From Newsgroup: comp.theory

keep in mind: all real TMs exist, undecidable machines do not exist.

see, if we do not have a general halting decider then there must be some
input machine L, which is the first machine in the full enumeration
who's halting semantics cannot be decided up for some kind of semantics
(like halting).

well, first off: all the proofs for undecidability use purely
hypothetical machines, which then are declared to not exist, so none of
those machines could be *real* machine L.

so what is this proposed non-hypothetical *real* machine L that then
cannot be decided?

and could that machine L even exist?

let's say someone found that limit L and demonstrated this property that
it cannot be decided upon by a halting decider ... but then next step in undecidable proofs is to declare the machine's non-existence, because an undecidable machine is also not a deterministic machine, which
ultimately contradicts the fact that this limit machine L was suppose to actually *exist*, so how could it ever exist?

and if the limit machine L does not actually exist, then how are TM
semantics not generally decidable???

good god guys, it's so tiring arguing against what is seemingly
irreconcilable nonsense. but bring it on my dudes, how do u think i'm
wrong this time???
--
a burnt out swe investigating into why our tooling doesn't involve
basic semantic proofs like halting analysis

please excuse my pseudo-pyscript,

~ nick

--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

dart200 kirjoitti 4.12.2025 klo 10.22:

keep in mind: all real TMs exist, undecidable machines do not exist.

see, if we do not have a general halting decider then there must be some input machine L, which is the first machine in the full enumeration
who's halting semantics cannot be decided up for some kind of semantics (like halting).

well, first off: all the proofs for undecidability use purely
hypothetical machines, which then are declared to not exist, so none of those machines could be *real* machine L.

Not true. There are proofs of undecidability of Turing's circularity
that son't use hypothetical machines but only quantification over
Turing machines.
--
Mikko
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 12/4/25 12:49 AM, Mikko wrote:

dart200 kirjoitti 4.12.2025 klo 10.22:

keep in mind: all real TMs exist, undecidable machines do not exist.

see, if we do not have a general halting decider then there must be
some input machine L, which is the first machine in the full
enumeration who's halting semantics cannot be decided up for some kind
of semantics (like halting).

well, first off: all the proofs for undecidability use purely
hypothetical machines, which then are declared to not exist, so none
of those machines could be *real* machine L.

Not true. There are proofs of undecidability of Turing's circularity
that son't use hypothetical machines but only quantification over
Turing machines.

like what example?

and u avoided most of the post
--
a burnt out swe investigating into why our tooling doesn't involve
basic semantic proofs like halting analysis

please excuse my pseudo-pyscript,

~ nick
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

dart200 kirjoitti 4.12.2025 klo 11.10:

On 12/4/25 12:49 AM, Mikko wrote:

dart200 kirjoitti 4.12.2025 klo 10.22:

keep in mind: all real TMs exist, undecidable machines do not exist.

see, if we do not have a general halting decider then there must be
some input machine L, which is the first machine in the full
enumeration who's halting semantics cannot be decided up for some
kind of semantics (like halting).

well, first off: all the proofs for undecidability use purely
hypothetical machines, which then are declared to not exist, so none
of those machines could be *real* machine L.

Not true. There are proofs of undecidability of Turing's circularity
that son't use hypothetical machines but only quantification over
Turing machines.

like what example?

The claim to be proven is: Every Turing machine fails as Turing
circulate decider.

One direct proof can be suumarized as:

For every Turing machine H one can sonstruct a counter example M so
that if H(M, M) accepts then M(M) runs forever and keeps writing
final symbols but if H(M, M) rejects then M(M) halts.

If H(M, M) neither accepts nor rejects it is not a Turing circularity
(nor any other) decider. If H(M, M) accepts then M(M) is not Turing
circular so H(M, M) is not a Turing circularity decider. If H(M, M)
rejects then M(M) is Turing circuilar so H(M, M) is not a Turing
circularity decider.

So for H is not a Turing circularity decider.

Because the proof was about every Turing machine H the conclusion is
that no Turing machine is a Turing circularity decider.
--
Mikko
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 12/4/25 3:22 AM, dart200 wrote:

keep in mind: all real TMs exist, undecidable machines do not exist.

But "Undecidability" isn't about a particular "machine", but about a
general problem, a total MAPPING of the (infinite) set of inputs to
there respective output. It is the statement that there can not exist a "Program" (as defined by the theory, which are finite definite
algorithms) that can recreate the mapping.

For halting, every given program is know to either halt or not, the
problem is to be able to universally give that answer correctly in
finite time. THAT can't be done (universally, i.e. for any possible
input machine).

see, if we do not have a general halting decider then there must be some input machine L, which is the first machine in the full enumeration
who's halting semantics cannot be decided up for some kind of semantics (like halting).

No, it means that for every machine in that enumeration, there is a
machine that it will give a wrong answer to (or fail to answer), and
what that input machine is, can very well differ depending on which
machine in the enumeration you are looking at.

well, first off: all the proofs for undecidability use purely
hypothetical machines, which then are declared to not exist, so none of those machines could be *real* machine L.

Not "ALL", but the classic one. and the input derived WOULD BE a real
machine if the decider it was built on was an actual machine.

so what is this proposed non-hypothetical *real* machine L that then
cannot be decided?

But that isn't the claim. It isn't that there is a specific machine L
that can't be decided, and in fact, there can't be such a machine, as
there are two poor deciders, we can all Yes, and No, that always answer
for every input their given answer, ONE of those MUST be right, so there
can not be a single specific machine that all get wrong.

That idea is just part of Peter Olcotts stupidity and misunderstanding.

and could that machine L even exist?

let's say someone found that limit L and demonstrated this property that
it cannot be decided upon by a halting decider ... but then next step in undecidable proofs is to declare the machine's non-existence, because an undecidable machine is also not a deterministic machine, which
ultimately contradicts the fact that this limit machine L was suppose to actually *exist*, so how could it ever exist?

and if the limit machine L does not actually exist, then how are TM semantics not generally decidable???

good god guys, it's so tiring arguing against what is seemingly irreconcilable nonsense. but bring it on my dudes, how do u think i'm
wrong this time???

And your problem he is you are working on the wrong problem, because
"someone" has spewed out so much misinformaiton that he has reduced the intelegence of the world.

The problem isn't that some given machine can't be decided if it halts
or not, but that for every machine that claims to be a decider, there
will be an input for which it gives the wrong answer, or it fails to
answers.

Now, a side effect of this fact, it becomes true that there exists some machine/input combinations that we can not know if they halt or not, but another side effect of this is we can't tell if a given machine is one
of them, as by definition any machine we can't know if it halts or not,
must be non-halting, as any halting machine can be proven to halt, just
by running it for enough steps.
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 12/5/25 5:31 PM, Richard Damon wrote:

On 12/4/25 3:22 AM, dart200 wrote:

keep in mind: all real TMs exist, undecidable machines do not exist.

But "Undecidability" isn't about a particular "machine", but about a
general problem, a total MAPPING of the (infinite) set of inputs to
there respective output. It is the statement that there can not exist a "Program" (as defined by the theory, which are finite definite
algorithms) that can recreate the mapping.

For halting, every given program is know to either halt or not, the
problem is to be able to universally give that answer correctly in
finite time. THAT can't be done (universally, i.e. for any possible
input machine).

see, if we do not have a general halting decider then there must be
some input machine L, which is the first machine in the full
enumeration who's halting semantics cannot be decided up for some kind
of semantics (like halting).

No, it means that for every machine in that enumeration, there is a
machine that it will give a wrong answer to (or fail to answer), and

let me boil this down:

all "proven" examples of what are actually hypothetical machines that
could not be decided upon, not only do not exist, they actually could
not exist... and therefore they *do not* and *will not* come up in a
full enumeration of machines

so what is the *real* example of a machine that demonstrably cannot be
decided upon???

if you tell me: look at these hypothetical undecidable machine that
cannot exist, but from that we can just extrapolate *real* forms of such machines that certainly can exist ... ???

but like ok, if ur so certain they *must* exist, what is an example of
one???

i'm not buying this whole if hypotheticals can be presented, then
certainly *real* variations of it exist ... where else would
hypothesizing about something just like fucking imply non-hypothetical
forms of it actually exist as real constructs???

what that input machine is, can very well differ depending on which
machine in the enumeration you are looking at.

well, first off: all the proofs for undecidability use purely
hypothetical machines, which then are declared to not exist, so none
of those machines could be *real* machine L.

Not "ALL", but the classic one. and the input derived WOULD BE a real machine if the decider it was built on was an actual machine.

so what is this proposed non-hypothetical *real* machine L that then
cannot be decided?

But that isn't the claim. It isn't that there is a specific machine L
that can't be decided, and in fact, there can't be such a machine, as
there are two poor deciders, we can all Yes, and No, that always answer
for every input their given answer, ONE of those MUST be right, so there
can not be a single specific machine that all get wrong.

That idea is just part of Peter Olcotts stupidity and misunderstanding.

and could that machine L even exist?

let's say someone found that limit L and demonstrated this property
that it cannot be decided upon by a halting decider ... but then next
step in undecidable proofs is to declare the machine's non-existence,
because an undecidable machine is also not a deterministic machine,
which ultimately contradicts the fact that this limit machine L was
suppose to actually *exist*, so how could it ever exist?

and if the limit machine L does not actually exist, then how are TM
semantics not generally decidable???

good god guys, it's so tiring arguing against what is seemingly
irreconcilable nonsense. but bring it on my dudes, how do u think i'm
wrong this time???

And your problem he is you are working on the wrong problem, because "someone" has spewed out so much misinformaiton that he has reduced the intelligence of the world.

no bro, please read this carefully: these really are my own thots that
i've mostly developed on my own without much external validation
anywhere. polcott is an interesting character, but we haven't yet seen
eye to eye enough for much influence to happen either way

unlike polcott, i'm personally not sure what to do about godel's incompleteness, and i'm not making claims about it because it's just
outside the scope i'm trying to address

i'm trying to address the theory of computing, not math as a whole

The problem isn't that some given machine can't be decided if it halts
or not, but that for every machine that claims to be a decider, there
will be an input for which it gives the wrong answer, or it fails to answers.

i know this is hard to really consider:

what is an example of a *real machine that exists*, where this behavior demonstrably happens???

sure you can throw around hypothetical examples of undecidable machines
all day long, i've spent a lot of time considering them myself, probably
more than you actually...

but like what about a *real* machine, that *actually exists*???

Now, a side effect of this fact, it becomes true that there exists some machine/input combinations that we can not know if they halt or not, but another side effect of this is we can't tell if a given machine is one
of them, as by definition any machine we can't know if it halts or not,
must be non-halting, as any halting machine can be proven to halt, just
by running it for enough steps.

honestly richard, i think i just stumbled right into a core
contradiction baked into the theory of computing that has gone almost
entirely unnoticed besides a few "cranks" on the internet,

none of which have put it so succinctly like i've done so in the last day
--
hi, i'm nick! let's end war 🙃

--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 12/6/2025 1:34 AM, dart200 wrote:

On 12/5/25 5:31 PM, Richard Damon wrote:

On 12/4/25 3:22 AM, dart200 wrote:

keep in mind: all real TMs exist, undecidable machines do not exist.

But "Undecidability" isn't about a particular "machine", but about a
general problem, a total MAPPING of the (infinite) set of inputs to
there respective output. It is the statement that there can not exist
a "Program" (as defined by the theory, which are finite definite
algorithms) that can recreate the mapping.

For halting, every given program is know to either halt or not, the
problem is to be able to universally give that answer correctly in
finite time. THAT can't be done (universally, i.e. for any possible
input machine).

see, if we do not have a general halting decider then there must be
some input machine L, which is the first machine in the full
enumeration who's halting semantics cannot be decided up for some
kind of semantics (like halting).

No, it means that for every machine in that enumeration, there is a
machine that it will give a wrong answer to (or fail to answer), and

let me boil this down:

all "proven" examples of what are actually hypothetical machines that
could not be decided upon, not only do not exist, they actually could
not exist... and therefore they *do not* and *will not* come up in a
full enumeration of machines

so what is the *real* example of a machine that demonstrably cannot be decided upon???

if you tell me: look at these hypothetical undecidable machine that
cannot exist, but from that we can just extrapolate *real* forms of such machines that certainly can exist ... ???

but like ok, if ur so certain they *must* exist, what is an example of one???

i'm not buying this whole if hypotheticals can be presented, then
certainly *real* variations of it exist ... where else would
hypothesizing about something just like fucking imply non-hypothetical
forms of it actually exist as real constructs???

what that input machine is, can very well differ depending on which
machine in the enumeration you are looking at.

well, first off: all the proofs for undecidability use purely
hypothetical machines, which then are declared to not exist, so none
of those machines could be *real* machine L.

Not "ALL", but the classic one. and the input derived WOULD BE a real
machine if the decider it was built on was an actual machine.

so what is this proposed non-hypothetical *real* machine L that then
cannot be decided?

But that isn't the claim. It isn't that there is a specific machine L
that can't be decided, and in fact, there can't be such a machine, as
there are two poor deciders, we can all Yes, and No, that always
answer for every input their given answer, ONE of those MUST be right,
so there can not be a single specific machine that all get wrong.

That idea is just part of Peter Olcotts stupidity and misunderstanding.

and could that machine L even exist?

let's say someone found that limit L and demonstrated this property
that it cannot be decided upon by a halting decider ... but then next
step in undecidable proofs is to declare the machine's non-existence,
because an undecidable machine is also not a deterministic machine,
which ultimately contradicts the fact that this limit machine L was
suppose to actually *exist*, so how could it ever exist?

and if the limit machine L does not actually exist, then how are TM
semantics not generally decidable???

good god guys, it's so tiring arguing against what is seemingly
irreconcilable nonsense. but bring it on my dudes, how do u think i'm
wrong this time???

And your problem he is you are working on the wrong problem, because
"someone" has spewed out so much misinformaiton that he has reduced
the intelligence of the world.

no bro, please read this carefully: these really are my own thots that
i've mostly developed on my own without much external validation
anywhere. polcott is an interesting character, but we haven't yet seen
eye to eye enough for much influence to happen either way

unlike polcott, i'm personally not sure what to do about godel's incompleteness, and i'm not making claims about it because it's just
outside the scope i'm trying to address

i'm trying to address the theory of computing, not math as a whole

The problem isn't that some given machine can't be decided if it halts
or not, but that for every machine that claims to be a decider, there
will be an input for which it gives the wrong answer, or it fails to
answers.

i know this is hard to really consider:

what is an example of a *real machine that exists*, where this behavior demonstrably happens???

sure you can throw around hypothetical examples of undecidable machines
all day long, i've spent a lot of time considering them myself, probably more than you actually...

but like what about a *real* machine, that *actually exists*???

Now, a side effect of this fact, it becomes true that there exists
some machine/input combinations that we can not know if they halt or
not, but another side effect of this is we can't tell if a given
machine is one of them, as by definition any machine we can't know if
it halts or not, must be non-halting, as any halting machine can be
proven to halt, just by running it for enough steps.

honestly richard, i think i just stumbled right into a core
contradiction baked into the theory of computing that has gone almost entirely unnoticed besides a few "cranks" on the internet,

none of which have put it so succinctly like i've done so in the last day

It looks like I am first to have fully refuted the Halting Problem
and Gödel's Incompleteness. They are both in the same paper.

https://www.researchgate.net/publication/398375553_Halting_Problem_Proof_Counter-Example_is_Isomorphic_to_the_Liar_Paradox
--
Copyright 2025 Olcott

My 28 year goal has been to make
"true on the basis of meaning" computable.

This required establishing a new foundation
for correct reasoning.
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 12/6/25 4:16 AM, olcott wrote:

On 12/6/2025 1:34 AM, dart200 wrote:

On 12/5/25 5:31 PM, Richard Damon wrote:

On 12/4/25 3:22 AM, dart200 wrote:

keep in mind: all real TMs exist, undecidable machines do not exist.

But "Undecidability" isn't about a particular "machine", but about a
general problem, a total MAPPING of the (infinite) set of inputs to
there respective output. It is the statement that there can not exist
a "Program" (as defined by the theory, which are finite definite
algorithms) that can recreate the mapping.

For halting, every given program is know to either halt or not, the
problem is to be able to universally give that answer correctly in
finite time. THAT can't be done (universally, i.e. for any possible
input machine).

see, if we do not have a general halting decider then there must be
some input machine L, which is the first machine in the full
enumeration who's halting semantics cannot be decided up for some
kind of semantics (like halting).

No, it means that for every machine in that enumeration, there is a
machine that it will give a wrong answer to (or fail to answer), and

let me boil this down:

all "proven" examples of what are actually hypothetical machines that
could not be decided upon, not only do not exist, they actually could
not exist... and therefore they *do not* and *will not* come up in a
full enumeration of machines

so what is the *real* example of a machine that demonstrably cannot be
decided upon???

if you tell me: look at these hypothetical undecidable machine that
cannot exist, but from that we can just extrapolate *real* forms of
such machines that certainly can exist ... ???

but like ok, if ur so certain they *must* exist, what is an example of
one???

i'm not buying this whole if hypotheticals can be presented, then
certainly *real* variations of it exist ... where else would
hypothesizing about something just like fucking imply non-hypothetical
forms of it actually exist as real constructs???

what that input machine is, can very well differ depending on which
machine in the enumeration you are looking at.

well, first off: all the proofs for undecidability use purely
hypothetical machines, which then are declared to not exist, so none
of those machines could be *real* machine L.

Not "ALL", but the classic one. and the input derived WOULD BE a real
machine if the decider it was built on was an actual machine.

so what is this proposed non-hypothetical *real* machine L that then
cannot be decided?

But that isn't the claim. It isn't that there is a specific machine L
that can't be decided, and in fact, there can't be such a machine, as
there are two poor deciders, we can all Yes, and No, that always
answer for every input their given answer, ONE of those MUST be
right, so there can not be a single specific machine that all get wrong. >>>
That idea is just part of Peter Olcotts stupidity and misunderstanding.

and could that machine L even exist?

let's say someone found that limit L and demonstrated this property
that it cannot be decided upon by a halting decider ... but then
next step in undecidable proofs is to declare the machine's non-
existence, because an undecidable machine is also not a
deterministic machine, which ultimately contradicts the fact that
this limit machine L was suppose to actually *exist*, so how could
it ever exist?

and if the limit machine L does not actually exist, then how are TM
semantics not generally decidable???

good god guys, it's so tiring arguing against what is seemingly
irreconcilable nonsense. but bring it on my dudes, how do u think
i'm wrong this time???

And your problem he is you are working on the wrong problem, because
"someone" has spewed out so much misinformaiton that he has reduced
the intelligence of the world.

no bro, please read this carefully: these really are my own thots that
i've mostly developed on my own without much external validation
anywhere. polcott is an interesting character, but we haven't yet seen
eye to eye enough for much influence to happen either way

unlike polcott, i'm personally not sure what to do about godel's
incompleteness, and i'm not making claims about it because it's just
outside the scope i'm trying to address

i'm trying to address the theory of computing, not math as a whole

The problem isn't that some given machine can't be decided if it
halts or not, but that for every machine that claims to be a decider,
there will be an input for which it gives the wrong answer, or it
fails to answers.

i know this is hard to really consider:

what is an example of a *real machine that exists*, where this
behavior demonstrably happens???

sure you can throw around hypothetical examples of undecidable
machines all day long, i've spent a lot of time considering them
myself, probably more than you actually...

but like what about a *real* machine, that *actually exists*???

Now, a side effect of this fact, it becomes true that there exists
some machine/input combinations that we can not know if they halt or
not, but another side effect of this is we can't tell if a given
machine is one of them, as by definition any machine we can't know if
it halts or not, must be non-halting, as any halting machine can be
proven to halt, just by running it for enough steps.

honestly richard, i think i just stumbled right into a core
contradiction baked into the theory of computing that has gone almost
entirely unnoticed besides a few "cranks" on the internet,

none of which have put it so succinctly like i've done so in the last day

It looks like I am first to have fully refuted the Halting Problem
and Gödel's Incompleteness. They are both in the same paper.

https://www.researchgate.net/ publication/398375553_Halting_Problem_Proof_Counter- Example_is_Isomorphic_to_the_Liar_Paradox

i'm not really refuting the halting problem there, rather presenting a fundamental contradiction with rejecting the premise of a general
halting deciders, namely that non-existent machines would exist

it doesn't impact godel's claims because the argument is at the level of computing machines, not more fundamentals claims
--
hi, i'm nick! let's end war 🙃

--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 12/6/2025 10:41 AM, dart200 wrote:

On 12/6/25 4:16 AM, olcott wrote:

On 12/6/2025 1:34 AM, dart200 wrote:

On 12/5/25 5:31 PM, Richard Damon wrote:

On 12/4/25 3:22 AM, dart200 wrote:

keep in mind: all real TMs exist, undecidable machines do not exist.

But "Undecidability" isn't about a particular "machine", but about a
general problem, a total MAPPING of the (infinite) set of inputs to
there respective output. It is the statement that there can not
exist a "Program" (as defined by the theory, which are finite
definite algorithms) that can recreate the mapping.

For halting, every given program is know to either halt or not, the
problem is to be able to universally give that answer correctly in
finite time. THAT can't be done (universally, i.e. for any possible
input machine).

see, if we do not have a general halting decider then there must be >>>>> some input machine L, which is the first machine in the full
enumeration who's halting semantics cannot be decided up for some
kind of semantics (like halting).

No, it means that for every machine in that enumeration, there is a
machine that it will give a wrong answer to (or fail to answer), and

let me boil this down:

all "proven" examples of what are actually hypothetical machines that
could not be decided upon, not only do not exist, they actually could
not exist... and therefore they *do not* and *will not* come up in a
full enumeration of machines

so what is the *real* example of a machine that demonstrably cannot
be decided upon???

if you tell me: look at these hypothetical undecidable machine that
cannot exist, but from that we can just extrapolate *real* forms of
such machines that certainly can exist ... ???

but like ok, if ur so certain they *must* exist, what is an example
of one???

i'm not buying this whole if hypotheticals can be presented, then
certainly *real* variations of it exist ... where else would
hypothesizing about something just like fucking imply non-
hypothetical forms of it actually exist as real constructs???

what that input machine is, can very well differ depending on which
machine in the enumeration you are looking at.

well, first off: all the proofs for undecidability use purely
hypothetical machines, which then are declared to not exist, so
none of those machines could be *real* machine L.

Not "ALL", but the classic one. and the input derived WOULD BE a
real machine if the decider it was built on was an actual machine.

so what is this proposed non-hypothetical *real* machine L that
then cannot be decided?

But that isn't the claim. It isn't that there is a specific machine
L that can't be decided, and in fact, there can't be such a machine,
as there are two poor deciders, we can all Yes, and No, that always
answer for every input their given answer, ONE of those MUST be
right, so there can not be a single specific machine that all get
wrong.

That idea is just part of Peter Olcotts stupidity and misunderstanding. >>>>

and could that machine L even exist?

let's say someone found that limit L and demonstrated this property >>>>> that it cannot be decided upon by a halting decider ... but then
next step in undecidable proofs is to declare the machine's non-
existence, because an undecidable machine is also not a
deterministic machine, which ultimately contradicts the fact that
this limit machine L was suppose to actually *exist*, so how could
it ever exist?

and if the limit machine L does not actually exist, then how are TM >>>>> semantics not generally decidable???

good god guys, it's so tiring arguing against what is seemingly
irreconcilable nonsense. but bring it on my dudes, how do u think
i'm wrong this time???

And your problem he is you are working on the wrong problem, because
"someone" has spewed out so much misinformaiton that he has reduced
the intelligence of the world.

no bro, please read this carefully: these really are my own thots
that i've mostly developed on my own without much external validation
anywhere. polcott is an interesting character, but we haven't yet
seen eye to eye enough for much influence to happen either way

unlike polcott, i'm personally not sure what to do about godel's
incompleteness, and i'm not making claims about it because it's just
outside the scope i'm trying to address

i'm trying to address the theory of computing, not math as a whole

The problem isn't that some given machine can't be decided if it
halts or not, but that for every machine that claims to be a
decider, there will be an input for which it gives the wrong answer,
or it fails to answers.

i know this is hard to really consider:

what is an example of a *real machine that exists*, where this
behavior demonstrably happens???

sure you can throw around hypothetical examples of undecidable
machines all day long, i've spent a lot of time considering them
myself, probably more than you actually...

but like what about a *real* machine, that *actually exists*???

Now, a side effect of this fact, it becomes true that there exists
some machine/input combinations that we can not know if they halt or
not, but another side effect of this is we can't tell if a given
machine is one of them, as by definition any machine we can't know
if it halts or not, must be non-halting, as any halting machine can
be proven to halt, just by running it for enough steps.

honestly richard, i think i just stumbled right into a core
contradiction baked into the theory of computing that has gone almost
entirely unnoticed besides a few "cranks" on the internet,

none of which have put it so succinctly like i've done so in the last
day

It looks like I am first to have fully refuted the Halting Problem
and Gödel's Incompleteness. They are both in the same paper.

https://www.researchgate.net/
publication/398375553_Halting_Problem_Proof_Counter-
Example_is_Isomorphic_to_the_Liar_Paradox

i'm not really refuting the halting problem there, rather presenting a fundamental contradiction with rejecting the premise of a general
halting deciders, namely that non-existent machines would exist

it doesn't impact godel's claims because the argument is at the level of computing machines, not more fundamentals claims

As my signature line now stipulates
My 28 year goal has been to make
"true on the basis of meaning" computable.

This can be directly implemented to make
LLM systems much more reliable.
--
Copyright 2025 Olcott

My 28 year goal has been to make
"true on the basis of meaning" computable.

This required establishing a new foundation
for correct reasoning.
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 12/6/2025 6:16 AM, olcott wrote:

On 12/6/2025 1:34 AM, dart200 wrote:

On 12/5/25 5:31 PM, Richard Damon wrote:

On 12/4/25 3:22 AM, dart200 wrote:

keep in mind: all real TMs exist, undecidable machines do not exist.

