On 12/10/2025 4:58 PM, wij wrote:
On Wed, 2025-12-10 at 16:43 -0600, polcott wrote:
When the halting problem requires a halt decider
to report on the behavior of a Turing machine
this is always a category error.
The corrected halting problem requires a Turing
machine decider to report in the behavior that
its finite string input specifies.
If you honestly admit you are solving POO Problem, everything is fine.
*It has take me 21 years to boil it down to this*
When the halting problem requires a halt decider
to report on the behavior of a Turing machine this
is always a category error.
The corrected halting problem requires a Turing
machine decider to report in the behavior that
its finite string input specifies.
Just an external observation:
A lot of tech innovations in software optimization area get discarded
from the very beginning because people who work on them perceive the
halting problem as a dogma. As result, certain practical things (in code analysis) are not even tried because it's assumed that they are bound by
the halting problem.
In practice, however, the halting problem is rarely a limitation. And
even when one hits it, they can safely discard a particular analysis
branch by marking it as inconclusive.
Halting problem for sure can be better framed to not sound as a dogma,
at least. In practice, algorithmic inconclusiveness has 0.001
probability, not a 100% guarantee as many engineers perceive it.
On 12/11/2025 12:03 AM, polcott wrote:
On 12/10/2025 4:58 PM, wij wrote:
On Wed, 2025-12-10 at 16:43 -0600, polcott wrote:
When the halting problem requires a halt decider
to report on the behavior of a Turing machine
this is always a category error.
The corrected halting problem requires a Turing
machine decider to report in the behavior that
its finite string input specifies.
If you honestly admit you are solving POO Problem, everything is fine.
*It has take me 21 years to boil it down to this*
When the halting problem requires a halt decider
to report on the behavior of a Turing machine this
is always a category error.
The corrected halting problem requires a Turing
machine decider to report in the behavior that
its finite string input specifies.
Just an external observation:
A lot of tech innovations in software optimization area get discarded
from the very beginning because people who work on them perceive the
halting problem as a dogma. As result, certain practical things (in code analysis) are not even tried because it's assumed that they are bound by
the halting problem.
In practice, however, the halting problem is rarely a limitation. And
even when one hits it, they can safely discard a particular analysis
branch by marking it as inconclusive.
Halting problem for sure can be better framed to not sound as a dogma,
at least. In practice, algorithmic inconclusiveness has 0.001
probability, not a 100% guarantee as many engineers perceive it.
On 12/11/2025 12:03 AM, polcott wrote:
On 12/10/2025 4:58 PM, wij wrote:
On Wed, 2025-12-10 at 16:43 -0600, polcott wrote:
When the halting problem requires a halt decider
to report on the behavior of a Turing machine
this is always a category error.
The corrected halting problem requires a Turing
machine decider to report in the behavior that
its finite string input specifies.
If you honestly admit you are solving POO Problem, everything is fine.
*It has take me 21 years to boil it down to this*
When the halting problem requires a halt decider
to report on the behavior of a Turing machine this
is always a category error.
The corrected halting problem requires a Turing
machine decider to report in the behavior that
its finite string input specifies.
Just an external observation:
A lot of tech innovations in software optimization area get discarded
from the very beginning because people who work on them perceive the
halting problem as a dogma.
On 06/01/2026 02:24, Oleksiy Gapotchenko wrote:
Just an external observation:
A lot of tech innovations in software optimization area get discarded
from the very beginning because people who work on them perceive the
halting problem as a dogma.
It is a dogma in the same sense as 2 * 3 = 6 is a dogma: a provably
true sentence of a certain theory.
On 1/5/26 4:24 PM, Oleksiy Gapotchenko wrote:
Just an external observation:
A lot of tech innovations in software optimization area get discarded
from the very beginning because people who work on them perceive the
halting problem as a dogma. As result, certain practical things (in
code analysis) are not even tried because it's assumed that they are
bound by the halting problem.
In practice, however, the halting problem is rarely a limitation. And
even when one hits it, they can safely discard a particular analysis
branch by marking it as inconclusive.
Halting problem for sure can be better framed to not sound as a dogma,
at least. In practice, algorithmic inconclusiveness has 0.001
probability, not a 100% guarantee as many engineers perceive it.
god it's been such a mind-fuck to unpack the halting problem,
but the halting problem does not mean that no algorithm exists for any
given machine, just that a "general" decider does not exist for all
machiens ...
heck it must be certain that for any given machine there must exist a partial decider that can decide on it ... because otherwise a paradox
would have to address all possible partial deciders in a computable
fashion and that runs up against it's own limit to classical computing. therefore some true decider must exist for any given machine that
exists ... we just can't funnel the knowledge thru a general interface.
i think the actual problem is the TM computing is not sufficient to
describe all computable relationships. TM computing is considered the gold-standard for what is computable, but we haven't actually proved that.
the CT-thesis is a thesis, not a proof. we've been treating it as a
law ... but we never actually justified that it should be law. this
whole time we've been discarding things like a general halting decidable because TM computing can be used to create paradoxes in regards to it,
but maybe the problem is that TM computing is not sufficient to describe
a general halting decider, not that a general halting decider is
impossible.
that's my new attack vector on the consensus understanding: the CT
thesis. i am to describe a general algo that *we* can obviously compute using deterministic steps, but such algo cannot be funneled thru a
general interface because TM computing will read and paradox it.
On 12/11/2025 12:03 AM, polcott wrote:
On 12/10/2025 4:58 PM, wij wrote:
On Wed, 2025-12-10 at 16:43 -0600, polcott wrote:
When the halting problem requires a halt decider
to report on the behavior of a Turing machine
this is always a category error.
The corrected halting problem requires a Turing
machine decider to report in the behavior that
its finite string input specifies.
If you honestly admit you are solving POO Problem, everything is fine. >>>>
*It has take me 21 years to boil it down to this*
When the halting problem requires a halt decider
to report on the behavior of a Turing machine this
is always a category error.
The corrected halting problem requires a Turing
machine decider to report in the behavior that
its finite string input specifies.
On 1/6/2026 1:47 AM, dart200 wrote:
On 1/5/26 4:24 PM, Oleksiy Gapotchenko wrote:
Just an external observation:
A lot of tech innovations in software optimization area get discarded
from the very beginning because people who work on them perceive the
halting problem as a dogma. As result, certain practical things (in
code analysis) are not even tried because it's assumed that they are
bound by the halting problem.
In practice, however, the halting problem is rarely a limitation. And
even when one hits it, they can safely discard a particular analysis
branch by marking it as inconclusive.
Halting problem for sure can be better framed to not sound as a
dogma, at least. In practice, algorithmic inconclusiveness has 0.001
probability, not a 100% guarantee as many engineers perceive it.
god it's been such a mind-fuck to unpack the halting problem,
but the halting problem does not mean that no algorithm exists for any
given machine, just that a "general" decider does not exist for all
machiens ...
heck it must be certain that for any given machine there must exist a
partial decider that can decide on it ... because otherwise a paradox
would have to address all possible partial deciders in a computable
fashion and that runs up against it's own limit to classical
computing. therefore some true decider must exist for any given
machine that exists ... we just can't funnel the knowledge thru a
general interface.
For every H there is a D such that D does the opposite
of whatever H reports. In this case use H1 on this D.
i think the actual problem is the TM computing is not sufficient to
describe all computable relationships. TM computing is considered the
gold-standard for what is computable, but we haven't actually proved
that.
the CT-thesis is a thesis, not a proof. we've been treating it as a
law ... but we never actually justified that it should be law. this
whole time we've been discarding things like a general halting
decidable because TM computing can be used to create paradoxes in
regards to it, but maybe the problem is that TM computing is not
sufficient to describe a general halting decider, not that a general
halting decider is impossible.
that's my new attack vector on the consensus understanding: the CT
thesis. i am to describe a general algo that *we* can obviously
compute using deterministic steps, but such algo cannot be funneled
thru a general interface because TM computing will read and paradox it.
On 12/11/2025 12:03 AM, polcott wrote:
On 12/10/2025 4:58 PM, wij wrote:
On Wed, 2025-12-10 at 16:43 -0600, polcott wrote:
When the halting problem requires a halt decider
to report on the behavior of a Turing machine
this is always a category error.
The corrected halting problem requires a Turing
machine decider to report in the behavior that
its finite string input specifies.
If you honestly admit you are solving POO Problem, everything is fine. >>>>>
*It has take me 21 years to boil it down to this*
When the halting problem requires a halt decider
to report on the behavior of a Turing machine this
is always a category error.
The corrected halting problem requires a Turing
machine decider to report in the behavior that
its finite string input specifies.
