On 5/8/26 12:19 AM, Mikko wrote:
On 07/05/2026 12:00, dart200 wrote:
On 5/7/26 12:18 AM, Mikko wrote:A machine is not a "diagonal".
On 06/05/2026 22:40, dart200 wrote:
On 5/6/26 12:55 AM, Mikko wrote:You should not say anything about the diagonal before you have defined >>>> it. Any use of the word before the definition is nonsense,.
On 05/05/2026 12:28, dart200 wrote:
On 5/5/26 1:25 AM, Mikko wrote:
On 04/05/2026 10:53, dart200 wrote:
On 5/3/26 11:15 PM, Mikko wrote:
On 03/05/2026 12:09, dart200 wrote:
On 5/3/26 12:53 AM, Mikko wrote:
On 02/05/2026 23:39, dart200 wrote:
On 4/19/26 10:58 AM, Richard Damon wrote:
On 4/19/26 1:21 PM, olcott wrote:
On 4/19/2026 3:59 AM, Mikko wrote:
On 18/04/2026 15:58, olcott wrote:
Unknown truths are not elements of the body of >>>>>>>>>>>>>>>>> knowledge is a semantic tautology. Did you think >>>>>>>>>>>>>>>>> that things that are unknown are known?
No, but that measn that for some sentences X True(X) is >>>>>>>>>>>>>>>> unknown and there
is no method to find out.
I don't know about philosophers but mathematicians and >>>>>>>>>>>>>>>> logicians don't
find it interesting if all you can say that all >>>>>>>>>>>>>>>> knowledge is knowable
and everything else is not.
Ross Finlayson, seemed to endlessly hedge on whether >>>>>>>>>>>>>>> or not the truth value of the Goldbach conjecture was >>>>>>>>>>>>>>> known. He seemed to think that there are alternative >>>>>>>>>>>>>>> analytical frameworks that make the question of whether >>>>>>>>>>>>>>> or not its truth value is known an ambiguous question. >>>>>>>>>>>>>>>
I needed to refer to unknown truth values specifically >>>>>>>>>>>>>>> because all "undecidability" when construed correctly >>>>>>>>>>>>>>> falls into one of two categories.
(a) Semantic incoherence
(b) Unknown truth values.
Nope.
Undecidability can not come from Semantic Incoherence, as >>>>>>>>>>>>>> the definition of Undecidability ia based on there being a >>>>>>>>>>>>>> coherent answer, just not one that can be determined by a >>>>>>>>>>>>>> computation.
richard richard richard, that is in-correct.
the undecidable problem turing described (as well as the >>>>>>>>>>>>> basic halting problem) involves a situations that have _no_ >>>>>>>>>>>>> coherent answer, not just one that can be known by not >>>>>>>>>>>>> computed ...
Turing proved that there are universal Turing machines. An >>>>>>>>>>>> universalTuring machine halts with some inputs and doesn't >>>>>>>>>>>> halt with any other
input. Every Turing machine that can be given the same input >>>>>>>>>>>> as an
universal Turing machine either fails to accept some input >>>>>>>>>>>> with which
that universal Turing machine halts or fails to reject some >>>>>>>>>>>> input with
which that universal Turing macnie does not halt.
dunno what ur saying here.
There is a way to find out if you can read.
i can't read if u can't explain
I can't explain the art of reading Common Language.
inturing hypothesized a diagonal computation that tries to put >>>>>>>>>>> the Nth digit from the Nth circle-free machine as the Nth >>>>>>>>>>> digit on this diagonal across all circle-free machine...
That is possible because there nither the machines nor digit >>>>>>>>>> positions
are more numerous than natural numbers.
yes, but then he argues it's impossible to compute the diagonal >>>>>>>>> because of the paradox that ensues when naively running the >>>>>>>>> classifier on the diagonal itself
It is impossible to have a Turing machine that computes a number >>>>>>>> that
no Turing machine can compute. But you can compute it if you can >>>>>>>> use
all (infinitely many) Turing machines.
no you can't.
Hard to test as I han't infinite many Turing machines. But it is
u don't need to test it, you can't define a total dovetailing
machine to compute turing's diagonal,
the H machine defined on p247 from his paper /on computable numbers/
the machine supposes to compute the "turing's diagonal" across circle-
free sequences, otherwise labeled as β' in the paper, defined at the
bottom of p246
On 5/8/2026 11:06 AM, dart200 wrote:
On 5/8/26 12:19 AM, Mikko wrote:
On 07/05/2026 12:00, dart200 wrote:
On 5/7/26 12:18 AM, Mikko wrote:A machine is not a "diagonal".
On 06/05/2026 22:40, dart200 wrote:
On 5/6/26 12:55 AM, Mikko wrote:You should not say anything about the diagonal before you have defined >>>>> it. Any use of the word before the definition is nonsense,.
On 05/05/2026 12:28, dart200 wrote:
On 5/5/26 1:25 AM, Mikko wrote:
On 04/05/2026 10:53, dart200 wrote:
On 5/3/26 11:15 PM, Mikko wrote:
On 03/05/2026 12:09, dart200 wrote:
On 5/3/26 12:53 AM, Mikko wrote:
On 02/05/2026 23:39, dart200 wrote:
On 4/19/26 10:58 AM, Richard Damon wrote:
On 4/19/26 1:21 PM, olcott wrote:
On 4/19/2026 3:59 AM, Mikko wrote:
On 18/04/2026 15:58, olcott wrote:
Unknown truths are not elements of the body of >>>>>>>>>>>>>>>>>> knowledge is a semantic tautology. Did you think >>>>>>>>>>>>>>>>>> that things that are unknown are known?
No, but that measn that for some sentences X True(X) is >>>>>>>>>>>>>>>>> unknown and there
is no method to find out.
I don't know about philosophers but mathematicians and >>>>>>>>>>>>>>>>> logicians don't
find it interesting if all you can say that all >>>>>>>>>>>>>>>>> knowledge is knowable
and everything else is not.
Ross Finlayson, seemed to endlessly hedge on whether >>>>>>>>>>>>>>>> or not the truth value of the Goldbach conjecture was >>>>>>>>>>>>>>>> known. He seemed to think that there are alternative >>>>>>>>>>>>>>>> analytical frameworks that make the question of whether >>>>>>>>>>>>>>>> or not its truth value is known an ambiguous question. >>>>>>>>>>>>>>>>
I needed to refer to unknown truth values specifically >>>>>>>>>>>>>>>> because all "undecidability" when construed correctly >>>>>>>>>>>>>>>> falls into one of two categories.
(a) Semantic incoherence
(b) Unknown truth values.
Nope.
Undecidability can not come from Semantic Incoherence, as >>>>>>>>>>>>>>> the definition of Undecidability ia based on there being >>>>>>>>>>>>>>> a coherent answer, just not one that can be determined by >>>>>>>>>>>>>>> a computation.
richard richard richard, that is in-correct.
the undecidable problem turing described (as well as the >>>>>>>>>>>>>> basic halting problem) involves a situations that have >>>>>>>>>>>>>> _no_ coherent answer, not just one that can be known by >>>>>>>>>>>>>> not computed ...
Turing proved that there are universal Turing machines. An >>>>>>>>>>>>> universalTuring machine halts with some inputs and doesn't >>>>>>>>>>>>> halt with any other
input. Every Turing machine that can be given the same >>>>>>>>>>>>> input as an
universal Turing machine either fails to accept some input >>>>>>>>>>>>> with which
that universal Turing machine halts or fails to reject some >>>>>>>>>>>>> input with
which that universal Turing macnie does not halt.
dunno what ur saying here.
There is a way to find out if you can read.
i can't read if u can't explain
I can't explain the art of reading Common Language.
inturing hypothesized a diagonal computation that tries to put >>>>>>>>>>>> the Nth digit from the Nth circle-free machine as the Nth >>>>>>>>>>>> digit on this diagonal across all circle-free machine... >>>>>>>>>>>That is possible because there nither the machines nor digit >>>>>>>>>>> positions
are more numerous than natural numbers.
yes, but then he argues it's impossible to compute the
diagonal because of the paradox that ensues when naively
running the classifier on the diagonal itself
It is impossible to have a Turing machine that computes a
number that
no Turing machine can compute. But you can compute it if you >>>>>>>>> can use
all (infinitely many) Turing machines.
no you can't.
Hard to test as I han't infinite many Turing machines. But it is
u don't need to test it, you can't define a total dovetailing
machine to compute turing's diagonal,
the H machine defined on p247 from his paper /on computable numbers/
the machine supposes to compute the "turing's diagonal" across circle-
free sequences, otherwise labeled as β' in the paper, defined at the
bottom of p246
Anything that any machine can possibly compute can
be computed by applying a finite set of finite string
transformation rules to a finite set of finite strings.
Everything else is simply out-of-scope for computation
like making a silk purse from a sow's ear.
On 5/8/26 9:58 AM, olcott wrote:
On 5/8/2026 11:06 AM, dart200 wrote:
On 5/8/26 12:19 AM, Mikko wrote:
On 07/05/2026 12:00, dart200 wrote:
On 5/7/26 12:18 AM, Mikko wrote:A machine is not a "diagonal".
On 06/05/2026 22:40, dart200 wrote:
On 5/6/26 12:55 AM, Mikko wrote:You should not say anything about the diagonal before you have
On 05/05/2026 12:28, dart200 wrote:u don't need to test it, you can't define a total dovetailing
On 5/5/26 1:25 AM, Mikko wrote:
On 04/05/2026 10:53, dart200 wrote:
On 5/3/26 11:15 PM, Mikko wrote:
On 03/05/2026 12:09, dart200 wrote:
On 5/3/26 12:53 AM, Mikko wrote:
On 02/05/2026 23:39, dart200 wrote:
On 4/19/26 10:58 AM, Richard Damon wrote:
On 4/19/26 1:21 PM, olcott wrote:
On 4/19/2026 3:59 AM, Mikko wrote:
On 18/04/2026 15:58, olcott wrote:
Unknown truths are not elements of the body of >>>>>>>>>>>>>>>>>>> knowledge is a semantic tautology. Did you think >>>>>>>>>>>>>>>>>>> that things that are unknown are known?
No, but that measn that for some sentences X True(X) >>>>>>>>>>>>>>>>>> is unknown and there
is no method to find out.
I don't know about philosophers but mathematicians and >>>>>>>>>>>>>>>>>> logicians don't
find it interesting if all you can say that all >>>>>>>>>>>>>>>>>> knowledge is knowable
and everything else is not.
Ross Finlayson, seemed to endlessly hedge on whether >>>>>>>>>>>>>>>>> or not the truth value of the Goldbach conjecture was >>>>>>>>>>>>>>>>> known. He seemed to think that there are alternative >>>>>>>>>>>>>>>>> analytical frameworks that make the question of whether >>>>>>>>>>>>>>>>> or not its truth value is known an ambiguous question. >>>>>>>>>>>>>>>>>
I needed to refer to unknown truth values specifically >>>>>>>>>>>>>>>>> because all "undecidability" when construed correctly >>>>>>>>>>>>>>>>> falls into one of two categories.
(a) Semantic incoherence
(b) Unknown truth values.
Nope.
Undecidability can not come from Semantic Incoherence, >>>>>>>>>>>>>>>> as the definition of Undecidability ia based on there >>>>>>>>>>>>>>>> being a coherent answer, just not one that can be >>>>>>>>>>>>>>>> determined by a computation.
richard richard richard, that is in-correct.
the undecidable problem turing described (as well as the >>>>>>>>>>>>>>> basic halting problem) involves a situations that have >>>>>>>>>>>>>>> _no_ coherent answer, not just one that can be known by >>>>>>>>>>>>>>> not computed ...
Turing proved that there are universal Turing machines. An >>>>>>>>>>>>>> universalTuring machine halts with some inputs and doesn't >>>>>>>>>>>>>> halt with any other
input. Every Turing machine that can be given the same >>>>>>>>>>>>>> input as an
universal Turing machine either fails to accept some input >>>>>>>>>>>>>> with which
that universal Turing machine halts or fails to reject >>>>>>>>>>>>>> some input with
which that universal Turing macnie does not halt.
dunno what ur saying here.
There is a way to find out if you can read.
i can't read if u can't explain
I can't explain the art of reading Common Language.
inturing hypothesized a diagonal computation that tries to >>>>>>>>>>>>> put the Nth digit from the Nth circle-free machine as the >>>>>>>>>>>>> Nth digit on this diagonal across all circle-free machine... >>>>>>>>>>>>That is possible because there nither the machines nor digit >>>>>>>>>>>> positions
are more numerous than natural numbers.
yes, but then he argues it's impossible to compute the
diagonal because of the paradox that ensues when naively >>>>>>>>>>> running the classifier on the diagonal itself
It is impossible to have a Turing machine that computes a >>>>>>>>>> number that
no Turing machine can compute. But you can compute it if you >>>>>>>>>> can use
all (infinitely many) Turing machines.
no you can't.
Hard to test as I han't infinite many Turing machines. But it is >>>>>>>
machine to compute turing's diagonal,
defined
it. Any use of the word before the definition is nonsense,.
the H machine defined on p247 from his paper /on computable numbers/
the machine supposes to compute the "turing's diagonal" across
circle- free sequences, otherwise labeled as β' in the paper, defined
at the bottom of p246
Anything that any machine can possibly compute can
be computed by applying a finite set of finite string
transformation rules to a finite set of finite strings.
Everything else is simply out-of-scope for computation
like making a silk purse from a sow's ear.
i believe the i mentally applied a finite set of string transformations
to decide that DD does in fact halt
On 5/8/2026 12:13 PM, dart200 wrote:
On 5/8/26 9:58 AM, olcott wrote:
On 5/8/2026 11:06 AM, dart200 wrote:
On 5/8/26 12:19 AM, Mikko wrote:
On 07/05/2026 12:00, dart200 wrote:
On 5/7/26 12:18 AM, Mikko wrote:
On 06/05/2026 22:40, dart200 wrote:
On 5/6/26 12:55 AM, Mikko wrote:You should not say anything about the diagonal before you have
On 05/05/2026 12:28, dart200 wrote:u don't need to test it, you can't define a total dovetailing >>>>>>>> machine to compute turing's diagonal,
On 5/5/26 1:25 AM, Mikko wrote:
On 04/05/2026 10:53, dart200 wrote:
On 5/3/26 11:15 PM, Mikko wrote:
On 03/05/2026 12:09, dart200 wrote:
On 5/3/26 12:53 AM, Mikko wrote:
On 02/05/2026 23:39, dart200 wrote:dunno what ur saying here.
On 4/19/26 10:58 AM, Richard Damon wrote:
On 4/19/26 1:21 PM, olcott wrote:
On 4/19/2026 3:59 AM, Mikko wrote:
On 18/04/2026 15:58, olcott wrote:
No, but that measn that for some sentences X True(X) >>>>>>>>>>>>>>>>>>> is unknown and there
Unknown truths are not elements of the body of >>>>>>>>>>>>>>>>>>>> knowledge is a semantic tautology. Did you think >>>>>>>>>>>>>>>>>>>> that things that are unknown are known? >>>>>>>>>>>>>>>>>>>
is no method to find out.