But "Undecidability" isn't about a particular "machine", but about a
general problem, a total MAPPING of the (infinite) set of inputs to
there respective output. It is the statement that there can not exist
a "Program" (as defined by the theory, which are finite definite
algorithms) that can recreate the mapping.

For halting, every given program is know to either halt or not, the
problem is to be able to universally give that answer correctly in
finite time. THAT can't be done (universally, i.e. for any possible
input machine).

see, if we do not have a general halting decider then there must be
some input machine L, which is the first machine in the full
enumeration who's halting semantics cannot be decided up for some
kind of semantics (like halting).

No, it means that for every machine in that enumeration, there is a
machine that it will give a wrong answer to (or fail to answer), and

let me boil this down:

all "proven" examples of what are actually hypothetical machines that
could not be decided upon, not only do not exist, they actually could
not exist... and therefore they *do not* and *will not* come up in a
full enumeration of machines

so what is the *real* example of a machine that demonstrably cannot be
decided upon???

if you tell me: look at these hypothetical undecidable machine that
cannot exist, but from that we can just extrapolate *real* forms of
such machines that certainly can exist ... ???

but like ok, if ur so certain they *must* exist, what is an example of
one???

i'm not buying this whole if hypotheticals can be presented, then
certainly *real* variations of it exist ... where else would
hypothesizing about something just like fucking imply non-hypothetical
forms of it actually exist as real constructs???

what that input machine is, can very well differ depending on which
machine in the enumeration you are looking at.

well, first off: all the proofs for undecidability use purely
hypothetical machines, which then are declared to not exist, so none
of those machines could be *real* machine L.

Not "ALL", but the classic one. and the input derived WOULD BE a real
machine if the decider it was built on was an actual machine.

so what is this proposed non-hypothetical *real* machine L that then
cannot be decided?

But that isn't the claim. It isn't that there is a specific machine L
that can't be decided, and in fact, there can't be such a machine, as
there are two poor deciders, we can all Yes, and No, that always
answer for every input their given answer, ONE of those MUST be
right, so there can not be a single specific machine that all get wrong. >>>
That idea is just part of Peter Olcotts stupidity and misunderstanding.

and could that machine L even exist?

let's say someone found that limit L and demonstrated this property
that it cannot be decided upon by a halting decider ... but then
next step in undecidable proofs is to declare the machine's non-
existence, because an undecidable machine is also not a
deterministic machine, which ultimately contradicts the fact that
this limit machine L was suppose to actually *exist*, so how could
it ever exist?

and if the limit machine L does not actually exist, then how are TM
semantics not generally decidable???

good god guys, it's so tiring arguing against what is seemingly
irreconcilable nonsense. but bring it on my dudes, how do u think
i'm wrong this time???

And your problem he is you are working on the wrong problem, because
"someone" has spewed out so much misinformaiton that he has reduced
the intelligence of the world.

no bro, please read this carefully: these really are my own thots that
i've mostly developed on my own without much external validation
anywhere. polcott is an interesting character, but we haven't yet seen
eye to eye enough for much influence to happen either way

unlike polcott, i'm personally not sure what to do about godel's
incompleteness, and i'm not making claims about it because it's just
outside the scope i'm trying to address

i'm trying to address the theory of computing, not math as a whole

The problem isn't that some given machine can't be decided if it
halts or not, but that for every machine that claims to be a decider,
there will be an input for which it gives the wrong answer, or it
fails to answers.

i know this is hard to really consider:

what is an example of a *real machine that exists*, where this
behavior demonstrably happens???

sure you can throw around hypothetical examples of undecidable
machines all day long, i've spent a lot of time considering them
myself, probably more than you actually...

but like what about a *real* machine, that *actually exists*???

Now, a side effect of this fact, it becomes true that there exists
some machine/input combinations that we can not know if they halt or
not, but another side effect of this is we can't tell if a given
machine is one of them, as by definition any machine we can't know if
it halts or not, must be non-halting, as any halting machine can be
proven to halt, just by running it for enough steps.

honestly richard, i think i just stumbled right into a core
contradiction baked into the theory of computing that has gone almost
entirely unnoticed besides a few "cranks" on the internet,

none of which have put it so succinctly like i've done so in the last day

It looks like I am first to have fully refuted the Halting Problem
and Gödel's Incompleteness. They are both in the same paper.

https://www.researchgate.net/ publication/398375553_Halting_Problem_Proof_Counter- Example_is_Isomorphic_to_the_Liar_Paradox

Halting Problem Proof Counter-Example is Isomorphic to the Liar Paradox https://philpapers.org/archive/OLCHPP-3.pdf
Same file without broken link
--
Copyright 2025 Olcott

My 28 year goal has been to make
"true on the basis of meaning" computable.

This required establishing a new foundation
for correct reasoning.
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 12/6/25 2:34 AM, dart200 wrote:

On 12/5/25 5:31 PM, Richard Damon wrote:

On 12/4/25 3:22 AM, dart200 wrote:

keep in mind: all real TMs exist, undecidable machines do not exist.

But "Undecidability" isn't about a particular "machine", but about a
general problem, a total MAPPING of the (infinite) set of inputs to
there respective output. It is the statement that there can not exist
a "Program" (as defined by the theory, which are finite definite
algorithms) that can recreate the mapping.

For halting, every given program is know to either halt or not, the
problem is to be able to universally give that answer correctly in
finite time. THAT can't be done (universally, i.e. for any possible
input machine).

see, if we do not have a general halting decider then there must be
some input machine L, which is the first machine in the full
enumeration who's halting semantics cannot be decided up for some
kind of semantics (like halting).

No, it means that for every machine in that enumeration, there is a
machine that it will give a wrong answer to (or fail to answer), and

let me boil this down:

all "proven" examples of what are actually hypothetical machines that
could not be decided upon, not only do not exist, they actually could
not exist... and therefore they *do not* and *will not* come up in a
full enumeration of machines

Where do you see that?

so what is the *real* example of a machine that demonstrably cannot be decided upon???

That isn't the question, so just a straw man. The issues isn't an
example, but the full question.

if you tell me: look at these hypothetical undecidable machine that
cannot exist, but from that we can just extrapolate *real* forms of such machines that certainly can exist ... ???

But that isn't what the proofs do.

All you are doing is showing a misunderstanding of the problem.

but like ok, if ur so certain they *must* exist, what is an example of one???

i'm not buying this whole if hypotheticals can be presented, then
certainly *real* variations of it exist ... where else would
hypothesizing about something just like fucking imply non-hypothetical
forms of it actually exist as real constructs???

And a proof can be made, that for *ANY* machine you can make and want to
claim to be a correct halt decider, I can make a machine and input to
give to it that it will get wrong.

Since I can do that for EVERY machine you make, there can not be a
machine that gets all input correct.

what that input machine is, can very well differ depending on which
machine in the enumeration you are looking at.

well, first off: all the proofs for undecidability use purely
hypothetical machines, which then are declared to not exist, so none
of those machines could be *real* machine L.

Not "ALL", but the classic one. and the input derived WOULD BE a real
machine if the decider it was built on was an actual machine.

so what is this proposed non-hypothetical *real* machine L that then
cannot be decided?

But that isn't the claim. It isn't that there is a specific machine L
that can't be decided, and in fact, there can't be such a machine, as
there are two poor deciders, we can all Yes, and No, that always
answer for every input their given answer, ONE of those MUST be right,
so there can not be a single specific machine that all get wrong.

That idea is just part of Peter Olcotts stupidity and misunderstanding.

and could that machine L even exist?

let's say someone found that limit L and demonstrated this property
that it cannot be decided upon by a halting decider ... but then next
step in undecidable proofs is to declare the machine's non-existence,
because an undecidable machine is also not a deterministic machine,
which ultimately contradicts the fact that this limit machine L was
suppose to actually *exist*, so how could it ever exist?

and if the limit machine L does not actually exist, then how are TM
semantics not generally decidable???

good god guys, it's so tiring arguing against what is seemingly
irreconcilable nonsense. but bring it on my dudes, how do u think i'm
wrong this time???

And your problem he is you are working on the wrong problem, because
"someone" has spewed out so much misinformaiton that he has reduced
the intelligence of the world.

no bro, please read this carefully: these really are my own thots that
i've mostly developed on my own without much external validation
anywhere. polcott is an interesting character, but we haven't yet seen
eye to eye enough for much influence to happen either way

Because it seems, you don't understand what the actual problem is, or
how the proof actually work.

unlike polcott, i'm personally not sure what to do about godel's incompleteness, and i'm not making claims about it because it's just
outside the scope i'm trying to address

So, you don't care about logic that has the power to express the Natural Numbers?

i'm trying to address the theory of computing, not math as a whole

But the theory of computing is based on logic that can express the
Natural numbers, and thus that part of mathematics comes in.

The problem isn't that some given machine can't be decided if it halts
or not, but that for every machine that claims to be a decider, there
will be an input for which it gives the wrong answer, or it fails to
answers.

i know this is hard to really consider:

what is an example of a *real machine that exists*, where this behavior demonstrably happens???

Since it is proven that there can't be a correct decider, what are you
asking for?

As I said, for *ANY* "Halt Decider" that you want to try to claim is universally correct, I can make an input that shows the claim to be wrong.

Your problem is you have the question backwards. It isn't that there is
a machine that no machine can get the right answer for, as that is
clearly wrong, but there is no machine that can always get the right answer.

I side affect of this, is that there WILL be machines that we can not
know the answer for, but we can't know if a given machine is one of
them, as knowing that lets you know what the answer is, as the only
unknowable halting state machines are non-halting, as ALL halting
machine can be shown to be halting by just running them till the halt.

sure you can throw around hypothetical examples of undecidable machines
all day long, i've spent a lot of time considering them myself, probably more than you actually...

And, as I have said, that isn't the concept to consider, as we can't
know that a machine is undecidable.

but like what about a *real* machine, that *actually exists*???

Which is an answer we can never know the answer to (at least possibly, I
am not sure if we can actually prove such an existance, only its
potential to exist)

Now, a side effect of this fact, it becomes true that there exists
some machine/input combinations that we can not know if they halt or
not, but another side effect of this is we can't tell if a given
machine is one of them, as by definition any machine we can't know if
it halts or not, must be non-halting, as any halting machine can be
proven to halt, just by running it for enough steps.

honestly richard, i think i just stumbled right into a core
contradiction baked into the theory of computing that has gone almost entirely unnoticed besides a few "cranks" on the internet,

none of which have put it so succinctly like i've done so in the last day

No, the problem is you keep on looking for that which the theory says is unknowable. We can show that there are machines that we can not know the halting property of, but we can never know if a machine is in that class.

We can know that no machine can be a correct decider, as for any claimed decider, we can show an input that it gets wrong. Thus no universally
correct deciders, which IS the question possed by the problem.
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 12/6/25 10:44 AM, Richard Damon wrote:

On 12/6/25 2:34 AM, dart200 wrote:

On 12/5/25 5:31 PM, Richard Damon wrote:

On 12/4/25 3:22 AM, dart200 wrote:

keep in mind: all real TMs exist, undecidable machines do not exist.

But "Undecidability" isn't about a particular "machine", but about a
general problem, a total MAPPING of the (infinite) set of inputs to
there respective output. It is the statement that there can not exist
a "Program" (as defined by the theory, which are finite definite
algorithms) that can recreate the mapping.

For halting, every given program is know to either halt or not, the
problem is to be able to universally give that answer correctly in
finite time. THAT can't be done (universally, i.e. for any possible
input machine).

see, if we do not have a general halting decider then there must be
some input machine L, which is the first machine in the full
enumeration who's halting semantics cannot be decided up for some
kind of semantics (like halting).

No, it means that for every machine in that enumeration, there is a
machine that it will give a wrong answer to (or fail to answer), and

let me boil this down:

all "proven" examples of what are actually hypothetical machines that
could not be decided upon, not only do not exist, they actually could
not exist... and therefore they *do not* and *will not* come up in a
full enumeration of machines

Where do you see that?

bro, none of the hypothetical machines talked about in undecidable
proofs are executable, because their result cannot be decided

what does machine: und = () -> halts(und) && loop_forever() do when
executed? if that cannot be decided, then it cannot be executed either, because execution requires a decision on the next state, for any given
current state.

therefore the logic as written is not a real machine, as all *real*
machines must be executable

so what is the *real* example of a machine that demonstrably cannot be
decided upon???

That isn't the question, so just a straw man. The issues isn't an
example, but the full question.

it's not a straw man, it's a consequence of declaring that undecidable machines exist preventing a general halting decider

ok ... so what is the first *real* machine that an attempt at creating a general halting decider cannot decide on ... ???

certainly there must be some kind maximally effective halting decider,
what is the first *real* *executable* machine U that said maximally
effective decision algorithm cannot decide upon??? what does that look
like?

because it can't look any of the machines discussed in the proofs ...
because those machines are all not executable, and therefore not real,
and therefore cannot manifest in a full enumeration of turing machines

if you tell me: look at these hypothetical undecidable machine that
cannot exist, but from that we can just extrapolate *real* forms of
such machines that certainly can exist ... ???

But that isn't what the proofs do.

All you are doing is showing a misunderstanding of the problem.

ur not recognizing the consequences of accepting the proofs as true

but like ok, if ur so certain they *must* exist, what is an example of
one???

i'm not buying this whole if hypotheticals can be presented, then
certainly *real* variations of it exist ... where else would
hypothesizing about something just like fucking imply non-hypothetical
forms of it actually exist as real constructs???

And a proof can be made, that for *ANY* machine you can make and want to claim to be a correct halt decider, I can make a machine and input to
give to it that it will get wrong.

right but can any of those machines actually run???

cause if not they don't exist.

and if so, they cannot actually appear in the full enumeration of machine,

and therefor a general halting decider, in regards to *real* machines,
does not actually have to deal with them

Since I can do that for EVERY machine you make, there can not be a
machine that gets all input correct.

what that input machine is, can very well differ depending on which
machine in the enumeration you are looking at.

well, first off: all the proofs for undecidability use purely
hypothetical machines, which then are declared to not exist, so none
of those machines could be *real* machine L.

Not "ALL", but the classic one. and the input derived WOULD BE a real
machine if the decider it was built on was an actual machine.

so what is this proposed non-hypothetical *real* machine L that then
cannot be decided?

But that isn't the claim. It isn't that there is a specific machine L
that can't be decided, and in fact, there can't be such a machine, as
there are two poor deciders, we can all Yes, and No, that always
answer for every input their given answer, ONE of those MUST be
right, so there can not be a single specific machine that all get wrong. >>>
That idea is just part of Peter Olcotts stupidity and misunderstanding.

and could that machine L even exist?

let's say someone found that limit L and demonstrated this property
that it cannot be decided upon by a halting decider ... but then
next step in undecidable proofs is to declare the machine's non-
existence, because an undecidable machine is also not a
deterministic machine, which ultimately contradicts the fact that
this limit machine L was suppose to actually *exist*, so how could
it ever exist?

and if the limit machine L does not actually exist, then how are TM
semantics not generally decidable???

good god guys, it's so tiring arguing against what is seemingly
irreconcilable nonsense. but bring it on my dudes, how do u think
i'm wrong this time???

And your problem he is you are working on the wrong problem, because
"someone" has spewed out so much misinformaiton that he has reduced
the intelligence of the world.

no bro, please read this carefully: these really are my own thots that
i've mostly developed on my own without much external validation
anywhere. polcott is an interesting character, but we haven't yet seen
eye to eye enough for much influence to happen either way

Because it seems, you don't understand what the actual problem is, or
how the proof actually work.

unlike polcott, i'm personally not sure what to do about godel's
incompleteness, and i'm not making claims about it because it's just
outside the scope i'm trying to address

So, you don't care about logic that has the power to express the Natural Numbers?

i'm trying to address the theory of computing, not math as a whole

But the theory of computing is based on logic that can express the
Natural numbers, and thus that part of mathematics comes in.

The problem isn't that some given machine can't be decided if it
halts or not, but that for every machine that claims to be a decider,
there will be an input for which it gives the wrong answer, or it
fails to answers.

i know this is hard to really consider:

what is an example of a *real machine that exists*, where this
behavior demonstrably happens???

Since it is proven that there can't be a correct decider, what are you asking for?

As I said, for *ANY* "Halt Decider" that you want to try to claim is universally correct, I can make an input that shows the claim to be wrong.

Your problem is you have the question backwards. It isn't that there is
a machine that no machine can get the right answer for, as that is
clearly wrong, but there is no machine that can always get the right
answer.

I side affect of this, is that there WILL be machines that we can not
know the answer for, but we can't know if a given machine is one of
them, as knowing that lets you know what the answer is, as the only unknowable halting state machines are non-halting, as ALL halting
machine can be shown to be halting by just running them till the halt.

sure you can throw around hypothetical examples of undecidable
machines all day long, i've spent a lot of time considering them
myself, probably more than you actually...

And, as I have said, that isn't the concept to consider, as we can't
know that a machine is undecidable.

but like what about a *real* machine, that *actually exists*???

Which is an answer we can never know the answer to (at least possibly, I
am not sure if we can actually prove such an existance, only its
potential to exist)

Now, a side effect of this fact, it becomes true that there exists
some machine/input combinations that we can not know if they halt or
not, but another side effect of this is we can't tell if a given
machine is one of them, as by definition any machine we can't know if
it halts or not, must be non-halting, as any halting machine can be
proven to halt, just by running it for enough steps.

honestly richard, i think i just stumbled right into a core
contradiction baked into the theory of computing that has gone almost
entirely unnoticed besides a few "cranks" on the internet,

none of which have put it so succinctly like i've done so in the last day

No, the problem is you keep on looking for that which the theory says is unknowable. We can show that there are machines that we can not know the halting property of, but we can never know if a machine is in that class.

We can know that no machine can be a correct decider, as for any claimed decider, we can show an input that it gets wrong. Thus no universally correct deciders, which IS the question possed by the problem.

--
a burnt out swe investigating into why our tooling doesn't involve
basic semantic proofs like halting analysis

please excuse my pseudo-pyscript,

~ nick
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 12/6/25 10:44 AM, Richard Damon wrote:

On 12/6/25 2:34 AM, dart200 wrote:

On 12/5/25 5:31 PM, Richard Damon wrote:

On 12/4/25 3:22 AM, dart200 wrote:

keep in mind: all real TMs exist, undecidable machines do not exist.

But "Undecidability" isn't about a particular "machine", but about a
general problem, a total MAPPING of the (infinite) set of inputs to
there respective output. It is the statement that there can not exist
a "Program" (as defined by the theory, which are finite definite
algorithms) that can recreate the mapping.

For halting, every given program is know to either halt or not, the
problem is to be able to universally give that answer correctly in
finite time. THAT can't be done (universally, i.e. for any possible
input machine).

see, if we do not have a general halting decider then there must be
some input machine L, which is the first machine in the full
enumeration who's halting semantics cannot be decided up for some
kind of semantics (like halting).

No, it means that for every machine in that enumeration, there is a
machine that it will give a wrong answer to (or fail to answer), and

let me boil this down:

all "proven" examples of what are actually hypothetical machines that
could not be decided upon, not only do not exist, they actually could
not exist... and therefore they *do not* and *will not* come up in a
full enumeration of machines

Where do you see that?

so what is the *real* example of a machine that demonstrably cannot be
decided upon???

That isn't the question, so just a straw man. The issues isn't an
example, but the full question.

if you tell me: look at these hypothetical undecidable machine that
cannot exist, but from that we can just extrapolate *real* forms of
such machines that certainly can exist ... ???

But that isn't what the proofs do.

All you are doing is showing a misunderstanding of the problem.

but like ok, if ur so certain they *must* exist, what is an example of
one???

i'm not buying this whole if hypotheticals can be presented, then
certainly *real* variations of it exist ... where else would
hypothesizing about something just like fucking imply non-hypothetical
forms of it actually exist as real constructs???

And a proof can be made, that for *ANY* machine you can make and want to claim to be a correct halt decider, I can make a machine and input to
give to it that it will get wrong.

Since I can do that for EVERY machine you make, there can not be a
machine that gets all input correct.

what that input machine is, can very well differ depending on which
machine in the enumeration you are looking at.

well, first off: all the proofs for undecidability use purely
hypothetical machines, which then are declared to not exist, so none
of those machines could be *real* machine L.

Not "ALL", but the classic one. and the input derived WOULD BE a real
machine if the decider it was built on was an actual machine.

so what is this proposed non-hypothetical *real* machine L that then
cannot be decided?

But that isn't the claim. It isn't that there is a specific machine L
that can't be decided, and in fact, there can't be such a machine, as
there are two poor deciders, we can all Yes, and No, that always
answer for every input their given answer, ONE of those MUST be
right, so there can not be a single specific machine that all get wrong. >>>
That idea is just part of Peter Olcotts stupidity and misunderstanding.

and could that machine L even exist?

let's say someone found that limit L and demonstrated this property
that it cannot be decided upon by a halting decider ... but then
next step in undecidable proofs is to declare the machine's non-
existence, because an undecidable machine is also not a
deterministic machine, which ultimately contradicts the fact that
this limit machine L was suppose to actually *exist*, so how could
it ever exist?

and if the limit machine L does not actually exist, then how are TM
semantics not generally decidable???

good god guys, it's so tiring arguing against what is seemingly
irreconcilable nonsense. but bring it on my dudes, how do u think
i'm wrong this time???

And your problem he is you are working on the wrong problem, because
"someone" has spewed out so much misinformaiton that he has reduced
the intelligence of the world.

no bro, please read this carefully: these really are my own thots that
i've mostly developed on my own without much external validation
anywhere. polcott is an interesting character, but we haven't yet seen
eye to eye enough for much influence to happen either way

Because it seems, you don't understand what the actual problem is, or
how the proof actually work.

unlike polcott, i'm personally not sure what to do about godel's
incompleteness, and i'm not making claims about it because it's just
outside the scope i'm trying to address

So, you don't care about logic that has the power to express the Natural Numbers?

i'm trying to address the theory of computing, not math as a whole

But the theory of computing is based on logic that can express the
Natural numbers, and thus that part of mathematics comes in.

The problem isn't that some given machine can't be decided if it
halts or not, but that for every machine that claims to be a decider,
there will be an input for which it gives the wrong answer, or it
fails to answers.

i know this is hard to really consider:

what is an example of a *real machine that exists*, where this
behavior demonstrably happens???

Since it is proven that there can't be a correct decider, what are you asking for?

As I said, for *ANY* "Halt Decider" that you want to try to claim is universally correct, I can make an input that shows the claim to be wrong.

Your problem is you have the question backwards. It isn't that there is
a machine that no machine can get the right answer for, as that is
clearly wrong, but there is no machine that can always get the right
answer.

I side affect of this, is that there WILL be machines that we can not
know the answer for, but we can't know if a given machine is one of
them, as knowing that lets you know what the answer is, as the only unknowable halting state machines are non-halting, as ALL halting
machine can be shown to be halting by just running them till the halt.

sure you can throw around hypothetical examples of undecidable
machines all day long, i've spent a lot of time considering them
myself, probably more than you actually...

And, as I have said, that isn't the concept to consider, as we can't
know that a machine is undecidable.

but like what about a *real* machine, that *actually exists*???

Which is an answer we can never know the answer to (at least possibly, I
am not sure if we can actually prove such an existance, only its
potential to exist)

Now, a side effect of this fact, it becomes true that there exists
some machine/input combinations that we can not know if they halt or
not, but another side effect of this is we can't tell if a given
machine is one of them, as by definition any machine we can't know if
it halts or not, must be non-halting, as any halting machine can be

bruh ... do u not recognize the inherent contradiction in say in all
machines which can't know the halting of ... must therefore be
non-halting???

like u literally just decided what they all must be after claiming they
are machiens which we cannot know the halting status of ...

proven to halt, just by running it for enough steps.

honestly richard, i think i just stumbled right into a core
contradiction baked into the theory of computing that has gone almost
entirely unnoticed besides a few "cranks" on the internet,

none of which have put it so succinctly like i've done so in the last day

No, the problem is you keep on looking for that which the theory says is unknowable. We can show that there are machines that we can not know the halting property of, but we can never know if a machine is in that class.

We can know that no machine can be a correct decider, as for any claimed decider, we can show an input that it gets wrong. Thus no universally correct deciders, which IS the question possed by the problem.

--
a burnt out swe investigating into why our tooling doesn't involve
basic semantic proofs like halting analysis

please excuse my pseudo-pyscript,

~ nick

--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 12/6/25 4:41 PM, dart200 wrote:

On 12/6/25 10:44 AM, Richard Damon wrote:

On 12/6/25 2:34 AM, dart200 wrote:

On 12/5/25 5:31 PM, Richard Damon wrote:

On 12/4/25 3:22 AM, dart200 wrote:

keep in mind: all real TMs exist, undecidable machines do not exist.

But "Undecidability" isn't about a particular "machine", but about a
general problem, a total MAPPING of the (infinite) set of inputs to
there respective output. It is the statement that there can not
exist a "Program" (as defined by the theory, which are finite
definite algorithms) that can recreate the mapping.

For halting, every given program is know to either halt or not, the
problem is to be able to universally give that answer correctly in
finite time. THAT can't be done (universally, i.e. for any possible
input machine).

see, if we do not have a general halting decider then there must be >>>>> some input machine L, which is the first machine in the full
enumeration who's halting semantics cannot be decided up for some
kind of semantics (like halting).

No, it means that for every machine in that enumeration, there is a
machine that it will give a wrong answer to (or fail to answer), and

let me boil this down:

all "proven" examples of what are actually hypothetical machines that
could not be decided upon, not only do not exist, they actually could
not exist... and therefore they *do not* and *will not* come up in a
full enumeration of machines

Where do you see that?

so what is the *real* example of a machine that demonstrably cannot
be decided upon???