On 1/6/26 5:26 PM, olcott wrote:
On 1/6/2026 1:47 AM, dart200 wrote:
On 1/5/26 4:24 PM, Oleksiy Gapotchenko wrote:
Just an external observation:
A lot of tech innovations in software optimization area get
discarded from the very beginning because people who work on them
perceive the halting problem as a dogma. As result, certain
practical things (in code analysis) are not even tried because it's
assumed that they are bound by the halting problem.
In practice, however, the halting problem is rarely a limitation.
And even when one hits it, they can safely discard a particular
analysis branch by marking it as inconclusive.
Halting problem for sure can be better framed to not sound as a
dogma, at least. In practice, algorithmic inconclusiveness has 0.001
probability, not a 100% guarantee as many engineers perceive it.
god it's been such a mind-fuck to unpack the halting problem,
but the halting problem does not mean that no algorithm exists for
any given machine, just that a "general" decider does not exist for
all machiens ...
heck it must be certain that for any given machine there must exist a
partial decider that can decide on it ... because otherwise a paradox
would have to address all possible partial deciders in a computable
fashion and that runs up against it's own limit to classical
computing. therefore some true decider must exist for any given
machine that exists ... we just can't funnel the knowledge thru a
general interface.
For every H there is a D such that D does the opposite
of whatever H reports. In this case use H1 on this D.
yes, the inability to correctly resolve halting thru a singular
interface is a flaw of TM computing, not an inherent algorithmic limit
On 1/6/2026 9:03 PM, dart200 wrote:
On 1/6/26 5:26 PM, olcott wrote:
On 1/6/2026 1:47 AM, dart200 wrote:
On 1/5/26 4:24 PM, Oleksiy Gapotchenko wrote:
Just an external observation:god it's been such a mind-fuck to unpack the halting problem,
A lot of tech innovations in software optimization area get
discarded from the very beginning because people who work on them
perceive the halting problem as a dogma. As result, certain
practical things (in code analysis) are not even tried because it's >>>>> assumed that they are bound by the halting problem.
In practice, however, the halting problem is rarely a limitation.
And even when one hits it, they can safely discard a particular
analysis branch by marking it as inconclusive.
Halting problem for sure can be better framed to not sound as a
dogma, at least. In practice, algorithmic inconclusiveness has
0.001 probability, not a 100% guarantee as many engineers perceive it. >>>>
but the halting problem does not mean that no algorithm exists for
any given machine, just that a "general" decider does not exist for
all machiens ...
heck it must be certain that for any given machine there must exist
a partial decider that can decide on it ... because otherwise a
paradox would have to address all possible partial deciders in a
computable fashion and that runs up against it's own limit to
classical computing. therefore some true decider must exist for any
given machine that exists ... we just can't funnel the knowledge
thru a general interface.
For every H there is a D such that D does the opposite
of whatever H reports. In this case use H1 on this D.
yes, the inability to correctly resolve halting thru a singular
interface is a flaw of TM computing, not an inherent algorithmic limit
No it is not that.
After spending 20,000 hours on this over 20 years
equivalent to ten full time years.
*if undecidability is correct then truth itself is broken*
*if undecidability is correct then truth itself is broken*
*if undecidability is correct then truth itself is broken*
*if undecidability is correct then truth itself is broken*
The simplest 100% correct resolution to the
actual definition of the Halting Problem
(that includes the counter-example input)
Is that (in the case of the counter-example input)
The halting problem asks a yes/no question
that has no correct yes/no answer.
*The HP asks an incorrect question*
*The HP asks an incorrect question*
*The HP asks an incorrect question*
*The HP asks an incorrect question*
We can only get to your idea of a different
interface when we change the definition of
that Halting Problem. The original problem
itself is simply incorrect.
*I proved the HP input is the same as the Liar Paradox back in 2004*
*I proved the HP input is the same as the Liar Paradox back in 2004*
*I proved the HP input is the same as the Liar Paradox back in 2004*
*I proved the HP input is the same as the Liar Paradox back in 2004*
function LoopIfYouSayItHalts (bool YouSayItHalts):
-a if YouSayItHalts () then
-a-a-a while true do {}
-a else
-a-a-a return false;
Does this program Halt?
(Your (YES or NO) answer is to be considered
-atranslated to Boolean as the function's input
-aparameter)
Please ONLY PROVIDE CORRECT ANSWERS!
https://groups.google.com/g/sci.logic/c/Hs78nMN6QZE/m/ID2rxwo__yQJ
On 1/6/26 8:33 PM, olcott wrote:
On 1/6/2026 9:03 PM, dart200 wrote:
On 1/6/26 5:26 PM, olcott wrote:
On 1/6/2026 1:47 AM, dart200 wrote:
On 1/5/26 4:24 PM, Oleksiy Gapotchenko wrote:
Just an external observation:
A lot of tech innovations in software optimization area get
discarded from the very beginning because people who work on them >>>>>> perceive the halting problem as a dogma. As result, certain
practical things (in code analysis) are not even tried because
it's assumed that they are bound by the halting problem.
In practice, however, the halting problem is rarely a limitation. >>>>>> And even when one hits it, they can safely discard a particular
analysis branch by marking it as inconclusive.
Halting problem for sure can be better framed to not sound as a
dogma, at least. In practice, algorithmic inconclusiveness has
0.001 probability, not a 100% guarantee as many engineers perceive >>>>>> it.
god it's been such a mind-fuck to unpack the halting problem,
but the halting problem does not mean that no algorithm exists for
any given machine, just that a "general" decider does not exist for >>>>> all machiens ...
heck it must be certain that for any given machine there must exist >>>>> a partial decider that can decide on it ... because otherwise a
paradox would have to address all possible partial deciders in a
computable fashion and that runs up against it's own limit to
classical computing. therefore some true decider must exist for any >>>>> given machine that exists ... we just can't funnel the knowledge
thru a general interface.
For every H there is a D such that D does the opposite
of whatever H reports. In this case use H1 on this D.
yes, the inability to correctly resolve halting thru a singular
interface is a flaw of TM computing, not an inherent algorithmic limit
No it is not that.
After spending 20,000 hours on this over 20 years
equivalent to ten full time years.
*if undecidability is correct then truth itself is broken*
*if undecidability is correct then truth itself is broken*
*if undecidability is correct then truth itself is broken*
*if undecidability is correct then truth itself is broken*
The simplest 100% correct resolution to the
actual definition of the Halting Problem
(that includes the counter-example input)
Is that (in the case of the counter-example input)
The halting problem asks a yes/no question
that has no correct yes/no answer.
i love how you agree with the consensus position but think u don't
*The HP asks an incorrect question*
*The HP asks an incorrect question*
*The HP asks an incorrect question*
*The HP asks an incorrect question*
We can only get to your idea of a different
interface when we change the definition of
that Halting Problem. The original problem
itself is simply incorrect.
the question's a fine expectation
TMs can't represent the answer tho, and that's the real problem
i think the actual problem is the TM computing is not sufficient to
describe all computable relationships.
On 1/6/2026 7:23 AM, Mikko wrote:
On 06/01/2026 02:24, Oleksiy Gapotchenko wrote:
Just an external observation:
A lot of tech innovations in software optimization area get discarded
from the very beginning because people who work on them perceive the
halting problem as a dogma.
It is a dogma in the same sense as 2 * 3 = 6 is a dogma: a provably
true sentence of a certain theory.
...We are therefore confronted with a proposition which
asserts its own unprovability. 15 rCa (G||del 1931:40-41)
G||del, Kurt 1931.
On Formally Undecidable Propositions of
Principia Mathematica And Related Systems
F reo G_F rao -4Prov_F (riLG_FriY)
"F proves that: G_F is equivalent to
G||del_Number(G_F) is not provable in F" https://plato.stanford.edu/entries/goedel-incompleteness/#FirIncTheCom
Stripping away the inessential baggage using a formal
language with its own self-reference operator and
provability operator (thus outside of arithmetic)
G := (F re4 G)-a-a // G asserts its own unprovability in F
A proof of G in F would be a sequence of inference
steps in F that prove that they themselves do not exist.
On 06/01/2026 16:02, olcott wrote:
On 1/6/2026 7:23 AM, Mikko wrote:
On 06/01/2026 02:24, Oleksiy Gapotchenko wrote:
Just an external observation:
A lot of tech innovations in software optimization area get
discarded from the very beginning because people who work on them
perceive the halting problem as a dogma.
It is a dogma in the same sense as 2 * 3 = 6 is a dogma: a provably
true sentence of a certain theory.
...We are therefore confronted with a proposition which
asserts its own unprovability. 15 rCa (G||del 1931:40-41)
G||del, Kurt 1931.
