent
- undecidable
since a partial recognizer only has two output: true/false, we merge
one of the decidable results with undecidable for the false output,
and we are left with a partial recognizer for the other decidable
result
And "Partial Recognizers" are well known and nothing new,
i suppose it's progress that we've gone from u repeatedly calling them
"liars" because they merge results, to "well known and nothing new"...
Well, people calling the "Deciders" and ignoring the partial are liars.
there's no way to produce a contradiction with such a machine. from
the reference of any given classifier an input can either be
decidedly decidable or not decidable. if it's decidedly decidable
the we can output the classification, if it's not decidable then we
cannot. there's no middle ground here to exploit for a contradiction
And the "contradiction" input just makes sure that its recognizer
can't decide on it, making sure it is just a partial recognizer.
as we iterate down the full enumeration of machines to build a
minimal turing complete subset, we can test each one for functional
non- equivalence against all previous found to be in that subset,
with a non- equivalence partial recognizer that outputs true iff
decidedly non- equivalent, or false iff decidedly equivalent OR not
decidable. only if a machine returns true when tested against all
previous machines in the subset is it then added to the minimal
turing complete subset. both machines with any decidable equivalence
or undecidability with respect to machines already in the subset are
therefore not put in the subset
And what good is this set. You don't know if it is even Turing
Complete Set (which it likely isn't).
if it can be proven that no paradoxical machine is the simplest of all
machines functionally equivalent to that paradoxical machine ...
then just excluding paradoxical machines does not reduce the
completeness of the minimal turing complete subset.
yes i get that i haven't proven that to u 🙄🙄🙄
The problem is the results of the "paradoxical" machine was never the problem, it was that the decider gave the wrong answer to it.
You seem to think there is something problematical about these
"paradoxical" machines in general.
It is just that it make one particular machine wrong, and that one
exists for every decider.
paradoxical machines are still produce computations ... just not >>>>>>>> computations that are unique in their functional result compared >>>>>>>> to non- paradoxical ones.
The problem is no machine is generically a "paradox". In the
proof, it is only a paradox to a particular machine that it refutes. >>>>>>>
The construction template (which isn't a machine, but a formula >>>>>>> to build a machine) is paradoxical to the Halt Decider API (which >>>>>>> again isn't a machine but a definition of the mapping for a
machine to generate).
You (like Peter) just confuse classes of machines with machines >>>>>>> themselves, which is just an error.
any machine in that class is a paradox
Then you consider truth to be a paradox, and paradox to be an
uncomputeable property.
no idea why u said that
Because the machine you just tried to classify, are really no
different if form than others you don't do so. Your criteria is based
on uncomputable values.
i apologize, that did not clarify anything to me
You are trying to make a class of machines that can't actually be computationally determined.
Looking at just the machine, there is nothing in it that says "I am a paradoxical machine", you first need to determine that it is using a sub-machine in a contrary manner, which means you need to be able to recognize that a machine is an attempt to be a halt decider.
| Sysop: | DaiTengu |
|---|---|
| Location: | Appleton, WI |
| Users: | 1,096 |
| Nodes: | 10 (0 / 10) |
| Uptime: | 398:57:36 |
| Calls: | 14,036 |
| Calls today: | 2 |
| Files: | 187,082 |
| D/L today: |
2,630 files (1,643M bytes) |
| Messages: | 2,479,108 |