I don't know about philosophers but mathematicians >>>>>>>>>>>>>>>>>>> and logicians don't
find it interesting if all you can say that all >>>>>>>>>>>>>>>>>>> knowledge is knowable
and everything else is not.
Ross Finlayson, seemed to endlessly hedge on whether >>>>>>>>>>>>>>>>>> or not the truth value of the Goldbach conjecture was >>>>>>>>>>>>>>>>>> known. He seemed to think that there are alternative >>>>>>>>>>>>>>>>>> analytical frameworks that make the question of whether >>>>>>>>>>>>>>>>>> or not its truth value is known an ambiguous question. >>>>>>>>>>>>>>>>>>
I needed to refer to unknown truth values specifically >>>>>>>>>>>>>>>>>> because all "undecidability" when construed correctly >>>>>>>>>>>>>>>>>> falls into one of two categories.
(a) Semantic incoherence
(b) Unknown truth values.
Nope.
Undecidability can not come from Semantic Incoherence, >>>>>>>>>>>>>>>>> as the definition of Undecidability ia based on there >>>>>>>>>>>>>>>>> being a coherent answer, just not one that can be >>>>>>>>>>>>>>>>> determined by a computation.
richard richard richard, that is in-correct.
the undecidable problem turing described (as well as the >>>>>>>>>>>>>>>> basic halting problem) involves a situations that have >>>>>>>>>>>>>>>> _no_ coherent answer, not just one that can be known by >>>>>>>>>>>>>>>> not computed ...
Turing proved that there are universal Turing machines. >>>>>>>>>>>>>>> An universalTuring machine halts with some inputs and >>>>>>>>>>>>>>> doesn't halt with any other
input. Every Turing machine that can be given the same >>>>>>>>>>>>>>> input as an
universal Turing machine either fails to accept some >>>>>>>>>>>>>>> input with which
that universal Turing machine halts or fails to reject >>>>>>>>>>>>>>> some input with
which that universal Turing macnie does not halt. >>>>>>>>>>>>>>
There is a way to find out if you can read.
i can't read if u can't explain
I can't explain the art of reading Common Language.
inturing hypothesized a diagonal computation that tries to >>>>>>>>>>>>>> put the Nth digit from the Nth circle-free machine as the >>>>>>>>>>>>>> Nth digit on this diagonal across all circle-free machine... >>>>>>>>>>>>>That is possible because there nither the machines nor >>>>>>>>>>>>> digit positions
are more numerous than natural numbers.
yes, but then he argues it's impossible to compute the >>>>>>>>>>>> diagonal because of the paradox that ensues when naively >>>>>>>>>>>> running the classifier on the diagonal itself
It is impossible to have a Turing machine that computes a >>>>>>>>>>> number that
no Turing machine can compute. But you can compute it if you >>>>>>>>>>> can use
all (infinitely many) Turing machines.
no you can't.
Hard to test as I han't infinite many Turing machines. But it is >>>>>>>>
defined
it. Any use of the word before the definition is nonsense,.
the H machine defined on p247 from his paper /on computable numbers/ >>>>> A machine is not a "diagonal".
the machine supposes to compute the "turing's diagonal" across
circle- free sequences, otherwise labeled as β' in the paper,
defined at the bottom of p246
Anything that any machine can possibly compute can
be computed by applying a finite set of finite string
transformation rules to a finite set of finite strings.
Everything else is simply out-of-scope for computation
like making a silk purse from a sow's ear.
i believe the i mentally applied a finite set of string
transformations to decide that DD does in fact halt
No one every simplified is down to its barest possible
essence before me. Also the entire body of knowledge
expressed in language can be encoded as finite relations
between finite strings.
This transforms all undecidability into
(a) Outside of the body of knowledge that can be expressed in language
(b) Semantically incoherent relations between finite strings.
All self-reference "paradox" is merely (b)
On 5/8/26 10:35 AM, olcott wrote:
On 5/8/2026 12:13 PM, dart200 wrote:
On 5/8/26 9:58 AM, olcott wrote:
On 5/8/2026 11:06 AM, dart200 wrote:
On 5/8/26 12:19 AM, Mikko wrote:
On 07/05/2026 12:00, dart200 wrote:
On 5/7/26 12:18 AM, Mikko wrote:
On 06/05/2026 22:40, dart200 wrote:
On 5/6/26 12:55 AM, Mikko wrote:You should not say anything about the diagonal before you have >>>>>>>> defined
On 05/05/2026 12:28, dart200 wrote:u don't need to test it, you can't define a total dovetailing >>>>>>>>> machine to compute turing's diagonal,
On 5/5/26 1:25 AM, Mikko wrote:
On 04/05/2026 10:53, dart200 wrote:
On 5/3/26 11:15 PM, Mikko wrote:
On 03/05/2026 12:09, dart200 wrote:
On 5/3/26 12:53 AM, Mikko wrote:
On 02/05/2026 23:39, dart200 wrote:dunno what ur saying here.
On 4/19/26 10:58 AM, Richard Damon wrote:
On 4/19/26 1:21 PM, olcott wrote:
On 4/19/2026 3:59 AM, Mikko wrote:
On 18/04/2026 15:58, olcott wrote:
No, but that measn that for some sentences X True(X) >>>>>>>>>>>>>>>>>>>> is unknown and there
Unknown truths are not elements of the body of >>>>>>>>>>>>>>>>>>>>> knowledge is a semantic tautology. Did you think >>>>>>>>>>>>>>>>>>>>> that things that are unknown are known? >>>>>>>>>>>>>>>>>>>>
is no method to find out.
I don't know about philosophers but mathematicians >>>>>>>>>>>>>>>>>>>> and logicians don't
find it interesting if all you can say that all >>>>>>>>>>>>>>>>>>>> knowledge is knowable
and everything else is not.
Ross Finlayson, seemed to endlessly hedge on whether >>>>>>>>>>>>>>>>>>> or not the truth value of the Goldbach conjecture was >>>>>>>>>>>>>>>>>>> known. He seemed to think that there are alternative >>>>>>>>>>>>>>>>>>> analytical frameworks that make the question of whether >>>>>>>>>>>>>>>>>>> or not its truth value is known an ambiguous question. >>>>>>>>>>>>>>>>>>>
I needed to refer to unknown truth values specifically >>>>>>>>>>>>>>>>>>> because all "undecidability" when construed correctly >>>>>>>>>>>>>>>>>>> falls into one of two categories.
(a) Semantic incoherence
(b) Unknown truth values.
Nope.
Undecidability can not come from Semantic Incoherence, >>>>>>>>>>>>>>>>>> as the definition of Undecidability ia based on there >>>>>>>>>>>>>>>>>> being a coherent answer, just not one that can be >>>>>>>>>>>>>>>>>> determined by a computation.
richard richard richard, that is in-correct. >>>>>>>>>>>>>>>>>
the undecidable problem turing described (as well as >>>>>>>>>>>>>>>>> the basic halting problem) involves a situations that >>>>>>>>>>>>>>>>> have _no_ coherent answer, not just one that can be >>>>>>>>>>>>>>>>> known by not computed ...
Turing proved that there are universal Turing machines. >>>>>>>>>>>>>>>> An universalTuring machine halts with some inputs and >>>>>>>>>>>>>>>> doesn't halt with any other
input. Every Turing machine that can be given the same >>>>>>>>>>>>>>>> input as an
universal Turing machine either fails to accept some >>>>>>>>>>>>>>>> input with which
that universal Turing machine halts or fails to reject >>>>>>>>>>>>>>>> some input with
which that universal Turing macnie does not halt. >>>>>>>>>>>>>>>
There is a way to find out if you can read.
i can't read if u can't explain
I can't explain the art of reading Common Language.
inturing hypothesized a diagonal computation that tries to >>>>>>>>>>>>>>> put the Nth digit from the Nth circle-free machine as the >>>>>>>>>>>>>>> Nth digit on this diagonal across all circle-free machine... >>>>>>>>>>>>>>That is possible because there nither the machines nor >>>>>>>>>>>>>> digit positions
are more numerous than natural numbers.
yes, but then he argues it's impossible to compute the >>>>>>>>>>>>> diagonal because of the paradox that ensues when naively >>>>>>>>>>>>> running the classifier on the diagonal itself
It is impossible to have a Turing machine that computes a >>>>>>>>>>>> number that
no Turing machine can compute. But you can compute it if you >>>>>>>>>>>> can use
all (infinitely many) Turing machines.
no you can't.
Hard to test as I han't infinite many Turing machines. But it is >>>>>>>>>
it. Any use of the word before the definition is nonsense,.
the H machine defined on p247 from his paper /on computable numbers/ >>>>>> A machine is not a "diagonal".
the machine supposes to compute the "turing's diagonal" across
circle- free sequences, otherwise labeled as β' in the paper,
defined at the bottom of p246
Anything that any machine can possibly compute can
be computed by applying a finite set of finite string
transformation rules to a finite set of finite strings.
Everything else is simply out-of-scope for computation
like making a silk purse from a sow's ear.
i believe the i mentally applied a finite set of string
transformations to decide that DD does in fact halt
No one every simplified is down to its barest possible
essence before me. Also the entire body of knowledge
expressed in language can be encoded as finite relations
between finite strings.
This transforms all undecidability into
(a) Outside of the body of knowledge that can be expressed in language
we know DD halts polcott, so clearly not outside the body of knowledge
that can be expressed in language
(b) Semantically incoherent relations between finite strings.
All self-reference "paradox" is merely (b)
On 5/8/26 9:58 AM, olcott wrote:
On 5/8/2026 11:06 AM, dart200 wrote:
On 5/8/26 12:19 AM, Mikko wrote:
On 07/05/2026 12:00, dart200 wrote:
On 5/7/26 12:18 AM, Mikko wrote:A machine is not a "diagonal".
On 06/05/2026 22:40, dart200 wrote:
On 5/6/26 12:55 AM, Mikko wrote:You should not say anything about the diagonal before you have
On 05/05/2026 12:28, dart200 wrote:u don't need to test it, you can't define a total dovetailing
On 5/5/26 1:25 AM, Mikko wrote:
On 04/05/2026 10:53, dart200 wrote:
On 5/3/26 11:15 PM, Mikko wrote:
On 03/05/2026 12:09, dart200 wrote:
On 5/3/26 12:53 AM, Mikko wrote:
On 02/05/2026 23:39, dart200 wrote:
On 4/19/26 10:58 AM, Richard Damon wrote:
On 4/19/26 1:21 PM, olcott wrote:
On 4/19/2026 3:59 AM, Mikko wrote:
On 18/04/2026 15:58, olcott wrote:
Unknown truths are not elements of the body of >>>>>>>>>>>>>>>>>>> knowledge is a semantic tautology. Did you think >>>>>>>>>>>>>>>>>>> that things that are unknown are known?
No, but that measn that for some sentences X True(X) >>>>>>>>>>>>>>>>>> is unknown and there
is no method to find out.
I don't know about philosophers but mathematicians and >>>>>>>>>>>>>>>>>> logicians don't
find it interesting if all you can say that all >>>>>>>>>>>>>>>>>> knowledge is knowable
and everything else is not.
Ross Finlayson, seemed to endlessly hedge on whether >>>>>>>>>>>>>>>>> or not the truth value of the Goldbach conjecture was >>>>>>>>>>>>>>>>> known. He seemed to think that there are alternative >>>>>>>>>>>>>>>>> analytical frameworks that make the question of whether >>>>>>>>>>>>>>>>> or not its truth value is known an ambiguous question. >>>>>>>>>>>>>>>>>
I needed to refer to unknown truth values specifically >>>>>>>>>>>>>>>>> because all "undecidability" when construed correctly >>>>>>>>>>>>>>>>> falls into one of two categories.
(a) Semantic incoherence
(b) Unknown truth values.
Nope.
Undecidability can not come from Semantic Incoherence, >>>>>>>>>>>>>>>> as the definition of Undecidability ia based on there >>>>>>>>>>>>>>>> being a coherent answer, just not one that can be >>>>>>>>>>>>>>>> determined by a computation.
richard richard richard, that is in-correct.
the undecidable problem turing described (as well as the >>>>>>>>>>>>>>> basic halting problem) involves a situations that have >>>>>>>>>>>>>>> _no_ coherent answer, not just one that can be known by >>>>>>>>>>>>>>> not computed ...
Turing proved that there are universal Turing machines. An >>>>>>>>>>>>>> universalTuring machine halts with some inputs and doesn't >>>>>>>>>>>>>> halt with any other
input. Every Turing machine that can be given the same >>>>>>>>>>>>>> input as an
universal Turing machine either fails to accept some input >>>>>>>>>>>>>> with which
that universal Turing machine halts or fails to reject >>>>>>>>>>>>>> some input with
which that universal Turing macnie does not halt.
dunno what ur saying here.
There is a way to find out if you can read.
i can't read if u can't explain
I can't explain the art of reading Common Language.
inturing hypothesized a diagonal computation that tries to >>>>>>>>>>>>> put the Nth digit from the Nth circle-free machine as the >>>>>>>>>>>>> Nth digit on this diagonal across all circle-free machine... >>>>>>>>>>>>That is possible because there nither the machines nor digit >>>>>>>>>>>> positions
are more numerous than natural numbers.
yes, but then he argues it's impossible to compute the
diagonal because of the paradox that ensues when naively >>>>>>>>>>> running the classifier on the diagonal itself
It is impossible to have a Turing machine that computes a >>>>>>>>>> number that
no Turing machine can compute. But you can compute it if you >>>>>>>>>> can use
all (infinitely many) Turing machines.
no you can't.
Hard to test as I han't infinite many Turing machines. But it is >>>>>>>
machine to compute turing's diagonal,
defined
it. Any use of the word before the definition is nonsense,.
the H machine defined on p247 from his paper /on computable numbers/
the machine supposes to compute the "turing's diagonal" across
circle- free sequences, otherwise labeled as β' in the paper, defined
at the bottom of p246
Anything that any machine can possibly compute can
be computed by applying a finite set of finite string
transformation rules to a finite set of finite strings.
Everything else is simply out-of-scope for computation
like making a silk purse from a sow's ear.
i believe the i mentally applied a finite set of string transformations
to decide that DD does in fact halt
On 5/8/2026 11:06 AM, dart200 wrote:
On 5/8/26 12:19 AM, Mikko wrote:
On 07/05/2026 12:00, dart200 wrote:
On 5/7/26 12:18 AM, Mikko wrote:A machine is not a "diagonal".
On 06/05/2026 22:40, dart200 wrote:
On 5/6/26 12:55 AM, Mikko wrote:You should not say anything about the diagonal before you have defined >>>>> it. Any use of the word before the definition is nonsense,.
On 05/05/2026 12:28, dart200 wrote:
On 5/5/26 1:25 AM, Mikko wrote:
On 04/05/2026 10:53, dart200 wrote:
On 5/3/26 11:15 PM, Mikko wrote:
On 03/05/2026 12:09, dart200 wrote:
On 5/3/26 12:53 AM, Mikko wrote:
On 02/05/2026 23:39, dart200 wrote:
On 4/19/26 10:58 AM, Richard Damon wrote:
On 4/19/26 1:21 PM, olcott wrote:
On 4/19/2026 3:59 AM, Mikko wrote:
On 18/04/2026 15:58, olcott wrote:
Unknown truths are not elements of the body of >>>>>>>>>>>>>>>>>> knowledge is a semantic tautology. Did you think >>>>>>>>>>>>>>>>>> that things that are unknown are known?