On Formally Undecidable Propositions of
Principia Mathematica And Related Systems
F reo G_F rao -4Prov_F (riLG_FriY)
"F proves that: G_F is equivalent to
G||del_Number(G_F) is not provable in F"
https://plato.stanford.edu/entries/goedel-incompleteness/#FirIncTheCom
Stripping away the inessential baggage using a formal
language with its own self-reference operator and
provability operator (thus outside of arithmetic)
G := (F re4 G)-a-a // G asserts its own unprovability in F
A proof of G in F would be a sequence of inference
steps in F that prove that they themselves do not exist.
From the way G is constructed it can be meta-proven that either
G is true and unprovable in F (which means that F is incomplete)
or G is false and provable in F (which means that F is inconsistent).
On 06/01/2026 09:47, dart200 wrote:
-a ...
i think the actual problem is the TM computing is not sufficient to
describe all computable relationships.
It is not. Although we don't know any way compute what is not Turing
computable, we can image a machine that can compute what a Turing
machine can't. Such machine can use a tape as an input and output
device as well as working storage just like Turing machine but has
additional instructions for operations that are not Turring computable.
While it is possible to imagine a halting decider for TUring machines implemented with an extended machine, a halting decider for all such
machines still requires that the decider can compute something that
none of the machines in its input domain can.
On 06/01/2026 09:47, dart200 wrote:
-a ...
i think the actual problem is the TM computing is not sufficient to
describe all computable relationships.
It is not. Although we don't know any way compute what is not Turing computable,
we can image a machine that can compute what a Turing
machine can't. Such machine can use a tape as an input and output
device as well as working storage just like Turing machine but has
additional instructions for operations that are not Turring computable.
While it is possible to imagine a halting decider for TUring machines implemented with an extended machine, a halting decider for all such
machines still requires that the decider can compute something that
none of the machines in its input domain can.
On 1/7/26 4:05 AM, Mikko wrote:
On 06/01/2026 09:47, dart200 wrote:
-a-a ...
i think the actual problem is the TM computing is not sufficient to
describe all computable relationships.
It is not. Although we don't know any way compute what is not Turing
if TM computing is not sufficient to describe all computable relationships,
then the CT-thesis is truly cooked, no???
On 1/7/2026 6:10 AM, Mikko wrote:
On 06/01/2026 16:02, olcott wrote:
On 1/6/2026 7:23 AM, Mikko wrote:
On 06/01/2026 02:24, Oleksiy Gapotchenko wrote:
Just an external observation:
A lot of tech innovations in software optimization area get
discarded from the very beginning because people who work on them
perceive the halting problem as a dogma.
It is a dogma in the same sense as 2 * 3 = 6 is a dogma: a provably
true sentence of a certain theory.
...We are therefore confronted with a proposition which
asserts its own unprovability. 15 rCa (G||del 1931:40-41)
G||del, Kurt 1931.
On Formally Undecidable Propositions of
Principia Mathematica And Related Systems
F reo G_F rao -4Prov_F (riLG_FriY)
"F proves that: G_F is equivalent to
G||del_Number(G_F) is not provable in F"
https://plato.stanford.edu/entries/goedel-incompleteness/#FirIncTheCom
Stripping away the inessential baggage using a formal
language with its own self-reference operator and
provability operator (thus outside of arithmetic)
G := (F re4 G)-a-a // G asserts its own unprovability in F
A proof of G in F would be a sequence of inference
steps in F that prove that they themselves do not exist.
-aFrom the way G is constructed it can be meta-proven that either
Did you hear me stutter ?
A proof of G in F would be a sequence of inference
steps in F that prove that they themselves do not exist.
On 07/01/2026 15:06, olcott wrote:
On 1/7/2026 6:10 AM, Mikko wrote:
On 06/01/2026 16:02, olcott wrote:
On 1/6/2026 7:23 AM, Mikko wrote:
On 06/01/2026 02:24, Oleksiy Gapotchenko wrote:
Just an external observation:
A lot of tech innovations in software optimization area get
discarded from the very beginning because people who work on them >>>>>> perceive the halting problem as a dogma.
It is a dogma in the same sense as 2 * 3 = 6 is a dogma: a provably
true sentence of a certain theory.
...We are therefore confronted with a proposition which
asserts its own unprovability. 15 rCa (G||del 1931:40-41)
G||del, Kurt 1931.
On Formally Undecidable Propositions of
Principia Mathematica And Related Systems
F reo G_F rao -4Prov_F (riLG_FriY)
"F proves that: G_F is equivalent to
G||del_Number(G_F) is not provable in F"
https://plato.stanford.edu/entries/goedel-incompleteness/#FirIncTheCom >>>>
Stripping away the inessential baggage using a formal
language with its own self-reference operator and
provability operator (thus outside of arithmetic)
G := (F re4 G)-a-a // G asserts its own unprovability in F
A proof of G in F would be a sequence of inference
steps in F that prove that they themselves do not exist.
-aFrom the way G is constructed it can be meta-proven that either
Did you hear me stutter ?
A proof of G in F would be a sequence of inference
steps in F that prove that they themselves do not exist.
An F where such sequence really exists then in that F both G and
the negation of G are provable.
In an F where such sequn|-nce does not exist G is unprovable by
definition. However it is meta-provable frome the way it is
constructed and therefore true in every interpretation where
the natural numbers contained in F have their standard properties.
On 1/8/2026 4:21 AM, Mikko wrote:
On 07/01/2026 15:06, olcott wrote:G := (F re4 G)-a-a // G asserts its own unprovability in F
On 1/7/2026 6:10 AM, Mikko wrote:
On 06/01/2026 16:02, olcott wrote:
On 1/6/2026 7:23 AM, Mikko wrote:
On 06/01/2026 02:24, Oleksiy Gapotchenko wrote:
Just an external observation:
A lot of tech innovations in software optimization area get
discarded from the very beginning because people who work on them >>>>>>> perceive the halting problem as a dogma.
It is a dogma in the same sense as 2 * 3 = 6 is a dogma: a provably >>>>>> true sentence of a certain theory.
...We are therefore confronted with a proposition which
asserts its own unprovability. 15 rCa (G||del 1931:40-41)
G||del, Kurt 1931.
On Formally Undecidable Propositions of
Principia Mathematica And Related Systems
F reo G_F rao -4Prov_F (riLG_FriY)
"F proves that: G_F is equivalent to
G||del_Number(G_F) is not provable in F"
https://plato.stanford.edu/entries/goedel-incompleteness/#FirIncTheCom >>>>>
Stripping away the inessential baggage using a formal
language with its own self-reference operator and
provability operator (thus outside of arithmetic)
G := (F re4 G)-a-a // G asserts its own unprovability in F
A proof of G in F would be a sequence of inference
steps in F that prove that they themselves do not exist.
-aFrom the way G is constructed it can be meta-proven that either
Did you hear me stutter ?
A proof of G in F would be a sequence of inference
steps in F that prove that they themselves do not exist.
An F where such sequence really exists then in that F both G and
the negation of G are provable.
A proof of G in F would be a sequence of inference
steps in F that prove that they themselves do not exist.
Does not exist because is contradicts itself.
On 08/01/2026 16:18, olcott wrote:
On 1/8/2026 4:21 AM, Mikko wrote:
On 07/01/2026 15:06, olcott wrote:G := (F re4 G)-a-a // G asserts its own unprovability in F
On 1/7/2026 6:10 AM, Mikko wrote:
On 06/01/2026 16:02, olcott wrote:
On 1/6/2026 7:23 AM, Mikko wrote:
On 06/01/2026 02:24, Oleksiy Gapotchenko wrote:
Just an external observation:
A lot of tech innovations in software optimization area get
discarded from the very beginning because people who work on
them perceive the halting problem as a dogma.
It is a dogma in the same sense as 2 * 3 = 6 is a dogma: a provably >>>>>>> true sentence of a certain theory.
...We are therefore confronted with a proposition which
asserts its own unprovability. 15 rCa (G||del 1931:40-41)
G||del, Kurt 1931.
On Formally Undecidable Propositions of
Principia Mathematica And Related Systems
F reo G_F rao -4Prov_F (riLG_FriY)
"F proves that: G_F is equivalent to
G||del_Number(G_F) is not provable in F"
https://plato.stanford.edu/entries/goedel-incompleteness/
#FirIncTheCom
Stripping away the inessential baggage using a formal
language with its own self-reference operator and
provability operator (thus outside of arithmetic)
G := (F re4 G)-a-a // G asserts its own unprovability in F
A proof of G in F would be a sequence of inference
steps in F that prove that they themselves do not exist.