That isn't the question, so just a straw man. The issues isn't an
example, but the full question.

if you tell me: look at these hypothetical undecidable machine that
cannot exist, but from that we can just extrapolate *real* forms of
such machines that certainly can exist ... ???

But that isn't what the proofs do.

All you are doing is showing a misunderstanding of the problem.

but like ok, if ur so certain they *must* exist, what is an example
of one???

i'm not buying this whole if hypotheticals can be presented, then
certainly *real* variations of it exist ... where else would
hypothesizing about something just like fucking imply non-
hypothetical forms of it actually exist as real constructs???

And a proof can be made, that for *ANY* machine you can make and want
to claim to be a correct halt decider, I can make a machine and input
to give to it that it will get wrong.

Since I can do that for EVERY machine you make, there can not be a
machine that gets all input correct.

what that input machine is, can very well differ depending on which
machine in the enumeration you are looking at.

well, first off: all the proofs for undecidability use purely
hypothetical machines, which then are declared to not exist, so
none of those machines could be *real* machine L.

Not "ALL", but the classic one. and the input derived WOULD BE a
real machine if the decider it was built on was an actual machine.

so what is this proposed non-hypothetical *real* machine L that
then cannot be decided?

But that isn't the claim. It isn't that there is a specific machine
L that can't be decided, and in fact, there can't be such a machine,
as there are two poor deciders, we can all Yes, and No, that always
answer for every input their given answer, ONE of those MUST be
right, so there can not be a single specific machine that all get
wrong.

That idea is just part of Peter Olcotts stupidity and misunderstanding. >>>>

and could that machine L even exist?

let's say someone found that limit L and demonstrated this property >>>>> that it cannot be decided upon by a halting decider ... but then
next step in undecidable proofs is to declare the machine's non-
existence, because an undecidable machine is also not a
deterministic machine, which ultimately contradicts the fact that
this limit machine L was suppose to actually *exist*, so how could
it ever exist?

and if the limit machine L does not actually exist, then how are TM >>>>> semantics not generally decidable???

good god guys, it's so tiring arguing against what is seemingly
irreconcilable nonsense. but bring it on my dudes, how do u think
i'm wrong this time???

And your problem he is you are working on the wrong problem, because
"someone" has spewed out so much misinformaiton that he has reduced
the intelligence of the world.

no bro, please read this carefully: these really are my own thots
that i've mostly developed on my own without much external validation
anywhere. polcott is an interesting character, but we haven't yet
seen eye to eye enough for much influence to happen either way

Because it seems, you don't understand what the actual problem is, or
how the proof actually work.

unlike polcott, i'm personally not sure what to do about godel's
incompleteness, and i'm not making claims about it because it's just
outside the scope i'm trying to address

So, you don't care about logic that has the power to express the
Natural Numbers?

i'm trying to address the theory of computing, not math as a whole

But the theory of computing is based on logic that can express the
Natural numbers, and thus that part of mathematics comes in.

The problem isn't that some given machine can't be decided if it
halts or not, but that for every machine that claims to be a
decider, there will be an input for which it gives the wrong answer,
or it fails to answers.

i know this is hard to really consider:

what is an example of a *real machine that exists*, where this
behavior demonstrably happens???

Since it is proven that there can't be a correct decider, what are you
asking for?

As I said, for *ANY* "Halt Decider" that you want to try to claim is
universally correct, I can make an input that shows the claim to be
wrong.

Your problem is you have the question backwards. It isn't that there
is a machine that no machine can get the right answer for, as that is
clearly wrong, but there is no machine that can always get the right
answer.

I side affect of this, is that there WILL be machines that we can not
know the answer for, but we can't know if a given machine is one of
them, as knowing that lets you know what the answer is, as the only
unknowable halting state machines are non-halting, as ALL halting
machine can be shown to be halting by just running them till the halt.

sure you can throw around hypothetical examples of undecidable
machines all day long, i've spent a lot of time considering them
myself, probably more than you actually...

And, as I have said, that isn't the concept to consider, as we can't
know that a machine is undecidable.

but like what about a *real* machine, that *actually exists*???

Which is an answer we can never know the answer to (at least possibly,
I am not sure if we can actually prove such an existance, only its
potential to exist)

Now, a side effect of this fact, it becomes true that there exists
some machine/input combinations that we can not know if they halt or
not, but another side effect of this is we can't tell if a given
machine is one of them, as by definition any machine we can't know
if it halts or not, must be non-halting, as any halting machine can be

bruh ... do u not recognize the inherent contradiction in say in all machines which can't know the halting of ... must therefore be non- halting???

What is the contradiction in that?

Do you understand the difference between knowABLE, and knowN.

Any machine that halts, can ALWAYS be proven it halts by running it
enough steps, as there must be some finite number of steps to run it
till it halts, as that is the DEFINITION of Halting, and a finite number
of steps makes a proof that gives knowledge.

like u literally just decided what they all must be after claiming they
are machiens which we cannot know the halting status of ...

Right, but we can't KNOW that we can't know their halting status. All we
can know is we haven't found the status YET. Not knowN can be either
halting or non-halting, halting if we haven't run it yet.

proven to halt, just by running it for enough steps.

honestly richard, i think i just stumbled right into a core
contradiction baked into the theory of computing that has gone almost
entirely unnoticed besides a few "cranks" on the internet,

none of which have put it so succinctly like i've done so in the last
day

No, the problem is you keep on looking for that which the theory says
is unknowable. We can show that there are machines that we can not
know the halting property of, but we can never know if a machine is in
that class.

We can know that no machine can be a correct decider, as for any
claimed decider, we can show an input that it gets wrong. Thus no
universally correct deciders, which IS the question possed by the
problem.

One way of looking at this, is we can take all machines, and we know
that they must fall into exactly 2 categories
Halting or
Non-Halting,

But ore knowledge of them divdes them into three categories:

Known Halting,
Known Non-Halting, or
Unknown Halting Status.

And this last category we know can consist of machines in 3 categories
(but we don't know which for a given machine):
Yet-to-be-known, but Knowable, Halting
Yet-to-be-known, but Knowable, Non-Halting
Not Knowable Non-Halting.

All Halting machines are Knowable, even if not-yet known, as running
them enough (but for a still finite number of steps) will reach the halt state, and thus it not yet being know is just because we haven't run it
far enough.

For the Yet-to-be-know but Knowable Non-Halting Machines, there exists a proof, to be discovered, that proves that it will not halt.

For the Unknowable machines, they can't be Halting, as we showed that
all halting machines are knowable by just running them long enough.
There is nothing that says we must be able to find a proof of
non-halting, and the fact that Halting is non-decidable seems to imply
that this category can't be empty, or our decider just needs to apply
the appropriate proof of non-halting to correctly decide. The fact that
there are an infinite number of possible proofs may allow this category
to be empty, but I am not sure you can prove that.

As I point out, It can't be possible to prove that a machine is in this unknowable category, as only non-halting machines can be unknowable, and
thus a proof that a machine is in this category can't be correct, or the
whole logic system is proven inconsistant. This is similar to the point
that Godel uses in his incompleteness proof, as if you could prove the sentence true, that proof creates the counter example that makes the
sentence false, thus no proof can exist.
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 12/6/2025 2:21 PM, Richard Damon wrote:
[...]

Think of a program that can sometimes halt, other times never halt.
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 12/4/2025 12:22 AM, dart200 wrote:

keep in mind: all real TMs exist, undecidable machines do not exist.

Can you predict a TRNG?

[...]
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 12/6/25 7:57 PM, Chris M. Thomasson wrote:

On 12/6/2025 2:21 PM, Richard Damon wrote:
[...]

Think of a program that can sometimes halt, other times never halt.

If that is for the same, it isn't a "Program" (aka an algorithm) in Computation Theory, whicb is what "Decidability" is defined in.
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 2025-12-06 at 14:16 olcott wrote a message with the subjec line
"I am first to have fully refuted the Halting Problem".

This subject line does not make sense. The expression "refuted the
Halting Problem" does not mean anything. To refute a claim means
to prove that the claim is false. But a problem does not claim and
is neither true or false. Therefore it is a category error to say
"refuted the Halting Problem".
--
Mikko
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

olcott kirjoitti 6.12.2025 klo 19.00:

As my signature line now stipulates
My 28 year goal has been to make
"true on the basis of meaning" computable.

You should first present a "proof of concept" version with very small
scope. For example, you could restrict to the following:

The language has, in addition to the symbols of logic with equivalence,
a constant symbol 1, a unary operator ', and a binary operator symbol *.

The basic truths are:

1. for every a, b, c: (a * b) * c = a * (b * c)
2. for every a: 1 * a = a and a * 1 = a
3. for every a: a * a' = 1 and a' * a = 1
4. for every a and b: a * b = b * a

Other truths are what can be inferred from above.

When you have solved that a good next step is to remove the basic truth
4. Then you can advance to systems with more functions and then to
systems that cover wider ranges of topics.
--
Mikko
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 12/6/2025 7:07 PM, Richard Damon wrote:

On 12/6/25 7:57 PM, Chris M. Thomasson wrote:

On 12/6/2025 2:21 PM, Richard Damon wrote:
[...]

Think of a program that can sometimes halt, other times never halt.

If that is for the same, it isn't a "Program" (aka an algorithm) in Computation Theory, whicb is what "Decidability" is defined in.

I thought my fuzzer was an algorithm that Computation Theory can handle.

1 HOME
5 PRINT "ct_dr_fuzz lol. ;^)"
6 P0 = 0
7 P1 = 0

10 REM Fuzzer... ;^)
20 A$ = "NOPE!"
30 IF RND(1) < .5 THEN A$ = "YES"

100 REM INPUT "Shall DD halt or not? " ; A$
110 PRINT "Shall DD halt or not? " ; A$
200 IF A$ = "YES" GOTO 666
300 P0 = P0 + 1
400 IF P0 > 0 AND P1 > 0 GOTO 1000
500 GOTO 10

666 PRINT "OK!"
667 P1 = P1 + 1
700 PRINT "NON_HALT P0 = "; P0
710 PRINT "HALT P1 = "; P1
720 IF P0 > 0 AND P1 > 0 GOTO 1000
730 PRINT "ALL PATHS FAILED TO BE HIT!"
740 GOTO 10


1000 REM Fin
1010 PRINT "FIN... All paths hit."
1020 PRINT "NON_HALT P0 = "; P0
1030 PRINT "HALT P1 = "; P1
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 12/6/25 2:21 PM, Richard Damon wrote:

On 12/6/25 4:41 PM, dart200 wrote:

On 12/6/25 10:44 AM, Richard Damon wrote:

On 12/6/25 2:34 AM, dart200 wrote:

On 12/5/25 5:31 PM, Richard Damon wrote:

On 12/4/25 3:22 AM, dart200 wrote:

keep in mind: all real TMs exist, undecidable machines do not exist. >>>>>

But "Undecidability" isn't about a particular "machine", but about
a general problem, a total MAPPING of the (infinite) set of inputs
to there respective output. It is the statement that there can not
exist a "Program" (as defined by the theory, which are finite
definite algorithms) that can recreate the mapping.

For halting, every given program is know to either halt or not, the >>>>> problem is to be able to universally give that answer correctly in
finite time. THAT can't be done (universally, i.e. for any possible >>>>> input machine).

see, if we do not have a general halting decider then there must
be some input machine L, which is the first machine in the full
enumeration who's halting semantics cannot be decided up for some >>>>>> kind of semantics (like halting).

No, it means that for every machine in that enumeration, there is a >>>>> machine that it will give a wrong answer to (or fail to answer), and >>>>

let me boil this down:

all "proven" examples of what are actually hypothetical machines
that could not be decided upon, not only do not exist, they actually
could not exist... and therefore they *do not* and *will not* come
up in a full enumeration of machines

Where do you see that?

so what is the *real* example of a machine that demonstrably cannot
be decided upon???

That isn't the question, so just a straw man. The issues isn't an
example, but the full question.

if you tell me: look at these hypothetical undecidable machine that
cannot exist, but from that we can just extrapolate *real* forms of
such machines that certainly can exist ... ???

But that isn't what the proofs do.

All you are doing is showing a misunderstanding of the problem.

but like ok, if ur so certain they *must* exist, what is an example
of one???

i'm not buying this whole if hypotheticals can be presented, then
certainly *real* variations of it exist ... where else would
hypothesizing about something just like fucking imply non-
hypothetical forms of it actually exist as real constructs???

And a proof can be made, that for *ANY* machine you can make and want
to claim to be a correct halt decider, I can make a machine and input
to give to it that it will get wrong.

Since I can do that for EVERY machine you make, there can not be a
machine that gets all input correct.

what that input machine is, can very well differ depending on which >>>>> machine in the enumeration you are looking at.

well, first off: all the proofs for undecidability use purely
hypothetical machines, which then are declared to not exist, so
none of those machines could be *real* machine L.

Not "ALL", but the classic one. and the input derived WOULD BE a
real machine if the decider it was built on was an actual machine.

so what is this proposed non-hypothetical *real* machine L that
then cannot be decided?

But that isn't the claim. It isn't that there is a specific machine >>>>> L that can't be decided, and in fact, there can't be such a
machine, as there are two poor deciders, we can all Yes, and No,
that always answer for every input their given answer, ONE of those >>>>> MUST be right, so there can not be a single specific machine that
all get wrong.

That idea is just part of Peter Olcotts stupidity and
misunderstanding.

and could that machine L even exist?

let's say someone found that limit L and demonstrated this
property that it cannot be decided upon by a halting decider ...
but then next step in undecidable proofs is to declare the
machine's non- existence, because an undecidable machine is also
not a deterministic machine, which ultimately contradicts the fact >>>>>> that this limit machine L was suppose to actually *exist*, so how >>>>>> could it ever exist?

and if the limit machine L does not actually exist, then how are
TM semantics not generally decidable???

good god guys, it's so tiring arguing against what is seemingly
irreconcilable nonsense. but bring it on my dudes, how do u think >>>>>> i'm wrong this time???

And your problem he is you are working on the wrong problem,
because "someone" has spewed out so much misinformaiton that he has >>>>> reduced the intelligence of the world.

no bro, please read this carefully: these really are my own thots
that i've mostly developed on my own without much external
validation anywhere. polcott is an interesting character, but we
haven't yet seen eye to eye enough for much influence to happen
either way

Because it seems, you don't understand what the actual problem is, or
how the proof actually work.

unlike polcott, i'm personally not sure what to do about godel's
incompleteness, and i'm not making claims about it because it's just
outside the scope i'm trying to address

So, you don't care about logic that has the power to express the
Natural Numbers?

i'm trying to address the theory of computing, not math as a whole

But the theory of computing is based on logic that can express the
Natural numbers, and thus that part of mathematics comes in.

The problem isn't that some given machine can't be decided if it
halts or not, but that for every machine that claims to be a
decider, there will be an input for which it gives the wrong
answer, or it fails to answers.

i know this is hard to really consider:

what is an example of a *real machine that exists*, where this
behavior demonstrably happens???

Since it is proven that there can't be a correct decider, what are
you asking for?

As I said, for *ANY* "Halt Decider" that you want to try to claim is
universally correct, I can make an input that shows the claim to be
wrong.

Your problem is you have the question backwards. It isn't that there
is a machine that no machine can get the right answer for, as that is
clearly wrong, but there is no machine that can always get the right
answer.

I side affect of this, is that there WILL be machines that we can not
know the answer for, but we can't know if a given machine is one of
them, as knowing that lets you know what the answer is, as the only
unknowable halting state machines are non-halting, as ALL halting
machine can be shown to be halting by just running them till the halt.

sure you can throw around hypothetical examples of undecidable
machines all day long, i've spent a lot of time considering them
myself, probably more than you actually...

And, as I have said, that isn't the concept to consider, as we can't
know that a machine is undecidable.

but like what about a *real* machine, that *actually exists*???

Which is an answer we can never know the answer to (at least
possibly, I am not sure if we can actually prove such an existance,
only its potential to exist)

Now, a side effect of this fact, it becomes true that there exists
some machine/input combinations that we can not know if they halt
or not, but another side effect of this is we can't tell if a given >>>>> machine is one of them, as by definition any machine we can't know
if it halts or not, must be non-halting, as any halting machine can be >>

bruh ... do u not recognize the inherent contradiction in say in all
machines which can't know the halting of ... must therefore be non-
halting???

What is the contradiction in that?

Do you understand the difference between knowABLE, and knowN.

Any machine that halts, can ALWAYS be proven it halts by running it
enough steps, as there must be some finite number of steps to run it
till it halts, as that is the DEFINITION of Halting, and a finite number
of steps makes a proof that gives knowledge.

like u literally just decided what they all must be after claiming
they are machiens which we cannot know the halting status of ...

Right, but we can't KNOW that we can't know their halting status. All we
can know is we haven't found the status YET. Not knowN can be either
halting or non-halting, halting if we haven't run it yet.

proven to halt, just by running it for enough steps.

honestly richard, i think i just stumbled right into a core
contradiction baked into the theory of computing that has gone
almost entirely unnoticed besides a few "cranks" on the internet,

none of which have put it so succinctly like i've done so in the
last day

No, the problem is you keep on looking for that which the theory says
is unknowable. We can show that there are machines that we can not
know the halting property of, but we can never know if a machine is
in that class.

We can know that no machine can be a correct decider, as for any
claimed decider, we can show an input that it gets wrong. Thus no
universally correct deciders, which IS the question possed by the
problem.

One way of looking at this, is we can take all machines, and we know
that they must fall into exactly 2 categories
Halting or
Non-Halting,

But ore knowledge of them divdes them into three categories:

Known Halting,
Known Non-Halting, or
Unknown Halting Status.

And this last category we know can consist of machines in 3 categories
(but we don't know which for a given machine):
Yet-to-be-known, but Knowable, Halting
Yet-to-be-known, but Knowable, Non-Halting
Not Knowable Non-Halting.

All Halting machines are Knowable, even if not-yet known, as running
them enough (but for a still finite number of steps) will reach the halt state, and thus it not yet being know is just because we haven't run it
far enough.

For the Yet-to-be-know but Knowable Non-Halting Machines, there exists a proof, to be discovered, that proves that it will not halt.

For the Unknowable machines, they can't be Halting, as we showed that
all halting machines are knowable by just running them long enough.
There is nothing that says we must be able to find a proof of non-
halting, and the fact that Halting is non-decidable seems to imply that
this category can't be empty, or our decider just needs to apply the appropriate proof of non-halting to correctly decide. The fact that
there are an infinite number of possible proofs may allow this category
to be empty, but I am not sure you can prove that.

As I point out, It can't be possible to prove that a machine is in this unknowable category, as only non-halting machines can be unknowable, and thus a proof that a machine is in this category can't be correct, or the whole logic system is proven inconsistant. This is similar to the point
that Godel uses in his incompleteness proof, as if you could prove the sentence true, that proof creates the counter example that makes the sentence false, thus no proof can exist.

great so u've ended up in the situation of certainly believing in
"unknowable" (yet certainly non-halting) machines,

that you can't even prove exist,

except for apparent demonstration with hypothetical machines that then
can't even exist,

i... just...

/that is fucking crazy bro/

*there has to be some machine L at which "unknowability" can be pointed
to*, why?? because we can partially decide this function, then there
must be some maximally partial decidable, and with that there *must* be
some *real* *existent* machine L which that maximally partial
decidability "breaks down" and cannot be decided upon!

if ur theory can't tolerate that, THEN ITS BROKEN NUMBNUTS

which it can't because if u could point that machine L, then according
to u we'd know it was a non-halting machine, which contradicts it being machine L. so machine L, the first point were maximum decidability
breaks down can't even be known!

you can't even tell me what form a machine looks like when it's
unknowable, because none of the arguments for undecidable machines
utilize machines *that actually exist*, and furthermore, if u could
point to one of these "unknowable" machines it would cease to be
unknowable!!

i'm sorry, this is like fucking believing in mathematical ghosts bro,

LOGIC HAS LEFT THE DISCUSSION
--
a burnt out swe investigating into why our tooling doesn't involve
basic semantic proofs like halting analysis

please excuse my pseudo-pyscript,

~ nick
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 12/7/25 4:59 PM, dart200 wrote:

On 12/6/25 2:21 PM, Richard Damon wrote:

On 12/6/25 4:41 PM, dart200 wrote:

On 12/6/25 10:44 AM, Richard Damon wrote:

On 12/6/25 2:34 AM, dart200 wrote:

On 12/5/25 5:31 PM, Richard Damon wrote:

On 12/4/25 3:22 AM, dart200 wrote:

keep in mind: all real TMs exist, undecidable machines do not exist. >>>>>>

But "Undecidability" isn't about a particular "machine", but about >>>>>> a general problem, a total MAPPING of the (infinite) set of inputs >>>>>> to there respective output. It is the statement that there can not >>>>>> exist a "Program" (as defined by the theory, which are finite
definite algorithms) that can recreate the mapping.

For halting, every given program is know to either halt or not,
the problem is to be able to universally give that answer
correctly in finite time. THAT can't be done (universally, i.e.
for any possible input machine).

see, if we do not have a general halting decider then there must >>>>>>> be some input machine L, which is the first machine in the full >>>>>>> enumeration who's halting semantics cannot be decided up for some >>>>>>> kind of semantics (like halting).

No, it means that for every machine in that enumeration, there is >>>>>> a machine that it will give a wrong answer to (or fail to answer), >>>>>> and

let me boil this down:

all "proven" examples of what are actually hypothetical machines
that could not be decided upon, not only do not exist, they
actually could not exist... and therefore they *do not* and *will
not* come up in a full enumeration of machines

Where do you see that?

so what is the *real* example of a machine that demonstrably cannot >>>>> be decided upon???

That isn't the question, so just a straw man. The issues isn't an
example, but the full question.

if you tell me: look at these hypothetical undecidable machine that >>>>> cannot exist, but from that we can just extrapolate *real* forms of >>>>> such machines that certainly can exist ... ???

But that isn't what the proofs do.

All you are doing is showing a misunderstanding of the problem.

but like ok, if ur so certain they *must* exist, what is an example >>>>> of one???

i'm not buying this whole if hypotheticals can be presented, then
certainly *real* variations of it exist ... where else would
hypothesizing about something just like fucking imply non-
hypothetical forms of it actually exist as real constructs???

And a proof can be made, that for *ANY* machine you can make and
want to claim to be a correct halt decider, I can make a machine and
input to give to it that it will get wrong.

Since I can do that for EVERY machine you make, there can not be a
machine that gets all input correct.

what that input machine is, can very well differ depending on
which machine in the enumeration you are looking at.

well, first off: all the proofs for undecidability use purely
hypothetical machines, which then are declared to not exist, so >>>>>>> none of those machines could be *real* machine L.

Not "ALL", but the classic one. and the input derived WOULD BE a
real machine if the decider it was built on was an actual machine. >>>>>>

so what is this proposed non-hypothetical *real* machine L that >>>>>>> then cannot be decided?

But that isn't the claim. It isn't that there is a specific
machine L that can't be decided, and in fact, there can't be such >>>>>> a machine, as there are two poor deciders, we can all Yes, and No, >>>>>> that always answer for every input their given answer, ONE of
those MUST be right, so there can not be a single specific machine >>>>>> that all get wrong.

That idea is just part of Peter Olcotts stupidity and
misunderstanding.

and could that machine L even exist?

let's say someone found that limit L and demonstrated this
property that it cannot be decided upon by a halting decider ... >>>>>>> but then next step in undecidable proofs is to declare the
machine's non- existence, because an undecidable machine is also >>>>>>> not a deterministic machine, which ultimately contradicts the
fact that this limit machine L was suppose to actually *exist*, >>>>>>> so how could it ever exist?

and if the limit machine L does not actually exist, then how are >>>>>>> TM semantics not generally decidable???

good god guys, it's so tiring arguing against what is seemingly >>>>>>> irreconcilable nonsense. but bring it on my dudes, how do u think >>>>>>> i'm wrong this time???

And your problem he is you are working on the wrong problem,
because "someone" has spewed out so much misinformaiton that he
has reduced the intelligence of the world.

no bro, please read this carefully: these really are my own thots
that i've mostly developed on my own without much external
validation anywhere. polcott is an interesting character, but we
haven't yet seen eye to eye enough for much influence to happen
either way

Because it seems, you don't understand what the actual problem is,
or how the proof actually work.

unlike polcott, i'm personally not sure what to do about godel's
incompleteness, and i'm not making claims about it because it's
just outside the scope i'm trying to address

So, you don't care about logic that has the power to express the
Natural Numbers?

i'm trying to address the theory of computing, not math as a whole

But the theory of computing is based on logic that can express the
Natural numbers, and thus that part of mathematics comes in.

The problem isn't that some given machine can't be decided if it
halts or not, but that for every machine that claims to be a
decider, there will be an input for which it gives the wrong
answer, or it fails to answers.

i know this is hard to really consider:

what is an example of a *real machine that exists*, where this
behavior demonstrably happens???

Since it is proven that there can't be a correct decider, what are
you asking for?

As I said, for *ANY* "Halt Decider" that you want to try to claim is
universally correct, I can make an input that shows the claim to be
wrong.

Your problem is you have the question backwards. It isn't that there
is a machine that no machine can get the right answer for, as that
is clearly wrong, but there is no machine that can always get the
right answer.

I side affect of this, is that there WILL be machines that we can
not know the answer for, but we can't know if a given machine is one
of them, as knowing that lets you know what the answer is, as the
only unknowable halting state machines are non-halting, as ALL
halting machine can be shown to be halting by just running them till
the halt.

sure you can throw around hypothetical examples of undecidable
machines all day long, i've spent a lot of time considering them
myself, probably more than you actually...

And, as I have said, that isn't the concept to consider, as we can't
know that a machine is undecidable.

but like what about a *real* machine, that *actually exists*???