No, but that measn that for some sentences X True(X) is >>>>>>>>>>>>>>>>> unknown and there
is no method to find out.
I don't know about philosophers but mathematicians and >>>>>>>>>>>>>>>>> logicians don't
find it interesting if all you can say that all >>>>>>>>>>>>>>>>> knowledge is knowable
and everything else is not.
Ross Finlayson, seemed to endlessly hedge on whether >>>>>>>>>>>>>>>> or not the truth value of the Goldbach conjecture was >>>>>>>>>>>>>>>> known. He seemed to think that there are alternative >>>>>>>>>>>>>>>> analytical frameworks that make the question of whether >>>>>>>>>>>>>>>> or not its truth value is known an ambiguous question. >>>>>>>>>>>>>>>>
I needed to refer to unknown truth values specifically >>>>>>>>>>>>>>>> because all "undecidability" when construed correctly >>>>>>>>>>>>>>>> falls into one of two categories.
(a) Semantic incoherence
(b) Unknown truth values.
Nope.
Undecidability can not come from Semantic Incoherence, as >>>>>>>>>>>>>>> the definition of Undecidability ia based on there being >>>>>>>>>>>>>>> a coherent answer, just not one that can be determined by >>>>>>>>>>>>>>> a computation.
richard richard richard, that is in-correct.
the undecidable problem turing described (as well as the >>>>>>>>>>>>>> basic halting problem) involves a situations that have >>>>>>>>>>>>>> _no_ coherent answer, not just one that can be known by >>>>>>>>>>>>>> not computed ...
Turing proved that there are universal Turing machines. An >>>>>>>>>>>>> universalTuring machine halts with some inputs and doesn't >>>>>>>>>>>>> halt with any other
input. Every Turing machine that can be given the same >>>>>>>>>>>>> input as an
universal Turing machine either fails to accept some input >>>>>>>>>>>>> with which
that universal Turing machine halts or fails to reject some >>>>>>>>>>>>> input with
which that universal Turing macnie does not halt.
dunno what ur saying here.
There is a way to find out if you can read.
i can't read if u can't explain
I can't explain the art of reading Common Language.
inturing hypothesized a diagonal computation that tries to put >>>>>>>>>>>> the Nth digit from the Nth circle-free machine as the Nth >>>>>>>>>>>> digit on this diagonal across all circle-free machine... >>>>>>>>>>>That is possible because there nither the machines nor digit >>>>>>>>>>> positions
are more numerous than natural numbers.
yes, but then he argues it's impossible to compute the
diagonal because of the paradox that ensues when naively
running the classifier on the diagonal itself
It is impossible to have a Turing machine that computes a
number that
no Turing machine can compute. But you can compute it if you >>>>>>>>> can use
all (infinitely many) Turing machines.
no you can't.
Hard to test as I han't infinite many Turing machines. But it is
u don't need to test it, you can't define a total dovetailing
machine to compute turing's diagonal,
the H machine defined on p247 from his paper /on computable numbers/
the machine supposes to compute the "turing's diagonal" across circle-
free sequences, otherwise labeled as β' in the paper, defined at the
bottom of p246
Anything that any machine can possibly compute can
be computed by applying a finite set of finite string
transformation rules to a finite set of finite strings.
Everything else is simply out-of-scope for computation
like making a silk purse from a sow's ear.
On 08/05/2026 19:58, olcott wrote:
On 5/8/2026 11:06 AM, dart200 wrote:
On 5/8/26 12:19 AM, Mikko wrote:
On 07/05/2026 12:00, dart200 wrote:
On 5/7/26 12:18 AM, Mikko wrote:A machine is not a "diagonal".
On 06/05/2026 22:40, dart200 wrote:
On 5/6/26 12:55 AM, Mikko wrote:You should not say anything about the diagonal before you have
On 05/05/2026 12:28, dart200 wrote:u don't need to test it, you can't define a total dovetailing
On 5/5/26 1:25 AM, Mikko wrote:
On 04/05/2026 10:53, dart200 wrote:
On 5/3/26 11:15 PM, Mikko wrote:
On 03/05/2026 12:09, dart200 wrote:
On 5/3/26 12:53 AM, Mikko wrote:
On 02/05/2026 23:39, dart200 wrote:
On 4/19/26 10:58 AM, Richard Damon wrote:
On 4/19/26 1:21 PM, olcott wrote:
On 4/19/2026 3:59 AM, Mikko wrote:
On 18/04/2026 15:58, olcott wrote:
Unknown truths are not elements of the body of >>>>>>>>>>>>>>>>>>> knowledge is a semantic tautology. Did you think >>>>>>>>>>>>>>>>>>> that things that are unknown are known?
No, but that measn that for some sentences X True(X) >>>>>>>>>>>>>>>>>> is unknown and there
is no method to find out.
I don't know about philosophers but mathematicians and >>>>>>>>>>>>>>>>>> logicians don't
find it interesting if all you can say that all >>>>>>>>>>>>>>>>>> knowledge is knowable
and everything else is not.
Ross Finlayson, seemed to endlessly hedge on whether >>>>>>>>>>>>>>>>> or not the truth value of the Goldbach conjecture was >>>>>>>>>>>>>>>>> known. He seemed to think that there are alternative >>>>>>>>>>>>>>>>> analytical frameworks that make the question of whether >>>>>>>>>>>>>>>>> or not its truth value is known an ambiguous question. >>>>>>>>>>>>>>>>>
I needed to refer to unknown truth values specifically >>>>>>>>>>>>>>>>> because all "undecidability" when construed correctly >>>>>>>>>>>>>>>>> falls into one of two categories.
(a) Semantic incoherence
(b) Unknown truth values.
Nope.
Undecidability can not come from Semantic Incoherence, >>>>>>>>>>>>>>>> as the definition of Undecidability ia based on there >>>>>>>>>>>>>>>> being a coherent answer, just not one that can be >>>>>>>>>>>>>>>> determined by a computation.
richard richard richard, that is in-correct.
the undecidable problem turing described (as well as the >>>>>>>>>>>>>>> basic halting problem) involves a situations that have >>>>>>>>>>>>>>> _no_ coherent answer, not just one that can be known by >>>>>>>>>>>>>>> not computed ...
Turing proved that there are universal Turing machines. An >>>>>>>>>>>>>> universalTuring machine halts with some inputs and doesn't >>>>>>>>>>>>>> halt with any other
input. Every Turing machine that can be given the same >>>>>>>>>>>>>> input as an
universal Turing machine either fails to accept some input >>>>>>>>>>>>>> with which
that universal Turing machine halts or fails to reject >>>>>>>>>>>>>> some input with
which that universal Turing macnie does not halt.
dunno what ur saying here.
There is a way to find out if you can read.
i can't read if u can't explain
I can't explain the art of reading Common Language.
inturing hypothesized a diagonal computation that tries to >>>>>>>>>>>>> put the Nth digit from the Nth circle-free machine as the >>>>>>>>>>>>> Nth digit on this diagonal across all circle-free machine... >>>>>>>>>>>>That is possible because there nither the machines nor digit >>>>>>>>>>>> positions
are more numerous than natural numbers.
yes, but then he argues it's impossible to compute the
diagonal because of the paradox that ensues when naively >>>>>>>>>>> running the classifier on the diagonal itself
It is impossible to have a Turing machine that computes a >>>>>>>>>> number that
no Turing machine can compute. But you can compute it if you >>>>>>>>>> can use
all (infinitely many) Turing machines.
no you can't.
Hard to test as I han't infinite many Turing machines. But it is >>>>>>>
machine to compute turing's diagonal,
defined
it. Any use of the word before the definition is nonsense,.
the H machine defined on p247 from his paper /on computable numbers/
the machine supposes to compute the "turing's diagonal" across
circle- free sequences, otherwise labeled as β' in the paper, defined
at the bottom of p246
Anything that any machine can possibly compute can
be computed by applying a finite set of finite string
transformation rules to a finite set of finite strings.
Everything else is simply out-of-scope for computation
like making a silk purse from a sow's ear.
That "everything else" includes many thigns that would be useful to
know. In particular, whether some useful function can be computed is
in that "everything else".
On 5/9/2026 3:30 AM, Mikko wrote:
On 08/05/2026 19:58, olcott wrote:
On 5/8/2026 11:06 AM, dart200 wrote:
On 5/8/26 12:19 AM, Mikko wrote:
On 07/05/2026 12:00, dart200 wrote:
On 5/7/26 12:18 AM, Mikko wrote:
On 06/05/2026 22:40, dart200 wrote:
On 5/6/26 12:55 AM, Mikko wrote:You should not say anything about the diagonal before you have
On 05/05/2026 12:28, dart200 wrote:u don't need to test it, you can't define a total dovetailing >>>>>>>> machine to compute turing's diagonal,
On 5/5/26 1:25 AM, Mikko wrote:
On 04/05/2026 10:53, dart200 wrote:
On 5/3/26 11:15 PM, Mikko wrote:
On 03/05/2026 12:09, dart200 wrote:
On 5/3/26 12:53 AM, Mikko wrote:
On 02/05/2026 23:39, dart200 wrote:dunno what ur saying here.
On 4/19/26 10:58 AM, Richard Damon wrote:
On 4/19/26 1:21 PM, olcott wrote:
On 4/19/2026 3:59 AM, Mikko wrote:
On 18/04/2026 15:58, olcott wrote:
No, but that measn that for some sentences X True(X) >>>>>>>>>>>>>>>>>>> is unknown and there
Unknown truths are not elements of the body of >>>>>>>>>>>>>>>>>>>> knowledge is a semantic tautology. Did you think >>>>>>>>>>>>>>>>>>>> that things that are unknown are known? >>>>>>>>>>>>>>>>>>>
is no method to find out.
I don't know about philosophers but mathematicians >>>>>>>>>>>>>>>>>>> and logicians don't
find it interesting if all you can say that all >>>>>>>>>>>>>>>>>>> knowledge is knowable
and everything else is not.
Ross Finlayson, seemed to endlessly hedge on whether >>>>>>>>>>>>>>>>>> or not the truth value of the Goldbach conjecture was >>>>>>>>>>>>>>>>>> known. He seemed to think that there are alternative >>>>>>>>>>>>>>>>>> analytical frameworks that make the question of whether >>>>>>>>>>>>>>>>>> or not its truth value is known an ambiguous question. >>>>>>>>>>>>>>>>>>
I needed to refer to unknown truth values specifically >>>>>>>>>>>>>>>>>> because all "undecidability" when construed correctly >>>>>>>>>>>>>>>>>> falls into one of two categories.
(a) Semantic incoherence
(b) Unknown truth values.
Nope.
Undecidability can not come from Semantic Incoherence, >>>>>>>>>>>>>>>>> as the definition of Undecidability ia based on there >>>>>>>>>>>>>>>>> being a coherent answer, just not one that can be >>>>>>>>>>>>>>>>> determined by a computation.
richard richard richard, that is in-correct.
the undecidable problem turing described (as well as the >>>>>>>>>>>>>>>> basic halting problem) involves a situations that have >>>>>>>>>>>>>>>> _no_ coherent answer, not just one that can be known by >>>>>>>>>>>>>>>> not computed ...
Turing proved that there are universal Turing machines. >>>>>>>>>>>>>>> An universalTuring machine halts with some inputs and >>>>>>>>>>>>>>> doesn't halt with any other
input. Every Turing machine that can be given the same >>>>>>>>>>>>>>> input as an
universal Turing machine either fails to accept some >>>>>>>>>>>>>>> input with which
that universal Turing machine halts or fails to reject >>>>>>>>>>>>>>> some input with
which that universal Turing macnie does not halt. >>>>>>>>>>>>>>
There is a way to find out if you can read.
i can't read if u can't explain
I can't explain the art of reading Common Language.
inturing hypothesized a diagonal computation that tries to >>>>>>>>>>>>>> put the Nth digit from the Nth circle-free machine as the >>>>>>>>>>>>>> Nth digit on this diagonal across all circle-free machine... >>>>>>>>>>>>>That is possible because there nither the machines nor >>>>>>>>>>>>> digit positions
are more numerous than natural numbers.
yes, but then he argues it's impossible to compute the >>>>>>>>>>>> diagonal because of the paradox that ensues when naively >>>>>>>>>>>> running the classifier on the diagonal itself
It is impossible to have a Turing machine that computes a >>>>>>>>>>> number that
no Turing machine can compute. But you can compute it if you >>>>>>>>>>> can use
all (infinitely many) Turing machines.
no you can't.
Hard to test as I han't infinite many Turing machines. But it is >>>>>>>>
defined
it. Any use of the word before the definition is nonsense,.
the H machine defined on p247 from his paper /on computable numbers/ >>>>> A machine is not a "diagonal".
the machine supposes to compute the "turing's diagonal" across
circle- free sequences, otherwise labeled as β' in the paper,
defined at the bottom of p246
Anything that any machine can possibly compute can
be computed by applying a finite set of finite string
transformation rules to a finite set of finite strings.
Everything else is simply out-of-scope for computation
like making a silk purse from a sow's ear.
That "everything else" includes many thigns that would be useful to
know. In particular, whether some useful function can be computed is
in that "everything else".
Like the truth value of: "This sentence is not true"
that has no truth value.
All self-reference "paradox" is equivalent to the
Liar Paradox and can be resolved by disallowing it
like ZFC disallowed Russell's "Paradox".
On 05/10/2026 12:10 AM, Mikko wrote:
On 09/05/2026 15:13, olcott wrote:
On 5/9/2026 3:30 AM, Mikko wrote:
On 08/05/2026 19:58, olcott wrote:
On 5/8/2026 11:06 AM, dart200 wrote:
On 5/8/26 12:19 AM, Mikko wrote:
On 07/05/2026 12:00, dart200 wrote:
On 5/7/26 12:18 AM, Mikko wrote:A machine is not a "diagonal".
On 06/05/2026 22:40, dart200 wrote:
On 5/6/26 12:55 AM, Mikko wrote:You should not say anything about the diagonal before you have >>>>>>>>> defined
On 05/05/2026 12:28, dart200 wrote:u don't need to test it, you can't define a total dovetailing >>>>>>>>>> machine to compute turing's diagonal,
On 5/5/26 1:25 AM, Mikko wrote:
On 04/05/2026 10:53, dart200 wrote:
On 5/3/26 11:15 PM, Mikko wrote:
On 03/05/2026 12:09, dart200 wrote:
On 5/3/26 12:53 AM, Mikko wrote:
On 02/05/2026 23:39, dart200 wrote:dunno what ur saying here.
On 4/19/26 10:58 AM, Richard Damon wrote: >>>>>>>>>>>>>>>>>>> On 4/19/26 1:21 PM, olcott wrote:
On 4/19/2026 3:59 AM, Mikko wrote:
On 18/04/2026 15:58, olcott wrote:
No, but that measn that for some sentences X True(X) >>>>>>>>>>>>>>>>>>>>> is unknown and there
Unknown truths are not elements of the body of >>>>>>>>>>>>>>>>>>>>>> knowledge is a semantic tautology. Did you think >>>>>>>>>>>>>>>>>>>>>> that things that are unknown are known? >>>>>>>>>>>>>>>>>>>>>
is no method to find out.