-aFrom the way G is constructed it can be meta-proven that either
Did you hear me stutter ?
A proof of G in F would be a sequence of inference
steps in F that prove that they themselves do not exist.
An F where such sequence really exists then in that F both G and
the negation of G are provable.
A proof of G in F would be a sequence of inference
steps in F that prove that they themselves do not exist.
Does not exist because is contradicts itself.
That conclusion needs the additional assumption that F is consistent,
which requires that the first order Peano arithmetic is consistent.
If F is not consistent then both G and its negation are provable in F.
The first order Peano arithmetic is believed to be sonsistent but its consistency is not proven.
On 07/01/2026 22:20, dart200 wrote:
On 1/7/26 4:05 AM, Mikko wrote:
On 06/01/2026 09:47, dart200 wrote:
-a-a ...
i think the actual problem is the TM computing is not sufficient to
describe all computable relationships.
It is not. Although we don't know any way compute what is not Turing
if TM computing is not sufficient to describe all computable
relationships,
then the CT-thesis is truly cooked, no???
In any case "cooked" is not the right word. The word "cooked" refers to
what has already happened or been done. What might be found out lanter
is irrelevant.
A method to compute something that is not Turing computable is not very useful when nobody knows it.
On 1/10/2026 3:25 AM, Mikko wrote:
On 08/01/2026 16:18, olcott wrote:
On 1/8/2026 4:21 AM, Mikko wrote:
On 07/01/2026 15:06, olcott wrote:G := (F re4 G)-a-a // G asserts its own unprovability in F
On 1/7/2026 6:10 AM, Mikko wrote:
On 06/01/2026 16:02, olcott wrote:
On 1/6/2026 7:23 AM, Mikko wrote:
On 06/01/2026 02:24, Oleksiy Gapotchenko wrote:
Just an external observation:
A lot of tech innovations in software optimization area get >>>>>>>>> discarded from the very beginning because people who work on >>>>>>>>> them perceive the halting problem as a dogma.
It is a dogma in the same sense as 2 * 3 = 6 is a dogma: a provably >>>>>>>> true sentence of a certain theory.
...We are therefore confronted with a proposition which
asserts its own unprovability. 15 rCa (G||del 1931:40-41)
G||del, Kurt 1931.
On Formally Undecidable Propositions of
Principia Mathematica And Related Systems
F reo G_F rao -4Prov_F (riLG_FriY)
"F proves that: G_F is equivalent to
G||del_Number(G_F) is not provable in F"
https://plato.stanford.edu/entries/goedel-incompleteness/
#FirIncTheCom
Stripping away the inessential baggage using a formal
language with its own self-reference operator and
provability operator (thus outside of arithmetic)
G := (F re4 G)-a-a // G asserts its own unprovability in F
A proof of G in F would be a sequence of inference
steps in F that prove that they themselves do not exist.
-aFrom the way G is constructed it can be meta-proven that either
Did you hear me stutter ?
A proof of G in F would be a sequence of inference
steps in F that prove that they themselves do not exist.
An F where such sequence really exists then in that F both G and
the negation of G are provable.
A proof of G in F would be a sequence of inference
steps in F that prove that they themselves do not nexist.
Does not exist because is contradicts itself.
That conclusion needs the additional assumption that F is consistent,
which requires that the first order Peano arithmetic is consistent.
It remains true for any proof system that does not
contradict itself.
If F is not consistent then both G and its negation are provable in F.
The first order Peano arithmetic is believed to be sonsistent but its
consistency is not proven.
The point is that after all these years no one ever
bothered to notice WHY G is unprovable in F. When
we do that then G||del Incompleteness falls apart.
*G is unprovable in F because its proof would contradict itself*
*G is unprovable in F because its proof would contradict itself*
*G is unprovable in F because its proof would contradict itself*
On 1/10/26 11:19 AM, olcott wrote:
On 1/10/2026 3:25 AM, Mikko wrote:
On 08/01/2026 16:18, olcott wrote:
On 1/8/2026 4:21 AM, Mikko wrote:
On 07/01/2026 15:06, olcott wrote:G := (F re4 G)-a-a // G asserts its own unprovability in F
On 1/7/2026 6:10 AM, Mikko wrote:
On 06/01/2026 16:02, olcott wrote:Did you hear me stutter ?
On 1/6/2026 7:23 AM, Mikko wrote:
On 06/01/2026 02:24, Oleksiy Gapotchenko wrote:
Just an external observation:
A lot of tech innovations in software optimization area get >>>>>>>>>> discarded from the very beginning because people who work on >>>>>>>>>> them perceive the halting problem as a dogma.
It is a dogma in the same sense as 2 * 3 = 6 is a dogma: a
provably
true sentence of a certain theory.
...We are therefore confronted with a proposition which
asserts its own unprovability. 15 rCa (G||del 1931:40-41)
G||del, Kurt 1931.
On Formally Undecidable Propositions of
Principia Mathematica And Related Systems
F reo G_F rao -4Prov_F (riLG_FriY)
"F proves that: G_F is equivalent to
G||del_Number(G_F) is not provable in F"
https://plato.stanford.edu/entries/goedel-incompleteness/
#FirIncTheCom
Stripping away the inessential baggage using a formal
language with its own self-reference operator and
provability operator (thus outside of arithmetic)
G := (F re4 G)-a-a // G asserts its own unprovability in F
A proof of G in F would be a sequence of inference
steps in F that prove that they themselves do not exist.
-aFrom the way G is constructed it can be meta-proven that either >>>>>>
A proof of G in F would be a sequence of inference
steps in F that prove that they themselves do not exist.
An F where such sequence really exists then in that F both G and
the negation of G are provable.
A proof of G in F would be a sequence of inference
steps in F that prove that they themselves do not nexist.
Does not exist because is contradicts itself.
That conclusion needs the additional assumption that F is consistent,
which requires that the first order Peano arithmetic is consistent.
It remains true for any proof system that does not
contradict itself.
If F is not consistent then both G and its negation are provable in F.
The first order Peano arithmetic is believed to be sonsistent but its
consistency is not proven.
The point is that after all these years no one ever
bothered to notice WHY G is unprovable in F. When
we do that then G||del Incompleteness falls apart.
*G is unprovable in F because its proof would contradict itself*
*G is unprovable in F because its proof would contradict itself*
*G is unprovable in F because its proof would contradict itself*
Right. so you can only have two of the following, and not all three:
1) Consistent.
2) Complete
3) Capable of supporting the Natural Numbers.
It seems the logic you can handle can't do the last, so yo are fine with your limited, but Complete and Consistant system.
On 1/10/2026 5:19 PM, Richard Damon wrote:
On 1/10/26 11:19 AM, olcott wrote:
On 1/10/2026 3:25 AM, Mikko wrote:
On 08/01/2026 16:18, olcott wrote:
On 1/8/2026 4:21 AM, Mikko wrote:
On 07/01/2026 15:06, olcott wrote:G := (F re4 G)-a-a // G asserts its own unprovability in F
On 1/7/2026 6:10 AM, Mikko wrote:
On 06/01/2026 16:02, olcott wrote:Did you hear me stutter ?
On 1/6/2026 7:23 AM, Mikko wrote:
On 06/01/2026 02:24, Oleksiy Gapotchenko wrote:
Just an external observation:
A lot of tech innovations in software optimization area get >>>>>>>>>>> discarded from the very beginning because people who work on >>>>>>>>>>> them perceive the halting problem as a dogma.
It is a dogma in the same sense as 2 * 3 = 6 is a dogma: a >>>>>>>>>> provably
true sentence of a certain theory.
...We are therefore confronted with a proposition which
asserts its own unprovability. 15 rCa (G||del 1931:40-41)
G||del, Kurt 1931.
On Formally Undecidable Propositions of
Principia Mathematica And Related Systems
F reo G_F rao -4Prov_F (riLG_FriY)
"F proves that: G_F is equivalent to
G||del_Number(G_F) is not provable in F"
https://plato.stanford.edu/entries/goedel-incompleteness/
#FirIncTheCom
Stripping away the inessential baggage using a formal
language with its own self-reference operator and
provability operator (thus outside of arithmetic)
G := (F re4 G)-a-a // G asserts its own unprovability in F
A proof of G in F would be a sequence of inference
steps in F that prove that they themselves do not exist.
-aFrom the way G is constructed it can be meta-proven that either >>>>>>>
A proof of G in F would be a sequence of inference
steps in F that prove that they themselves do not exist.
An F where such sequence really exists then in that F both G and
the negation of G are provable.
A proof of G in F would be a sequence of inference
steps in F that prove that they themselves do not nexist.
Does not exist because is contradicts itself.