Which is an answer we can never know the answer to (at least
possibly, I am not sure if we can actually prove such an existance,
only its potential to exist)

Now, a side effect of this fact, it becomes true that there exists >>>>>> some machine/input combinations that we can not know if they halt >>>>>> or not, but another side effect of this is we can't tell if a
given machine is one of them, as by definition any machine we
can't know if it halts or not, must be non-halting, as any halting >>>>>> machine can be

bruh ... do u not recognize the inherent contradiction in say in all
machines which can't know the halting of ... must therefore be non-
halting???

What is the contradiction in that?

Do you understand the difference between knowABLE, and knowN.

Any machine that halts, can ALWAYS be proven it halts by running it
enough steps, as there must be some finite number of steps to run it
till it halts, as that is the DEFINITION of Halting, and a finite
number of steps makes a proof that gives knowledge.

like u literally just decided what they all must be after claiming
they are machiens which we cannot know the halting status of ...

Right, but we can't KNOW that we can't know their halting status. All
we can know is we haven't found the status YET. Not knowN can be
either halting or non-halting, halting if we haven't run it yet.

proven to halt, just by running it for enough steps.

honestly richard, i think i just stumbled right into a core
contradiction baked into the theory of computing that has gone
almost entirely unnoticed besides a few "cranks" on the internet,

none of which have put it so succinctly like i've done so in the
last day

No, the problem is you keep on looking for that which the theory
says is unknowable. We can show that there are machines that we can
not know the halting property of, but we can never know if a machine
is in that class.

We can know that no machine can be a correct decider, as for any
claimed decider, we can show an input that it gets wrong. Thus no
universally correct deciders, which IS the question possed by the
problem.

One way of looking at this, is we can take all machines, and we know
that they must fall into exactly 2 categories
Halting or
Non-Halting,

But ore knowledge of them divdes them into three categories:

Known Halting,
Known Non-Halting, or
Unknown Halting Status.

And this last category we know can consist of machines in 3 categories
(but we don't know which for a given machine):
Yet-to-be-known, but Knowable, Halting
Yet-to-be-known, but Knowable, Non-Halting
Not Knowable Non-Halting.

All Halting machines are Knowable, even if not-yet known, as running
them enough (but for a still finite number of steps) will reach the
halt state, and thus it not yet being know is just because we haven't
run it far enough.

For the Yet-to-be-know but Knowable Non-Halting Machines, there exists
a proof, to be discovered, that proves that it will not halt.

For the Unknowable machines, they can't be Halting, as we showed that
all halting machines are knowable by just running them long enough.
There is nothing that says we must be able to find a proof of non-
halting, and the fact that Halting is non-decidable seems to imply
that this category can't be empty, or our decider just needs to apply
the appropriate proof of non-halting to correctly decide. The fact
that there are an infinite number of possible proofs may allow this
category to be empty, but I am not sure you can prove that.

As I point out, It can't be possible to prove that a machine is in
this unknowable category, as only non-halting machines can be
unknowable, and thus a proof that a machine is in this category can't
be correct, or the whole logic system is proven inconsistant. This is
similar to the point that Godel uses in his incompleteness proof, as
if you could prove the sentence true, that proof creates the counter
example that makes the sentence false, thus no proof can exist.

great so u've ended up in the situation of certainly believing in "unknowable" (yet certainly non-halting) machines,

that you can't even prove exist,

I don't need to prove they exist, as that isn't what the problem is
talking about.

Undecidabiity just means that you can't make a decider that gets all the answers right, and THAT is fully provable with a simple proof.

The meta-logic to show that there exists some machines that we CAN'T
know, is a different problem, and much more complicated.

except for apparent demonstration with hypothetical machines that then
can't even exist,

i... just...

/that is fucking crazy bro/

It is the reasonable outcome of the fact that is reasonable to prove,
that there can never be a machine that decides all input correctly, and
thus the Halting Problem is undecidable.

*there has to be some machine L at which "unknowability" can be pointed
to*, why?? because we can partially decide this function, then there
must be some maximally partial decidable, and with that there *must* be
some *real* *existent* machine L which that maximally partial
decidability "breaks down" and cannot be decided upon!

Nope. To prove that it is undecidable, you just need to prove that no
decider gets all answers right.

It is theoretically conceivable that there could be a proof that can be discovered, but only after a potentially infinite search, for every machine.

if ur theory can't tolerate that, THEN ITS BROKEN NUMBNUTS

My theory can't tolerate what? That we might be able to know the answer
to every possible instance, but that knowledge can't come from a finite machine?

which it can't because if u could point that machine L, then according
to u we'd know it was a non-halting machine, which contradicts it being machine L. so machine L, the first point were maximum decidability
breaks down can't even be known!

Right, we can't possible KNOW that a given machine is unknowable. As the meta-information defines the value of the question.

Nothing wrong with that, it is just a property of unknowable things.

you can't even tell me what form a machine looks like when it's
unknowable, because none of the arguments for undecidable machines
utilize machines *that actually exist*, and furthermore, if u could
point to one of these "unknowable" machines it would cease to be unknowable!!

So? You seem to be hung up on the side issue of the existance of
unkmowable machines. We CAN say some things about their behavior, just
not enough to know if a given machine is unknowable. This just comes
from the incompleteness of logic in powerful enough systems.

i'm sorry, this is like fucking believing in mathematical ghosts bro,

LOGIC HAS LEFT THE DISCUSSION

Only for you. it seems you just can't handle talking about things that
are unknowable. By their nature, logic can't tell us much about them,
only if the can/might exists. We know that there MUST be statements that
are unprovable in truth value, and from more advance proofs, that even
as we go down layers of meta-logic that might be able to prove some statements, there will ALWAYS be some statements that are unprovable,
and if they are unprovable in ALL systems, they are unknowable.
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From Newsgroup: comp.theory

On 12/7/25 4:32 PM, Chris M. Thomasson wrote:

On 12/6/2025 7:07 PM, Richard Damon wrote:

On 12/6/25 7:57 PM, Chris M. Thomasson wrote:

On 12/6/2025 2:21 PM, Richard Damon wrote:
[...]

Think of a program that can sometimes halt, other times never halt.

If that is for the same, it isn't a "Program" (aka an algorithm) in
Computation Theory, whicb is what "Decidability" is defined in.

I thought my fuzzer was an algorithm that Computation Theory can handle.

Nope, as it has an non-determinism/non-input that affects its behavior. Computation theory is about the mapping of input to output, so any non-determinism or dependency of a "non-input" isn't allowed, as the
machine no longer "compute" a mapping.

There ARE variants of computation theory that handles such machines, but
not about individual runs, but about the collection of all runs. They
"branch" the path at each non-deterministic point, and look at the final result, using a couple of different criteria.

Some ask if ANY path halts, if so the machine is considered Halting.

Some ask if ALL paths eventually halt, and that is required to be
halting, if it might not ever halt with a non-vanishing probability,
then it is non-halting.

Some determine the probability of each of the final states (or
non-halting) and that distribution is the answer.

Single runs of non-deterministic machines just are not considered
interesting for the theory.

1 HOME
5 PRINT "ct_dr_fuzz lol. ;^)"
6 P0 = 0
7 P1 = 0

10 REM Fuzzer... ;^)
20 A$ = "NOPE!"
30 IF RND(1) < .5 THEN A$ = "YES"

100 REM INPUT "Shall DD halt or not? " ; A$
110 PRINT "Shall DD halt or not? " ; A$
200 IF A$ = "YES" GOTO 666
300 P0 = P0 + 1
400 IF P0 > 0 AND P1 > 0 GOTO 1000
500 GOTO 10

666 PRINT "OK!"
667 P1 = P1 + 1
700 PRINT "NON_HALT P0 = "; P0
710 PRINT "HALT P1 = "; P1
720 IF P0 > 0 AND P1 > 0 GOTO 1000
730 PRINT "ALL PATHS FAILED TO BE HIT!"
740 GOTO 10

1000 REM Fin
1010 PRINT "FIN... All paths hit."
1020 PRINT "NON_HALT P0 = "; P0
1030 PRINT "HALT P1 = "; P1

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From Newsgroup: comp.theory

On 12/7/25 2:41 PM, Richard Damon wrote:

On 12/7/25 4:59 PM, dart200 wrote:

On 12/6/25 2:21 PM, Richard Damon wrote:

On 12/6/25 4:41 PM, dart200 wrote:

On 12/6/25 10:44 AM, Richard Damon wrote:

On 12/6/25 2:34 AM, dart200 wrote:

On 12/5/25 5:31 PM, Richard Damon wrote:

On 12/4/25 3:22 AM, dart200 wrote:

keep in mind: all real TMs exist, undecidable machines do not >>>>>>>> exist.

But "Undecidability" isn't about a particular "machine", but
about a general problem, a total MAPPING of the (infinite) set of >>>>>>> inputs to there respective output. It is the statement that there >>>>>>> can not exist a "Program" (as defined by the theory, which are
finite definite algorithms) that can recreate the mapping.

For halting, every given program is know to either halt or not, >>>>>>> the problem is to be able to universally give that answer
correctly in finite time. THAT can't be done (universally, i.e. >>>>>>> for any possible input machine).

see, if we do not have a general halting decider then there must >>>>>>>> be some input machine L, which is the first machine in the full >>>>>>>> enumeration who's halting semantics cannot be decided up for
some kind of semantics (like halting).

No, it means that for every machine in that enumeration, there is >>>>>>> a machine that it will give a wrong answer to (or fail to
answer), and

let me boil this down:

all "proven" examples of what are actually hypothetical machines
that could not be decided upon, not only do not exist, they
actually could not exist... and therefore they *do not* and *will >>>>>> not* come up in a full enumeration of machines

Where do you see that?

so what is the *real* example of a machine that demonstrably
cannot be decided upon???

That isn't the question, so just a straw man. The issues isn't an
example, but the full question.

if you tell me: look at these hypothetical undecidable machine
that cannot exist, but from that we can just extrapolate *real*
forms of such machines that certainly can exist ... ???

But that isn't what the proofs do.

All you are doing is showing a misunderstanding of the problem.

but like ok, if ur so certain they *must* exist, what is an
example of one???

i'm not buying this whole if hypotheticals can be presented, then >>>>>> certainly *real* variations of it exist ... where else would
hypothesizing about something just like fucking imply non-
hypothetical forms of it actually exist as real constructs???

And a proof can be made, that for *ANY* machine you can make and
want to claim to be a correct halt decider, I can make a machine
and input to give to it that it will get wrong.

Since I can do that for EVERY machine you make, there can not be a
machine that gets all input correct.

what that input machine is, can very well differ depending on
which machine in the enumeration you are looking at.

well, first off: all the proofs for undecidability use purely >>>>>>>> hypothetical machines, which then are declared to not exist, so >>>>>>>> none of those machines could be *real* machine L.

Not "ALL", but the classic one. and the input derived WOULD BE a >>>>>>> real machine if the decider it was built on was an actual machine. >>>>>>>

so what is this proposed non-hypothetical *real* machine L that >>>>>>>> then cannot be decided?

But that isn't the claim. It isn't that there is a specific
machine L that can't be decided, and in fact, there can't be such >>>>>>> a machine, as there are two poor deciders, we can all Yes, and
No, that always answer for every input their given answer, ONE of >>>>>>> those MUST be right, so there can not be a single specific
machine that all get wrong.

That idea is just part of Peter Olcotts stupidity and
misunderstanding.

and could that machine L even exist?

let's say someone found that limit L and demonstrated this
property that it cannot be decided upon by a halting decider ... >>>>>>>> but then next step in undecidable proofs is to declare the
machine's non- existence, because an undecidable machine is also >>>>>>>> not a deterministic machine, which ultimately contradicts the >>>>>>>> fact that this limit machine L was suppose to actually *exist*, >>>>>>>> so how could it ever exist?

and if the limit machine L does not actually exist, then how are >>>>>>>> TM semantics not generally decidable???

good god guys, it's so tiring arguing against what is seemingly >>>>>>>> irreconcilable nonsense. but bring it on my dudes, how do u
think i'm wrong this time???

And your problem he is you are working on the wrong problem,
because "someone" has spewed out so much misinformaiton that he >>>>>>> has reduced the intelligence of the world.

no bro, please read this carefully: these really are my own thots >>>>>> that i've mostly developed on my own without much external
validation anywhere. polcott is an interesting character, but we
haven't yet seen eye to eye enough for much influence to happen
either way

Because it seems, you don't understand what the actual problem is,
or how the proof actually work.

unlike polcott, i'm personally not sure what to do about godel's
incompleteness, and i'm not making claims about it because it's
just outside the scope i'm trying to address

So, you don't care about logic that has the power to express the
Natural Numbers?

i'm trying to address the theory of computing, not math as a whole

But the theory of computing is based on logic that can express the
Natural numbers, and thus that part of mathematics comes in.

The problem isn't that some given machine can't be decided if it >>>>>>> halts or not, but that for every machine that claims to be a
decider, there will be an input for which it gives the wrong
answer, or it fails to answers.

i know this is hard to really consider:

what is an example of a *real machine that exists*, where this
behavior demonstrably happens???

Since it is proven that there can't be a correct decider, what are
you asking for?

As I said, for *ANY* "Halt Decider" that you want to try to claim
is universally correct, I can make an input that shows the claim to >>>>> be wrong.

Your problem is you have the question backwards. It isn't that
there is a machine that no machine can get the right answer for, as >>>>> that is clearly wrong, but there is no machine that can always get
the right answer.

I side affect of this, is that there WILL be machines that we can
not know the answer for, but we can't know if a given machine is
one of them, as knowing that lets you know what the answer is, as
the only unknowable halting state machines are non-halting, as ALL
halting machine can be shown to be halting by just running them
till the halt.

sure you can throw around hypothetical examples of undecidable
machines all day long, i've spent a lot of time considering them
myself, probably more than you actually...

And, as I have said, that isn't the concept to consider, as we
can't know that a machine is undecidable.

but like what about a *real* machine, that *actually exists*???

Which is an answer we can never know the answer to (at least
possibly, I am not sure if we can actually prove such an existance, >>>>> only its potential to exist)

Now, a side effect of this fact, it becomes true that there
exists some machine/input combinations that we can not know if
they halt or not, but another side effect of this is we can't
tell if a given machine is one of them, as by definition any
machine we can't know if it halts or not, must be non-halting, as >>>>>>> any halting machine can be

bruh ... do u not recognize the inherent contradiction in say in all
machines which can't know the halting of ... must therefore be non-
halting???

What is the contradiction in that?

Do you understand the difference between knowABLE, and knowN.

Any machine that halts, can ALWAYS be proven it halts by running it
enough steps, as there must be some finite number of steps to run it
till it halts, as that is the DEFINITION of Halting, and a finite
number of steps makes a proof that gives knowledge.

like u literally just decided what they all must be after claiming
they are machiens which we cannot know the halting status of ...

Right, but we can't KNOW that we can't know their halting status. All
we can know is we haven't found the status YET. Not knowN can be
either halting or non-halting, halting if we haven't run it yet.

proven to halt, just by running it for enough steps.

honestly richard, i think i just stumbled right into a core
contradiction baked into the theory of computing that has gone
almost entirely unnoticed besides a few "cranks" on the internet,

none of which have put it so succinctly like i've done so in the
last day

No, the problem is you keep on looking for that which the theory
says is unknowable. We can show that there are machines that we can >>>>> not know the halting property of, but we can never know if a
machine is in that class.

We can know that no machine can be a correct decider, as for any
claimed decider, we can show an input that it gets wrong. Thus no
universally correct deciders, which IS the question possed by the
problem.

One way of looking at this, is we can take all machines, and we know
that they must fall into exactly 2 categories
Halting or
Non-Halting,

But ore knowledge of them divdes them into three categories:

Known Halting,
Known Non-Halting, or
Unknown Halting Status.

And this last category we know can consist of machines in 3
categories (but we don't know which for a given machine):
Yet-to-be-known, but Knowable, Halting
Yet-to-be-known, but Knowable, Non-Halting
Not Knowable Non-Halting.

All Halting machines are Knowable, even if not-yet known, as running
them enough (but for a still finite number of steps) will reach the
halt state, and thus it not yet being know is just because we haven't
run it far enough.

For the Yet-to-be-know but Knowable Non-Halting Machines, there
exists a proof, to be discovered, that proves that it will not halt.

For the Unknowable machines, they can't be Halting, as we showed that
all halting machines are knowable by just running them long enough.
There is nothing that says we must be able to find a proof of non-
halting, and the fact that Halting is non-decidable seems to imply
that this category can't be empty, or our decider just needs to apply
the appropriate proof of non-halting to correctly decide. The fact
that there are an infinite number of possible proofs may allow this
category to be empty, but I am not sure you can prove that.

As I point out, It can't be possible to prove that a machine is in
this unknowable category, as only non-halting machines can be
unknowable, and thus a proof that a machine is in this category can't
be correct, or the whole logic system is proven inconsistant. This is
similar to the point that Godel uses in his incompleteness proof, as
if you could prove the sentence true, that proof creates the counter
example that makes the sentence false, thus no proof can exist.

great so u've ended up in the situation of certainly believing in
"unknowable" (yet certainly non-halting) machines,

that you can't even prove exist,

I don't need to prove they exist, as that isn't what the problem is
talking about.

Undecidabiity just means that you can't make a decider that gets all the answers right, and THAT is fully provable with a simple proof.

The meta-logic to show that there exists some machines that we CAN'T
know, is a different problem, and much more complicated.

except for apparent demonstration with hypothetical machines that then
can't even exist,

i... just...

/that is fucking crazy bro/

It is the reasonable outcome of the fact that is reasonable to prove,
that there can never be a machine that decides all input correctly, and
thus the Halting Problem is undecidable.

*there has to be some machine L at which "unknowability" can be
pointed to*, why?? because we can partially decide this function, then
there must be some maximally partial decidable, and with that there
*must* be some *real* *existent* machine L which that maximally
partial decidability "breaks down" and cannot be decided upon!

Nope. To prove that it is undecidable, you just need to prove that no decider gets all answers right.

It is theoretically conceivable that there could be a proof that can be discovered, but only after a potentially infinite search, for every
machine.

if ur theory can't tolerate that, THEN ITS BROKEN NUMBNUTS

My theory can't tolerate what? That we might be able to know the answer
to every possible instance, but that knowledge can't come from a finite machine?

which it can't because if u could point that machine L, then according
to u we'd know it was a non-halting machine, which contradicts it
being machine L. so machine L, the first point were maximum
decidability breaks down can't even be known!

Right, we can't possible KNOW that a given machine is unknowable. As the meta-information defines the value of the question.

Nothing wrong with that, it is just a property of unknowable things.

you can't even tell me what form a machine looks like when it's
unknowable, because none of the arguments for undecidable machines
utilize machines *that actually exist*, and furthermore, if u could
point to one of these "unknowable" machines it would cease to be
unknowable!!

So? You seem to be hung up on the side issue of the existance of
unkmowable machines. We CAN say some things about their behavior, just
not enough to know if a given machine is unknowable. This just comes
from the incompleteness of logic in powerful enough systems.

i'm sorry, this is like fucking believing in mathematical ghosts bro,

LOGIC HAS LEFT THE DISCUSSION

Only for you. it seems you just can't handle talking about things that
are unknowable. By their nature, logic can't tell us much about them,
only if the can/might exists. We know that there MUST be statements that
are unprovable in truth value, and from more advance proofs, that even
as we go down layers of meta-logic that might be able to prove some statements, there will ALWAYS be some statements that are unprovable,
and if they are unprovable in ALL systems, they are unknowable.

yah bro u keep going on about those unknowable limits to decidability
that u can't even point to a *real* example of because being able to do
so would contradict the premise that this unknowable limit even exists
in the first place!

god damn bro
--
a burnt out swe investigating into why our tooling doesn't involve
basic semantic proofs like halting analysis

please excuse my pseudo-pyscript,

~ nick
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From Newsgroup: comp.theory

On 06/12/2025 17:00, olcott wrote:

As my signature line now stipulates
My 28 year goal has been to make
"true on the basis of meaning" computable.

Do you really mean "truthy" on the basis of meaning?
I'd argue "true on the basis of meaning" can only every be truthy, but
"truthy on the basis of meaning" could, perhaps, become true.
--
Tristan Wibberley

The message body is Copyright (C) 2025 Tristan Wibberley except
citations and quotations noted. All Rights Reserved except that you may,
of course, cite it academically giving credit to me, distribute it
verbatim as part of a usenet system or its archives, and use it to
promote my greatness and general superiority without misrepresentation
of my opinions other than my opinion of my greatness and general
superiority which you _may_ misrepresent. You definitely MAY NOT train
any production AI system with it but you may train experimental AI that
will only be used for evaluation of the AI methods it implements.

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From Newsgroup: comp.theory

dart200 <user7160@newsgrouper.org.invalid> writes:

keep in mind: all real TMs exist, undecidable machines do not exist.

Is a "real TM" any different to a TM? If so, on what way? What is an undecidable machine (or, for that matter, a decidable machine)? I can't
keep this in mind if I don't know what your terms mean.

see, if we do not have a general halting decider then there must be some input machine L, which is the first machine in the full enumeration who's halting semantics cannot be decided up for some kind of semantics (like halting).

The theory of desirability is all about sets. Sets are or are not
decidable. The set of TMs that halt (on, say, an empty tape) is not
decidable, for example. Unless you choose to use conventional terms or
define some new terms precisely, you will just be writing
technical-sounding nonsense.

well, first off: all the proofs for undecidability use purely hypothetical machines, which then are declared to not exist, so none of those machines could be *real* machine L.

I very much doubt you know all the proofs about undecidability. I doubt
you know even all the proofs of the undecidability of the set of halting
TMs. I don't.

so what is this proposed non-hypothetical *real* machine L that then cannot be decided?

See above. What is a real TM as opposed to a TM as usually defined?

and could that machine L even exist?

Does any TM exist? TMs are, after all, just mathematical objects. If
you accept that mathematical objects (like the set of primes) exist,
then every TM exists.

let's say someone found that limit L and demonstrated this property that it cannot be decided upon by a halting decider ... but then next step in undecidable proofs is to declare the machine's non-existence, because an undecidable machine is also not a deterministic machine, which ultimately contradicts the fact that this limit machine L was suppose to actually *exist*, so how could it ever exist?

You might want to read some more proofs about TMs and halting.

and if the limit machine L does not actually exist, then how are TM
semantics not generally decidable???

good god guys, it's so tiring arguing against what is seemingly irreconcilable nonsense. but bring it on my dudes, how do u think i'm wrong this time???

I sympathise. But I get tired with people who don't define their terms
and argue about a topic they don't appear to have studied.
--
Ben.
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From Newsgroup: comp.theory

On 12/7/25 6:21 PM, dart200 wrote:

On 12/7/25 2:41 PM, Richard Damon wrote:

On 12/7/25 4:59 PM, dart200 wrote:

On 12/6/25 2:21 PM, Richard Damon wrote:

On 12/6/25 4:41 PM, dart200 wrote:

On 12/6/25 10:44 AM, Richard Damon wrote:

On 12/6/25 2:34 AM, dart200 wrote:

On 12/5/25 5:31 PM, Richard Damon wrote:

On 12/4/25 3:22 AM, dart200 wrote:

keep in mind: all real TMs exist, undecidable machines do not >>>>>>>>> exist.

But "Undecidability" isn't about a particular "machine", but
about a general problem, a total MAPPING of the (infinite) set >>>>>>>> of inputs to there respective output. It is the statement that >>>>>>>> there can not exist a "Program" (as defined by the theory, which >>>>>>>> are finite definite algorithms) that can recreate the mapping. >>>>>>>>
For halting, every given program is know to either halt or not, >>>>>>>> the problem is to be able to universally give that answer
correctly in finite time. THAT can't be done (universally, i.e. >>>>>>>> for any possible input machine).

see, if we do not have a general halting decider then there >>>>>>>>> must be some input machine L, which is the first machine in the >>>>>>>>> full enumeration who's halting semantics cannot be decided up >>>>>>>>> for some kind of semantics (like halting).

No, it means that for every machine in that enumeration, there >>>>>>>> is a machine that it will give a wrong answer to (or fail to
answer), and

let me boil this down:

all "proven" examples of what are actually hypothetical machines >>>>>>> that could not be decided upon, not only do not exist, they
actually could not exist... and therefore they *do not* and *will >>>>>>> not* come up in a full enumeration of machines

Where do you see that?

so what is the *real* example of a machine that demonstrably
cannot be decided upon???

That isn't the question, so just a straw man. The issues isn't an >>>>>> example, but the full question.

if you tell me: look at these hypothetical undecidable machine
that cannot exist, but from that we can just extrapolate *real* >>>>>>> forms of such machines that certainly can exist ... ???

But that isn't what the proofs do.

All you are doing is showing a misunderstanding of the problem.

but like ok, if ur so certain they *must* exist, what is an
example of one???

i'm not buying this whole if hypotheticals can be presented, then >>>>>>> certainly *real* variations of it exist ... where else would
hypothesizing about something just like fucking imply non-
hypothetical forms of it actually exist as real constructs???

And a proof can be made, that for *ANY* machine you can make and
want to claim to be a correct halt decider, I can make a machine
and input to give to it that it will get wrong.

Since I can do that for EVERY machine you make, there can not be a >>>>>> machine that gets all input correct.

what that input machine is, can very well differ depending on >>>>>>>> which machine in the enumeration you are looking at.

well, first off: all the proofs for undecidability use purely >>>>>>>>> hypothetical machines, which then are declared to not exist, so >>>>>>>>> none of those machines could be *real* machine L.

Not "ALL", but the classic one. and the input derived WOULD BE a >>>>>>>> real machine if the decider it was built on was an actual machine. >>>>>>>>

so what is this proposed non-hypothetical *real* machine L that >>>>>>>>> then cannot be decided?

But that isn't the claim. It isn't that there is a specific
machine L that can't be decided, and in fact, there can't be
such a machine, as there are two poor deciders, we can all Yes, >>>>>>>> and No, that always answer for every input their given answer, >>>>>>>> ONE of those MUST be right, so there can not be a single
specific machine that all get wrong.