I don't know about philosophers but mathematicians >>>>>>>>>>>>>>>>>>>>> and logicians don't
find it interesting if all you can say that all >>>>>>>>>>>>>>>>>>>>> knowledge is knowable
and everything else is not.
Ross Finlayson, seemed to endlessly hedge on whether >>>>>>>>>>>>>>>>>>>> or not the truth value of the Goldbach conjecture was >>>>>>>>>>>>>>>>>>>> known. He seemed to think that there are alternative >>>>>>>>>>>>>>>>>>>> analytical frameworks that make the question of whether >>>>>>>>>>>>>>>>>>>> or not its truth value is known an ambiguous question. >>>>>>>>>>>>>>>>>>>>
I needed to refer to unknown truth values specifically >>>>>>>>>>>>>>>>>>>> because all "undecidability" when construed correctly >>>>>>>>>>>>>>>>>>>> falls into one of two categories.
(a) Semantic incoherence
(b) Unknown truth values.
Nope.
Undecidability can not come from Semantic Incoherence, >>>>>>>>>>>>>>>>>>> as the definition of Undecidability ia based on there >>>>>>>>>>>>>>>>>>> being a coherent answer, just not one that can be >>>>>>>>>>>>>>>>>>> determined by a computation.
richard richard richard, that is in-correct. >>>>>>>>>>>>>>>>>>
the undecidable problem turing described (as well as >>>>>>>>>>>>>>>>>> the basic halting problem) involves a situations that >>>>>>>>>>>>>>>>>> have _no_ coherent answer, not just one that can be >>>>>>>>>>>>>>>>>> known by not computed ...
Turing proved that there are universal Turing machines. >>>>>>>>>>>>>>>>> An universalTuring machine halts with some inputs and >>>>>>>>>>>>>>>>> doesn't halt with any other
input. Every Turing machine that can be given the same >>>>>>>>>>>>>>>>> input as an
universal Turing machine either fails to accept some >>>>>>>>>>>>>>>>> input with which
that universal Turing machine halts or fails to reject >>>>>>>>>>>>>>>>> some input with
which that universal Turing macnie does not halt. >>>>>>>>>>>>>>>>
There is a way to find out if you can read.
i can't read if u can't explain
I can't explain the art of reading Common Language.
inturing hypothesized a diagonal computation that tries to >>>>>>>>>>>>>>>> put the Nth digit from the Nth circle-free machine as the >>>>>>>>>>>>>>>> Nth digit on this diagonal across all circle-free >>>>>>>>>>>>>>>> machine...
That is possible because there nither the machines nor >>>>>>>>>>>>>>> digit positions
are more numerous than natural numbers.
yes, but then he argues it's impossible to compute the >>>>>>>>>>>>>> diagonal because of the paradox that ensues when naively >>>>>>>>>>>>>> running the classifier on the diagonal itself
It is impossible to have a Turing machine that computes a >>>>>>>>>>>>> number that
no Turing machine can compute. But you can compute it if you >>>>>>>>>>>>> can use
all (infinitely many) Turing machines.
no you can't.
Hard to test as I han't infinite many Turing machines. But it is >>>>>>>>>>
it. Any use of the word before the definition is nonsense,.
the H machine defined on p247 from his paper /on computable
numbers/
the machine supposes to compute the "turing's diagonal" across
circle- free sequences, otherwise labeled as β' in the paper,
defined at the bottom of p246
Anything that any machine can possibly compute can
be computed by applying a finite set of finite string
transformation rules to a finite set of finite strings.
Everything else is simply out-of-scope for computation
like making a silk purse from a sow's ear.
That "everything else" includes many thigns that would be useful to
know. In particular, whether some useful function can be computed is
in that "everything else".
Like the truth value of: "This sentence is not true"
that has no truth value.
I don't think knowing the truth value of that would be useful. At least
not for any important purpose.
All self-reference "paradox" is equivalent to the
Liar Paradox and can be resolved by disallowing it
like ZFC disallowed Russell's "Paradox".
Whether something is a self-reference depends on interpretation. In an
uninterpreted formal language there are no references and therefore no
self-references, which is the simplest way to avoid paradoxes by self-
reference.
Even without any self-reference a theory can be inconsistent. Russell's
paradox is simply an inconsistency.
Another way to look at that quantification over finitely-many elements
brings another one, is providing "increment" or "successor" as a
natural fact of quantification instead of it being "defined" as
what later gives a model of Peano (or Presburger) arithmetic,
though that those are really only models of ordinals, since
integers themselves have the integral moduli.
So, one way to look at that is that Russell's "paradox" or really
any account of quantification over what would make numbers
illustrates that numbers make more numbers.
That quantifying over numbers brings more numbers is just a fact
that numbers have and that the action does - then for somebody
like Mirimanoff who simply notes that after the "ordinary",
i.e. as by the finite ordinals, is the "extra-ordinary',
yet, "Russell's paradox" can start with an empty set and
find another one, that contains itself.
So, you either make for freedom of expansion of comprehension,
and numbers aren't paradoxical, or you don't.
Many keep the account simple with "there's no infinite".
Here though that's considered retro-finitism after
something like "Russell's retro-thesis" and ignorant.
On 5/8/2026 1:40 PM, dart200 wrote:
On 5/8/26 10:35 AM, olcott wrote:
On 5/8/2026 12:13 PM, dart200 wrote:
On 5/8/26 9:58 AM, olcott wrote:
On 5/8/2026 11:06 AM, dart200 wrote:
On 5/8/26 12:19 AM, Mikko wrote:
On 07/05/2026 12:00, dart200 wrote:
On 5/7/26 12:18 AM, Mikko wrote:A machine is not a "diagonal".
On 06/05/2026 22:40, dart200 wrote:
On 5/6/26 12:55 AM, Mikko wrote:You should not say anything about the diagonal before you have >>>>>>>>> defined
On 05/05/2026 12:28, dart200 wrote:u don't need to test it, you can't define a total dovetailing >>>>>>>>>> machine to compute turing's diagonal,
On 5/5/26 1:25 AM, Mikko wrote:
On 04/05/2026 10:53, dart200 wrote:
On 5/3/26 11:15 PM, Mikko wrote:
On 03/05/2026 12:09, dart200 wrote:
On 5/3/26 12:53 AM, Mikko wrote:
On 02/05/2026 23:39, dart200 wrote:dunno what ur saying here.
On 4/19/26 10:58 AM, Richard Damon wrote: >>>>>>>>>>>>>>>>>>> On 4/19/26 1:21 PM, olcott wrote:
On 4/19/2026 3:59 AM, Mikko wrote:
On 18/04/2026 15:58, olcott wrote:
No, but that measn that for some sentences X >>>>>>>>>>>>>>>>>>>>> True(X) is unknown and there
Unknown truths are not elements of the body of >>>>>>>>>>>>>>>>>>>>>> knowledge is a semantic tautology. Did you think >>>>>>>>>>>>>>>>>>>>>> that things that are unknown are known? >>>>>>>>>>>>>>>>>>>>>
is no method to find out.
I don't know about philosophers but mathematicians >>>>>>>>>>>>>>>>>>>>> and logicians don't
find it interesting if all you can say that all >>>>>>>>>>>>>>>>>>>>> knowledge is knowable
and everything else is not.
Ross Finlayson, seemed to endlessly hedge on whether >>>>>>>>>>>>>>>>>>>> or not the truth value of the Goldbach conjecture was >>>>>>>>>>>>>>>>>>>> known. He seemed to think that there are alternative >>>>>>>>>>>>>>>>>>>> analytical frameworks that make the question of whether >>>>>>>>>>>>>>>>>>>> or not its truth value is known an ambiguous question. >>>>>>>>>>>>>>>>>>>>
I needed to refer to unknown truth values specifically >>>>>>>>>>>>>>>>>>>> because all "undecidability" when construed correctly >>>>>>>>>>>>>>>>>>>> falls into one of two categories.
(a) Semantic incoherence
(b) Unknown truth values.
Nope.
Undecidability can not come from Semantic >>>>>>>>>>>>>>>>>>> Incoherence, as the definition of Undecidability ia >>>>>>>>>>>>>>>>>>> based on there being a coherent answer, just not one >>>>>>>>>>>>>>>>>>> that can be determined by a computation.
richard richard richard, that is in-correct. >>>>>>>>>>>>>>>>>>
the undecidable problem turing described (as well as >>>>>>>>>>>>>>>>>> the basic halting problem) involves a situations that >>>>>>>>>>>>>>>>>> have _no_ coherent answer, not just one that can be >>>>>>>>>>>>>>>>>> known by not computed ...
Turing proved that there are universal Turing machines. >>>>>>>>>>>>>>>>> An universalTuring machine halts with some inputs and >>>>>>>>>>>>>>>>> doesn't halt with any other
input. Every Turing machine that can be given the same >>>>>>>>>>>>>>>>> input as an
universal Turing machine either fails to accept some >>>>>>>>>>>>>>>>> input with which
that universal Turing machine halts or fails to reject >>>>>>>>>>>>>>>>> some input with
which that universal Turing macnie does not halt. >>>>>>>>>>>>>>>>
There is a way to find out if you can read.
i can't read if u can't explain
I can't explain the art of reading Common Language.
inturing hypothesized a diagonal computation that tries to >>>>>>>>>>>>>>>> put the Nth digit from the Nth circle-free machine as >>>>>>>>>>>>>>>> the Nth digit on this diagonal across all circle-free >>>>>>>>>>>>>>>> machine...
That is possible because there nither the machines nor >>>>>>>>>>>>>>> digit positions
are more numerous than natural numbers.
yes, but then he argues it's impossible to compute the >>>>>>>>>>>>>> diagonal because of the paradox that ensues when naively >>>>>>>>>>>>>> running the classifier on the diagonal itself
It is impossible to have a Turing machine that computes a >>>>>>>>>>>>> number that
no Turing machine can compute. But you can compute it if >>>>>>>>>>>>> you can use
all (infinitely many) Turing machines.
no you can't.
Hard to test as I han't infinite many Turing machines. But it is >>>>>>>>>>
it. Any use of the word before the definition is nonsense,.
the H machine defined on p247 from his paper /on computable
numbers/
the machine supposes to compute the "turing's diagonal" across
circle- free sequences, otherwise labeled as β' in the paper,
defined at the bottom of p246
Anything that any machine can possibly compute can
be computed by applying a finite set of finite string
transformation rules to a finite set of finite strings.
Everything else is simply out-of-scope for computation
like making a silk purse from a sow's ear.
i believe the i mentally applied a finite set of string
transformations to decide that DD does in fact halt
No one every simplified is down to its barest possible
essence before me. Also the entire body of knowledge
expressed in language can be encoded as finite relations
between finite strings.
This transforms all undecidability into
(a) Outside of the body of knowledge that can be expressed in language
we know DD halts polcott, so clearly not outside the body of knowledge
that can be expressed in language
No it is fucked up bullshit like:
"This sentence is not true" (see b below)
(b) Semantically incoherent relations between finite strings.
All self-reference "paradox" is merely (b)
On 5/8/26 12:01 PM, olcott wrote:
On 5/8/2026 1:40 PM, dart200 wrote:
On 5/8/26 10:35 AM, olcott wrote:
On 5/8/2026 12:13 PM, dart200 wrote:
On 5/8/26 9:58 AM, olcott wrote:
On 5/8/2026 11:06 AM, dart200 wrote:
On 5/8/26 12:19 AM, Mikko wrote:
On 07/05/2026 12:00, dart200 wrote:
On 5/7/26 12:18 AM, Mikko wrote:A machine is not a "diagonal".
On 06/05/2026 22:40, dart200 wrote:
On 5/6/26 12:55 AM, Mikko wrote:You should not say anything about the diagonal before you have >>>>>>>>>> defined
On 05/05/2026 12:28, dart200 wrote:
On 5/5/26 1:25 AM, Mikko wrote:
On 04/05/2026 10:53, dart200 wrote:
On 5/3/26 11:15 PM, Mikko wrote:
On 03/05/2026 12:09, dart200 wrote:
On 5/3/26 12:53 AM, Mikko wrote:
On 02/05/2026 23:39, dart200 wrote:dunno what ur saying here.
On 4/19/26 10:58 AM, Richard Damon wrote: >>>>>>>>>>>>>>>>>>>> On 4/19/26 1:21 PM, olcott wrote:
richard richard richard, that is in-correct. >>>>>>>>>>>>>>>>>>>On 4/19/2026 3:59 AM, Mikko wrote:
On 18/04/2026 15:58, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>
Unknown truths are not elements of the body of >>>>>>>>>>>>>>>>>>>>>>> knowledge is a semantic tautology. Did you think >>>>>>>>>>>>>>>>>>>>>>> that things that are unknown are known? >>>>>>>>>>>>>>>>>>>>>>No, but that measn that for some sentences X >>>>>>>>>>>>>>>>>>>>>> True(X) is unknown and there
is no method to find out.
I don't know about philosophers but mathematicians >>>>>>>>>>>>>>>>>>>>>> and logicians don't
find it interesting if all you can say that all >>>>>>>>>>>>>>>>>>>>>> knowledge is knowable
and everything else is not.
Ross Finlayson, seemed to endlessly hedge on whether >>>>>>>>>>>>>>>>>>>>> or not the truth value of the Goldbach conjecture was >>>>>>>>>>>>>>>>>>>>> known. He seemed to think that there are alternative >>>>>>>>>>>>>>>>>>>>> analytical frameworks that make the question of >>>>>>>>>>>>>>>>>>>>> whether
or not its truth value is known an ambiguous question. >>>>>>>>>>>>>>>>>>>>>
I needed to refer to unknown truth values specifically >>>>>>>>>>>>>>>>>>>>> because all "undecidability" when construed correctly >>>>>>>>>>>>>>>>>>>>> falls into one of two categories.
(a) Semantic incoherence
(b) Unknown truth values.
Nope.
Undecidability can not come from Semantic >>>>>>>>>>>>>>>>>>>> Incoherence, as the definition of Undecidability ia >>>>>>>>>>>>>>>>>>>> based on there being a coherent answer, just not one >>>>>>>>>>>>>>>>>>>> that can be determined by a computation. >>>>>>>>>>>>>>>>>>>
the undecidable problem turing described (as well as >>>>>>>>>>>>>>>>>>> the basic halting problem) involves a situations that >>>>>>>>>>>>>>>>>>> have _no_ coherent answer, not just one that can be >>>>>>>>>>>>>>>>>>> known by not computed ...