That conclusion needs the additional assumption that F is consistent,
which requires that the first order Peano arithmetic is consistent.
It remains true for any proof system that does not
contradict itself.
If F is not consistent then both G and its negation are provable in F. >>>> The first order Peano arithmetic is believed to be sonsistent but its
consistency is not proven.
The point is that after all these years no one ever
bothered to notice WHY G is unprovable in F. When
we do that then G||del Incompleteness falls apart.
*G is unprovable in F because its proof would contradict itself*
*G is unprovable in F because its proof would contradict itself*
*G is unprovable in F because its proof would contradict itself*
Right. so you can only have two of the following, and not all three:
1) Consistent.
2) Complete
3) Capable of supporting the Natural Numbers.
It seems the logic you can handle can't do the last, so yo are fine
with your limited, but Complete and Consistant system.
Not at all. G||del incorrectly conflates true in meta-math
with true in math. Proof Theoretic Semantics rejects this.
Proof Conditional Semantics is misguided.
On 1/10/26 7:16 PM, olcott wrote:
On 1/10/2026 5:19 PM, Richard Damon wrote:
On 1/10/26 11:19 AM, olcott wrote:
On 1/10/2026 3:25 AM, Mikko wrote:
On 08/01/2026 16:18, olcott wrote:
On 1/8/2026 4:21 AM, Mikko wrote:
On 07/01/2026 15:06, olcott wrote:G := (F re4 G)-a-a // G asserts its own unprovability in F
On 1/7/2026 6:10 AM, Mikko wrote:
On 06/01/2026 16:02, olcott wrote:Did you hear me stutter ?
On 1/6/2026 7:23 AM, Mikko wrote:
On 06/01/2026 02:24, Oleksiy Gapotchenko wrote:
Just an external observation:
A lot of tech innovations in software optimization area get >>>>>>>>>>>> discarded from the very beginning because people who work on >>>>>>>>>>>> them perceive the halting problem as a dogma.
It is a dogma in the same sense as 2 * 3 = 6 is a dogma: a >>>>>>>>>>> provably
true sentence of a certain theory.
...We are therefore confronted with a proposition which
asserts its own unprovability. 15 rCa (G||del 1931:40-41)
G||del, Kurt 1931.
On Formally Undecidable Propositions of
Principia Mathematica And Related Systems
F reo G_F rao -4Prov_F (riLG_FriY)
"F proves that: G_F is equivalent to
G||del_Number(G_F) is not provable in F"
https://plato.stanford.edu/entries/goedel-incompleteness/ >>>>>>>>>> #FirIncTheCom
Stripping away the inessential baggage using a formal
language with its own self-reference operator and
provability operator (thus outside of arithmetic)
G := (F re4 G)-a-a // G asserts its own unprovability in F >>>>>>>>>>
A proof of G in F would be a sequence of inference
steps in F that prove that they themselves do not exist.
-aFrom the way G is constructed it can be meta-proven that either >>>>>>>>
A proof of G in F would be a sequence of inference
steps in F that prove that they themselves do not exist.
An F where such sequence really exists then in that F both G and >>>>>>> the negation of G are provable.
A proof of G in F would be a sequence of inference
steps in F that prove that they themselves do not nexist.
Does not exist because is contradicts itself.
That conclusion needs the additional assumption that F is consistent, >>>>> which requires that the first order Peano arithmetic is consistent.
It remains true for any proof system that does not
contradict itself.
If F is not consistent then both G and its negation are provable in F. >>>>> The first order Peano arithmetic is believed to be sonsistent but its >>>>> consistency is not proven.
The point is that after all these years no one ever
bothered to notice WHY G is unprovable in F. When
we do that then G||del Incompleteness falls apart.
*G is unprovable in F because its proof would contradict itself*
*G is unprovable in F because its proof would contradict itself*
*G is unprovable in F because its proof would contradict itself*
Right. so you can only have two of the following, and not all three:
1) Consistent.
2) Complete
3) Capable of supporting the Natural Numbers.
It seems the logic you can handle can't do the last, so yo are fine
with your limited, but Complete and Consistant system.
Not at all. G||del incorrectly conflates true in meta-math
with true in math. Proof Theoretic Semantics rejects this.
Proof Conditional Semantics is misguided.
Nope, it weems you think math doesn't work.
On 1/10/2026 3:25 AM, Mikko wrote:
On 08/01/2026 16:18, olcott wrote:
On 1/8/2026 4:21 AM, Mikko wrote:
On 07/01/2026 15:06, olcott wrote:G := (F re4 G)-a-a // G asserts its own unprovability in F
On 1/7/2026 6:10 AM, Mikko wrote:
On 06/01/2026 16:02, olcott wrote:
On 1/6/2026 7:23 AM, Mikko wrote:
On 06/01/2026 02:24, Oleksiy Gapotchenko wrote:
Just an external observation:
A lot of tech innovations in software optimization area get >>>>>>>>> discarded from the very beginning because people who work on >>>>>>>>> them perceive the halting problem as a dogma.
It is a dogma in the same sense as 2 * 3 = 6 is a dogma: a provably >>>>>>>> true sentence of a certain theory.
...We are therefore confronted with a proposition which
asserts its own unprovability. 15 rCa (G||del 1931:40-41)
G||del, Kurt 1931.
On Formally Undecidable Propositions of
Principia Mathematica And Related Systems
F reo G_F rao -4Prov_F (riLG_FriY)
"F proves that: G_F is equivalent to
G||del_Number(G_F) is not provable in F"
https://plato.stanford.edu/entries/goedel-incompleteness/
#FirIncTheCom
Stripping away the inessential baggage using a formal
language with its own self-reference operator and
provability operator (thus outside of arithmetic)
G := (F re4 G)-a-a // G asserts its own unprovability in F
A proof of G in F would be a sequence of inference
steps in F that prove that they themselves do not exist.
-aFrom the way G is constructed it can be meta-proven that either
Did you hear me stutter ?
A proof of G in F would be a sequence of inference
steps in F that prove that they themselves do not exist.
An F where such sequence really exists then in that F both G and
the negation of G are provable.
A proof of G in F would be a sequence of inference
steps in F that prove that they themselves do not exist.
Does not exist because is contradicts itself.
That conclusion needs the additional assumption that F is consistent,
which requires that the first order Peano arithmetic is consistent.
It remains true for any proof system that does not
contradict itself.
On 1/10/2026 6:35 PM, Richard Damon wrote:
On 1/10/26 7:16 PM, olcott wrote:
On 1/10/2026 5:19 PM, Richard Damon wrote:
On 1/10/26 11:19 AM, olcott wrote:
On 1/10/2026 3:25 AM, Mikko wrote:
On 08/01/2026 16:18, olcott wrote:It remains true for any proof system that does not
On 1/8/2026 4:21 AM, Mikko wrote:
On 07/01/2026 15:06, olcott wrote:G := (F re4 G)-a-a // G asserts its own unprovability in F
On 1/7/2026 6:10 AM, Mikko wrote:
On 06/01/2026 16:02, olcott wrote:Did you hear me stutter ?
On 1/6/2026 7:23 AM, Mikko wrote:
On 06/01/2026 02:24, Oleksiy Gapotchenko wrote:
Just an external observation:
A lot of tech innovations in software optimization area get >>>>>>>>>>>>> discarded from the very beginning because people who work >>>>>>>>>>>>> on them perceive the halting problem as a dogma.
It is a dogma in the same sense as 2 * 3 = 6 is a dogma: a >>>>>>>>>>>> provably
true sentence of a certain theory.
...We are therefore confronted with a proposition which
asserts its own unprovability. 15 rCa (G||del 1931:40-41) >>>>>>>>>>>
G||del, Kurt 1931.
On Formally Undecidable Propositions of
Principia Mathematica And Related Systems
F reo G_F rao -4Prov_F (riLG_FriY)
"F proves that: G_F is equivalent to
G||del_Number(G_F) is not provable in F"
https://plato.stanford.edu/entries/goedel-incompleteness/ >>>>>>>>>>> #FirIncTheCom
Stripping away the inessential baggage using a formal
language with its own self-reference operator and
provability operator (thus outside of arithmetic)
G := (F re4 G)-a-a // G asserts its own unprovability in F >>>>>>>>>>>
A proof of G in F would be a sequence of inference
steps in F that prove that they themselves do not exist.
-aFrom the way G is constructed it can be meta-proven that either >>>>>>>>>
A proof of G in F would be a sequence of inference
steps in F that prove that they themselves do not exist.
An F where such sequence really exists then in that F both G and >>>>>>>> the negation of G are provable.
A proof of G in F would be a sequence of inference
steps in F that prove that they themselves do not nexist.
Does not exist because is contradicts itself.