That idea is just part of Peter Olcotts stupidity and
misunderstanding.

and could that machine L even exist?

let's say someone found that limit L and demonstrated this
property that it cannot be decided upon by a halting
decider ... but then next step in undecidable proofs is to
declare the machine's non- existence, because an undecidable >>>>>>>>> machine is also not a deterministic machine, which ultimately >>>>>>>>> contradicts the fact that this limit machine L was suppose to >>>>>>>>> actually *exist*, so how could it ever exist?

and if the limit machine L does not actually exist, then how >>>>>>>>> are TM semantics not generally decidable???

good god guys, it's so tiring arguing against what is seemingly >>>>>>>>> irreconcilable nonsense. but bring it on my dudes, how do u >>>>>>>>> think i'm wrong this time???

And your problem he is you are working on the wrong problem,
because "someone" has spewed out so much misinformaiton that he >>>>>>>> has reduced the intelligence of the world.

no bro, please read this carefully: these really are my own thots >>>>>>> that i've mostly developed on my own without much external
validation anywhere. polcott is an interesting character, but we >>>>>>> haven't yet seen eye to eye enough for much influence to happen >>>>>>> either way

Because it seems, you don't understand what the actual problem is, >>>>>> or how the proof actually work.

unlike polcott, i'm personally not sure what to do about godel's >>>>>>> incompleteness, and i'm not making claims about it because it's >>>>>>> just outside the scope i'm trying to address

So, you don't care about logic that has the power to express the
Natural Numbers?

i'm trying to address the theory of computing, not math as a whole >>>>>>

But the theory of computing is based on logic that can express the >>>>>> Natural numbers, and thus that part of mathematics comes in.

The problem isn't that some given machine can't be decided if it >>>>>>>> halts or not, but that for every machine that claims to be a
decider, there will be an input for which it gives the wrong
answer, or it fails to answers.

i know this is hard to really consider:

what is an example of a *real machine that exists*, where this
behavior demonstrably happens???

Since it is proven that there can't be a correct decider, what are >>>>>> you asking for?

As I said, for *ANY* "Halt Decider" that you want to try to claim >>>>>> is universally correct, I can make an input that shows the claim
to be wrong.

Your problem is you have the question backwards. It isn't that
there is a machine that no machine can get the right answer for,
as that is clearly wrong, but there is no machine that can always >>>>>> get the right answer.

I side affect of this, is that there WILL be machines that we can >>>>>> not know the answer for, but we can't know if a given machine is
one of them, as knowing that lets you know what the answer is, as >>>>>> the only unknowable halting state machines are non-halting, as ALL >>>>>> halting machine can be shown to be halting by just running them
till the halt.

sure you can throw around hypothetical examples of undecidable
machines all day long, i've spent a lot of time considering them >>>>>>> myself, probably more than you actually...

And, as I have said, that isn't the concept to consider, as we
can't know that a machine is undecidable.

but like what about a *real* machine, that *actually exists*???

Which is an answer we can never know the answer to (at least
possibly, I am not sure if we can actually prove such an
existance, only its potential to exist)

Now, a side effect of this fact, it becomes true that there
exists some machine/input combinations that we can not know if >>>>>>>> they halt or not, but another side effect of this is we can't >>>>>>>> tell if a given machine is one of them, as by definition any
machine we can't know if it halts or not, must be non-halting, >>>>>>>> as any halting machine can be

bruh ... do u not recognize the inherent contradiction in say in
all machines which can't know the halting of ... must therefore be
non- halting???

What is the contradiction in that?

Do you understand the difference between knowABLE, and knowN.

Any machine that halts, can ALWAYS be proven it halts by running it
enough steps, as there must be some finite number of steps to run it
till it halts, as that is the DEFINITION of Halting, and a finite
number of steps makes a proof that gives knowledge.

like u literally just decided what they all must be after claiming
they are machiens which we cannot know the halting status of ...

Right, but we can't KNOW that we can't know their halting status.
All we can know is we haven't found the status YET. Not knowN can be
either halting or non-halting, halting if we haven't run it yet.

proven to halt, just by running it for enough steps.

honestly richard, i think i just stumbled right into a core
contradiction baked into the theory of computing that has gone
almost entirely unnoticed besides a few "cranks" on the internet, >>>>>>>
none of which have put it so succinctly like i've done so in the >>>>>>> last day

No, the problem is you keep on looking for that which the theory
says is unknowable. We can show that there are machines that we
can not know the halting property of, but we can never know if a
machine is in that class.

We can know that no machine can be a correct decider, as for any
claimed decider, we can show an input that it gets wrong. Thus no >>>>>> universally correct deciders, which IS the question possed by the >>>>>> problem.

One way of looking at this, is we can take all machines, and we know
that they must fall into exactly 2 categories
Halting or
Non-Halting,

But ore knowledge of them divdes them into three categories:

Known Halting,
Known Non-Halting, or
Unknown Halting Status.

And this last category we know can consist of machines in 3
categories (but we don't know which for a given machine):
Yet-to-be-known, but Knowable, Halting
Yet-to-be-known, but Knowable, Non-Halting
Not Knowable Non-Halting.

All Halting machines are Knowable, even if not-yet known, as running
them enough (but for a still finite number of steps) will reach the
halt state, and thus it not yet being know is just because we
haven't run it far enough.

For the Yet-to-be-know but Knowable Non-Halting Machines, there
exists a proof, to be discovered, that proves that it will not halt.

For the Unknowable machines, they can't be Halting, as we showed
that all halting machines are knowable by just running them long
enough. There is nothing that says we must be able to find a proof
of non- halting, and the fact that Halting is non-decidable seems to
imply that this category can't be empty, or our decider just needs
to apply the appropriate proof of non-halting to correctly decide.
The fact that there are an infinite number of possible proofs may
allow this category to be empty, but I am not sure you can prove that. >>>>
As I point out, It can't be possible to prove that a machine is in
this unknowable category, as only non-halting machines can be
unknowable, and thus a proof that a machine is in this category
can't be correct, or the whole logic system is proven inconsistant.
This is similar to the point that Godel uses in his incompleteness
proof, as if you could prove the sentence true, that proof creates
the counter example that makes the sentence false, thus no proof can
exist.

great so u've ended up in the situation of certainly believing in
"unknowable" (yet certainly non-halting) machines,

that you can't even prove exist,

I don't need to prove they exist, as that isn't what the problem is
talking about.

Undecidabiity just means that you can't make a decider that gets all
the answers right, and THAT is fully provable with a simple proof.

The meta-logic to show that there exists some machines that we CAN'T
know, is a different problem, and much more complicated.

except for apparent demonstration with hypothetical machines that
then can't even exist,

i... just...

/that is fucking crazy bro/

It is the reasonable outcome of the fact that is reasonable to prove,
that there can never be a machine that decides all input correctly,
and thus the Halting Problem is undecidable.

*there has to be some machine L at which "unknowability" can be
pointed to*, why?? because we can partially decide this function,
then there must be some maximally partial decidable, and with that
there *must* be some *real* *existent* machine L which that maximally
partial decidability "breaks down" and cannot be decided upon!

Nope. To prove that it is undecidable, you just need to prove that no
decider gets all answers right.

It is theoretically conceivable that there could be a proof that can
be discovered, but only after a potentially infinite search, for every
machine.

if ur theory can't tolerate that, THEN ITS BROKEN NUMBNUTS

My theory can't tolerate what? That we might be able to know the
answer to every possible instance, but that knowledge can't come from
a finite machine?

which it can't because if u could point that machine L, then
according to u we'd know it was a non-halting machine, which
contradicts it being machine L. so machine L, the first point were
maximum decidability breaks down can't even be known!

Right, we can't possible KNOW that a given machine is unknowable. As
the meta-information defines the value of the question.

Nothing wrong with that, it is just a property of unknowable things.

you can't even tell me what form a machine looks like when it's
unknowable, because none of the arguments for undecidable machines
utilize machines *that actually exist*, and furthermore, if u could
point to one of these "unknowable" machines it would cease to be
unknowable!!

So? You seem to be hung up on the side issue of the existance of
unkmowable machines. We CAN say some things about their behavior, just
not enough to know if a given machine is unknowable. This just comes
from the incompleteness of logic in powerful enough systems.

i'm sorry, this is like fucking believing in mathematical ghosts bro,

LOGIC HAS LEFT THE DISCUSSION

Only for you. it seems you just can't handle talking about things that
are unknowable. By their nature, logic can't tell us much about them,
only if the can/might exists. We know that there MUST be statements
that are unprovable in truth value, and from more advance proofs, that
even as we go down layers of meta-logic that might be able to prove
some statements, there will ALWAYS be some statements that are
unprovable, and if they are unprovable in ALL systems, they are
unknowable.

yah bro u keep going on about those unknowable limits to decidability
that u can't even point to a *real* example of because being able to do
so would contradict the premise that this unknowable limit even exists
in the first place!

god damn bro

Because Turing PROVED that the Halting Problem can't be computed, thus,
the limit exists.

We may not be able to precisely define the line betweem computable and non-computable (or decidable vs non-decidable), but we know it exists as
we have things know to be on both sides.

We have a number of general propositions that have been proven to be uncomputable/undecidable, like the Halting Problem.

When we narrow the question to a specific machine, that machine can fall
into 3 camps.

Known to Halt.
Known to Never Halt.
Unknown in behavior (but we know it will either halt of not).

The question of knowABILITY is tougher, as it is easy to prove we know
an answer (if we do) as knowing the answer shows it is knowable.

Showing that some things might be knowable but not currently know is
possible, but that does NOT mean we can answer the knowability question
for all things that are knowable.

Why are you so stuck in the fact that between the domain of the
decidable and the undeciable there is a band of "we don't know" that
might contain some things that "we can't know".

This is part of the problem of working in infinite spaces, you can
always end up with a piece you don't know about.
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From Newsgroup: comp.theory

On 12/7/2025 7:26 PM, Tristan Wibberley wrote:

On 06/12/2025 17:00, olcott wrote:

As my signature line now stipulates
My 28 year goal has been to make
"true on the basis of meaning" computable.

Do you really mean "truthy" on the basis of meaning?
I'd argue "true on the basis of meaning" can only every be truthy, but "truthy on the basis of meaning" could, perhaps, become true.

In other words we cannot be certain
that the integer five is a number?
--
Copyright 2025 Olcott<br><br>

My 28 year goal has been to make <br>
"true on the basis of meaning" computable.<br><br>

This required establishing a new foundation<br>
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From Newsgroup: comp.theory

On 12/7/25 6:42 PM, Richard Damon wrote:

On 12/7/25 6:21 PM, dart200 wrote:

On 12/7/25 2:41 PM, Richard Damon wrote:

On 12/7/25 4:59 PM, dart200 wrote:

On 12/6/25 2:21 PM, Richard Damon wrote:

On 12/6/25 4:41 PM, dart200 wrote:

On 12/6/25 10:44 AM, Richard Damon wrote:

On 12/6/25 2:34 AM, dart200 wrote:

On 12/5/25 5:31 PM, Richard Damon wrote:

On 12/4/25 3:22 AM, dart200 wrote:

keep in mind: all real TMs exist, undecidable machines do not >>>>>>>>>> exist.

But "Undecidability" isn't about a particular "machine", but >>>>>>>>> about a general problem, a total MAPPING of the (infinite) set >>>>>>>>> of inputs to there respective output. It is the statement that >>>>>>>>> there can not exist a "Program" (as defined by the theory,
which are finite definite algorithms) that can recreate the >>>>>>>>> mapping.

For halting, every given program is know to either halt or not, >>>>>>>>> the problem is to be able to universally give that answer
correctly in finite time. THAT can't be done (universally, i.e. >>>>>>>>> for any possible input machine).

see, if we do not have a general halting decider then there >>>>>>>>>> must be some input machine L, which is the first machine in >>>>>>>>>> the full enumeration who's halting semantics cannot be decided >>>>>>>>>> up for some kind of semantics (like halting).

No, it means that for every machine in that enumeration, there >>>>>>>>> is a machine that it will give a wrong answer to (or fail to >>>>>>>>> answer), and

let me boil this down:

all "proven" examples of what are actually hypothetical machines >>>>>>>> that could not be decided upon, not only do not exist, they
actually could not exist... and therefore they *do not* and
*will not* come up in a full enumeration of machines

Where do you see that?

so what is the *real* example of a machine that demonstrably
cannot be decided upon???

That isn't the question, so just a straw man. The issues isn't an >>>>>>> example, but the full question.

if you tell me: look at these hypothetical undecidable machine >>>>>>>> that cannot exist, but from that we can just extrapolate *real* >>>>>>>> forms of such machines that certainly can exist ... ???

But that isn't what the proofs do.

All you are doing is showing a misunderstanding of the problem.

but like ok, if ur so certain they *must* exist, what is an
example of one???

i'm not buying this whole if hypotheticals can be presented,
then certainly *real* variations of it exist ... where else
would hypothesizing about something just like fucking imply non- >>>>>>>> hypothetical forms of it actually exist as real constructs???

And a proof can be made, that for *ANY* machine you can make and >>>>>>> want to claim to be a correct halt decider, I can make a machine >>>>>>> and input to give to it that it will get wrong.

Since I can do that for EVERY machine you make, there can not be >>>>>>> a machine that gets all input correct.

what that input machine is, can very well differ depending on >>>>>>>>> which machine in the enumeration you are looking at.

well, first off: all the proofs for undecidability use purely >>>>>>>>>> hypothetical machines, which then are declared to not exist, >>>>>>>>>> so none of those machines could be *real* machine L.

Not "ALL", but the classic one. and the input derived WOULD BE >>>>>>>>> a real machine if the decider it was built on was an actual >>>>>>>>> machine.

so what is this proposed non-hypothetical *real* machine L >>>>>>>>>> that then cannot be decided?

But that isn't the claim. It isn't that there is a specific >>>>>>>>> machine L that can't be decided, and in fact, there can't be >>>>>>>>> such a machine, as there are two poor deciders, we can all Yes, >>>>>>>>> and No, that always answer for every input their given answer, >>>>>>>>> ONE of those MUST be right, so there can not be a single
specific machine that all get wrong.

That idea is just part of Peter Olcotts stupidity and
misunderstanding.

and could that machine L even exist?

let's say someone found that limit L and demonstrated this >>>>>>>>>> property that it cannot be decided upon by a halting
decider ... but then next step in undecidable proofs is to >>>>>>>>>> declare the machine's non- existence, because an undecidable >>>>>>>>>> machine is also not a deterministic machine, which ultimately >>>>>>>>>> contradicts the fact that this limit machine L was suppose to >>>>>>>>>> actually *exist*, so how could it ever exist?

and if the limit machine L does not actually exist, then how >>>>>>>>>> are TM semantics not generally decidable???

good god guys, it's so tiring arguing against what is
seemingly irreconcilable nonsense. but bring it on my dudes, >>>>>>>>>> how do u think i'm wrong this time???

And your problem he is you are working on the wrong problem, >>>>>>>>> because "someone" has spewed out so much misinformaiton that he >>>>>>>>> has reduced the intelligence of the world.

no bro, please read this carefully: these really are my own
thots that i've mostly developed on my own without much external >>>>>>>> validation anywhere. polcott is an interesting character, but we >>>>>>>> haven't yet seen eye to eye enough for much influence to happen >>>>>>>> either way

Because it seems, you don't understand what the actual problem
is, or how the proof actually work.

unlike polcott, i'm personally not sure what to do about godel's >>>>>>>> incompleteness, and i'm not making claims about it because it's >>>>>>>> just outside the scope i'm trying to address

So, you don't care about logic that has the power to express the >>>>>>> Natural Numbers?

i'm trying to address the theory of computing, not math as a whole >>>>>>>

But the theory of computing is based on logic that can express
the Natural numbers, and thus that part of mathematics comes in. >>>>>>>

The problem isn't that some given machine can't be decided if >>>>>>>>> it halts or not, but that for every machine that claims to be a >>>>>>>>> decider, there will be an input for which it gives the wrong >>>>>>>>> answer, or it fails to answers.

i know this is hard to really consider:

what is an example of a *real machine that exists*, where this >>>>>>>> behavior demonstrably happens???

Since it is proven that there can't be a correct decider, what
are you asking for?

As I said, for *ANY* "Halt Decider" that you want to try to claim >>>>>>> is universally correct, I can make an input that shows the claim >>>>>>> to be wrong.

Your problem is you have the question backwards. It isn't that
there is a machine that no machine can get the right answer for, >>>>>>> as that is clearly wrong, but there is no machine that can always >>>>>>> get the right answer.

I side affect of this, is that there WILL be machines that we can >>>>>>> not know the answer for, but we can't know if a given machine is >>>>>>> one of them, as knowing that lets you know what the answer is, as >>>>>>> the only unknowable halting state machines are non-halting, as
ALL halting machine can be shown to be halting by just running
them till the halt.

sure you can throw around hypothetical examples of undecidable >>>>>>>> machines all day long, i've spent a lot of time considering them >>>>>>>> myself, probably more than you actually...

And, as I have said, that isn't the concept to consider, as we
can't know that a machine is undecidable.

but like what about a *real* machine, that *actually exists*??? >>>>>>>

Which is an answer we can never know the answer to (at least
possibly, I am not sure if we can actually prove such an
existance, only its potential to exist)

Now, a side effect of this fact, it becomes true that there >>>>>>>>> exists some machine/input combinations that we can not know if >>>>>>>>> they halt or not, but another side effect of this is we can't >>>>>>>>> tell if a given machine is one of them, as by definition any >>>>>>>>> machine we can't know if it halts or not, must be non-halting, >>>>>>>>> as any halting machine can be

bruh ... do u not recognize the inherent contradiction in say in
all machines which can't know the halting of ... must therefore be >>>>>> non- halting???

What is the contradiction in that?

Do you understand the difference between knowABLE, and knowN.

Any machine that halts, can ALWAYS be proven it halts by running it >>>>> enough steps, as there must be some finite number of steps to run
it till it halts, as that is the DEFINITION of Halting, and a
finite number of steps makes a proof that gives knowledge.

like u literally just decided what they all must be after claiming >>>>>> they are machiens which we cannot know the halting status of ...

Right, but we can't KNOW that we can't know their halting status.
All we can know is we haven't found the status YET. Not knowN can
be either halting or non-halting, halting if we haven't run it yet.

proven to halt, just by running it for enough steps.

honestly richard, i think i just stumbled right into a core
contradiction baked into the theory of computing that has gone >>>>>>>> almost entirely unnoticed besides a few "cranks" on the internet, >>>>>>>>
none of which have put it so succinctly like i've done so in the >>>>>>>> last day

No, the problem is you keep on looking for that which the theory >>>>>>> says is unknowable. We can show that there are machines that we >>>>>>> can not know the halting property of, but we can never know if a >>>>>>> machine is in that class.

We can know that no machine can be a correct decider, as for any >>>>>>> claimed decider, we can show an input that it gets wrong. Thus no >>>>>>> universally correct deciders, which IS the question possed by the >>>>>>> problem.

One way of looking at this, is we can take all machines, and we
know that they must fall into exactly 2 categories
Halting or
Non-Halting,

But ore knowledge of them divdes them into three categories:

Known Halting,
Known Non-Halting, or
Unknown Halting Status.

And this last category we know can consist of machines in 3
categories (but we don't know which for a given machine):
Yet-to-be-known, but Knowable, Halting
Yet-to-be-known, but Knowable, Non-Halting
Not Knowable Non-Halting.

All Halting machines are Knowable, even if not-yet known, as
running them enough (but for a still finite number of steps) will
reach the halt state, and thus it not yet being know is just
because we haven't run it far enough.

For the Yet-to-be-know but Knowable Non-Halting Machines, there
exists a proof, to be discovered, that proves that it will not halt. >>>>>
For the Unknowable machines, they can't be Halting, as we showed
that all halting machines are knowable by just running them long
enough. There is nothing that says we must be able to find a proof
of non- halting, and the fact that Halting is non-decidable seems
to imply that this category can't be empty, or our decider just
needs to apply the appropriate proof of non-halting to correctly
decide. The fact that there are an infinite number of possible
proofs may allow this category to be empty, but I am not sure you
can prove that.

As I point out, It can't be possible to prove that a machine is in
this unknowable category, as only non-halting machines can be
unknowable, and thus a proof that a machine is in this category
can't be correct, or the whole logic system is proven inconsistant. >>>>> This is similar to the point that Godel uses in his incompleteness
proof, as if you could prove the sentence true, that proof creates
the counter example that makes the sentence false, thus no proof
can exist.

great so u've ended up in the situation of certainly believing in
"unknowable" (yet certainly non-halting) machines,

that you can't even prove exist,

I don't need to prove they exist, as that isn't what the problem is
talking about.

Undecidabiity just means that you can't make a decider that gets all
the answers right, and THAT is fully provable with a simple proof.

The meta-logic to show that there exists some machines that we CAN'T
know, is a different problem, and much more complicated.

except for apparent demonstration with hypothetical machines that
then can't even exist,

i... just...

/that is fucking crazy bro/

It is the reasonable outcome of the fact that is reasonable to prove,
that there can never be a machine that decides all input correctly,
and thus the Halting Problem is undecidable.

*there has to be some machine L at which "unknowability" can be
pointed to*, why?? because we can partially decide this function,
then there must be some maximally partial decidable, and with that
there *must* be some *real* *existent* machine L which that
maximally partial decidability "breaks down" and cannot be decided
upon!

Nope. To prove that it is undecidable, you just need to prove that no
decider gets all answers right.

It is theoretically conceivable that there could be a proof that can
be discovered, but only after a potentially infinite search, for
every machine.

if ur theory can't tolerate that, THEN ITS BROKEN NUMBNUTS

My theory can't tolerate what? That we might be able to know the
answer to every possible instance, but that knowledge can't come from
a finite machine?

which it can't because if u could point that machine L, then
according to u we'd know it was a non-halting machine, which
contradicts it being machine L. so machine L, the first point were
maximum decidability breaks down can't even be known!

Right, we can't possible KNOW that a given machine is unknowable. As
the meta-information defines the value of the question.

Nothing wrong with that, it is just a property of unknowable things.

you can't even tell me what form a machine looks like when it's
unknowable, because none of the arguments for undecidable machines
utilize machines *that actually exist*, and furthermore, if u could
point to one of these "unknowable" machines it would cease to be
unknowable!!

So? You seem to be hung up on the side issue of the existance of
unkmowable machines. We CAN say some things about their behavior,
just not enough to know if a given machine is unknowable. This just
comes from the incompleteness of logic in powerful enough systems.

i'm sorry, this is like fucking believing in mathematical ghosts bro,

LOGIC HAS LEFT THE DISCUSSION

Only for you. it seems you just can't handle talking about things
that are unknowable. By their nature, logic can't tell us much about
them, only if the can/might exists. We know that there MUST be
statements that are unprovable in truth value, and from more advance
proofs, that even as we go down layers of meta-logic that might be
able to prove some statements, there will ALWAYS be some statements
that are unprovable, and if they are unprovable in ALL systems, they
are unknowable.

yah bro u keep going on about those unknowable limits to decidability
that u can't even point to a *real* example of because being able to
do so would contradict the premise that this unknowable limit even
exists in the first place!

god damn bro

Because Turing PROVED that the Halting Problem can't be computed, thus,
the limit exists.

We may not be able to precisely define the line betweem computable and non-computable (or decidable vs non-decidable), but we know it exists as
we have things know to be on both sides.

We have a number of general propositions that have been proven to be uncomputable/undecidable, like the Halting Problem.

When we narrow the question to a specific machine, that machine can fall into 3 camps.

Known to Halt.
Known to Never Halt.
Unknown in behavior (but we know it will either halt of not).

The question of knowABILITY is tougher, as it is easy to prove we know
an answer (if we do) as knowing the answer shows it is knowable.

Showing that some things might be knowable but not currently know is possible, but that does NOT mean we can answer the knowability question
for all things that are knowable.

Why are you so stuck in the fact that between the domain of the
decidable and the undeciable there is a band of "we don't know" that
might contain some things that "we can't know".

This is part of the problem of working in infinite spaces, you can
always end up with a piece you don't know about.

u put urself in a mathematical jam,

can't actually show me what one of these apparently non-halting machines
with "unknown" behavior actually looks like because then ur theory falls apart, despite the fact we can in fact emuerate over all machines ...

so idk wtf u think u'r actually talking about there buddy
--
a burnt out swe investigating into why our tooling doesn't involve
basic semantic proofs like halting analysis

please excuse my pseudo-pyscript,

~ nick
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 12/7/25 5:46 PM, Ben Bacarisse wrote:

dart200 <user7160@newsgrouper.org.invalid> writes:

keep in mind: all real TMs exist, undecidable machines do not exist.

Is a "real TM" any different to a TM? If so, on what way? What is an undecidable machine (or, for that matter, a decidable machine)? I can't
keep this in mind if I don't know what your terms mean.

see, if we do not have a general halting decider then there must be some
input machine L, which is the first machine in the full enumeration who's
halting semantics cannot be decided up for some kind of semantics (like
halting).

The theory of desirability is all about sets. Sets are or are not
decidable. The set of TMs that halt (on, say, an empty tape) is not decidable, for example. Unless you choose to use conventional terms or define some new terms precisely, you will just be writing
technical-sounding nonsense.

all the example of machines that cannot be decided into the set of
halting or non-halting machines are then declared to not exist ... so
they can't come up in the actual enumeration of machines.

well, first off: all the proofs for undecidability use purely hypothetical >> machines, which then are declared to not exist, so none of those machines
could be *real* machine L.

I very much doubt you know all the proofs about undecidability. I doubt
you know even all the proofs of the undecidability of the set of halting
TMs. I don't.

so what is this proposed non-hypothetical *real* machine L that then cannot >> be decided?

See above. What is a real TM as opposed to a TM as usually defined?

real TMs come up in the full enumerations. the hypothetical TMs
discussed in undecidability proofs do not exist, and therefore cannot
appear in full enumerations

and could that machine L even exist?