Turing proved that there are universal Turing >>>>>>>>>>>>>>>>>> machines. An universalTuring machine halts with some >>>>>>>>>>>>>>>>>> inputs and doesn't halt with any other
input. Every Turing machine that can be given the same >>>>>>>>>>>>>>>>>> input as an
universal Turing machine either fails to accept some >>>>>>>>>>>>>>>>>> input with which
that universal Turing machine halts or fails to reject >>>>>>>>>>>>>>>>>> some input with
which that universal Turing macnie does not halt. >>>>>>>>>>>>>>>>>
There is a way to find out if you can read.
i can't read if u can't explain
I can't explain the art of reading Common Language. >>>>>>>>>>>>>>
inturing hypothesized a diagonal computation that tries >>>>>>>>>>>>>>>>> to put the Nth digit from the Nth circle-free machine >>>>>>>>>>>>>>>>> as the Nth digit on this diagonal across all >>>>>>>>>>>>>>>>> circle-free machine...
That is possible because there nither the machines nor >>>>>>>>>>>>>>>> digit positions
are more numerous than natural numbers.
yes, but then he argues it's impossible to compute the >>>>>>>>>>>>>>> diagonal because of the paradox that ensues when naively >>>>>>>>>>>>>>> running the classifier on the diagonal itself
It is impossible to have a Turing machine that computes a >>>>>>>>>>>>>> number that
no Turing machine can compute. But you can compute it if >>>>>>>>>>>>>> you can use
all (infinitely many) Turing machines.
no you can't.
Hard to test as I han't infinite many Turing machines. But >>>>>>>>>>>> it is
u don't need to test it, you can't define a total dovetailing >>>>>>>>>>> machine to compute turing's diagonal,
it. Any use of the word before the definition is nonsense,.
the H machine defined on p247 from his paper /on computable >>>>>>>>> numbers/
the machine supposes to compute the "turing's diagonal" across
circle- free sequences, otherwise labeled as β' in the paper,
defined at the bottom of p246
Anything that any machine can possibly compute can
be computed by applying a finite set of finite string
transformation rules to a finite set of finite strings.
Everything else is simply out-of-scope for computation
like making a silk purse from a sow's ear.
i believe the i mentally applied a finite set of string
transformations to decide that DD does in fact halt
No one every simplified is down to its barest possible
essence before me. Also the entire body of knowledge
expressed in language can be encoded as finite relations
between finite strings.
This transforms all undecidability into
(a) Outside of the body of knowledge that can be expressed in language
we know DD halts polcott, so clearly not outside the body of
knowledge that can be expressed in language
No it is fucked up bullshit like:
"This sentence is not true" (see b below)
are you saying u don't understand that DD maps to the semantic property
of "halting" polcott??
On 5/8/26 12:01 PM, olcott wrote:
On 5/8/2026 1:40 PM, dart200 wrote:
On 5/8/26 10:35 AM, olcott wrote:
On 5/8/2026 12:13 PM, dart200 wrote:
On 5/8/26 9:58 AM, olcott wrote:
On 5/8/2026 11:06 AM, dart200 wrote:
On 5/8/26 12:19 AM, Mikko wrote:
On 07/05/2026 12:00, dart200 wrote:
On 5/7/26 12:18 AM, Mikko wrote:A machine is not a "diagonal".
On 06/05/2026 22:40, dart200 wrote:
On 5/6/26 12:55 AM, Mikko wrote:You should not say anything about the diagonal before you have >>>>>>>>>> defined
On 05/05/2026 12:28, dart200 wrote:
On 5/5/26 1:25 AM, Mikko wrote:
On 04/05/2026 10:53, dart200 wrote:
On 5/3/26 11:15 PM, Mikko wrote:
On 03/05/2026 12:09, dart200 wrote:
On 5/3/26 12:53 AM, Mikko wrote:
On 02/05/2026 23:39, dart200 wrote:dunno what ur saying here.
On 4/19/26 10:58 AM, Richard Damon wrote: >>>>>>>>>>>>>>>>>>>> On 4/19/26 1:21 PM, olcott wrote:
richard richard richard, that is in-correct. >>>>>>>>>>>>>>>>>>>On 4/19/2026 3:59 AM, Mikko wrote:
On 18/04/2026 15:58, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>
Unknown truths are not elements of the body of >>>>>>>>>>>>>>>>>>>>>>> knowledge is a semantic tautology. Did you think >>>>>>>>>>>>>>>>>>>>>>> that things that are unknown are known? >>>>>>>>>>>>>>>>>>>>>>No, but that measn that for some sentences X >>>>>>>>>>>>>>>>>>>>>> True(X) is unknown and there
is no method to find out.
I don't know about philosophers but mathematicians >>>>>>>>>>>>>>>>>>>>>> and logicians don't
find it interesting if all you can say that all >>>>>>>>>>>>>>>>>>>>>> knowledge is knowable
and everything else is not.
Ross Finlayson, seemed to endlessly hedge on whether >>>>>>>>>>>>>>>>>>>>> or not the truth value of the Goldbach conjecture was >>>>>>>>>>>>>>>>>>>>> known. He seemed to think that there are alternative >>>>>>>>>>>>>>>>>>>>> analytical frameworks that make the question of >>>>>>>>>>>>>>>>>>>>> whether
or not its truth value is known an ambiguous question. >>>>>>>>>>>>>>>>>>>>>
I needed to refer to unknown truth values specifically >>>>>>>>>>>>>>>>>>>>> because all "undecidability" when construed correctly >>>>>>>>>>>>>>>>>>>>> falls into one of two categories.
(a) Semantic incoherence
(b) Unknown truth values.
Nope.
Undecidability can not come from Semantic >>>>>>>>>>>>>>>>>>>> Incoherence, as the definition of Undecidability ia >>>>>>>>>>>>>>>>>>>> based on there being a coherent answer, just not one >>>>>>>>>>>>>>>>>>>> that can be determined by a computation. >>>>>>>>>>>>>>>>>>>
the undecidable problem turing described (as well as >>>>>>>>>>>>>>>>>>> the basic halting problem) involves a situations that >>>>>>>>>>>>>>>>>>> have _no_ coherent answer, not just one that can be >>>>>>>>>>>>>>>>>>> known by not computed ...
Turing proved that there are universal Turing >>>>>>>>>>>>>>>>>> machines. An universalTuring machine halts with some >>>>>>>>>>>>>>>>>> inputs and doesn't halt with any other
input. Every Turing machine that can be given the same >>>>>>>>>>>>>>>>>> input as an
universal Turing machine either fails to accept some >>>>>>>>>>>>>>>>>> input with which
that universal Turing machine halts or fails to reject >>>>>>>>>>>>>>>>>> some input with
which that universal Turing macnie does not halt. >>>>>>>>>>>>>>>>>
There is a way to find out if you can read.
i can't read if u can't explain
I can't explain the art of reading Common Language. >>>>>>>>>>>>>>
inturing hypothesized a diagonal computation that tries >>>>>>>>>>>>>>>>> to put the Nth digit from the Nth circle-free machine >>>>>>>>>>>>>>>>> as the Nth digit on this diagonal across all circle- >>>>>>>>>>>>>>>>> free machine...
That is possible because there nither the machines nor >>>>>>>>>>>>>>>> digit positions
are more numerous than natural numbers.
yes, but then he argues it's impossible to compute the >>>>>>>>>>>>>>> diagonal because of the paradox that ensues when naively >>>>>>>>>>>>>>> running the classifier on the diagonal itself
It is impossible to have a Turing machine that computes a >>>>>>>>>>>>>> number that
no Turing machine can compute. But you can compute it if >>>>>>>>>>>>>> you can use
all (infinitely many) Turing machines.
no you can't.
Hard to test as I han't infinite many Turing machines. But >>>>>>>>>>>> it is
u don't need to test it, you can't define a total dovetailing >>>>>>>>>>> machine to compute turing's diagonal,
it. Any use of the word before the definition is nonsense,.
the H machine defined on p247 from his paper /on computable >>>>>>>>> numbers/
the machine supposes to compute the "turing's diagonal" across
circle- free sequences, otherwise labeled as β' in the paper,
defined at the bottom of p246
Anything that any machine can possibly compute can
be computed by applying a finite set of finite string
transformation rules to a finite set of finite strings.
Everything else is simply out-of-scope for computation
like making a silk purse from a sow's ear.
i believe the i mentally applied a finite set of string
transformations to decide that DD does in fact halt
No one every simplified is down to its barest possible
essence before me. Also the entire body of knowledge
expressed in language can be encoded as finite relations
between finite strings.
This transforms all undecidability into
(a) Outside of the body of knowledge that can be expressed in language
we know DD halts polcott, so clearly not outside the body of
knowledge that can be expressed in language
No it is fucked up bullshit like:
"This sentence is not true" (see b below)
are you saying u don't understand that DD maps to the semantic property
of "halting" polcott??
(b) Semantically incoherent relations between finite strings.
All self-reference "paradox" is merely (b)
dart200 wrote:^^^^^^^^^^^^^^^^^^^
On 5/8/26 12:01 PM, olcott wrote:
On 5/8/2026 1:40 PM, dart200 wrote:
On 5/8/26 10:35 AM, olcott wrote:
On 5/8/2026 12:13 PM, dart200 wrote:we know DD halts polcott, so clearly not outside the body of
On 5/8/26 9:58 AM, olcott wrote:
On 5/8/2026 11:06 AM, dart200 wrote:
On 5/8/26 12:19 AM, Mikko wrote:
On 07/05/2026 12:00, dart200 wrote:
On 5/7/26 12:18 AM, Mikko wrote:A machine is not a "diagonal".
On 06/05/2026 22:40, dart200 wrote:the H machine defined on p247 from his paper /on computable >>>>>>>>>> numbers/
On 5/6/26 12:55 AM, Mikko wrote:You should not say anything about the diagonal before you >>>>>>>>>>> have defined
On 05/05/2026 12:28, dart200 wrote:
On 5/5/26 1:25 AM, Mikko wrote:
On 04/05/2026 10:53, dart200 wrote:
On 5/3/26 11:15 PM, Mikko wrote:
On 03/05/2026 12:09, dart200 wrote:
On 5/3/26 12:53 AM, Mikko wrote:
On 02/05/2026 23:39, dart200 wrote:dunno what ur saying here.
On 4/19/26 10:58 AM, Richard Damon wrote: >>>>>>>>>>>>>>>>>>>>> On 4/19/26 1:21 PM, olcott wrote:
richard richard richard, that is in-correct. >>>>>>>>>>>>>>>>>>>>On 4/19/2026 3:59 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>> On 18/04/2026 15:58, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>
Unknown truths are not elements of the body of >>>>>>>>>>>>>>>>>>>>>>>> knowledge is a semantic tautology. Did you think >>>>>>>>>>>>>>>>>>>>>>>> that things that are unknown are known? >>>>>>>>>>>>>>>>>>>>>>>No, but that measn that for some sentences X >>>>>>>>>>>>>>>>>>>>>>> True(X) is unknown and there
is no method to find out.
I don't know about philosophers but >>>>>>>>>>>>>>>>>>>>>>> mathematicians and logicians don't >>>>>>>>>>>>>>>>>>>>>>> find it interesting if all you can say that all >>>>>>>>>>>>>>>>>>>>>>> knowledge is knowable
and everything else is not.
Ross Finlayson, seemed to endlessly hedge on whether >>>>>>>>>>>>>>>>>>>>>> or not the truth value of the Goldbach conjecture was >>>>>>>>>>>>>>>>>>>>>> known. He seemed to think that there are alternative >>>>>>>>>>>>>>>>>>>>>> analytical frameworks that make the question of >>>>>>>>>>>>>>>>>>>>>> whether
or not its truth value is known an ambiguous >>>>>>>>>>>>>>>>>>>>>> question.
I needed to refer to unknown truth values >>>>>>>>>>>>>>>>>>>>>> specifically
because all "undecidability" when construed correctly >>>>>>>>>>>>>>>>>>>>>> falls into one of two categories.
(a) Semantic incoherence
(b) Unknown truth values.
Nope.
Undecidability can not come from Semantic >>>>>>>>>>>>>>>>>>>>> Incoherence, as the definition of Undecidability ia >>>>>>>>>>>>>>>>>>>>> based on there being a coherent answer, just not >>>>>>>>>>>>>>>>>>>>> one that can be determined by a computation. >>>>>>>>>>>>>>>>>>>>
the undecidable problem turing described (as well as >>>>>>>>>>>>>>>>>>>> the basic halting problem) involves a situations >>>>>>>>>>>>>>>>>>>> that have _no_ coherent answer, not just one that >>>>>>>>>>>>>>>>>>>> can be known by not computed ...
Turing proved that there are universal Turing >>>>>>>>>>>>>>>>>>> machines. An universalTuring machine halts with some >>>>>>>>>>>>>>>>>>> inputs and doesn't halt with any other
input. Every Turing machine that can be given the >>>>>>>>>>>>>>>>>>> same input as an
universal Turing machine either fails to accept some >>>>>>>>>>>>>>>>>>> input with which
that universal Turing machine halts or fails to >>>>>>>>>>>>>>>>>>> reject some input with
which that universal Turing macnie does not halt. >>>>>>>>>>>>>>>>>>
There is a way to find out if you can read.
i can't read if u can't explain
I can't explain the art of reading Common Language. >>>>>>>>>>>>>>>
inturing hypothesized a diagonal computation that tries >>>>>>>>>>>>>>>>>> to put the Nth digit from the Nth circle-free machine >>>>>>>>>>>>>>>>>> as the Nth digit on this diagonal across all circle- >>>>>>>>>>>>>>>>>> free machine...
That is possible because there nither the machines nor >>>>>>>>>>>>>>>>> digit positions
are more numerous than natural numbers.
yes, but then he argues it's impossible to compute the >>>>>>>>>>>>>>>> diagonal because of the paradox that ensues when naively >>>>>>>>>>>>>>>> running the classifier on the diagonal itself
It is impossible to have a Turing machine that computes a >>>>>>>>>>>>>>> number that
no Turing machine can compute. But you can compute it if >>>>>>>>>>>>>>> you can use
all (infinitely many) Turing machines.
no you can't.
Hard to test as I han't infinite many Turing machines. But >>>>>>>>>>>>> it is
u don't need to test it, you can't define a total
dovetailing machine to compute turing's diagonal,
it. Any use of the word before the definition is nonsense,. >>>>>>>>>
the machine supposes to compute the "turing's diagonal" across >>>>>>>> circle- free sequences, otherwise labeled as β' in the paper, >>>>>>>> defined at the bottom of p246
Anything that any machine can possibly compute can
be computed by applying a finite set of finite string
transformation rules to a finite set of finite strings.
Everything else is simply out-of-scope for computation
like making a silk purse from a sow's ear.
i believe the i mentally applied a finite set of string
transformations to decide that DD does in fact halt
No one every simplified is down to its barest possible
essence before me. Also the entire body of knowledge
expressed in language can be encoded as finite relations
between finite strings.
This transforms all undecidability into
(a) Outside of the body of knowledge that can be expressed in language >>>>
knowledge that can be expressed in language
No it is fucked up bullshit like:
"This sentence is not true" (see b below)
are you saying u don't understand that DD maps to the semantic
property of "halting" polcott??
No I'm saying
that M/RR changes by any small movement of a pebble within
the earth's makeup. There are millions of vehicles driving around on the earth's surface altering the calculation. What's there to pinpointing G?
What's next, setting down an ice-cold coca-cola and marveling at
different temperature readings upon it?