That conclusion needs the additional assumption that F is consistent, >>>>>> which requires that the first order Peano arithmetic is consistent. >>>>>
contradict itself.
If F is not consistent then both G and its negation are provable
in F.
The first order Peano arithmetic is believed to be sonsistent but its >>>>>> consistency is not proven.
The point is that after all these years no one ever
bothered to notice WHY G is unprovable in F. When
we do that then G||del Incompleteness falls apart.
*G is unprovable in F because its proof would contradict itself*
*G is unprovable in F because its proof would contradict itself*
*G is unprovable in F because its proof would contradict itself*
Right. so you can only have two of the following, and not all three:
1) Consistent.
2) Complete
3) Capable of supporting the Natural Numbers.
It seems the logic you can handle can't do the last, so yo are fine
with your limited, but Complete and Consistant system.
Not at all. G||del incorrectly conflates true in meta-math
with true in math. Proof Theoretic Semantics rejects this.
Proof Conditional Semantics is misguided.
Nope, it weems you think math doesn't work.
Proof Theoretic Semantics agrees with me you are
going by Proof Conditional Semantics.
On 1/6/26 5:26 PM, olcott wrote:
On 1/6/2026 1:47 AM, dart200 wrote:
On 1/5/26 4:24 PM, Oleksiy Gapotchenko wrote:
Just an external observation:
A lot of tech innovations in software optimization area get
discarded from the very beginning because people who work on them
perceive the halting problem as a dogma. As result, certain
practical things (in code analysis) are not even tried because it's
assumed that they are bound by the halting problem.
In practice, however, the halting problem is rarely a limitation.
And even when one hits it, they can safely discard a particular
analysis branch by marking it as inconclusive.
Halting problem for sure can be better framed to not sound as a
dogma, at least. In practice, algorithmic inconclusiveness has 0.001
probability, not a 100% guarantee as many engineers perceive it.
god it's been such a mind-fuck to unpack the halting problem,
but the halting problem does not mean that no algorithm exists for
any given machine, just that a "general" decider does not exist for
all machiens ...
heck it must be certain that for any given machine there must exist a
partial decider that can decide on it ... because otherwise a paradox
would have to address all possible partial deciders in a computable
fashion and that runs up against it's own limit to classical
computing. therefore some true decider must exist for any given
machine that exists ... we just can't funnel the knowledge thru a
general interface.
For every H there is a D such that D does the opposite
of whatever H reports. In this case use H1 on this D.
yes, the inability to correctly resolve halting thru a singular
interface is a flaw of TM computing, not an inherent algorithmic limit
i think the actual problem is the TM computing is not sufficient to
describe all computable relationships. TM computing is considered the
gold-standard for what is computable, but we haven't actually proved
that.
the CT-thesis is a thesis, not a proof. we've been treating it as a
law ... but we never actually justified that it should be law. this
whole time we've been discarding things like a general halting
decidable because TM computing can be used to create paradoxes in
regards to it, but maybe the problem is that TM computing is not
sufficient to describe a general halting decider, not that a general
halting decider is impossible.
that's my new attack vector on the consensus understanding: the CT
thesis. i am to describe a general algo that *we* can obviously
compute using deterministic steps, but such algo cannot be funneled
thru a general interface because TM computing will read and paradox it.
On 12/11/2025 12:03 AM, polcott wrote:
On 12/10/2025 4:58 PM, wij wrote:
On Wed, 2025-12-10 at 16:43 -0600, polcott wrote:
When the halting problem requires a halt decider
to report on the behavior of a Turing machine
this is always a category error.
The corrected halting problem requires a Turing
machine decider to report in the behavior that
its finite string input specifies.
If you honestly admit you are solving POO Problem, everything is
fine.
*It has take me 21 years to boil it down to this*
When the halting problem requires a halt decider
to report on the behavior of a Turing machine this
is always a category error.
The corrected halting problem requires a Turing
machine decider to report in the behavior that
its finite string input specifies.
On 1/6/2026 9:03 PM, dart200 wrote:
On 1/6/26 5:26 PM, olcott wrote:
On 1/6/2026 1:47 AM, dart200 wrote:
On 1/5/26 4:24 PM, Oleksiy Gapotchenko wrote:
Just an external observation:god it's been such a mind-fuck to unpack the halting problem,
A lot of tech innovations in software optimization area get
discarded from the very beginning because people who work on them
perceive the halting problem as a dogma. As result, certain
practical things (in code analysis) are not even tried because it's >>>>> assumed that they are bound by the halting problem.
In practice, however, the halting problem is rarely a limitation.
And even when one hits it, they can safely discard a particular
analysis branch by marking it as inconclusive.
Halting problem for sure can be better framed to not sound as a
dogma, at least. In practice, algorithmic inconclusiveness has
0.001 probability, not a 100% guarantee as many engineers perceive it. >>>>
but the halting problem does not mean that no algorithm exists for
any given machine, just that a "general" decider does not exist for
all machiens ...
heck it must be certain that for any given machine there must exist
a partial decider that can decide on it ... because otherwise a
paradox would have to address all possible partial deciders in a
computable fashion and that runs up against it's own limit to
classical computing. therefore some true decider must exist for any
given machine that exists ... we just can't funnel the knowledge
thru a general interface.
For every H there is a D such that D does the opposite
of whatever H reports. In this case use H1 on this D.
yes, the inability to correctly resolve halting thru a singular
interface is a flaw of TM computing, not an inherent algorithmic limit
No it is not that.
After spending 20,000 hours on this over 20 years
equivalent to ten full time years.
*if undecidability is correct then truth itself is broken*
*if undecidability is correct then truth itself is broken*
*if undecidability is correct then truth itself is broken*
*if undecidability is correct then truth itself is broken*
The simplest 100% correct resolution to the
actual definition of the Halting Problem
(that includes the counter-example input)
Is that (in the case of the counter-example input)
The halting problem asks a yes/no question
that has no correct yes/no answer.
*The HP asks an incorrect question*
*The HP asks an incorrect question*
*The HP asks an incorrect question*
*The HP asks an incorrect question*
We can only get to your idea of a different
interface when we change the definition of
that Halting Problem. The original problem
itself is simply incorrect.
*I proved the HP input is the same as the Liar Paradox back in 2004*
*I proved the HP input is the same as the Liar Paradox back in 2004*
*I proved the HP input is the same as the Liar Paradox back in 2004*
*I proved the HP input is the same as the Liar Paradox back in 2004*
function LoopIfYouSayItHalts (bool YouSayItHalts):
-a if YouSayItHalts () then
-a-a-a while true do {}
-a else
-a-a-a return false;
Does this program Halt?
(Your (YES or NO) answer is to be considered
-atranslated to Boolean as the function's input
-aparameter)
Please ONLY PROVIDE CORRECT ANSWERS!
https://groups.google.com/g/sci.logic/c/Hs78nMN6QZE/m/ID2rxwo__yQJ
On 1/6/26 10:03 PM, dart200 wrote:
On 1/6/26 5:26 PM, olcott wrote:
On 1/6/2026 1:47 AM, dart200 wrote:
On 1/5/26 4:24 PM, Oleksiy Gapotchenko wrote:
Just an external observation:god it's been such a mind-fuck to unpack the halting problem,
A lot of tech innovations in software optimization area get
discarded from the very beginning because people who work on them
perceive the halting problem as a dogma. As result, certain
practical things (in code analysis) are not even tried because it's >>>>> assumed that they are bound by the halting problem.
In practice, however, the halting problem is rarely a limitation.
And even when one hits it, they can safely discard a particular
analysis branch by marking it as inconclusive.
Halting problem for sure can be better framed to not sound as a
dogma, at least. In practice, algorithmic inconclusiveness has
0.001 probability, not a 100% guarantee as many engineers perceive it. >>>>
but the halting problem does not mean that no algorithm exists for
any given machine, just that a "general" decider does not exist for
all machiens ...
heck it must be certain that for any given machine there must exist
a partial decider that can decide on it ... because otherwise a
paradox would have to address all possible partial deciders in a
computable fashion and that runs up against it's own limit to
classical computing. therefore some true decider must exist for any
given machine that exists ... we just can't funnel the knowledge
thru a general interface.
For every H there is a D such that D does the opposite
of whatever H reports. In this case use H1 on this D.
yes, the inability to correctly resolve halting thru a singular
interface is a flaw of TM computing, not an inherent algorithmic limit
Nope, because the proof doesn't actually need to talk about HOW the
decider actually made its decision, and thus not limited to Turing
Machines.
All it needs is that the decider be limited by the rules of a computation.