Does any TM exist? TMs are, after all, just mathematical objects. If
you accept that mathematical objects (like the set of primes) exist,
then every TM exists.

TMs that exist come up in the full enumeration of machine, which is necessarily possible given that machine description are finite objects.

let's say someone found that limit L and demonstrated this property that it >> cannot be decided upon by a halting decider ... but then next step in
undecidable proofs is to declare the machine's non-existence, because an
undecidable machine is also not a deterministic machine, which ultimately
contradicts the fact that this limit machine L was suppose to actually
*exist*, so how could it ever exist?

You might want to read some more proofs about TMs and halting.

dude an "undecidable" machine cannot exist, as it's behavior is
undeterminable which contradicts the deterministic nature of TMs

these hypothetical machines which we present as unclassifiable are also
not real machines.

what are *real* machines, that we can actually iterate upon in the full enumeration of machines, that are *provably* unclassifiable???

and if the limit machine L does not actually exist, then how are TM
semantics not generally decidable???

good god guys, it's so tiring arguing against what is seemingly
irreconcilable nonsense. but bring it on my dudes, how do u think i'm wrong >> this time???

I sympathise. But I get tired with people who don't define their terms
and argue about a topic they don't appear to have studied.

cut that gaslighting shit out bro
--
a burnt out swe investigating into why our tooling doesn't involve
basic semantic proofs like halting analysis

please excuse my pseudo-pyscript,

~ nick
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 08/12/2025 03:17, olcott wrote:

On 12/7/2025 7:26 PM, Tristan Wibberley wrote:

On 06/12/2025 17:00, olcott wrote:

As my signature line now stipulates
My 28 year goal has been to make
"true on the basis of meaning" computable.

Do you really mean "truthy" on the basis of meaning?
I'd argue "true on the basis of meaning" can only every be truthy, but
"truthy on the basis of meaning" could, perhaps, become true.

In other words we cannot be certain
that the integer five is a number?

that "the integer five" refers to a number. exactly
--
Tristan Wibberley

The message body is Copyright (C) 2025 Tristan Wibberley except
citations and quotations noted. All Rights Reserved except that you may,
of course, cite it academically giving credit to me, distribute it
verbatim as part of a usenet system or its archives, and use it to
promote my greatness and general superiority without misrepresentation
of my opinions other than my opinion of my greatness and general
superiority which you _may_ misrepresent. You definitely MAY NOT train
any production AI system with it but you may train experimental AI that
will only be used for evaluation of the AI methods it implements.

--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 08/12/2025 04:37, dart200 wrote:

On 12/7/25 5:46 PM, Ben Bacarisse wrote:

dart200 <user7160@newsgrouper.org.invalid> writes:

keep in mind: all real TMs exist, undecidable machines do not exist.

Is a "real TM" any different to a TM?  If so, on what way?  What is an
undecidable machine (or, for that matter, a decidable machine)?  I can't
keep this in mind if I don't know what your terms mean.

dart200 - you cunningly avoided answering the above, making all the rest
a pointless read, and thus a pointless write.
--
Tristan Wibberley

The message body is Copyright (C) 2025 Tristan Wibberley except
citations and quotations noted. All Rights Reserved except that you may,
of course, cite it academically giving credit to me, distribute it
verbatim as part of a usenet system or its archives, and use it to
promote my greatness and general superiority without misrepresentation
of my opinions other than my opinion of my greatness and general
superiority which you _may_ misrepresent. You definitely MAY NOT train
any production AI system with it but you may train experimental AI that
will only be used for evaluation of the AI methods it implements.

--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 12/7/25 11:28 PM, dart200 wrote:

On 12/7/25 6:42 PM, Richard Damon wrote:

Because Turing PROVED that the Halting Problem can't be computed,
thus, the limit exists.

We may not be able to precisely define the line betweem computable and
non-computable (or decidable vs non-decidable), but we know it exists
as we have things know to be on both sides.

We have a number of general propositions that have been proven to be
uncomputable/undecidable, like the Halting Problem.

When we narrow the question to a specific machine, that machine can
fall into 3 camps.

Known to Halt.
Known to Never Halt.
Unknown in behavior (but we know it will either halt of not).

The question of knowABILITY is tougher, as it is easy to prove we know
an answer (if we do) as knowing the answer shows it is knowable.

Showing that some things might be knowable but not currently know is
possible, but that does NOT mean we can answer the knowability
question for all things that are knowable.

Why are you so stuck in the fact that between the domain of the
decidable and the undeciable there is a band of "we don't know" that
might contain some things that "we can't know".

This is part of the problem of working in infinite spaces, you can
always end up with a piece you don't know about.

u put urself in a mathematical jam,

can't actually show me what one of these apparently non-halting machines with "unknown" behavior actually looks like because then ur theory falls apart, despite the fact we can in fact emuerate over all machines ...

so idk wtf u think u'r actually talking about there buddy

But I don't need to talk about machines with unknowable results, as they aren't the topic of the problem.

It seems you are stuck in a Naive Set Theory system that insists on
having Sets based on just a description of them.

What I am talking about is that we can prove that there can not exist of
a finite algorithm that will always tell if any finite algorithn it is
given the full description of will reach an answer or not.

Since such a decider doesn't exist, we of course can't "describe" it,
except by point out its absence.

Yes, we can enumerate over all machines, and divide them into 3 classes,

Known to Halt,
Known to not Halt.
We don't know (possibly just yet) what they do.

In that last class, there may be some that we can prove that with more
work we CAN determine if they will halt or not, but there will be some
which we can't (perhaps yet) determine if we can do that.

So, the set of machines which we can not know their behavior is not a
valid set to talk about except in a Naive Set theory, which will itself
be inconsistant. The fact you keep on harping about that set says you
don't understand the problem with it.

Your logic seems to be based on trying to solve Russel's Teapot, which
is just a logic error. It just shows that there are things whose
existance / non-existence just are not practically knowable.
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 12/7/25 11:37 PM, dart200 wrote:

dude an "undecidable" machine cannot exist, as it's behavior is undeterminable which contradicts the deterministic nature of TMs

That is an incorrect reasoning.

The "undecidable machine" (if they do exist) are fully deterministic,
but just run from an infinite number of steps, and for which no
reduction is available for use to determine that in a finite number of
steps.

How do you intend to KNOW in a finite amount of work, which is a
limitation of all knowledge, something that takes infinite work to
determine.

Deterministic doesn't mean finite, or reducible to finite.
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 12/8/2025 12:36 AM, Tristan Wibberley wrote:

On 08/12/2025 03:17, olcott wrote:

On 12/7/2025 7:26 PM, Tristan Wibberley wrote:

On 06/12/2025 17:00, olcott wrote:

As my signature line now stipulates
My 28 year goal has been to make
"true on the basis of meaning" computable.

Do you really mean "truthy" on the basis of meaning?
I'd argue "true on the basis of meaning" can only every be truthy, but
"truthy on the basis of meaning" could, perhaps, become true.

In other words we cannot be certain
that the integer five is a number?

that "the integer five" refers to a number. exactly

The body of general knowledge that can be expressed in
language includes all of the details of every published
definition in a knowledge ontology type hierarchy.
Each atomic fact of the actual world.

This is stored as formalized natural language such as
Rudolf Carnap Meaning Postulates, Montague Grammar of
natural language semantics, or the CycL language of the
Cyc project's knowledge ontology.

Some aspects of this knowledge might also be stored in
some other formal language that may be more compact
and succinct for mathematical notions.
--
Copyright 2025 Olcott<br><br>

My 28 year goal has been to make <br>
"true on the basis of meaning" computable.<br><br>

This required establishing a new foundation<br>
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 12/8/25 1:48 AM, Tristan Wibberley wrote:

On 08/12/2025 04:37, dart200 wrote:

On 12/7/25 5:46 PM, Ben Bacarisse wrote:

dart200 <user7160@newsgrouper.org.invalid> writes:

keep in mind: all real TMs exist, undecidable machines do not exist.

Is a "real TM" any different to a TM?  If so, on what way?  What is an >>> undecidable machine (or, for that matter, a decidable machine)?  I can't >>> keep this in mind if I don't know what your terms mean.

dart200 - you cunningly avoided answering the above, making all the rest
a pointless read, and thus a pointless write.

i'm pretty sure i answer it several times over in the rest of the post,
so that's why u read the whole post numbnuts ...

anyways, the hypothetical machines we talk about in undecidable proofs
are not real deterministic machines because deterministic machines must
remain determinable at every step of the computation, which those
undecidable machines aren't.

these machines which remap themselves based on the response they get
from a decider do not have determinable behavior, so they cannot be deterministic, and cannot come up in the enumeration of machines.

what do *actual* undecidable machines look like???

so far ion my discussion with richard he's concluded *real* machines
which cannot be classified into the set of programs that halt/not, are
all non-halting machines that cannot be specifically identified or else
we'd know they are non-halting machines, breaking the conclusion they
are undecidable machines.

that's where we are at in computing: undecidable spooks which can't be specifically identified lest they'd stop being the undecidable spooks
that they are
--
a burnt out swe investigating into why our tooling doesn't involve
basic semantic proofs like halting analysis

please excuse my pseudo-pyscript,

~ nick
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 12/8/25 4:31 AM, Richard Damon wrote:

On 12/7/25 11:28 PM, dart200 wrote:

On 12/7/25 6:42 PM, Richard Damon wrote:

Because Turing PROVED that the Halting Problem can't be computed,
thus, the limit exists.

We may not be able to precisely define the line betweem computable
and non-computable (or decidable vs non-decidable), but we know it
exists as we have things know to be on both sides.

We have a number of general propositions that have been proven to be
uncomputable/undecidable, like the Halting Problem.

When we narrow the question to a specific machine, that machine can
fall into 3 camps.

Known to Halt.
Known to Never Halt.
Unknown in behavior (but we know it will either halt of not).

The question of knowABILITY is tougher, as it is easy to prove we
know an answer (if we do) as knowing the answer shows it is knowable.

Showing that some things might be knowable but not currently know is
possible, but that does NOT mean we can answer the knowability
question for all things that are knowable.

Why are you so stuck in the fact that between the domain of the
decidable and the undeciable there is a band of "we don't know" that
might contain some things that "we can't know".

This is part of the problem of working in infinite spaces, you can
always end up with a piece you don't know about.

u put urself in a mathematical jam,

can't actually show me what one of these apparently non-halting
machines with "unknown" behavior actually looks like because then ur
theory falls apart, despite the fact we can in fact emuerate over all
machines ...

so idk wtf u think u'r actually talking about there buddy

But I don't need to talk about machines with unknowable results, as they aren't the topic of the problem.

... what??? the halting problem is literally ur proof they exist, how
are they not the topic???

It seems you are stuck in a Naive Set Theory system that insists on
having Sets based on just a description of them.

and ur stuck on believing in machine ghosts

What I am talking about is that we can prove that there can not exist of
a finite algorithm that will always tell if any finite algorithn it is
given the full description of will reach an answer or not.

but u can't give me a what logical structure a finite algorithm would
provably fail in, because all the hypothetical failures demonstrated in undecidability proofs *DO NOT EXIST*

Since such a decider doesn't exist, we of course can't "describe" it,
except by point out its absence.

Yes, we can enumerate over all machines, and divide them into 3 classes,

Known to Halt,
Known to not Halt.
We don't know (possibly just yet) what they do.

In that last class, there may be some that we can prove that with more
work we CAN determine if they will halt or not, but there will be some
which we can't (perhaps yet) determine if we can do that.

well apparently that set will contain machines we *cannot* *ever* know,
that we *cannot* *know* that we *cannot* *know*, so you can't even show
me the form of the machine that is not mappable, ur just presuming it exists

So, the set of machines which we can not know their behavior is not a
valid set to talk about except in a Naive Set theory, which will itself
be inconsistant. The fact you keep on harping about that set says you
don't understand the problem with it.

this is computing theory bro, it's a lot more constrained a possibility
space than set theory theory, set theory needs to encompass infinite
sets of real numbers ... computing does not

Your logic seems to be based on trying to solve Russel's Teapot, which

ur claiming there's certainly a fucking teapot out there that *can't* be
found or else it wouldn't exist!

is just a logic error. It just shows that there are things whose
existance / non-existence just are not practically knowable.

--
a burnt out swe investigating into why our tooling doesn't involve
basic semantic proofs like halting analysis

please excuse my pseudo-pyscript,

~ nick
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 12/8/25 4:35 AM, Richard Damon wrote:

On 12/7/25 11:37 PM, dart200 wrote:

dude an "undecidable" machine cannot exist, as it's behavior is
undeterminable which contradicts the deterministic nature of TMs

That is an incorrect reasoning.

The "undecidable machine" (if they do exist) are fully deterministic,
but just run from an infinite number of steps, and for which no
reduction is available for use to determine that in a finite number of steps.

How do you intend to KNOW in a finite amount of work, which is a
limitation of all knowledge, something that takes infinite work to determine.

Deterministic doesn't mean finite, or reducible to finite.

because undecidability proofs don't have anything to do with infinite
work, the all involve hypothesized machines which cannot be classified,
and therefore also cannot actually exist

see this is the crux of the issue: proofs of "undecidable" machines
supposedly disprove the halting algo in order to disprove the existance
of said undecidable machines ... but in the wake of disproving the
halting algo ur left with at least one machine that must be undecidable ...

which defeats the purpose of the proof

it's a self-defeating concept that has been held onto for almost a
century for some ungodly reason that you will not specify
--
a burnt out swe investigating into why our tooling doesn't involve
basic semantic proofs like halting analysis

please excuse my pseudo-pyscript,

~ nick
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 12/8/25 1:02 PM, dart200 wrote:

On 12/8/25 4:35 AM, Richard Damon wrote:

On 12/7/25 11:37 PM, dart200 wrote:

dude an "undecidable" machine cannot exist, as it's behavior is
undeterminable which contradicts the deterministic nature of TMs

That is an incorrect reasoning.

The "undecidable machine" (if they do exist) are fully deterministic,
but just run from an infinite number of steps, and for which no
reduction is available for use to determine that in a finite number of
steps.

How do you intend to KNOW in a finite amount of work, which is a
limitation of all knowledge, something that takes infinite work to
determine.

Deterministic doesn't mean finite, or reducible to finite.

because undecidability proofs don't have anything to do with infinite
work, the all involve hypothesized machines which cannot be classified,

and this can be shown in finite time,

and therefore also cannot actually exist

see this is the crux of the issue: proofs of "undecidable" machines supposedly disprove the halting algo in order to disprove the existance
of said undecidable machines ... but in the wake of disproving the
halting algo ur left with at least one machine that must be undecidable ...

which defeats the purpose of the proof

it's a self-defeating concept that has been held onto for almost a
century for some ungodly reason that you will not specify

--
a burnt out swe investigating into why our tooling doesn't involve
basic semantic proofs like halting analysis

please excuse my pseudo-pyscript,

~ nick
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 12/8/25 4:02 PM, dart200 wrote:

On 12/8/25 4:35 AM, Richard Damon wrote:

On 12/7/25 11:37 PM, dart200 wrote:

dude an "undecidable" machine cannot exist, as it's behavior is
undeterminable which contradicts the deterministic nature of TMs

That is an incorrect reasoning.

The "undecidable machine" (if they do exist) are fully deterministic,
but just run from an infinite number of steps, and for which no
reduction is available for use to determine that in a finite number of
steps.

How do you intend to KNOW in a finite amount of work, which is a
limitation of all knowledge, something that takes infinite work to
determine.

Deterministic doesn't mean finite, or reducible to finite.

because undecidability proofs don't have anything to do with infinite
work, the all involve hypothesized machines which cannot be classified,
and therefore also cannot actually exist

Nope, show me one that does that!

They all show that for every decider, we can make an input that it will
get wrong, and that input is DIFFERENT for each decider.

see this is the crux of the issue: proofs of "undecidable" machines supposedly disprove the halting algo in order to disprove the existance
of said undecidable machines ... but in the wake of disproving the
halting algo ur left with at least one machine that must be undecidable ...

No, the crux is you don't understand what you are reading.

which defeats the purpose of the proof

Nope, just shows you are stuck on a strawman.

it's a self-defeating concept that has been held onto for almost a
century for some ungodly reason that you will not specify

Again, where do the proofs actually do what you claim, create a SINGLE
machine that no decider can handle?

It seems you don't understand what a machine actually is.
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 12/8/25 2:51 PM, dart200 wrote:

On 12/8/25 4:31 AM, Richard Damon wrote:

On 12/7/25 11:28 PM, dart200 wrote:

On 12/7/25 6:42 PM, Richard Damon wrote:

Because Turing PROVED that the Halting Problem can't be computed,
thus, the limit exists.

We may not be able to precisely define the line betweem computable
and non-computable (or decidable vs non-decidable), but we know it
exists as we have things know to be on both sides.

We have a number of general propositions that have been proven to be
uncomputable/undecidable, like the Halting Problem.

When we narrow the question to a specific machine, that machine can
fall into 3 camps.

Known to Halt.
Known to Never Halt.
Unknown in behavior (but we know it will either halt of not).

The question of knowABILITY is tougher, as it is easy to prove we
know an answer (if we do) as knowing the answer shows it is knowable.

Showing that some things might be knowable but not currently know is
possible, but that does NOT mean we can answer the knowability
question for all things that are knowable.

Why are you so stuck in the fact that between the domain of the
decidable and the undeciable there is a band of "we don't know" that
might contain some things that "we can't know".

This is part of the problem of working in infinite spaces, you can
always end up with a piece you don't know about.

u put urself in a mathematical jam,

can't actually show me what one of these apparently non-halting
machines with "unknown" behavior actually looks like because then ur
theory falls apart, despite the fact we can in fact emuerate over all
machines ...

so idk wtf u think u'r actually talking about there buddy

But I don't need to talk about machines with unknowable results, as
they aren't the topic of the problem.

... what??? the halting problem is literally ur proof they exist, how
are they not the topic???

Nope. It seems you don't understand the words I am using.

It seems you are stuck in a Naive Set Theory system that insists on
having Sets based on just a description of them.

and ur stuck on believing in machine ghosts

Nope, I believe your ghosts exist, but they are not the based of the
actual proof.

Which is that a "Correct Halt Decider" is the ghost, as we can show the existance of an input (that varies based on the decider we are talking
about) that it will get wrong.

What I am talking about is that we can prove that there can not exist
of a finite algorithm that will always tell if any finite algorithn it
is given the full description of will reach an answer or not.

but u can't give me a what logical structure a finite algorithm would provably fail in, because all the hypothetical failures demonstrated in undecidability proofs *DO NOT EXIST*

Sure, for any finite halt decision algorithm, to decide on an algorithm
that uses that algorithm, and then does the opposite.

All algorithms need to fail for that form of input, which again, is a DIFFERENT input for every claimed decider.

We don't need to find a single input that all fail on, just that every
decider fails on at least one input, and the one they fail on can be
different for every decider.

Since such a decider doesn't exist, we of course can't "describe" it,
except by point out its absence.

Yes, we can enumerate over all machines, and divide them into 3 classes,

Known to Halt,
Known to not Halt.
We don't know (possibly just yet) what they do.

In that last class, there may be some that we can prove that with more
work we CAN determine if they will halt or not, but there will be some
which we can't (perhaps yet) determine if we can do that.

well apparently that set will contain machines we *cannot* *ever* know,
that we *cannot* *know* that we *cannot* *know*, so you can't even show
me the form of the machine that is not mappable, ur just presuming it
exists

What "Set"? That is the problem, you can't construct that set by any consistent set theory.

You need to rely on "Naive" set theory to build your set, you end up
with inconsistant logic.

So, the set of machines which we can not know their behavior is not a
valid set to talk about except in a Naive Set theory, which will
itself be inconsistant. The fact you keep on harping about that set
says you don't understand the problem with it.

this is computing theory bro, it's a lot more constrained a possibility space than set theory theory, set theory needs to encompass infinite
sets of real numbers ... computing does not

So? If you can't build the set, you can't use it in your arguement.

Your logic seems to be based on trying to solve Russel's Teapot, which

ur claiming there's certainly a fucking teapot out there that *can't* be found or else it wouldn't exist!

Nope, my comment was that there might be a teapot out there, the
unknowable machine. I don't need the unknowable machine to prove undecidability.

It seems you are just stuck looking at the case that I point out might
exists, and just ignore the fact that you keep on misusing the terminology.

is just a logic error. It just shows that there are things whose
existance / non-existence just are not practically knowable.

--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 12/8/25 4:13 PM, Richard Damon wrote:

On 12/8/25 2:51 PM, dart200 wrote:

On 12/8/25 4:31 AM, Richard Damon wrote:

On 12/7/25 11:28 PM, dart200 wrote:

On 12/7/25 6:42 PM, Richard Damon wrote:

Because Turing PROVED that the Halting Problem can't be computed,
thus, the limit exists.

We may not be able to precisely define the line betweem computable
and non-computable (or decidable vs non-decidable), but we know it
exists as we have things know to be on both sides.

We have a number of general propositions that have been proven to
be uncomputable/undecidable, like the Halting Problem.

When we narrow the question to a specific machine, that machine can >>>>> fall into 3 camps.

Known to Halt.
Known to Never Halt.
Unknown in behavior (but we know it will either halt of not).

The question of knowABILITY is tougher, as it is easy to prove we
know an answer (if we do) as knowing the answer shows it is knowable. >>>>>
Showing that some things might be knowable but not currently know
is possible, but that does NOT mean we can answer the knowability
question for all things that are knowable.

Why are you so stuck in the fact that between the domain of the
decidable and the undeciable there is a band of "we don't know"
that might contain some things that "we can't know".

This is part of the problem of working in infinite spaces, you can
always end up with a piece you don't know about.

u put urself in a mathematical jam,

can't actually show me what one of these apparently non-halting
machines with "unknown" behavior actually looks like because then ur
theory falls apart, despite the fact we can in fact emuerate over
all machines ...

so idk wtf u think u'r actually talking about there buddy

But I don't need to talk about machines with unknowable results, as
they aren't the topic of the problem.

... what??? the halting problem is literally ur proof they exist, how
are they not the topic???

Nope. It seems you don't understand the words I am using.

It seems you are stuck in a Naive Set Theory system that insists on
having Sets based on just a description of them.

and ur stuck on believing in machine ghosts

Nope, I believe your ghosts exist, but they are not the based of the
actual proof.

Which is that a "Correct Halt Decider" is the ghost, as we can show the existance of an input (that varies based on the decider we are talking about) that it will get wrong.

after which u declare that problem to not actually exist and defeat ur
own proof's meaning,

and try to make up for this by supposing (but not actually
demonstrating) that there must be instead some ghost machines that look nothing like the paradoxes you construct (because those *cant* exist),
but if we could point to or describe specifically in any way, that would
also self-defeat their existence!

my god the kind of shit the theory of computing has been blowing up
their asshole for the past century:

wanking on about unknowable, yet non-halting ghost machines none can
ever discover lest their theory unravel into a puff of irreconcilable smoke!

imagine believing in limitations that can't even be known!

What I am talking about is that we can prove that there can not exist
of a finite algorithm that will always tell if any finite algorithn
it is given the full description of will reach an answer or not.

but u can't give me a what logical structure a finite algorithm would
provably fail in, because all the hypothetical failures demonstrated
in undecidability proofs *DO NOT EXIST*

Sure, for any finite halt decision algorithm, to decide on an algorithm
that uses that algorithm, and then does the opposite.

i asked for a non-hypothetical example that actually exists

All algorithms need to fail for that form of input, which again, is a DIFFERENT input for every claimed decider.

We don't need to find a single input that all fail on, just that every decider fails on at least one input, and the one they fail on can be different for every decider.

Since such a decider doesn't exist, we of course can't "describe" it,
except by point out its absence.

Yes, we can enumerate over all machines, and divide them into 3 classes, >>>
Known to Halt,
Known to not Halt.
We don't know (possibly just yet) what they do.

In that last class, there may be some that we can prove that with
more work we CAN determine if they will halt or not, but there will
be some which we can't (perhaps yet) determine if we can do that.

well apparently that set will contain machines we *cannot* *ever*
know, that we *cannot* *know* that we *cannot* *know*, so you can't
even show me the form of the machine that is not mappable, ur just
presuming it exists

What "Set"? That is the problem, you can't construct that set by any consistent set theory.

You need to rely on "Naive" set theory to build your set, you end up
with inconsistant logic.

So, the set of machines which we can not know their behavior is not a
valid set to talk about except in a Naive Set theory, which will
itself be inconsistant. The fact you keep on harping about that set
says you don't understand the problem with it.

this is computing theory bro, it's a lot more constrained a
possibility space than set theory theory, set theory needs to
encompass infinite sets of real numbers ... computing does not

So? If you can't build the set, you can't use it in your arguement.

Your logic seems to be based on trying to solve Russel's Teapot, which

ur claiming there's certainly a fucking teapot out there that *can't*
be found or else it wouldn't exist!

Nope, my comment was that there might be a teapot out there, the

MIGHT?!?! BRO, you claim there *MUST* be one ... holy shit bro

ur not operating on speculation, u are proposing there exists a *hard*
and *certain* but *unknowable* teapot that would cease to exist if it
were ever found...

and ignore the fact we can certainly enumerate over it. we can infact
write this teapot down, we apparently just can't know the teapot is the
teapot we're looking for

the state of computing theory is mind numbingly ghastly

unknowable machine. I don't need the unknowable machine to prove undecidability.

It seems you are just stuck looking at the case that I point out might exists, and just ignore the fact that you keep on misusing the terminology.

is just a logic error. It just shows that there are things whose
existance / non-existence just are not practically knowable.

--
hi, i'm nick! let's end war 🙃

--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 12/8/25 3:49 PM, Richard Damon wrote:

On 12/8/25 4:02 PM, dart200 wrote:

On 12/8/25 4:35 AM, Richard Damon wrote:

On 12/7/25 11:37 PM, dart200 wrote:

dude an "undecidable" machine cannot exist, as it's behavior is
undeterminable which contradicts the deterministic nature of TMs

That is an incorrect reasoning.