On 10/05/2026 22:06, olcott wrote:
On 5/10/2026 2:10 AM, Mikko wrote:
On 09/05/2026 15:13, olcott wrote:
On 5/9/2026 3:30 AM, Mikko wrote:
On 08/05/2026 19:58, olcott wrote:
On 5/8/2026 11:06 AM, dart200 wrote:
On 5/8/26 12:19 AM, Mikko wrote:
On 07/05/2026 12:00, dart200 wrote:
On 5/7/26 12:18 AM, Mikko wrote:A machine is not a "diagonal".
On 06/05/2026 22:40, dart200 wrote:
On 5/6/26 12:55 AM, Mikko wrote:You should not say anything about the diagonal before you have >>>>>>>>>> defined
On 05/05/2026 12:28, dart200 wrote:
On 5/5/26 1:25 AM, Mikko wrote:
On 04/05/2026 10:53, dart200 wrote:
On 5/3/26 11:15 PM, Mikko wrote:
On 03/05/2026 12:09, dart200 wrote:
On 5/3/26 12:53 AM, Mikko wrote:
On 02/05/2026 23:39, dart200 wrote:dunno what ur saying here.
On 4/19/26 10:58 AM, Richard Damon wrote: >>>>>>>>>>>>>>>>>>>> On 4/19/26 1:21 PM, olcott wrote:
richard richard richard, that is in-correct. >>>>>>>>>>>>>>>>>>>On 4/19/2026 3:59 AM, Mikko wrote:
On 18/04/2026 15:58, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>
Unknown truths are not elements of the body of >>>>>>>>>>>>>>>>>>>>>>> knowledge is a semantic tautology. Did you think >>>>>>>>>>>>>>>>>>>>>>> that things that are unknown are known? >>>>>>>>>>>>>>>>>>>>>>No, but that measn that for some sentences X >>>>>>>>>>>>>>>>>>>>>> True(X) is unknown and there
is no method to find out.
I don't know about philosophers but mathematicians >>>>>>>>>>>>>>>>>>>>>> and logicians don't
find it interesting if all you can say that all >>>>>>>>>>>>>>>>>>>>>> knowledge is knowable
and everything else is not.
Ross Finlayson, seemed to endlessly hedge on whether >>>>>>>>>>>>>>>>>>>>> or not the truth value of the Goldbach conjecture was >>>>>>>>>>>>>>>>>>>>> known. He seemed to think that there are alternative >>>>>>>>>>>>>>>>>>>>> analytical frameworks that make the question of >>>>>>>>>>>>>>>>>>>>> whether
or not its truth value is known an ambiguous question. >>>>>>>>>>>>>>>>>>>>>
I needed to refer to unknown truth values specifically >>>>>>>>>>>>>>>>>>>>> because all "undecidability" when construed correctly >>>>>>>>>>>>>>>>>>>>> falls into one of two categories.
(a) Semantic incoherence
(b) Unknown truth values.
Nope.
Undecidability can not come from Semantic >>>>>>>>>>>>>>>>>>>> Incoherence, as the definition of Undecidability ia >>>>>>>>>>>>>>>>>>>> based on there being a coherent answer, just not one >>>>>>>>>>>>>>>>>>>> that can be determined by a computation. >>>>>>>>>>>>>>>>>>>
the undecidable problem turing described (as well as >>>>>>>>>>>>>>>>>>> the basic halting problem) involves a situations that >>>>>>>>>>>>>>>>>>> have _no_ coherent answer, not just one that can be >>>>>>>>>>>>>>>>>>> known by not computed ...
Turing proved that there are universal Turing >>>>>>>>>>>>>>>>>> machines. An universalTuring machine halts with some >>>>>>>>>>>>>>>>>> inputs and doesn't halt with any other
input. Every Turing machine that can be given the same >>>>>>>>>>>>>>>>>> input as an
universal Turing machine either fails to accept some >>>>>>>>>>>>>>>>>> input with which
that universal Turing machine halts or fails to reject >>>>>>>>>>>>>>>>>> some input with
which that universal Turing macnie does not halt. >>>>>>>>>>>>>>>>>
There is a way to find out if you can read.
i can't read if u can't explain
I can't explain the art of reading Common Language. >>>>>>>>>>>>>>
inturing hypothesized a diagonal computation that tries >>>>>>>>>>>>>>>>> to put the Nth digit from the Nth circle-free machine >>>>>>>>>>>>>>>>> as the Nth digit on this diagonal across all circle- >>>>>>>>>>>>>>>>> free machine...
That is possible because there nither the machines nor >>>>>>>>>>>>>>>> digit positions
are more numerous than natural numbers.
yes, but then he argues it's impossible to compute the >>>>>>>>>>>>>>> diagonal because of the paradox that ensues when naively >>>>>>>>>>>>>>> running the classifier on the diagonal itself
It is impossible to have a Turing machine that computes a >>>>>>>>>>>>>> number that
no Turing machine can compute. But you can compute it if >>>>>>>>>>>>>> you can use
all (infinitely many) Turing machines.
no you can't.
Hard to test as I han't infinite many Turing machines. But >>>>>>>>>>>> it is
u don't need to test it, you can't define a total dovetailing >>>>>>>>>>> machine to compute turing's diagonal,
it. Any use of the word before the definition is nonsense,.
the H machine defined on p247 from his paper /on computable >>>>>>>>> numbers/
the machine supposes to compute the "turing's diagonal" across
circle- free sequences, otherwise labeled as β' in the paper,
defined at the bottom of p246
Anything that any machine can possibly compute can
be computed by applying a finite set of finite string
transformation rules to a finite set of finite strings.
Everything else is simply out-of-scope for computation
like making a silk purse from a sow's ear.
That "everything else" includes many thigns that would be useful to
know. In particular, whether some useful function can be computed is >>>>> in that "everything else".
Like the truth value of: "This sentence is not true"
that has no truth value.
I don't think knowing the truth value of that would be useful. At least
not for any important purpose.
Knowing that all undecidability is merely semantic
incoherence enables:
"true on the basis of meaning expressed in language"
to be reliably computable for the entire body of knowledge.
We don't have the knowledge that all undecidability is merely semantic incoherence, and can't know because we already know that there is undecidability that is not semantic incoherence. FOr example the
axiom system
∀x (1⋅x = x)
∀x (x⋅1 = x)
∀x∀y∀z (x⋅(y⋅z) = (x⋅y)⋅z)
∀x∃y (x⋅y = 1)
∀x∃y (y⋅x = 1)
is useful for many purposes. But there are sentences like
∀x∃y (x⋅y = y⋅x)
that are undecidable in that system. But there is notiong semantically incoherent in that example or similar ones.
The truth about climate change and election fraud could
be computed.
Not without real world information.
Of course you may postulate that
the climate is immutable or that there was massimbe undetected fraud
in the last or some earlier election but that is not what the word "knowledge" means.
LLMs could become reliable truth tellers.
They don't became other than what they are made to be. IF truthfullness
is not a design crterion it will not be a feature.
All self-reference "paradox" is equivalent to the
Liar Paradox and can be resolved by disallowing it
like ZFC disallowed Russell's "Paradox".
Whether something is a self-reference depends on interpretation. In an
uninterpreted formal language there are no references and therefore no
self-references, which is the simplest way to avoid paradoxes by self-
reference.
Even without any self-reference a theory can be inconsistent.
Russell's paradox is simply an inconsistency.
Likewise with all undecidability within the body
of knowledge that can be expressed as language.
No, per definition an inconcistency is decidable so it is not an undecidability.
RP is merely the only instance of pathological
self-reference (PSR) that was correctly rejected.
Russell's paradox is not an undecidability.
HP counter-example input is another instance of PSR.
The halting problem counter-example is neither an undecidability nor an incconsistency.
And there is no self-reference in it. The halting
problem counter-example is simply a Turing machine. A Truring machine
cannot contain any reference to any Turing machine so it cannot contain
a self-reference. A Turing machine is not and does not contain any claim
so it is not and does not contain any undecidability or inconsistency.
On 5/11/2026 2:24 AM, Mikko wrote:
On 10/05/2026 22:06, olcott wrote:
On 5/10/2026 2:10 AM, Mikko wrote:
On 09/05/2026 15:13, olcott wrote:
On 5/9/2026 3:30 AM, Mikko wrote:
On 08/05/2026 19:58, olcott wrote:
On 5/8/2026 11:06 AM, dart200 wrote:
On 5/8/26 12:19 AM, Mikko wrote:
On 07/05/2026 12:00, dart200 wrote:
On 5/7/26 12:18 AM, Mikko wrote:A machine is not a "diagonal".
On 06/05/2026 22:40, dart200 wrote:the H machine defined on p247 from his paper /on computable >>>>>>>>>> numbers/
On 5/6/26 12:55 AM, Mikko wrote:You should not say anything about the diagonal before you >>>>>>>>>>> have defined
On 05/05/2026 12:28, dart200 wrote:
On 5/5/26 1:25 AM, Mikko wrote:
On 04/05/2026 10:53, dart200 wrote:
On 5/3/26 11:15 PM, Mikko wrote:
On 03/05/2026 12:09, dart200 wrote:
On 5/3/26 12:53 AM, Mikko wrote:
On 02/05/2026 23:39, dart200 wrote:dunno what ur saying here.
On 4/19/26 10:58 AM, Richard Damon wrote: >>>>>>>>>>>>>>>>>>>>> On 4/19/26 1:21 PM, olcott wrote:
richard richard richard, that is in-correct. >>>>>>>>>>>>>>>>>>>>On 4/19/2026 3:59 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>> On 18/04/2026 15:58, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>
Unknown truths are not elements of the body of >>>>>>>>>>>>>>>>>>>>>>>> knowledge is a semantic tautology. Did you think >>>>>>>>>>>>>>>>>>>>>>>> that things that are unknown are known? >>>>>>>>>>>>>>>>>>>>>>>No, but that measn that for some sentences X >>>>>>>>>>>>>>>>>>>>>>> True(X) is unknown and there
is no method to find out.
I don't know about philosophers but >>>>>>>>>>>>>>>>>>>>>>> mathematicians and logicians don't >>>>>>>>>>>>>>>>>>>>>>> find it interesting if all you can say that all >>>>>>>>>>>>>>>>>>>>>>> knowledge is knowable
and everything else is not.
Ross Finlayson, seemed to endlessly hedge on whether >>>>>>>>>>>>>>>>>>>>>> or not the truth value of the Goldbach conjecture was >>>>>>>>>>>>>>>>>>>>>> known. He seemed to think that there are alternative >>>>>>>>>>>>>>>>>>>>>> analytical frameworks that make the question of >>>>>>>>>>>>>>>>>>>>>> whether
or not its truth value is known an ambiguous >>>>>>>>>>>>>>>>>>>>>> question.
I needed to refer to unknown truth values >>>>>>>>>>>>>>>>>>>>>> specifically
because all "undecidability" when construed correctly >>>>>>>>>>>>>>>>>>>>>> falls into one of two categories.
(a) Semantic incoherence
(b) Unknown truth values.
Nope.
Undecidability can not come from Semantic >>>>>>>>>>>>>>>>>>>>> Incoherence, as the definition of Undecidability ia >>>>>>>>>>>>>>>>>>>>> based on there being a coherent answer, just not >>>>>>>>>>>>>>>>>>>>> one that can be determined by a computation. >>>>>>>>>>>>>>>>>>>>
the undecidable problem turing described (as well as >>>>>>>>>>>>>>>>>>>> the basic halting problem) involves a situations >>>>>>>>>>>>>>>>>>>> that have _no_ coherent answer, not just one that >>>>>>>>>>>>>>>>>>>> can be known by not computed ...
Turing proved that there are universal Turing >>>>>>>>>>>>>>>>>>> machines. An universalTuring machine halts with some >>>>>>>>>>>>>>>>>>> inputs and doesn't halt with any other
input. Every Turing machine that can be given the >>>>>>>>>>>>>>>>>>> same input as an
universal Turing machine either fails to accept some >>>>>>>>>>>>>>>>>>> input with which
that universal Turing machine halts or fails to >>>>>>>>>>>>>>>>>>> reject some input with
which that universal Turing macnie does not halt. >>>>>>>>>>>>>>>>>>
There is a way to find out if you can read.
i can't read if u can't explain
I can't explain the art of reading Common Language. >>>>>>>>>>>>>>>
inturing hypothesized a diagonal computation that tries >>>>>>>>>>>>>>>>>> to put the Nth digit from the Nth circle-free machine >>>>>>>>>>>>>>>>>> as the Nth digit on this diagonal across all circle- >>>>>>>>>>>>>>>>>> free machine...
That is possible because there nither the machines nor >>>>>>>>>>>>>>>>> digit positions
are more numerous than natural numbers.
yes, but then he argues it's impossible to compute the >>>>>>>>>>>>>>>> diagonal because of the paradox that ensues when naively >>>>>>>>>>>>>>>> running the classifier on the diagonal itself
It is impossible to have a Turing machine that computes a >>>>>>>>>>>>>>> number that
no Turing machine can compute. But you can compute it if >>>>>>>>>>>>>>> you can use
all (infinitely many) Turing machines.
no you can't.
Hard to test as I han't infinite many Turing machines. But >>>>>>>>>>>>> it is
u don't need to test it, you can't define a total
dovetailing machine to compute turing's diagonal,
it. Any use of the word before the definition is nonsense,. >>>>>>>>>
the machine supposes to compute the "turing's diagonal" across >>>>>>>> circle- free sequences, otherwise labeled as β' in the paper, >>>>>>>> defined at the bottom of p246
Anything that any machine can possibly compute can
be computed by applying a finite set of finite string
transformation rules to a finite set of finite strings.
Everything else is simply out-of-scope for computation
like making a silk purse from a sow's ear.
That "everything else" includes many thigns that would be useful to >>>>>> know. In particular, whether some useful function can be computed is >>>>>> in that "everything else".
Like the truth value of: "This sentence is not true"
that has no truth value.
I don't think knowing the truth value of that would be useful. At least >>>> not for any important purpose.
Knowing that all undecidability is merely semantic
incoherence enables:
"true on the basis of meaning expressed in language"
to be reliably computable for the entire body of knowledge.
We don't have the knowledge that all undecidability is merely semantic
incoherence, and can't know because we already know that there is
undecidability that is not semantic incoherence. FOr example the
axiom system
∀x (1⋅x = x)
1.5 != 5 ∴ you are wrong and I am couinting the rest as gibberish
∀x (x⋅1 = x)
∀x∀y∀z (x⋅(y⋅z) = (x⋅y)⋅z)
∀x∃y (x⋅y = 1)
∀x∃y (y⋅x = 1)
is useful for many purposes. But there are sentences like
∀x∃y (x⋅y = y⋅x)
that are undecidable in that system. But there is notiong semantically
incoherent in that example or similar ones.
The truth about climate change and election fraud could
be computed.
Not without real world information.
Yes, so what?
All knowledge that can be expressed in language would
include the exact (x,y,z) coordinates of every atom of your
body relative to the exact center of the Earth every millisecond.
Because this degree of detail is not physically implementable
to implement my system we exclude most specific details. It
is a system of general knowledge of about 200 petabytes.
Of course you may postulate that
the climate is immutable or that there was massimbe undetected fraud
in the last or some earlier election but that is not what the word
"knowledge" means.