All the arguements against the proof seem to begin with the error that
the decider can be changed after the fact and such change changes the
input to match, but that breaks the fundamental property of
computations, that they are fixed algorithms
The proof shows that the SPECIFIC decider that the input was made from
will get the wrong answer, and we can make such an input for ANY
specific decider, and thus no decider can get all answers correct.
That the input HAS a correct answer (just the opposite of what that
specific decider gives) shows that there IS a correct answer, so there
is nothing wrong about the question of its halting, and thus a non-
answer like "its behavior is contrary" is valid.
Everyone trying to make the arguements just shows they don't understand
the basics of what a computation is.
On 1/12/26 4:06 AM, Richard Damon wrote:
On 1/6/26 10:03 PM, dart200 wrote:
On 1/6/26 5:26 PM, olcott wrote:
On 1/6/2026 1:47 AM, dart200 wrote:
On 1/5/26 4:24 PM, Oleksiy Gapotchenko wrote:
Just an external observation:
A lot of tech innovations in software optimization area get
discarded from the very beginning because people who work on them >>>>>> perceive the halting problem as a dogma. As result, certain
practical things (in code analysis) are not even tried because
it's assumed that they are bound by the halting problem.
In practice, however, the halting problem is rarely a limitation. >>>>>> And even when one hits it, they can safely discard a particular
analysis branch by marking it as inconclusive.
Halting problem for sure can be better framed to not sound as a
dogma, at least. In practice, algorithmic inconclusiveness has
0.001 probability, not a 100% guarantee as many engineers perceive >>>>>> it.
god it's been such a mind-fuck to unpack the halting problem,
but the halting problem does not mean that no algorithm exists for
any given machine, just that a "general" decider does not exist for >>>>> all machiens ...
heck it must be certain that for any given machine there must exist >>>>> a partial decider that can decide on it ... because otherwise a
paradox would have to address all possible partial deciders in a
computable fashion and that runs up against it's own limit to
classical computing. therefore some true decider must exist for any >>>>> given machine that exists ... we just can't funnel the knowledge
thru a general interface.
For every H there is a D such that D does the opposite
of whatever H reports. In this case use H1 on this D.
yes, the inability to correctly resolve halting thru a singular
interface is a flaw of TM computing, not an inherent algorithmic limit
Nope, because the proof doesn't actually need to talk about HOW the
decider actually made its decision, and thus not limited to Turing
Machines.
All it needs is that the decider be limited by the rules of a
computation.
All the arguements against the proof seem to begin with the error that
the decider can be changed after the fact and such change changes the
input to match, but that breaks the fundamental property of
computations, that they are fixed algorithms
The proof shows that the SPECIFIC decider that the input was made from
will get the wrong answer, and we can make such an input for ANY
specific decider, and thus no decider can get all answers correct.
That the input HAS a correct answer (just the opposite of what that
specific decider gives) shows that there IS a correct answer, so there
is nothing wrong about the question of its halting, and thus a non-
answer like "its behavior is contrary" is valid.
Everyone trying to make the arguements just shows they don't
understand the basics of what a computation is.
missed ya dick!
given that deciders are inherently part of the execution path they are deciding on ... ofc deciders can modify their behavior based on an input which they are included within, like they can modify their behavior
based on the properties of the input.
this is how partial deciders can intelligently block on responding to
input that cannot be answered thru their particular interface.
i'm not aware of any method that can prove a partial decider can't be
more efficient that brute force, because again, they can block when encountering a paradox specific to their interface.
furthermore this doesn't disprove a general algorithm backing the
partial deciders, all the general algorithm needs is a "self" input
which identifies the particular interface it's computing for. this
general algo for partial deciders will have three outputs: HALTS, LOOPS,
and PARADOX. when partial deciders receive PARADOX back from their algo
run they will then just loop forever to never respond.
yes i'm aware "interfaces" are complete descriptions of a partial
decider, and that's what i mean by passing in a self. the partial
decider must have a quine that allows it to recognize itself, and it
passes this into the general algo.
"but i can loop over all partial deciders to produce a paradox" ... uhh
no you can't? traditional computing cannot iterate over all functionally equivalent machines, so it certainly can't iterate over all almost functionally equivalent machines, so you cannot claim to produce a
general paradox for the general algo as such a computation is outside
the scope of classical computing limits.
i await to see how you purposefully misunderstand this
On 1/12/26 5:09 PM, dart200 wrote:
On 1/12/26 4:06 AM, Richard Damon wrote:
On 1/6/26 10:03 PM, dart200 wrote:
On 1/6/26 5:26 PM, olcott wrote:
On 1/6/2026 1:47 AM, dart200 wrote:
On 1/5/26 4:24 PM, Oleksiy Gapotchenko wrote:
Just an external observation:
A lot of tech innovations in software optimization area get
discarded from the very beginning because people who work on them >>>>>>> perceive the halting problem as a dogma. As result, certain
practical things (in code analysis) are not even tried because
it's assumed that they are bound by the halting problem.
In practice, however, the halting problem is rarely a limitation. >>>>>>> And even when one hits it, they can safely discard a particular >>>>>>> analysis branch by marking it as inconclusive.
Halting problem for sure can be better framed to not sound as a >>>>>>> dogma, at least. In practice, algorithmic inconclusiveness has
0.001 probability, not a 100% guarantee as many engineers
perceive it.
god it's been such a mind-fuck to unpack the halting problem,
but the halting problem does not mean that no algorithm exists for >>>>>> any given machine, just that a "general" decider does not exist
for all machiens ...
heck it must be certain that for any given machine there must
exist a partial decider that can decide on it ... because
otherwise a paradox would have to address all possible partial
deciders in a computable fashion and that runs up against it's own >>>>>> limit to classical computing. therefore some true decider must
exist for any given machine that exists ... we just can't funnel
the knowledge thru a general interface.
For every H there is a D such that D does the opposite
of whatever H reports. In this case use H1 on this D.
yes, the inability to correctly resolve halting thru a singular
interface is a flaw of TM computing, not an inherent algorithmic limit >>>>
Nope, because the proof doesn't actually need to talk about HOW the
decider actually made its decision, and thus not limited to Turing
Machines.
All it needs is that the decider be limited by the rules of a
computation.
All the arguements against the proof seem to begin with the error
that the decider can be changed after the fact and such change
changes the input to match, but that breaks the fundamental property
of computations, that they are fixed algorithms
The proof shows that the SPECIFIC decider that the input was made
from will get the wrong answer, and we can make such an input for ANY
specific decider, and thus no decider can get all answers correct.
That the input HAS a correct answer (just the opposite of what that
specific decider gives) shows that there IS a correct answer, so
there is nothing wrong about the question of its halting, and thus a
non- answer like "its behavior is contrary" is valid.
Everyone trying to make the arguements just shows they don't
understand the basics of what a computation is.
missed ya dick!
given that deciders are inherently part of the execution path they are
deciding on ... ofc deciders can modify their behavior based on an
input which they are included within, like they can modify their
behavior based on the properties of the input.
No, that behavior had to always have been in them, and thus seen by the "pathological" input.
this is how partial deciders can intelligently block on responding to
input that cannot be answered thru their particular interface.
i'm not aware of any method that can prove a partial decider can't be
more efficient that brute force, because again, they can block when
encountering a paradox specific to their interface.
How does "brute force" determine non-halting?
And nothing in the theory disagrees with partial halt deciders existing, they just can NEVER give an answer to the pathological program based on them, as if they give an answer, it will be wrong.
furthermore this doesn't disprove a general algorithm backing the
partial deciders, all the general algorithm needs is a "self" input
which identifies the particular interface it's computing for. this
general algo for partial deciders will have three outputs: HALTS,
LOOPS, and PARADOX. when partial deciders receive PARADOX back from
their algo run they will then just loop forever to never respond.
Sure it does.
The problem is it doesn't get a "self" input, and by its nature. it
can't determine if the input is just using a computational equivalent of itself that doesn't match its idea of what it looks like.
This FACT just breaks you concept, as you just assume you can detect
what is proven to be undetectable in full generality.
And, even if it CAN detect that the input is using a copy of itself,
that doesn't help it as it still can't get the right answer, and the
pathological input based on your general algorithm effectively uses
copies of all the algorithms it enumerates, so NONE of them can give the right answer.
yes i'm aware "interfaces" are complete descriptions of a partial
decider, and that's what i mean by passing in a self. the partial
decider must have a quine that allows it to recognize itself, and it
passes this into the general algo.
Nope, an "Interface" is NOT a complete description of ANY machine, so
you are just showing you are fundamentally incorrect in your basis.
You can't "run" and "interface", only an actual program that implements it.