The "undecidable machine" (if they do exist) are fully deterministic,
but just run from an infinite number of steps, and for which no
reduction is available for use to determine that in a finite number
of steps.

How do you intend to KNOW in a finite amount of work, which is a
limitation of all knowledge, something that takes infinite work to
determine.

Deterministic doesn't mean finite, or reducible to finite.

because undecidability proofs don't have anything to do with infinite
work, the all involve hypothesized machines which cannot be
classified, and therefore also cannot actually exist

Nope, show me one that does that!

They all show that for every decider, we can make an input that it will
get wrong, and that input is DIFFERENT for each decider.

BUT THEN U CLAIM THE DECIDER DOESN'T EXIST SO, SO THAT INPUT DOESN'T
EXIST, THE PROBLEM OF IRRECONCILABLE INPUT DOESN'T EXIST IN THE REAL ENUMERATION OF MACHINES

you then just overgeneralize this problem to the rest of computing and fallacious just assume there is some other (but apparently unknowable)
means to produce an input that could fool any attempt to decide on only
*real* machines

that's the fundamental error ur making: an overgeneralization fallacy

see this is the crux of the issue: proofs of "undecidable" machines
supposedly disprove the halting algo in order to disprove the
existance of said undecidable machines ... but in the wake of
disproving the halting algo ur left with at least one machine that
must be undecidable ...

No, the crux is you don't understand what you are reading.

which defeats the purpose of the proof

Nope, just shows you are stuck on a strawman.

it's a self-defeating concept that has been held onto for almost a
century for some ungodly reason that you will not specify

Again, where do the proofs actually do what you claim, create a SINGLE machine that no decider can handle?

It seems you don't understand what a machine actually is.

--
a burnt out swe investigating into why our tooling doesn't involve
basic semantic proofs like halting analysis

please excuse my pseudo-pyscript,

~ nick
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 12/8/25 8:30 PM, dart200 wrote:

On 12/8/25 4:13 PM, Richard Damon wrote:

On 12/8/25 2:51 PM, dart200 wrote:

On 12/8/25 4:31 AM, Richard Damon wrote:

On 12/7/25 11:28 PM, dart200 wrote:

On 12/7/25 6:42 PM, Richard Damon wrote:

Because Turing PROVED that the Halting Problem can't be computed, >>>>>> thus, the limit exists.

We may not be able to precisely define the line betweem computable >>>>>> and non-computable (or decidable vs non-decidable), but we know it >>>>>> exists as we have things know to be on both sides.

We have a number of general propositions that have been proven to >>>>>> be uncomputable/undecidable, like the Halting Problem.

When we narrow the question to a specific machine, that machine
can fall into 3 camps.

Known to Halt.
Known to Never Halt.
Unknown in behavior (but we know it will either halt of not).

The question of knowABILITY is tougher, as it is easy to prove we >>>>>> know an answer (if we do) as knowing the answer shows it is knowable. >>>>>>
Showing that some things might be knowable but not currently know >>>>>> is possible, but that does NOT mean we can answer the knowability >>>>>> question for all things that are knowable.

Why are you so stuck in the fact that between the domain of the
decidable and the undeciable there is a band of "we don't know"
that might contain some things that "we can't know".

This is part of the problem of working in infinite spaces, you can >>>>>> always end up with a piece you don't know about.

u put urself in a mathematical jam,

can't actually show me what one of these apparently non-halting
machines with "unknown" behavior actually looks like because then
ur theory falls apart, despite the fact we can in fact emuerate
over all machines ...

so idk wtf u think u'r actually talking about there buddy

But I don't need to talk about machines with unknowable results, as
they aren't the topic of the problem.

... what??? the halting problem is literally ur proof they exist, how
are they not the topic???

Nope. It seems you don't understand the words I am using.

It seems you are stuck in a Naive Set Theory system that insists on
having Sets based on just a description of them.

and ur stuck on believing in machine ghosts

Nope, I believe your ghosts exist, but they are not the based of the
actual proof.

Which is that a "Correct Halt Decider" is the ghost, as we can show
the existance of an input (that varies based on the decider we are
talking about) that it will get wrong.

after which u declare that problem to not actually exist and defeat ur
own proof's meaning,

I never said the PROBLEM doesn't exist, just that no decider can
correctly answer the problem for all inputs.

Maybe you don't understand the nature of problems and answers.

and try to make up for this by supposing (but not actually
demonstrating) that there must be instead some ghost machines that look nothing like the paradoxes you construct (because those *cant* exist),
but if we could point to or describe specifically in any way, that would also self-defeat their existence!

Where did I use these ghost machines?

my god the kind of shit the theory of computing has been blowing up
their asshole for the past century:

The only shit is what is in your head, not understand what is being said.

wanking on about unknowable, yet non-halting ghost machines none can
ever discover lest their theory unravel into a puff of irreconcilable
smoke!

it seems you are stuck in your ghosts

imagine believing in limitations that can't even be known!

Why do you say that?

The limitation is well know, that the halting function can not be computed.

This means that EVERY attempt to compute it will give some wrong answers.

That doesn't mean there needs to be a specific input that we can't know
its halting, even if that might be an implication of that fact.

For the proposition, the existance of such a machine isn't important.

It seems you have a problem with "abstract" concepts, like having to
look at the answers for ALL inputs for the decider to meet the requirements.

Note, very specifically, for a given machine, there ALWAYS is a machine
that correctly answer for it, we just might not know which machine it is
that gives the answer. The the problem of Halting for just a specific
machine is not uncomputable, even if we don't know the answer, all that
means is we can't tell which machines were right and which were wrong.

What I am talking about is that we can prove that there can not
exist of a finite algorithm that will always tell if any finite
algorithn it is given the full description of will reach an answer
or not.

but u can't give me a what logical structure a finite algorithm would
provably fail in, because all the hypothetical failures demonstrated
in undecidability proofs *DO NOT EXIST*

Sure, for any finite halt decision algorithm, to decide on an
algorithm that uses that algorithm, and then does the opposite.

i asked for a non-hypothetical example that actually exists

Of what?

It seems you are stuck on a strawman.

The non-hypothetical example is that "Halting" is not decidable, as
there can not exist a machine that gets the right answer for every
possible machine given to it.

What is a non-hypothetical example of something said not to exist?

Can you give me a non-hypothetical example of an even number greater
than 2 that is prime?

All algorithms need to fail for that form of input, which again, is a
DIFFERENT input for every claimed decider.

We don't need to find a single input that all fail on, just that every
decider fails on at least one input, and the one they fail on can be
different for every decider.

Since such a decider doesn't exist, we of course can't "describe"
it, except by point out its absence.

Yes, we can enumerate over all machines, and divide them into 3
classes,

Known to Halt,
Known to not Halt.
We don't know (possibly just yet) what they do.

In that last class, there may be some that we can prove that with
more work we CAN determine if they will halt or not, but there will
be some which we can't (perhaps yet) determine if we can do that.

well apparently that set will contain machines we *cannot* *ever*
know, that we *cannot* *know* that we *cannot* *know*, so you can't
even show me the form of the machine that is not mappable, ur just
presuming it exists

What "Set"? That is the problem, you can't construct that set by any
consistent set theory.

You need to rely on "Naive" set theory to build your set, you end up
with inconsistant logic.

So, the set of machines which we can not know their behavior is not
a valid set to talk about except in a Naive Set theory, which will
itself be inconsistant. The fact you keep on harping about that set
says you don't understand the problem with it.

this is computing theory bro, it's a lot more constrained a
possibility space than set theory theory, set theory needs to
encompass infinite sets of real numbers ... computing does not

So? If you can't build the set, you can't use it in your arguement.

Your logic seems to be based on trying to solve Russel's Teapot, which >>>

ur claiming there's certainly a fucking teapot out there that *can't*
be found or else it wouldn't exist!

Nope, my comment was that there might be a teapot out there, the

MIGHT?!?! BRO, you claim there *MUST* be one ... holy shit bro

No, where did I say that an undecidable machine must exist?

I claim that no decider can get every input correct, and THAT is the definition that makes the problem uncomputable.

I point out that this seems to imply that there likely is some machine
that we can't know if it halts or not, and an implication of that unknowability is that that machine (if it exists) must not halt.

ur not operating on speculation, u are proposing there exists a *hard*
and *certain* but *unknowable* teapot that would cease to exist if it
were ever found...

Nope, I don't need the "teapot" to exist for Halting to not be computab;le.

and ignore the fact we can certainly enumerate over it. we can infact
write this teapot down, we apparently just can't know the teapot is the teapot we're looking for

Ok, then what even number greater than 2 can not be written as the sum
of two primes?

the state of computing theory is mind numbingly ghastly

Nope, your understanding of it is.

unknowable machine. I don't need the unknowable machine to prove
undecidability.

It seems you are just stuck looking at the case that I point out might
exists, and just ignore the fact that you keep on misusing the
terminology.

is just a logic error. It just shows that there are things whose
existance / non-existence just are not practically knowable.

--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 12/8/25 8:52 PM, dart200 wrote:

On 12/8/25 3:49 PM, Richard Damon wrote:

On 12/8/25 4:02 PM, dart200 wrote:

On 12/8/25 4:35 AM, Richard Damon wrote:

On 12/7/25 11:37 PM, dart200 wrote:

dude an "undecidable" machine cannot exist, as it's behavior is
undeterminable which contradicts the deterministic nature of TMs

That is an incorrect reasoning.

The "undecidable machine" (if they do exist) are fully
deterministic, but just run from an infinite number of steps, and
for which no reduction is available for use to determine that in a
finite number of steps.

How do you intend to KNOW in a finite amount of work, which is a
limitation of all knowledge, something that takes infinite work to
determine.

Deterministic doesn't mean finite, or reducible to finite.

because undecidability proofs don't have anything to do with infinite
work, the all involve hypothesized machines which cannot be
classified, and therefore also cannot actually exist

Nope, show me one that does that!

They all show that for every decider, we can make an input that it
will get wrong, and that input is DIFFERENT for each decider.

BUT THEN U CLAIM THE DECIDER DOESN'T EXIST SO, SO THAT INPUT DOESN'T
EXIST, THE PROBLEM OF IRRECONCILABLE INPUT DOESN'T EXIST IN THE REAL ENUMERATION OF MACHINES

Then I guess you are admitting that you can't even CLAIM a decider might
be a halt decider. We only need a decider that CLAIMS to be a halt
decider to prove it wrong, or maybe even that there can't be anything
that would be called a decider.

The claim is that given any machine you want to try to call a halt
decider, I can prove you wrong by showing you a definite input that
makes it wrong.

The RESULT of being able to do that is that we can show that no decider
can exist that gets the right answer for all inputs.

I don't need to make an input for a decider that doesn't exist.

you then just overgeneralize this problem to the rest of computing and fallacious just assume there is some other (but apparently unknowable)
means to produce an input that could fool any attempt to decide on only *real* machines

Nope. But then, the Halting Problem doesn't make direct claims about any
other computation problem. Since one properly defined problem isn't computable, we know that SOME problems are not computable.

What have I "overgeneralize", are you thinking I am making things up
like Olcott does?

that's the fundamental error ur making: an overgeneralization fallacy

Nope, it seems you are using the stupidity fallacy, or maybe just the strawbrain fallacy.

--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 12/8/25 6:24 PM, Richard Damon wrote:

On 12/8/25 8:30 PM, dart200 wrote:

On 12/8/25 4:13 PM, Richard Damon wrote:

On 12/8/25 2:51 PM, dart200 wrote:

On 12/8/25 4:31 AM, Richard Damon wrote:

On 12/7/25 11:28 PM, dart200 wrote:

On 12/7/25 6:42 PM, Richard Damon wrote:

Because Turing PROVED that the Halting Problem can't be computed, >>>>>>> thus, the limit exists.

We may not be able to precisely define the line betweem
computable and non-computable (or decidable vs non-decidable),
but we know it exists as we have things know to be on both sides. >>>>>>>
We have a number of general propositions that have been proven to >>>>>>> be uncomputable/undecidable, like the Halting Problem.

When we narrow the question to a specific machine, that machine >>>>>>> can fall into 3 camps.

Known to Halt.
Known to Never Halt.
Unknown in behavior (but we know it will either halt of not).

The question of knowABILITY is tougher, as it is easy to prove we >>>>>>> know an answer (if we do) as knowing the answer shows it is
knowable.

Showing that some things might be knowable but not currently know >>>>>>> is possible, but that does NOT mean we can answer the knowability >>>>>>> question for all things that are knowable.

Why are you so stuck in the fact that between the domain of the >>>>>>> decidable and the undeciable there is a band of "we don't know" >>>>>>> that might contain some things that "we can't know".

This is part of the problem of working in infinite spaces, you
can always end up with a piece you don't know about.

u put urself in a mathematical jam,

can't actually show me what one of these apparently non-halting
machines with "unknown" behavior actually looks like because then >>>>>> ur theory falls apart, despite the fact we can in fact emuerate
over all machines ...

so idk wtf u think u'r actually talking about there buddy

But I don't need to talk about machines with unknowable results, as >>>>> they aren't the topic of the problem.

... what??? the halting problem is literally ur proof they exist,
how are they not the topic???

Nope. It seems you don't understand the words I am using.

It seems you are stuck in a Naive Set Theory system that insists on >>>>> having Sets based on just a description of them.

and ur stuck on believing in machine ghosts

Nope, I believe your ghosts exist, but they are not the based of the
actual proof.

Which is that a "Correct Halt Decider" is the ghost, as we can show
the existance of an input (that varies based on the decider we are
talking about) that it will get wrong.

after which u declare that problem to not actually exist and defeat ur
own proof's meaning,

I never said the PROBLEM doesn't exist, just that no decider can
correctly answer the problem for all inputs.

Maybe you don't understand the nature of problems and answers.

and try to make up for this by supposing (but not actually
demonstrating) that there must be instead some ghost machines that
look nothing like the paradoxes you construct (because those *cant*
exist), but if we could point to or describe specifically in any way,
that would also self-defeat their existence!

Where did I use these ghost machines?

my god the kind of shit the theory of computing has been blowing up
their asshole for the past century:

The only shit is what is in your head, not understand what is being said.

wanking on about unknowable, yet non-halting ghost machines none can
ever discover lest their theory unravel into a puff of irreconcilable
smoke!

it seems you are stuck in your ghosts

imagine believing in limitations that can't even be known!

Why do you say that?

The limitation is well know, that the halting function can not be computed.

This means that EVERY attempt to compute it will give some wrong answers.

That doesn't mean there needs to be a specific input that we can't know
its halting, even if that might be an implication of that fact.

For the proposition, the existance of such a machine isn't important.

It seems you have a problem with "abstract" concepts, like having to
look at the answers for ALL inputs for the decider to meet the
requirements.

Note, very specifically, for a given machine, there ALWAYS is a machine
that correctly answer for it, we just might not know which machine it is that gives the answer. The the problem of Halting for just a specific machine is not uncomputable, even if we don't know the answer, all that means is we can't tell which machines were right and which were wrong.

What I am talking about is that we can prove that there can not
exist of a finite algorithm that will always tell if any finite
algorithn it is given the full description of will reach an answer
or not.

but u can't give me a what logical structure a finite algorithm
would provably fail in, because all the hypothetical failures
demonstrated in undecidability proofs *DO NOT EXIST*

Sure, for any finite halt decision algorithm, to decide on an
algorithm that uses that algorithm, and then does the opposite.

i asked for a non-hypothetical example that actually exists

Of what?

It seems you are stuck on a strawman.

The non-hypothetical example is that "Halting" is not decidable, as
there can not exist a machine that gets the right answer for every
possible machine given to it.

What is a non-hypothetical example of something said not to exist?

nononono, the undecidable machine *must* exist if halting cannot be
fully decided upon ...

Can you give me a non-hypothetical example of an even number greater
than 2 that is prime?

All algorithms need to fail for that form of input, which again, is a
DIFFERENT input for every claimed decider.

We don't need to find a single input that all fail on, just that
every decider fails on at least one input, and the one they fail on
can be different for every decider.

Since such a decider doesn't exist, we of course can't "describe"
it, except by point out its absence.

Yes, we can enumerate over all machines, and divide them into 3
classes,

Known to Halt,
Known to not Halt.
We don't know (possibly just yet) what they do.

In that last class, there may be some that we can prove that with
more work we CAN determine if they will halt or not, but there will >>>>> be some which we can't (perhaps yet) determine if we can do that.

well apparently that set will contain machines we *cannot* *ever*
know, that we *cannot* *know* that we *cannot* *know*, so you can't
even show me the form of the machine that is not mappable, ur just
presuming it exists

What "Set"? That is the problem, you can't construct that set by any
consistent set theory.

You need to rely on "Naive" set theory to build your set, you end up
with inconsistant logic.

So, the set of machines which we can not know their behavior is not >>>>> a valid set to talk about except in a Naive Set theory, which will
itself be inconsistant. The fact you keep on harping about that set >>>>> says you don't understand the problem with it.

this is computing theory bro, it's a lot more constrained a
possibility space than set theory theory, set theory needs to
encompass infinite sets of real numbers ... computing does not

So? If you can't build the set, you can't use it in your arguement.

Your logic seems to be based on trying to solve Russel's Teapot, which >>>>

ur claiming there's certainly a fucking teapot out there that
*can't* be found or else it wouldn't exist!

Nope, my comment was that there might be a teapot out there, the

MIGHT?!?! BRO, you claim there *MUST* be one ... holy shit bro

No, where did I say that an undecidable machine must exist?

I claim that no decider can get every input correct, and THAT is the definition that makes the problem uncomputable.

THEREFORE some machines must exist that said decider cannot decide upon:

the "undecidable" machines,

that can't look anything like the hypothetical machines in
undecidability proofs that don't actually exist???

I point out that this seems to imply that there likely is some machine
that we can't know if it halts or not, and an implication of that unknowability is that that machine (if it exists) must not halt.

you only speculate it must exist, but the speculation goes so far as to
claim that speculation is the best we can do, that we cannot even
specifically know what form of machine it is ... or ur whole freaking
theory here falls apart

ur not operating on speculation, u are proposing there exists a *hard*
and *certain* but *unknowable* teapot that would cease to exist if it
were ever found...

Nope, I don't need the "teapot" to exist for Halting to not be computab;le.

yeah u do: if a decider cannot handle ever input, then there must exist
the input that the decider cannot handle

u are asserting that the teapot *must* exist, and go so far as to claim
that even if we can look at it (which we can, because we can enumerate
all machines, err "teapots"), we just can't know that the teapot is the specific teapot we're looking for

and ignore the fact we can certainly enumerate over it. we can infact
write this teapot down, we apparently just can't know the teapot is
the teapot we're looking for

Ok, then what even number greater than 2 can not be written as the sum
of two primes?

the state of computing theory is mind numbingly ghastly

Nope, your understanding of it is.

i don't buy into claims of fundamentally unknowable ghosts that *must*
exist bro

unknowable machine. I don't need the unknowable machine to prove
undecidability.

It seems you are just stuck looking at the case that I point out
might exists, and just ignore the fact that you keep on misusing the
terminology.

is just a logic error. It just shows that there are things whose
existance / non-existence just are not practically knowable.

--
a burnt out swe investigating into why our tooling doesn't involve
basic semantic proofs like halting analysis

please excuse my pseudo-pyscript,

~ nick
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 12/8/25 10:06 PM, dart200 wrote:

On 12/8/25 6:24 PM, Richard Damon wrote:

On 12/8/25 8:30 PM, dart200 wrote:

On 12/8/25 4:13 PM, Richard Damon wrote:

On 12/8/25 2:51 PM, dart200 wrote:

On 12/8/25 4:31 AM, Richard Damon wrote:

On 12/7/25 11:28 PM, dart200 wrote:

On 12/7/25 6:42 PM, Richard Damon wrote:

Because Turing PROVED that the Halting Problem can't be
computed, thus, the limit exists.

We may not be able to precisely define the line betweem
computable and non-computable (or decidable vs non-decidable), >>>>>>>> but we know it exists as we have things know to be on both sides. >>>>>>>>
We have a number of general propositions that have been proven >>>>>>>> to be uncomputable/undecidable, like the Halting Problem.

When we narrow the question to a specific machine, that machine >>>>>>>> can fall into 3 camps.

Known to Halt.
Known to Never Halt.
Unknown in behavior (but we know it will either halt of not).

The question of knowABILITY is tougher, as it is easy to prove >>>>>>>> we know an answer (if we do) as knowing the answer shows it is >>>>>>>> knowable.

Showing that some things might be knowable but not currently
know is possible, but that does NOT mean we can answer the
knowability question for all things that are knowable.

Why are you so stuck in the fact that between the domain of the >>>>>>>> decidable and the undeciable there is a band of "we don't know" >>>>>>>> that might contain some things that "we can't know".

This is part of the problem of working in infinite spaces, you >>>>>>>> can always end up with a piece you don't know about.

u put urself in a mathematical jam,

can't actually show me what one of these apparently non-halting >>>>>>> machines with "unknown" behavior actually looks like because then >>>>>>> ur theory falls apart, despite the fact we can in fact emuerate >>>>>>> over all machines ...

so idk wtf u think u'r actually talking about there buddy

But I don't need to talk about machines with unknowable results,
as they aren't the topic of the problem.

... what??? the halting problem is literally ur proof they exist,
how are they not the topic???

Nope. It seems you don't understand the words I am using.

It seems you are stuck in a Naive Set Theory system that insists
on having Sets based on just a description of them.

and ur stuck on believing in machine ghosts

Nope, I believe your ghosts exist, but they are not the based of the
actual proof.

Which is that a "Correct Halt Decider" is the ghost, as we can show
the existance of an input (that varies based on the decider we are
talking about) that it will get wrong.

after which u declare that problem to not actually exist and defeat
ur own proof's meaning,

I never said the PROBLEM doesn't exist, just that no decider can
correctly answer the problem for all inputs.

Maybe you don't understand the nature of problems and answers.

and try to make up for this by supposing (but not actually
demonstrating) that there must be instead some ghost machines that
look nothing like the paradoxes you construct (because those *cant*
exist), but if we could point to or describe specifically in any way,
that would also self-defeat their existence!

Where did I use these ghost machines?

my god the kind of shit the theory of computing has been blowing up
their asshole for the past century:

The only shit is what is in your head, not understand what is being said.

wanking on about unknowable, yet non-halting ghost machines none can
ever discover lest their theory unravel into a puff of irreconcilable
smoke!

it seems you are stuck in your ghosts

imagine believing in limitations that can't even be known!

Why do you say that?

The limitation is well know, that the halting function can not be
computed.

This means that EVERY attempt to compute it will give some wrong answers.

That doesn't mean there needs to be a specific input that we can't
know its halting, even if that might be an implication of that fact.

For the proposition, the existance of such a machine isn't important.

It seems you have a problem with "abstract" concepts, like having to
look at the answers for ALL inputs for the decider to meet the
requirements.

Note, very specifically, for a given machine, there ALWAYS is a
machine that correctly answer for it, we just might not know which
machine it is that gives the answer. The the problem of Halting for
just a specific machine is not uncomputable, even if we don't know the
answer, all that means is we can't tell which machines were right and
which were wrong.

What I am talking about is that we can prove that there can not
exist of a finite algorithm that will always tell if any finite
algorithn it is given the full description of will reach an answer >>>>>> or not.

but u can't give me a what logical structure a finite algorithm
would provably fail in, because all the hypothetical failures
demonstrated in undecidability proofs *DO NOT EXIST*

Sure, for any finite halt decision algorithm, to decide on an
algorithm that uses that algorithm, and then does the opposite.

i asked for a non-hypothetical example that actually exists

Of what?

It seems you are stuck on a strawman.

The non-hypothetical example is that "Halting" is not decidable, as
there can not exist a machine that gets the right answer for every
possible machine given to it.

What is a non-hypothetical example of something said not to exist?

nononono, the undecidable machine *must* exist if halting cannot be
fully decided upon ...

Can you give me a non-hypothetical example of an even number greater
than 2 that is prime?

All algorithms need to fail for that form of input, which again, is
a DIFFERENT input for every claimed decider.

We don't need to find a single input that all fail on, just that
every decider fails on at least one input, and the one they fail on
can be different for every decider.

Since such a decider doesn't exist, we of course can't "describe" >>>>>> it, except by point out its absence.

Yes, we can enumerate over all machines, and divide them into 3
classes,

Known to Halt,
Known to not Halt.
We don't know (possibly just yet) what they do.

In that last class, there may be some that we can prove that with >>>>>> more work we CAN determine if they will halt or not, but there
will be some which we can't (perhaps yet) determine if we can do
that.

well apparently that set will contain machines we *cannot* *ever*
know, that we *cannot* *know* that we *cannot* *know*, so you can't >>>>> even show me the form of the machine that is not mappable, ur just
presuming it exists

What "Set"? That is the problem, you can't construct that set by any
consistent set theory.

You need to rely on "Naive" set theory to build your set, you end up
with inconsistant logic.

So, the set of machines which we can not know their behavior is
not a valid set to talk about except in a Naive Set theory, which >>>>>> will itself be inconsistant. The fact you keep on harping about
that set says you don't understand the problem with it.

this is computing theory bro, it's a lot more constrained a
possibility space than set theory theory, set theory needs to
encompass infinite sets of real numbers ... computing does not

So? If you can't build the set, you can't use it in your arguement.

Your logic seems to be based on trying to solve Russel's Teapot,
which

ur claiming there's certainly a fucking teapot out there that
*can't* be found or else it wouldn't exist!

Nope, my comment was that there might be a teapot out there, the

MIGHT?!?! BRO, you claim there *MUST* be one ... holy shit bro

No, where did I say that an undecidable machine must exist?

I claim that no decider can get every input correct, and THAT is the
definition that makes the problem uncomputable.