The key elements of election fraud are two things:
(a) There was no actual evidence of election fraud
that could have possibly changed the results.
All self-reference "paradox" is equivalent to the
Liar Paradox and can be resolved by disallowing it
like ZFC disallowed Russell's "Paradox".
Whether something is a self-reference depends on interpretation. In an >>>> uninterpreted formal language there are no references and therefore no >>>> self-references, which is the simplest way to avoid paradoxes by self- >>>> reference.
Even without any self-reference a theory can be inconsistent.
Russell's paradox is simply an inconsistency.
Likewise with all undecidability within the body
of knowledge that can be expressed as language.
No, per definition an inconcistency is decidable so it is not an
undecidability.
RP is merely the only instance of pathological
self-reference (PSR) that was correctly rejected.
Russell's paradox is not an undecidability.
It was until ZFC refuted it.
HP counter-example input is another instance of PSR.
The halting problem counter-example is neither an undecidability nor an
incconsistency.
In computability theory and computational complexity
theory, an undecidable problem is a decision problem
for which it is proved to be impossible to construct
an algorithm that always leads to a correct yes-or-no answer. https://en.wikipedia.org/wiki/Undecidable_problem
And there is no self-reference in it. The halting
Can a halt decider H provide a yes/no answer to the
question: Does my input D halt? When the input D does
the opposite of whatever answer that the halt decider
H returns?
On 2026-05-12 07:32, olcott wrote:
On 5/12/2026 2:05 AM, Mikko wrote:
On 11/05/2026 14:44, olcott wrote:
On 5/11/2026 2:24 AM, Mikko wrote:
On 10/05/2026 22:06, olcott wrote:
We don't have the knowledge that all undecidability is merely semantic >>>>> incoherence, and can't know because we already know that there is
undecidability that is not semantic incoherence. FOr example the
axiom system
∀x (1⋅x = x)
1.5 != 5 ∴ you are wrong and I am couinting the rest as gibberish
Middle dot is a commonly used mathematical operator. In this context
where the purpose of the operation is not specified some other symbols
are often used instead, like ∘ or ∙, or operands are just put side by >>> side with no operator between.
If commonly used mathematics is gibberish to you then we many safely
conclude that you have nothing useful to offer to the groups you
posted to.
∀x (x⋅1 = x)
∀x∀y∀z (x⋅(y⋅z) = (x⋅y)⋅z)
∀x∃y (x⋅y = 1)
∀x∃y (y⋅x = 1)
is useful for many purposes. But there are sentences like
∀x∃y (x⋅y = y⋅x)
that are undecidable in that system. But there is notiong semantically >>>>> incoherent in that example or similar ones.
I'm curious to know how you would actually address Mikko's point here.
He's pointed out the rather obvious error in your reading comprehension,
but you've simply glossed over the example.
In what sense is ∀x∃y (x⋅y = y⋅x) "semantically incoherent"?
André
On 12/05/2026 16:32, olcott wrote:
On 5/12/2026 2:05 AM, Mikko wrote:
On 11/05/2026 14:44, olcott wrote:
On 5/11/2026 2:24 AM, Mikko wrote:
On 10/05/2026 22:06, olcott wrote:
On 5/10/2026 2:10 AM, Mikko wrote:
On 09/05/2026 15:13, olcott wrote:
On 5/9/2026 3:30 AM, Mikko wrote:
On 08/05/2026 19:58, olcott wrote:
On 5/8/2026 11:06 AM, dart200 wrote:
On 5/8/26 12:19 AM, Mikko wrote:
On 07/05/2026 12:00, dart200 wrote:
On 5/7/26 12:18 AM, Mikko wrote:A machine is not a "diagonal".
On 06/05/2026 22:40, dart200 wrote:the H machine defined on p247 from his paper /on computable >>>>>>>>>>>>> numbers/
On 5/6/26 12:55 AM, Mikko wrote:it. Any use of the word before the definition is nonsense,. >>>>>>>>>>>>
On 05/05/2026 12:28, dart200 wrote:
On 5/5/26 1:25 AM, Mikko wrote:
On 04/05/2026 10:53, dart200 wrote:
On 5/3/26 11:15 PM, Mikko wrote:
On 03/05/2026 12:09, dart200 wrote:i can't read if u can't explain
On 5/3/26 12:53 AM, Mikko wrote:
On 02/05/2026 23:39, dart200 wrote: >>>>>>>>>>>>>>>>>>>>>>> On 4/19/26 10:58 AM, Richard Damon wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 4/19/26 1:21 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 4/19/2026 3:59 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 18/04/2026 15:58, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>dunno what ur saying here.
Turing proved that there are universal Turing >>>>>>>>>>>>>>>>>>>>>> machines. An universalTuring machine halts with >>>>>>>>>>>>>>>>>>>>>> some inputs and doesn't halt with any other >>>>>>>>>>>>>>>>>>>>>> input. Every Turing machine that can be given the >>>>>>>>>>>>>>>>>>>>>> same input as anrichard richard richard, that is in-correct. >>>>>>>>>>>>>>>>>>>>>>>Unknown truths are not elements of the body of >>>>>>>>>>>>>>>>>>>>>>>>>>> knowledge is a semantic tautology. Did you think >>>>>>>>>>>>>>>>>>>>>>>>>>> that things that are unknown are known? >>>>>>>>>>>>>>>>>>>>>>>>>>No, but that measn that for some sentences X >>>>>>>>>>>>>>>>>>>>>>>>>> True(X) is unknown and there >>>>>>>>>>>>>>>>>>>>>>>>>> is no method to find out.
I don't know about philosophers but >>>>>>>>>>>>>>>>>>>>>>>>>> mathematicians and logicians don't >>>>>>>>>>>>>>>>>>>>>>>>>> find it interesting if all you can say that >>>>>>>>>>>>>>>>>>>>>>>>>> all knowledge is knowable
and everything else is not. >>>>>>>>>>>>>>>>>>>>>>>>>>
Ross Finlayson, seemed to endlessly hedge on >>>>>>>>>>>>>>>>>>>>>>>>> whether
or not the truth value of the Goldbach >>>>>>>>>>>>>>>>>>>>>>>>> conjecture was
known. He seemed to think that there are >>>>>>>>>>>>>>>>>>>>>>>>> alternative
analytical frameworks that make the question of >>>>>>>>>>>>>>>>>>>>>>>>> whether
or not its truth value is known an ambiguous >>>>>>>>>>>>>>>>>>>>>>>>> question.
I needed to refer to unknown truth values >>>>>>>>>>>>>>>>>>>>>>>>> specifically
because all "undecidability" when construed >>>>>>>>>>>>>>>>>>>>>>>>> correctly
falls into one of two categories. >>>>>>>>>>>>>>>>>>>>>>>>> (a) Semantic incoherence
(b) Unknown truth values.
Nope.
Undecidability can not come from Semantic >>>>>>>>>>>>>>>>>>>>>>>> Incoherence, as the definition of Undecidability >>>>>>>>>>>>>>>>>>>>>>>> ia based on there being a coherent answer, just >>>>>>>>>>>>>>>>>>>>>>>> not one that can be determined by a computation. >>>>>>>>>>>>>>>>>>>>>>>
the undecidable problem turing described (as well >>>>>>>>>>>>>>>>>>>>>>> as the basic halting problem) involves a >>>>>>>>>>>>>>>>>>>>>>> situations that have _no_ coherent answer, not >>>>>>>>>>>>>>>>>>>>>>> just one that can be known by not computed ... >>>>>>>>>>>>>>>>>>>>>>
universal Turing machine either fails to accept >>>>>>>>>>>>>>>>>>>>>> some input with which
that universal Turing machine halts or fails to >>>>>>>>>>>>>>>>>>>>>> reject some input with
which that universal Turing macnie does not halt. >>>>>>>>>>>>>>>>>>>>>
There is a way to find out if you can read. >>>>>>>>>>>>>>>>>>>
I can't explain the art of reading Common Language. >>>>>>>>>>>>>>>>>>
It is impossible to have a Turing machine that >>>>>>>>>>>>>>>>>> computes a number thatyes, but then he argues it's impossible to compute >>>>>>>>>>>>>>>>>>> the diagonal because of the paradox that ensues when >>>>>>>>>>>>>>>>>>> naively running the classifier on the diagonal itself >>>>>>>>>>>>>>>>>> inturing hypothesized a diagonal computation that >>>>>>>>>>>>>>>>>>>>> tries to put the Nth digit from the Nth circle-free >>>>>>>>>>>>>>>>>>>>> machine as the Nth digit on this diagonal across >>>>>>>>>>>>>>>>>>>>> all circle- free machine...
That is possible because there nither the machines >>>>>>>>>>>>>>>>>>>> nor digit positions
are more numerous than natural numbers. >>>>>>>>>>>>>>>>>>>
no Turing machine can compute. But you can compute it >>>>>>>>>>>>>>>>>> if you can use
all (infinitely many) Turing machines.
no you can't.
Hard to test as I han't infinite many Turing machines. >>>>>>>>>>>>>>>> But it is
u don't need to test it, you can't define a total >>>>>>>>>>>>>>> dovetailing machine to compute turing's diagonal, >>>>>>>>>>>>>> You should not say anything about the diagonal before you >>>>>>>>>>>>>> have defined
the machine supposes to compute the "turing's diagonal" >>>>>>>>>>> across circle- free sequences, otherwise labeled as β' in the >>>>>>>>>>> paper, defined at the bottom of p246
Anything that any machine can possibly compute can
be computed by applying a finite set of finite string
transformation rules to a finite set of finite strings.
Everything else is simply out-of-scope for computation
like making a silk purse from a sow's ear.
That "everything else" includes many thigns that would be
useful to
know. In particular, whether some useful function can be
computed is
in that "everything else".
Like the truth value of: "This sentence is not true"
that has no truth value.
I don't think knowing the truth value of that would be useful. At >>>>>>> least
not for any important purpose.
Knowing that all undecidability is merely semantic
incoherence enables:
"true on the basis of meaning expressed in language"
to be reliably computable for the entire body of knowledge.
We don't have the knowledge that all undecidability is merely semantic >>>>> incoherence, and can't know because we already know that there is
undecidability that is not semantic incoherence. FOr example the
axiom system
∀x (1⋅x = x)
1.5 != 5 ∴ you are wrong and I am couinting the rest as gibberish
Middle dot is a commonly used mathematical operator. In this context
where the purpose of the operation is not specified some other symbols
are often used instead, like ∘ or ∙, or operands are just put side by >>> side with no operator between.
If commonly used mathematics is gibberish to you then we many safely
conclude that you have nothing useful to offer to the groups you
posted to.
∀x (x⋅1 = x)
∀x∀y∀z (x⋅(y⋅z) = (x⋅y)⋅z)
∀x∃y (x⋅y = 1)
∀x∃y (y⋅x = 1)
is useful for many purposes. But there are sentences like
∀x∃y (x⋅y = y⋅x)
that are undecidable in that system. But there is notiong semantically >>>>> incoherent in that example or similar ones.
The truth about climate change and election fraud could
be computed.
Not without real world information.
Yes, so what?
So the biggest problem is not how to compute but how to get and verify
the relevant real world infomration.
A set of "atomic facts" does exist. We only nee to write> them all down.
THat is a lot of work that can never be completed.
The place to start would be published textbooks.
How long does it take to read all texbooks published in one year?
Then peer reviewed papers.
Now long does it take to read all reviewed papers published in one year?
Then published newspaper articles.
How long does it take to read all newspaper articles publised in one
year?
And what to do with the "atomic facts" that conflict each other?
All knowledge that can be expressed in language would
include the exact (x,y,z) coordinates of every atom of your
body relative to the exact center of the Earth every millisecond.
Because this degree of detail is not physically implementable
to implement my system we exclude most specific details. It
is a system of general knowledge of about 200 petabytes.
Of course you may postulate that
the climate is immutable or that there was massimbe undetected fraud >>>>> in the last or some earlier election but that is not what the word
"knowledge" means.
The key elements of election fraud are two things:
(a) There was no actual evidence of election fraud
that could have possibly changed the results.
The key element of elction fraud is to find a vulnerability in the
election procedure.
There has only been 1620 total documented cases in the USA
in the last 30 years. Every investigation into fraud by
audits found a few more votes against Trump than prior to
the audit. Each of the 60 election fraud cases Trump lost.
He lost because his lawyers could not tell the wild stories
that he was telling the public without getting themselves
convicted of perjury.
These these fact were unconvincing seems to prove that
his supporters are in a cult.
But not that there were no fraud performed skillfully enough to avoid detection. What was found was only small unintentional errors that
nobody tried to hide.
All self-reference "paradox" is equivalent to the
Liar Paradox and can be resolved by disallowing it
like ZFC disallowed Russell's "Paradox".
Whether something is a self-reference depends on interpretation. >>>>>>> In an
uninterpreted formal language there are no references and
therefore no
self-references, which is the simplest way to avoid paradoxes by >>>>>>> self-
reference.
Even without any self-reference a theory can be inconsistent.
Russell's paradox is simply an inconsistency.
Likewise with all undecidability within the body
of knowledge that can be expressed as language.
No, per definition an inconcistency is decidable so it is not an
undecidability.
RP is merely the only instance of pathological
self-reference (PSR) that was correctly rejected.
Russell's paradox is not an undecidability.
It was until ZFC refuted it.
No, it never was. The possibility to decide it was always there. That
nobody discovered it before Russell is irrelevant.
The fact is that we did at one time have Russell's
self reference "paradox" and we no longer has it
because its incoherence was rejected by ZFC.
We still have it and its relatives. The naive set theory
is still
inconsistent. We have ZF and other new set tehories that don't
have it. Sometimes it would be nice to have an unversal set but
there is none in ZF.
HP counter-example input is another instance of PSR.
The halting problem counter-example is neither an undecidability
nor an
incconsistency.
In computability theory and computational complexity
theory, an undecidable problem is a decision problem
for which it is proved to be impossible to construct
an algorithm that always leads to a correct yes-or-no answer.
https://en.wikipedia.org/wiki/Undecidable_problem
There is a note on the top of the page noting that the article needs
additional citations for verification. This means that the page is
not as relable as typical Wikipedia pages. In particular, the quoted
text is not quite correct.
But the quoted text is irrelevant anyway. In logic "undecidability"
means that a sentence and its negation are unprovable in some thoery.
When we switch the proof theoretic semantics then
unprovable means ungrounded thus meaningless.
When we use a theory for some serious purpose then inability to solve
a problem means we must think harder and wider. For example, it may
turn out that a partial solution is sufficient, or we can determine
that our soultion method, although not proven correct, works in every
case we have tested, so we can trust it does not fail too often.
Going outside of PA in a separate model of PA
has always only been a mere ruse.
What we really need to know is not PA but the natural numbers. If
PA does not answer some question then it is better to look for an
asnwer elsewhere. A set theory might be a good place because an
important use of natural numbers is cardinalities of finite sets.