"but i can loop over all partial deciders to produce a paradox" ...
uhh no you can't? traditional computing cannot iterate over all
functionally equivalent machines, so it certainly can't iterate over
all almost functionally equivalent machines, so you cannot claim to
produce a general paradox for the general algo as such a computation
is outside the scope of classical computing limits.
So, you just admitting you can't use an emumerated list of partial
deciders to get the answer.
The pathological program doesn't need to enumerate the deciders, it just needs to user what you make your final decider, which can only partially enumerate the partial deciders.
i await to see how you purposefully misunderstand this
It seems you are the one that doesn't understand.
Programs can't CHANGE there behavior, they HAVE specific behavior that depends on the input, and ALWAYS have that behavior for that input.
The definition of a computation means it can't squirrel away the fact
that it was once used on this particular input, and needs to do
something different, which is what is needed to CHANGE their behavior.
On 1/12/26 7:16 PM, Richard Damon wrote:
On 1/12/26 5:09 PM, dart200 wrote:
On 1/12/26 4:06 AM, Richard Damon wrote:
On 1/6/26 10:03 PM, dart200 wrote:
On 1/6/26 5:26 PM, olcott wrote:
On 1/6/2026 1:47 AM, dart200 wrote:
On 1/5/26 4:24 PM, Oleksiy Gapotchenko wrote:
Just an external observation:
A lot of tech innovations in software optimization area get
discarded from the very beginning because people who work on
them perceive the halting problem as a dogma. As result, certain >>>>>>>> practical things (in code analysis) are not even tried because >>>>>>>> it's assumed that they are bound by the halting problem.
In practice, however, the halting problem is rarely a
limitation. And even when one hits it, they can safely discard a >>>>>>>> particular analysis branch by marking it as inconclusive.
Halting problem for sure can be better framed to not sound as a >>>>>>>> dogma, at least. In practice, algorithmic inconclusiveness has >>>>>>>> 0.001 probability, not a 100% guarantee as many engineers
perceive it.
god it's been such a mind-fuck to unpack the halting problem,
but the halting problem does not mean that no algorithm exists
for any given machine, just that a "general" decider does not
exist for all machiens ...
heck it must be certain that for any given machine there must
exist a partial decider that can decide on it ... because
otherwise a paradox would have to address all possible partial
deciders in a computable fashion and that runs up against it's
own limit to classical computing. therefore some true decider
must exist for any given machine that exists ... we just can't
funnel the knowledge thru a general interface.
For every H there is a D such that D does the opposite
of whatever H reports. In this case use H1 on this D.
yes, the inability to correctly resolve halting thru a singular
interface is a flaw of TM computing, not an inherent algorithmic limit >>>>>
Nope, because the proof doesn't actually need to talk about HOW the
decider actually made its decision, and thus not limited to Turing
Machines.
All it needs is that the decider be limited by the rules of a
computation.
All the arguements against the proof seem to begin with the error
that the decider can be changed after the fact and such change
changes the input to match, but that breaks the fundamental property
of computations, that they are fixed algorithms
The proof shows that the SPECIFIC decider that the input was made
from will get the wrong answer, and we can make such an input for
ANY specific decider, and thus no decider can get all answers correct. >>>>
That the input HAS a correct answer (just the opposite of what that
specific decider gives) shows that there IS a correct answer, so
there is nothing wrong about the question of its halting, and thus a
non- answer like "its behavior is contrary" is valid.
Everyone trying to make the arguements just shows they don't
understand the basics of what a computation is.
missed ya dick!
given that deciders are inherently part of the execution path they
are deciding on ... ofc deciders can modify their behavior based on
an input which they are included within, like they can modify their
behavior based on the properties of the input.
No, that behavior had to always have been in them, and thus seen by
the "pathological" input.
this is how partial deciders can intelligently block on responding to
input that cannot be answered thru their particular interface.
i'm not aware of any method that can prove a partial decider can't be
more efficient that brute force, because again, they can block when
encountering a paradox specific to their interface.
How does "brute force" determine non-halting?
well it does for the halting computations (bounded time, bounded space),
and proper infinite loops (unbounded time, bounded space),
just not runaway infinite computation (unbounded time, unbounded space)
And nothing in the theory disagrees with partial halt deciders
existing, they just can NEVER give an answer to the pathological
program based on them, as if they give an answer, it will be wrong.
which means: for any given machine, there is a decider out there that
must decide correctly on it. so, for any given machine there is a method that does correctly decide on it without ever given any wrong answers to
any other machine (tho it may not give answers at times).
as a man, i'm not subject to having my output read and contradicted like turing machine deciders are. i'm not subject to having to block
indefinitely because some input is pathological to me. and because some method must exist that can correct decide on any given input... i can
know that method for any given input, and therefor i can decide on any
given input.
this is why i'm really starting to think the ct-thesis is cooked. you
say i can't do that because turing machines can't do that ... but
where's the proof that turing machine encompass all of computing? why am
i limited by the absolute nonsense that is turing machines producing pathological input to themselves?
because turing machines *are* the fundamentals of computation??? but
again: that's just an assumption. we never proved it, yet here you are treating it like unquestionable law.
that's the flaw bro, one we've been sitting on for almost a century. i
don't even have a proof to deconstruct, it's literally just an
assumption, so all i need to do is construct the scenarios where
something is obviously generally computable, but that computation cannot
be generally expressed thru a turing machine computation input/ouput specification.
furthermore this doesn't disprove a general algorithm backing the
partial deciders, all the general algorithm needs is a "self" input
which identifies the particular interface it's computing for. this
general algo for partial deciders will have three outputs: HALTS,
LOOPS, and PARADOX. when partial deciders receive PARADOX back from
their algo run they will then just loop forever to never respond.
Sure it does.
The problem is it doesn't get a "self" input, and by its nature. it
i'm defining the algo, so i say it does
can't determine if the input is just using a computational equivalent
of itself that doesn't match its idea of what it looks like.
This FACT just breaks you concept, as you just assume you can detect
what is proven to be undetectable in full generality.
using the very paradox i'm trying to solve, so that's begging the
question. it's really kinda sad how much begging the question is going
on in the fundamental theory of computing
And, even if it CAN detect that the input is using a copy of itself,
that doesn't help it as it still can't get the right answer, and the
it's general algo to the partial deciders - all it needs to do is either
it returns PARADOX in which case the partial decider decides to loop(),
or maybe we can just extract that functionality into the general partial algo itself...
pathological input based on your general algorithm effectively uses
copies of all the algorithms it enumerates, so NONE of them can give
the right answer.
yes i'm aware "interfaces" are complete descriptions of a partial
decider, and that's what i mean by passing in a self. the partial
decider must have a quine that allows it to recognize itself, and it
passes this into the general algo.
Nope, an "Interface" is NOT a complete description of ANY machine, so
you are just showing you are fundamentally incorrect in your basis.
You can't "run" and "interface", only an actual program that
implements it.
sure, but all the partial decider do is construct a self-reference using
a quine and pass that along with the input to a common backing
algorithm. all valid partial deciders will need accurate quines in order
to ascertain where their output feedbacks into affect the prediction
they are making.
and yes the partial deciders do contain full descriptions of the common backing algo, but they still really do just act as an interface to that common algo
they act like an exposed API/interface into the common algo
"but i can loop over all partial deciders to produce a paradox" ...
uhh no you can't? traditional computing cannot iterate over all
functionally equivalent machines, so it certainly can't iterate over
all almost functionally equivalent machines, so you cannot claim to
produce a general paradox for the general algo as such a computation
is outside the scope of classical computing limits.
So, you just admitting you can't use an emumerated list of partial
deciders to get the answer.
which is fine, it's just not necessary
The pathological program doesn't need to enumerate the deciders, it
just needs to user what you make your final decider, which can only
partially enumerate the partial deciders.
it would in order to break the general algo across all self's. the self
acts as the fixed point of reference to which the decision is made ...
and while no fixed point can decide on all input, for any given input
there is a fixed point of self that can decide on that input. and this
can be encapsulated into a general algorithm that encapsulated a general procedure even if any given fixed point of self is not general.
therefore a general algo exists, even if any particular fixed point of decision making is contradicted.
dear god, why is computing theory is such a shit show? cause we've been almost blindly following what the forefathers of computing said?
i await to see how you purposefully misunderstand this
It seems you are the one that doesn't understand.
Programs can't CHANGE there behavior, they HAVE specific behavior that
depends on the input, and ALWAYS have that behavior for that input.
The definition of a computation means it can't squirrel away the fact
that it was once used on this particular input, and needs to do
something different, which is what is needed to CHANGE their behavior.
i'm aware, i'm not really sure why ur reapting that
and i await ur further purposeful misunderstanding
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