THEREFORE some machines must exist that said decider cannot decide upon:

the "undecidable" machines,

Nope, because nothing says that machine can't be decider by other machines.

that can't look anything like the hypothetical machines in
undecidability proofs that don't actually exist???

Nope, THAT decider didn't give the correct answer, not that NO machine
cna give the correct answer.

You seem to have a fundamental problem with qualifiers.

I point out that this seems to imply that there likely is some machine
that we can't know if it halts or not, and an implication of that
unknowability is that that machine (if it exists) must not halt.

you only speculate it must exist, but the speculation goes so far as to claim that speculation is the best we can do, that we cannot even specifically know what form of machine it is ... or ur whole freaking
theory here falls apart

No, for a given machine, we have the recipe to build the input that it
will get wrong.

Thus, for any existing machine you want to claim to be a prospective
halt decider, I can show an input that it gets wrong.

ur not operating on speculation, u are proposing there exists a
*hard* and *certain* but *unknowable* teapot that would cease to
exist if it were ever found...

Nope, I don't need the "teapot" to exist for Halting to not be
computab;le.

yeah u do: if a decider cannot handle ever input, then there must exist
the input that the decider cannot handle

No I don't, as I can provide a physically demonstratable input for ANY
machine you want to put forward.

I don't need to find that elusive unknowable machine.

u are asserting that the teapot *must* exist, and go so far as to claim
that even if we can look at it (which we can, because we can enumerate
all machines, err "teapots"), we just can't know that the teapot is the specific teapot we're looking for

That the teapot must exist is a RESULT of the fact that we can show that
the problem is uncomputable. If we had an algorithm that allowed us to
KNOW the behavior of every machine, then we could make the input on
whatever that algorithm that we used to know about machines, and that algorithm would be wrong about that machine.

and ignore the fact we can certainly enumerate over it. we can infact
write this teapot down, we apparently just can't know the teapot is
the teapot we're looking for

Ok, then what even number greater than 2 can not be written as the sum
of two primes?

the state of computing theory is mind numbingly ghastly

Nope, your understanding of it is.

i don't buy into claims of fundamentally unknowable ghosts that *must*
exist bro

That is your problem.

What can you PROVE about it?

How do you handle the fact that you can't make a correct decider for ALL inputs?

How can you KNOW the answer, if you can't make an algorithm to tell you?

Your problem is you don't understand how knowledge comes about.
Knowledge comes form things that are computable/provable. The fact we
can show that some things can not be computed/proven means that some
things can not be known.

One of the problems is that while we can know what we know, we can't
tell out of what we don't know can't be known, and which might
eventually become known. You seem to want to lable this lack of
knowledge a "ghost", when it is just reality.

unknowable machine. I don't need the unknowable machine to prove
undecidability.

It seems you are just stuck looking at the case that I point out
might exists, and just ignore the fact that you keep on misusing the
terminology.

is just a logic error. It just shows that there are things whose
existance / non-existence just are not practically knowable.

--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 12/8/25 7:19 PM, Richard Damon wrote:

On 12/8/25 10:06 PM, dart200 wrote:

On 12/8/25 6:24 PM, Richard Damon wrote:

On 12/8/25 8:30 PM, dart200 wrote:

On 12/8/25 4:13 PM, Richard Damon wrote:

On 12/8/25 2:51 PM, dart200 wrote:

On 12/8/25 4:31 AM, Richard Damon wrote:

On 12/7/25 11:28 PM, dart200 wrote:

On 12/7/25 6:42 PM, Richard Damon wrote:

Because Turing PROVED that the Halting Problem can't be
computed, thus, the limit exists.

We may not be able to precisely define the line betweem
computable and non-computable (or decidable vs non-decidable), >>>>>>>>> but we know it exists as we have things know to be on both sides. >>>>>>>>>
We have a number of general propositions that have been proven >>>>>>>>> to be uncomputable/undecidable, like the Halting Problem.

When we narrow the question to a specific machine, that machine >>>>>>>>> can fall into 3 camps.

Known to Halt.
Known to Never Halt.
Unknown in behavior (but we know it will either halt of not). >>>>>>>>>
The question of knowABILITY is tougher, as it is easy to prove >>>>>>>>> we know an answer (if we do) as knowing the answer shows it is >>>>>>>>> knowable.

Showing that some things might be knowable but not currently >>>>>>>>> know is possible, but that does NOT mean we can answer the
knowability question for all things that are knowable.

Why are you so stuck in the fact that between the domain of the >>>>>>>>> decidable and the undeciable there is a band of "we don't know" >>>>>>>>> that might contain some things that "we can't know".

This is part of the problem of working in infinite spaces, you >>>>>>>>> can always end up with a piece you don't know about.

u put urself in a mathematical jam,

can't actually show me what one of these apparently non-halting >>>>>>>> machines with "unknown" behavior actually looks like because
then ur theory falls apart, despite the fact we can in fact
emuerate over all machines ...

so idk wtf u think u'r actually talking about there buddy

But I don't need to talk about machines with unknowable results, >>>>>>> as they aren't the topic of the problem.

... what??? the halting problem is literally ur proof they exist, >>>>>> how are they not the topic???

Nope. It seems you don't understand the words I am using.

It seems you are stuck in a Naive Set Theory system that insists >>>>>>> on having Sets based on just a description of them.

and ur stuck on believing in machine ghosts

Nope, I believe your ghosts exist, but they are not the based of
the actual proof.

Which is that a "Correct Halt Decider" is the ghost, as we can show >>>>> the existance of an input (that varies based on the decider we are
talking about) that it will get wrong.

after which u declare that problem to not actually exist and defeat
ur own proof's meaning,

I never said the PROBLEM doesn't exist, just that no decider can
correctly answer the problem for all inputs.

Maybe you don't understand the nature of problems and answers.

and try to make up for this by supposing (but not actually
demonstrating) that there must be instead some ghost machines that
look nothing like the paradoxes you construct (because those *cant*
exist), but if we could point to or describe specifically in any
way, that would also self-defeat their existence!

Where did I use these ghost machines?

my god the kind of shit the theory of computing has been blowing up
their asshole for the past century:

The only shit is what is in your head, not understand what is being
said.

wanking on about unknowable, yet non-halting ghost machines none can
ever discover lest their theory unravel into a puff of
irreconcilable smoke!

it seems you are stuck in your ghosts

imagine believing in limitations that can't even be known!

Why do you say that?

The limitation is well know, that the halting function can not be
computed.

This means that EVERY attempt to compute it will give some wrong
answers.

That doesn't mean there needs to be a specific input that we can't
know its halting, even if that might be an implication of that fact.

For the proposition, the existance of such a machine isn't important.

It seems you have a problem with "abstract" concepts, like having to
look at the answers for ALL inputs for the decider to meet the
requirements.

Note, very specifically, for a given machine, there ALWAYS is a
machine that correctly answer for it, we just might not know which
machine it is that gives the answer. The the problem of Halting for
just a specific machine is not uncomputable, even if we don't know
the answer, all that means is we can't tell which machines were right
and which were wrong.

What I am talking about is that we can prove that there can not >>>>>>> exist of a finite algorithm that will always tell if any finite >>>>>>> algorithn it is given the full description of will reach an
answer or not.

but u can't give me a what logical structure a finite algorithm
would provably fail in, because all the hypothetical failures
demonstrated in undecidability proofs *DO NOT EXIST*

Sure, for any finite halt decision algorithm, to decide on an
algorithm that uses that algorithm, and then does the opposite.

i asked for a non-hypothetical example that actually exists

Of what?

It seems you are stuck on a strawman.

The non-hypothetical example is that "Halting" is not decidable, as
there can not exist a machine that gets the right answer for every
possible machine given to it.

What is a non-hypothetical example of something said not to exist?

nononono, the undecidable machine *must* exist if halting cannot be
fully decided upon ...

Can you give me a non-hypothetical example of an even number greater
than 2 that is prime?

All algorithms need to fail for that form of input, which again, is >>>>> a DIFFERENT input for every claimed decider.

We don't need to find a single input that all fail on, just that
every decider fails on at least one input, and the one they fail on >>>>> can be different for every decider.

Since such a decider doesn't exist, we of course can't "describe" >>>>>>> it, except by point out its absence.

Yes, we can enumerate over all machines, and divide them into 3 >>>>>>> classes,

Known to Halt,
Known to not Halt.
We don't know (possibly just yet) what they do.

In that last class, there may be some that we can prove that with >>>>>>> more work we CAN determine if they will halt or not, but there
will be some which we can't (perhaps yet) determine if we can do >>>>>>> that.

well apparently that set will contain machines we *cannot* *ever* >>>>>> know, that we *cannot* *know* that we *cannot* *know*, so you
can't even show me the form of the machine that is not mappable,
ur just presuming it exists

What "Set"? That is the problem, you can't construct that set by
any consistent set theory.

You need to rely on "Naive" set theory to build your set, you end
up with inconsistant logic.

So, the set of machines which we can not know their behavior is >>>>>>> not a valid set to talk about except in a Naive Set theory, which >>>>>>> will itself be inconsistant. The fact you keep on harping about >>>>>>> that set says you don't understand the problem with it.

this is computing theory bro, it's a lot more constrained a
possibility space than set theory theory, set theory needs to
encompass infinite sets of real numbers ... computing does not

So? If you can't build the set, you can't use it in your arguement.

Your logic seems to be based on trying to solve Russel's Teapot, >>>>>>> which

ur claiming there's certainly a fucking teapot out there that
*can't* be found or else it wouldn't exist!

Nope, my comment was that there might be a teapot out there, the

MIGHT?!?! BRO, you claim there *MUST* be one ... holy shit bro

No, where did I say that an undecidable machine must exist?

I claim that no decider can get every input correct, and THAT is the
definition that makes the problem uncomputable.

THEREFORE some machines must exist that said decider cannot decide upon:

the "undecidable" machines,

Nope, because nothing says that machine can't be decider by other machines.

that's also just fucking speculation on ur part since you can't even
point to this machine which cannot be decided by one partial decider,
but can be by another

that can't look anything like the hypothetical machines in
undecidability proofs that don't actually exist???

Nope, THAT decider didn't give the correct answer, not that NO machine
cna give the correct answer.

when it comes to hypothesized undecidable proofs ... no machine can
correctly decide:

und = () -> halts(und) && loop_forever(), not just halts()

so know ur just fucking cherry-picking behavior randomly without proof
or a system to justify it because it suits the world view u've been
taught for this point in the discussion

and ur feel confident to not justify anything with specifics... because
if u could actually point to *real* examples of machines that cannot be decided, then ur fucking theory fucking falls apart

holy fuck, i can't believe this kinda trash is the consensus

You seem to have a fundamental problem with qualifiers.

cut that gaslighting shit out bro

I point out that this seems to imply that there likely is some
machine that we can't know if it halts or not, and an implication of
that unknowability is that that machine (if it exists) must not halt.

you only speculate it must exist, but the speculation goes so far as
to claim that speculation is the best we can do, that we cannot even
specifically know what form of machine it is ... or ur whole freaking
theory here falls apart

No, for a given machine, we have the recipe to build the input that it
will get wrong.

but none of fucking hypotheticals actually exist!!! what about deciding
on *only* machines that actually exist???

i'm imaging u asking next: "how do you limit the input to only machines
that exist???"

like, WHAT IN THE FUCK!??? only machines that exist in the full
enumeration, actually exist!

Thus, for any existing machine you want to claim to be a prospective
halt decider, I can show an input that it gets wrong.

ur not operating on speculation, u are proposing there exists a
*hard* and *certain* but *unknowable* teapot that would cease to
exist if it were ever found...

Nope, I don't need the "teapot" to exist for Halting to not be
computab;le.

yeah u do: if a decider cannot handle ever input, then there must
exist the input that the decider cannot handle

No I don't, as I can provide a physically demonstratable input for ANY machine you want to put forward.

I don't need to find that elusive unknowable machine.

u just need to speculate endlessly about it and assert it's truth,
because ur so convinced that ur broken ass theory of computing is coherent

u are asserting that the teapot *must* exist, and go so far as to
claim that even if we can look at it (which we can, because we can
enumerate all machines, err "teapots"), we just can't know that the
teapot is the specific teapot we're looking for

That the teapot must exist is a RESULT of the fact that we can show that
the problem is uncomputable. If we had an algorithm that allowed us to
KNOW the behavior of every machine, then we could make the input on
whatever that algorithm that we used to know about machines, and that algorithm would be wrong about that machine.

or maybe theory is just broken instead of fixing it, u shoved it under a fucking rug for the last century in fear of machines that you do nothing
more than speculate about

and ignore the fact we can certainly enumerate over it. we can
infact write this teapot down, we apparently just can't know the
teapot is the teapot we're looking for

Ok, then what even number greater than 2 can not be written as the
sum of two primes?

the state of computing theory is mind numbingly ghastly

Nope, your understanding of it is.

i don't buy into claims of fundamentally unknowable ghosts that *must*
exist bro

That is your problem.

What can you PROVE about it?

How do you handle the fact that you can't make a correct decider for ALL inputs?

How can you KNOW the answer, if you can't make an algorithm to tell you?

Your problem is you don't understand how knowledge comes about.
Knowledge comes form things that are computable/provable. The fact we
can show that some things can not be computed/proven means that some
things can not be known.

One of the problems is that while we can know what we know, we can't
tell out of what we don't know can't be known, and which might
eventually become known. You seem to want to lable this lack of
knowledge a "ghost", when it is just reality.

unknowable machine. I don't need the unknowable machine to prove
undecidability.

It seems you are just stuck looking at the case that I point out
might exists, and just ignore the fact that you keep on misusing
the terminology.

is just a logic error. It just shows that there are things whose >>>>>>> existance / non-existence just are not practically knowable.

--
a burnt out swe investigating into why our tooling doesn't involve
basic semantic proofs like halting analysis

please excuse my pseudo-pyscript,

~ nick
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 12/8/2025 9:38 PM, dart200 wrote:

*You have support for this in high places*

The Halting Paradox
Bill Stoddart

6 Conclusions
The idea of a universal halting test seems reasonable,
but cannot be formalised as a consistent specification.
It has no model and does not exist as a conceptual object.
Assuming its conceptual existence leads to a paradox.

https://arxiv.org/pdf/1906.05340
--
Copyright 2025 Olcott

My 28 year goal has been to make
"true on the basis of meaning" computable.

This required establishing a new foundation
for correct reasoning.
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.theory

On 12/8/25 10:38 PM, dart200 wrote:

On 12/8/25 7:19 PM, Richard Damon wrote:

On 12/8/25 10:06 PM, dart200 wrote:

On 12/8/25 6:24 PM, Richard Damon wrote:

On 12/8/25 8:30 PM, dart200 wrote:

On 12/8/25 4:13 PM, Richard Damon wrote:

On 12/8/25 2:51 PM, dart200 wrote:

On 12/8/25 4:31 AM, Richard Damon wrote:

On 12/7/25 11:28 PM, dart200 wrote:

On 12/7/25 6:42 PM, Richard Damon wrote:

Because Turing PROVED that the Halting Problem can't be
computed, thus, the limit exists.

We may not be able to precisely define the line betweem
computable and non-computable (or decidable vs non-decidable), >>>>>>>>>> but we know it exists as we have things know to be on both sides. >>>>>>>>>>
We have a number of general propositions that have been proven >>>>>>>>>> to be uncomputable/undecidable, like the Halting Problem.

When we narrow the question to a specific machine, that
machine can fall into 3 camps.

Known to Halt.
Known to Never Halt.
Unknown in behavior (but we know it will either halt of not). >>>>>>>>>>
The question of knowABILITY is tougher, as it is easy to prove >>>>>>>>>> we know an answer (if we do) as knowing the answer shows it is >>>>>>>>>> knowable.

Showing that some things might be knowable but not currently >>>>>>>>>> know is possible, but that does NOT mean we can answer the >>>>>>>>>> knowability question for all things that are knowable.

Why are you so stuck in the fact that between the domain of >>>>>>>>>> the decidable and the undeciable there is a band of "we don't >>>>>>>>>> know" that might contain some things that "we can't know". >>>>>>>>>>
This is part of the problem of working in infinite spaces, you >>>>>>>>>> can always end up with a piece you don't know about.

u put urself in a mathematical jam,

can't actually show me what one of these apparently non-halting >>>>>>>>> machines with "unknown" behavior actually looks like because >>>>>>>>> then ur theory falls apart, despite the fact we can in fact >>>>>>>>> emuerate over all machines ...

so idk wtf u think u'r actually talking about there buddy

But I don't need to talk about machines with unknowable results, >>>>>>>> as they aren't the topic of the problem.

... what??? the halting problem is literally ur proof they exist, >>>>>>> how are they not the topic???

Nope. It seems you don't understand the words I am using.

It seems you are stuck in a Naive Set Theory system that insists >>>>>>>> on having Sets based on just a description of them.

and ur stuck on believing in machine ghosts

Nope, I believe your ghosts exist, but they are not the based of
the actual proof.

Which is that a "Correct Halt Decider" is the ghost, as we can
show the existance of an input (that varies based on the decider
we are talking about) that it will get wrong.

after which u declare that problem to not actually exist and defeat >>>>> ur own proof's meaning,

I never said the PROBLEM doesn't exist, just that no decider can
correctly answer the problem for all inputs.

Maybe you don't understand the nature of problems and answers.

and try to make up for this by supposing (but not actually
demonstrating) that there must be instead some ghost machines that
look nothing like the paradoxes you construct (because those *cant* >>>>> exist), but if we could point to or describe specifically in any
way, that would also self-defeat their existence!

Where did I use these ghost machines?

my god the kind of shit the theory of computing has been blowing up >>>>> their asshole for the past century:

The only shit is what is in your head, not understand what is being
said.

wanking on about unknowable, yet non-halting ghost machines none
can ever discover lest their theory unravel into a puff of
irreconcilable smoke!

it seems you are stuck in your ghosts

imagine believing in limitations that can't even be known!

Why do you say that?

The limitation is well know, that the halting function can not be
computed.

This means that EVERY attempt to compute it will give some wrong
answers.

That doesn't mean there needs to be a specific input that we can't
know its halting, even if that might be an implication of that fact.

For the proposition, the existance of such a machine isn't important.

It seems you have a problem with "abstract" concepts, like having to
look at the answers for ALL inputs for the decider to meet the
requirements.

Note, very specifically, for a given machine, there ALWAYS is a
machine that correctly answer for it, we just might not know which
machine it is that gives the answer. The the problem of Halting for
just a specific machine is not uncomputable, even if we don't know
the answer, all that means is we can't tell which machines were
right and which were wrong.

What I am talking about is that we can prove that there can not >>>>>>>> exist of a finite algorithm that will always tell if any finite >>>>>>>> algorithn it is given the full description of will reach an
answer or not.

but u can't give me a what logical structure a finite algorithm >>>>>>> would provably fail in, because all the hypothetical failures
demonstrated in undecidability proofs *DO NOT EXIST*

Sure, for any finite halt decision algorithm, to decide on an
algorithm that uses that algorithm, and then does the opposite.

i asked for a non-hypothetical example that actually exists

Of what?

It seems you are stuck on a strawman.

The non-hypothetical example is that "Halting" is not decidable, as
there can not exist a machine that gets the right answer for every
possible machine given to it.

What is a non-hypothetical example of something said not to exist?

nononono, the undecidable machine *must* exist if halting cannot be
fully decided upon ...

Can you give me a non-hypothetical example of an even number greater
than 2 that is prime?

All algorithms need to fail for that form of input, which again,
is a DIFFERENT input for every claimed decider.

We don't need to find a single input that all fail on, just that
every decider fails on at least one input, and the one they fail
on can be different for every decider.

Since such a decider doesn't exist, we of course can't
"describe" it, except by point out its absence.

Yes, we can enumerate over all machines, and divide them into 3 >>>>>>>> classes,

Known to Halt,
Known to not Halt.
We don't know (possibly just yet) what they do.

In that last class, there may be some that we can prove that
with more work we CAN determine if they will halt or not, but >>>>>>>> there will be some which we can't (perhaps yet) determine if we >>>>>>>> can do that.

well apparently that set will contain machines we *cannot* *ever* >>>>>>> know, that we *cannot* *know* that we *cannot* *know*, so you
can't even show me the form of the machine that is not mappable, >>>>>>> ur just presuming it exists

What "Set"? That is the problem, you can't construct that set by
any consistent set theory.

You need to rely on "Naive" set theory to build your set, you end >>>>>> up with inconsistant logic.

So, the set of machines which we can not know their behavior is >>>>>>>> not a valid set to talk about except in a Naive Set theory,
which will itself be inconsistant. The fact you keep on harping >>>>>>>> about that set says you don't understand the problem with it.

this is computing theory bro, it's a lot more constrained a
possibility space than set theory theory, set theory needs to
encompass infinite sets of real numbers ... computing does not

So? If you can't build the set, you can't use it in your arguement. >>>>>>

Your logic seems to be based on trying to solve Russel's Teapot, >>>>>>>> which

ur claiming there's certainly a fucking teapot out there that
*can't* be found or else it wouldn't exist!

Nope, my comment was that there might be a teapot out there, the

MIGHT?!?! BRO, you claim there *MUST* be one ... holy shit bro

No, where did I say that an undecidable machine must exist?

I claim that no decider can get every input correct, and THAT is the
definition that makes the problem uncomputable.

THEREFORE some machines must exist that said decider cannot decide upon: >>>
the "undecidable" machines,

Nope, because nothing says that machine can't be decider by other
machines.

that's also just fucking speculation on ur part since you can't even
point to this machine which cannot be decided by one partial decider,
but can be by another

???

Given Machine H is chosen as one partial decider then the machine:

H^(d): if H(d, d) returns halting, loop forever
else halt.

Then H^(H^) will show that H was wrong for H(H^, H^)

How is that not showing the machine which that machine can not decider.

It seems you are stuck on your strawman with confused qualification that
NO machine can decide that input correctly, but that isn't the claim,
only that this particular one doesn't.

The fact that I can ALWAYS make such a machine for ANY decider you may
want to create means that:

For ALL deciders H, there exist an input H^ that that particual H gets
wrong.

THus, but the logic of qualifies, this means that there does not exist
any H that gets the correct answer for all inputs.

that can't look anything like the hypothetical machines in
undecidability proofs that don't actually exist???

Nope, THAT decider didn't give the correct answer, not that NO machine
cna give the correct answer.

when it comes to hypothesized undecidable proofs ... no machine can correctly decide:

und = () -> halts(und) && loop_forever(), not just halts()

Note, this und isn't a machine until a particular Halts is chosen, and
DOES show that any prospecive Halt Decider can't be an always correct
halt decider.

Thus, you yourself just showed the input for the GIVEN decider "halts"

so know ur just fucking cherry-picking behavior randomly without proof
or a system to justify it because it suits the world view u've been
taught for this point in the discussion

No, we know your brain is just mush, as you just demonstrated the point
you claimed couldn't be shown.

and ur feel confident to not justify anything with specifics... because
if u could actually point to *real* examples of machines that cannot be decided, then ur fucking theory fucking falls apart

And what isn't specific about your "und" template.

Note, you err in calling it a machine, as it isn't a machine until
paired with a particular "halts" decider.

holy fuck, i can't believe this kinda trash is the consensus

Yes, I can't believe how you keep on repeating your error of not knowing
what you are talking about,

You seem to have a fundamental problem with qualifiers.

cut that gaslighting shit out bro

What gaslighting?

You just proved the point you said couldn't be shown, but you can't
recognize it.

I point out that this seems to imply that there likely is some
machine that we can't know if it halts or not, and an implication of
that unknowability is that that machine (if it exists) must not halt.

you only speculate it must exist, but the speculation goes so far as
to claim that speculation is the best we can do, that we cannot even
specifically know what form of machine it is ... or ur whole freaking
theory here falls apart

No, for a given machine, we have the recipe to build the input that it
will get wrong.

but none of fucking hypotheticals actually exist!!! what about deciding
on *only* machines that actually exist???

but "halt" isn't just a hypothetical, it is the placeholder for ANY
decider you want to try to claim.

i'm imaging u asking next: "how do you limit the input to only machines
that exist???"

Because the all do, at least if your claimed halt exist.

If you admit that there is not possible halt to exist, then you have
agreed to the proposition and don't need further proof.

like, WHAT IN THE FUCK!??? only machines that exist in the full
enumeration, actually exist!

Right, and non of them give the right answer to the und built from them,
so none of them can be a correct halt decider.

Thus, for any existing machine you want to claim to be a prospective
halt decider, I can show an input that it gets wrong.

ur not operating on speculation, u are proposing there exists a
*hard* and *certain* but *unknowable* teapot that would cease to
exist if it were ever found...

Nope, I don't need the "teapot" to exist for Halting to not be
computab;le.

yeah u do: if a decider cannot handle ever input, then there must
exist the input that the decider cannot handle

No I don't, as I can provide a physically demonstratable input for ANY
machine you want to put forward.

I don't need to find that elusive unknowable machine.

u just need to speculate endlessly about it and assert it's truth,
because ur so convinced that ur broken ass theory of computing is coherent

Because it IS true, and your problem is you don't understand the logic
of universals.

If I can show that ALL are incorrect, I have shown that NONE are correct.

If you are looking for an example form that "none", you don't understand
how logic works.

u are asserting that the teapot *must* exist, and go so far as to
claim that even if we can look at it (which we can, because we can
enumerate all machines, err "teapots"), we just can't know that the
teapot is the specific teapot we're looking for

That the teapot must exist is a RESULT of the fact that we can show
that the problem is uncomputable. If we had an algorithm that allowed
us to KNOW the behavior of every machine, then we could make the input
on whatever that algorithm that we used to know about machines, and
that algorithm would be wrong about that machine.

or maybe theory is just broken instead of fixing it, u shoved it under a fucking rug for the last century in fear of machines that you do nothing more than speculate about

If your idea of "fixing" a system is to just declair it broken, you are showing your stupidity.

All you are doing is showing your ignorance.

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