On 2026-05-13 05:18, olcott wrote:
On 5/12/2026 10:02 PM, André G. Isaak wrote:
On 2026-05-12 07:32, olcott wrote:
On 5/12/2026 2:05 AM, Mikko wrote:
On 11/05/2026 14:44, olcott wrote:
On 5/11/2026 2:24 AM, Mikko wrote:
On 10/05/2026 22:06, olcott wrote:
Middle dot is a commonly used mathematical operator. In this context >>>>> where the purpose of the operation is not specified some other symbols >>>>> are often used instead, like ∘ or ∙, or operands are just put side by >>>>> side with no operator between.We don't have the knowledge that all undecidability is merely
semantic
incoherence, and can't know because we already know that there is >>>>>>> undecidability that is not semantic incoherence. FOr example the >>>>>>> axiom system
∀x (1⋅x = x)
1.5 != 5 ∴ you are wrong and I am couinting the rest as gibberish >>>>>
If commonly used mathematics is gibberish to you then we many safely >>>>> conclude that you have nothing useful to offer to the groups you
posted to.
∀x (x⋅1 = x)
∀x∀y∀z (x⋅(y⋅z) = (x⋅y)⋅z)
∀x∃y (x⋅y = 1)
∀x∃y (y⋅x = 1)
is useful for many purposes. But there are sentences like
∀x∃y (x⋅y = y⋅x)
that are undecidable in that system. But there is notiong
semantically
incoherent in that example or similar ones.
I'm curious to know how you would actually address Mikko's point
here. He's pointed out the rather obvious error in your reading
comprehension, but you've simply glossed over the example.
In what sense is ∀x∃y (x⋅y = y⋅x) "semantically incoherent"?
André
Decimal point versus multiplication operator?
If it is a decimal point then it is incoherent.
Obviously its nor a decimal point. He gave you the actual axioms which define the dot operator, so there should be no dispute as to its meaning.
The point is that ∀x∃y (x⋅y = y⋅x) is not decidable from those axioms,yet it is clearly semantically coherent.
André
On 2026-05-13 08:20, olcott wrote:
On 5/13/2026 6:56 AM, André G. Isaak wrote:
On 2026-05-13 05:18, olcott wrote:
On 5/12/2026 10:02 PM, André G. Isaak wrote:
On 2026-05-12 07:32, olcott wrote:
On 5/12/2026 2:05 AM, Mikko wrote:
On 11/05/2026 14:44, olcott wrote:
On 5/11/2026 2:24 AM, Mikko wrote:
On 10/05/2026 22:06, olcott wrote:
Middle dot is a commonly used mathematical operator. In this context >>>>>>> where the purpose of the operation is not specified some otherWe don't have the knowledge that all undecidability is merely >>>>>>>>> semantic
incoherence, and can't know because we already know that there is >>>>>>>>> undecidability that is not semantic incoherence. FOr example the >>>>>>>>> axiom system
∀x (1⋅x = x)
1.5 != 5 ∴ you are wrong and I am couinting the rest as gibberish >>>>>>>
symbols
are often used instead, like ∘ or ∙, or operands are just put >>>>>>> side by
side with no operator between.
If commonly used mathematics is gibberish to you then we many safely >>>>>>> conclude that you have nothing useful to offer to the groups you >>>>>>> posted to.
∀x (x⋅1 = x)
∀x∀y∀z (x⋅(y⋅z) = (x⋅y)⋅z)
∀x∃y (x⋅y = 1)
∀x∃y (y⋅x = 1)
is useful for many purposes. But there are sentences like
∀x∃y (x⋅y = y⋅x)
that are undecidable in that system. But there is notiong
semantically
incoherent in that example or similar ones.
I'm curious to know how you would actually address Mikko's point
here. He's pointed out the rather obvious error in your reading
comprehension, but you've simply glossed over the example.
In what sense is ∀x∃y (x⋅y = y⋅x) "semantically incoherent"? >>>>>
André
Decimal point versus multiplication operator?
If it is a decimal point then it is incoherent.
Obviously its nor a decimal point. He gave you the actual axioms
which define the dot operator, so there should be no dispute as to
its meaning.
The point is that ∀x∃y (x⋅y = y⋅x) is not decidable from those
axioms,yet it is clearly semantically coherent.
André
∀x∃y (x⋅y = y⋅x) is proven true by ∀x∀y (x⋅y = y⋅x)
which is proven true by the commutative property of multiplication.
https://people.hsc.edu/faculty-staff/blins/classes/fall18/math105/
Examples/AlgebraAxioms.pdf
But then you're introducing a new axiom which isn't part of the set of axioms which he introduced.
Therefore, you're not dealing with the same
theory.
The point is that ∀x∃y (x⋅y = y⋅x) is undecidable in the theory which he presented. Whether it is decidable in some other theory isn't really germane to the discussion.
André
On 5/10/2026 1:12 PM, phoenix wrote:
dart200 wrote:^^^^^^^^^^^^^^^^^^^
On 5/8/26 12:01 PM, olcott wrote:
On 5/8/2026 1:40 PM, dart200 wrote:
On 5/8/26 10:35 AM, olcott wrote:
On 5/8/2026 12:13 PM, dart200 wrote:
On 5/8/26 9:58 AM, olcott wrote:
On 5/8/2026 11:06 AM, dart200 wrote:
On 5/8/26 12:19 AM, Mikko wrote:
On 07/05/2026 12:00, dart200 wrote:
On 5/7/26 12:18 AM, Mikko wrote:A machine is not a "diagonal".
On 06/05/2026 22:40, dart200 wrote:the H machine defined on p247 from his paper /on computable >>>>>>>>>>> numbers/
On 5/6/26 12:55 AM, Mikko wrote:You should not say anything about the diagonal before you >>>>>>>>>>>> have defined
On 05/05/2026 12:28, dart200 wrote:
On 5/5/26 1:25 AM, Mikko wrote:
On 04/05/2026 10:53, dart200 wrote:
On 5/3/26 11:15 PM, Mikko wrote:
On 03/05/2026 12:09, dart200 wrote:i can't read if u can't explain
On 5/3/26 12:53 AM, Mikko wrote:
On 02/05/2026 23:39, dart200 wrote:dunno what ur saying here.
On 4/19/26 10:58 AM, Richard Damon wrote: >>>>>>>>>>>>>>>>>>>>>> On 4/19/26 1:21 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>> On 4/19/2026 3:59 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 18/04/2026 15:58, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>
richard richard richard, that is in-correct. >>>>>>>>>>>>>>>>>>>>>Unknown truths are not elements of the body of >>>>>>>>>>>>>>>>>>>>>>>>> knowledge is a semantic tautology. Did you think >>>>>>>>>>>>>>>>>>>>>>>>> that things that are unknown are known? >>>>>>>>>>>>>>>>>>>>>>>>No, but that measn that for some sentences X >>>>>>>>>>>>>>>>>>>>>>>> True(X) is unknown and there
is no method to find out.
I don't know about philosophers but >>>>>>>>>>>>>>>>>>>>>>>> mathematicians and logicians don't >>>>>>>>>>>>>>>>>>>>>>>> find it interesting if all you can say that all >>>>>>>>>>>>>>>>>>>>>>>> knowledge is knowable
and everything else is not.
Ross Finlayson, seemed to endlessly hedge on whether >>>>>>>>>>>>>>>>>>>>>>> or not the truth value of the Goldbach conjecture >>>>>>>>>>>>>>>>>>>>>>> was
known. He seemed to think that there are alternative >>>>>>>>>>>>>>>>>>>>>>> analytical frameworks that make the question of >>>>>>>>>>>>>>>>>>>>>>> whether
or not its truth value is known an ambiguous >>>>>>>>>>>>>>>>>>>>>>> question.
I needed to refer to unknown truth values >>>>>>>>>>>>>>>>>>>>>>> specifically
because all "undecidability" when construed >>>>>>>>>>>>>>>>>>>>>>> correctly
falls into one of two categories. >>>>>>>>>>>>>>>>>>>>>>> (a) Semantic incoherence
(b) Unknown truth values.
Nope.
Undecidability can not come from Semantic >>>>>>>>>>>>>>>>>>>>>> Incoherence, as the definition of Undecidability >>>>>>>>>>>>>>>>>>>>>> ia based on there being a coherent answer, just >>>>>>>>>>>>>>>>>>>>>> not one that can be determined by a computation. >>>>>>>>>>>>>>>>>>>>>
the undecidable problem turing described (as well >>>>>>>>>>>>>>>>>>>>> as the basic halting problem) involves a situations >>>>>>>>>>>>>>>>>>>>> that have _no_ coherent answer, not just one that >>>>>>>>>>>>>>>>>>>>> can be known by not computed ...
Turing proved that there are universal Turing >>>>>>>>>>>>>>>>>>>> machines. An universalTuring machine halts with some >>>>>>>>>>>>>>>>>>>> inputs and doesn't halt with any other >>>>>>>>>>>>>>>>>>>> input. Every Turing machine that can be given the >>>>>>>>>>>>>>>>>>>> same input as an
universal Turing machine either fails to accept some >>>>>>>>>>>>>>>>>>>> input with which
that universal Turing machine halts or fails to >>>>>>>>>>>>>>>>>>>> reject some input with
which that universal Turing macnie does not halt. >>>>>>>>>>>>>>>>>>>
There is a way to find out if you can read. >>>>>>>>>>>>>>>>>
I can't explain the art of reading Common Language. >>>>>>>>>>>>>>>>
It is impossible to have a Turing machine that computes >>>>>>>>>>>>>>>> a number thatturing hypothesized a diagonal computation that tries >>>>>>>>>>>>>>>>>>> to put the Nth digit from the Nth circle-free machine >>>>>>>>>>>>>>>>>>> as the Nth digit on this diagonal across all circle- >>>>>>>>>>>>>>>>>>> free machine...
That is possible because there nither the machines nor >>>>>>>>>>>>>>>>>> digit positions
are more numerous than natural numbers.
yes, but then he argues it's impossible to compute the >>>>>>>>>>>>>>>>> diagonal because of the paradox that ensues when >>>>>>>>>>>>>>>>> naively running the classifier on the diagonal itself >>>>>>>>>>>>>>>> in
no Turing machine can compute. But you can compute it if >>>>>>>>>>>>>>>> you can use
all (infinitely many) Turing machines.
no you can't.
Hard to test as I han't infinite many Turing machines. But >>>>>>>>>>>>>> it is
u don't need to test it, you can't define a total
dovetailing machine to compute turing's diagonal,
it. Any use of the word before the definition is nonsense,. >>>>>>>>>>
the machine supposes to compute the "turing's diagonal" across >>>>>>>>> circle- free sequences, otherwise labeled as β' in the paper, >>>>>>>>> defined at the bottom of p246
Anything that any machine can possibly compute can
be computed by applying a finite set of finite string
transformation rules to a finite set of finite strings.
Everything else is simply out-of-scope for computation
like making a silk purse from a sow's ear.
i believe the i mentally applied a finite set of string
transformations to decide that DD does in fact halt
No one every simplified is down to its barest possible
essence before me. Also the entire body of knowledge
expressed in language can be encoded as finite relations
between finite strings.
This transforms all undecidability into
(a) Outside of the body of knowledge that can be expressed in
language
we know DD halts polcott, so clearly not outside the body of
knowledge that can be expressed in language
No it is fucked up bullshit like:
"This sentence is not true" (see b below)
are you saying u don't understand that DD maps to the semantic
property of "halting" polcott??
No I'm saying
^^^^^^^^^^^^^^^^^^^
So you are a nym shift olcott thing? Are you? phoenix?
that M/RR changes by any small movement of a pebble within the earth's
makeup. There are millions of vehicles driving around on the earth's
surface altering the calculation. What's there to pinpointing G?
What's next, setting down an ice-cold coca-cola and marveling at
different temperature readings upon it?
On 2026-05-13 09:28, olcott wrote:
On 5/13/2026 9:38 AM, André G. Isaak wrote:
On 2026-05-13 08:20, olcott wrote:
On 5/13/2026 6:56 AM, André G. Isaak wrote:
On 2026-05-13 05:18, olcott wrote:
On 5/12/2026 10:02 PM, André G. Isaak wrote:
On 2026-05-12 07:32, olcott wrote:
On 5/12/2026 2:05 AM, Mikko wrote:
On 11/05/2026 14:44, olcott wrote:
On 5/11/2026 2:24 AM, Mikko wrote:
On 10/05/2026 22:06, olcott wrote:
Middle dot is a commonly used mathematical operator. In this >>>>>>>>> contextWe don't have the knowledge that all undecidability is merely >>>>>>>>>>> semantic
incoherence, and can't know because we already know that >>>>>>>>>>> there is
undecidability that is not semantic incoherence. FOr example the >>>>>>>>>>> axiom system
∀x (1⋅x = x)
1.5 != 5 ∴ you are wrong and I am couinting the rest as gibberish >>>>>>>>>
where the purpose of the operation is not specified some other >>>>>>>>> symbols
are often used instead, like ∘ or ∙, or operands are just put >>>>>>>>> side by
side with no operator between.
If commonly used mathematics is gibberish to you then we many >>>>>>>>> safely
conclude that you have nothing useful to offer to the groups you >>>>>>>>> posted to.
∀x (x⋅1 = x)
∀x∀y∀z (x⋅(y⋅z) = (x⋅y)⋅z)
∀x∃y (x⋅y = 1)
∀x∃y (y⋅x = 1)
is useful for many purposes. But there are sentences like >>>>>>>>>>>
∀x∃y (x⋅y = y⋅x)
that are undecidable in that system. But there is notiong >>>>>>>>>>> semantically
incoherent in that example or similar ones.
I'm curious to know how you would actually address Mikko's point >>>>>>> here. He's pointed out the rather obvious error in your reading >>>>>>> comprehension, but you've simply glossed over the example.
In what sense is ∀x∃y (x⋅y = y⋅x) "semantically incoherent"? >>>>>>>
André
Decimal point versus multiplication operator?
If it is a decimal point then it is incoherent.
Obviously its nor a decimal point. He gave you the actual axioms
which define the dot operator, so there should be no dispute as to
its meaning.
The point is that ∀x∃y (x⋅y = y⋅x) is not decidable from those >>>>> axioms,yet it is clearly semantically coherent.
André
∀x∃y (x⋅y = y⋅x) is proven true by ∀x∀y (x⋅y = y⋅x)
which is proven true by the commutative property of multiplication.
https://people.hsc.edu/faculty-staff/blins/classes/fall18/math105/
Examples/AlgebraAxioms.pdf
But then you're introducing a new axiom which isn't part of the set
of axioms which he introduced.
My thesis:
The entire body of knowledge that can be expressed
in language can be encoded as relations between finite strings.
And how 'bout them Mets?
Therefore, you're not dealing with the same theory.
*The entire body of knowledge that can be expressed in language*
... is an ill-defined set which only exists in your mind. There's over 8 billion people on earth, all of whom believe different, often
contradictory things. And, with the exception of theorems of formal
systems, there is nothing that we know with absolute certainty. Only
varying degrees of certainty, but for every given fact you won't get a universal consensus on exactly how certain we are of that fact.
Formal systems operate over a *fixed* set of axioms. The set of
knowledge is not fixed, but constantly changing. But the results you are attempting to challenge (Gödels theorem, etc.) all apply to *formal* systems based on fixed sets of axioms rather than some fluid and vaguely defined body of knowledge.
Is the scope. That some knucklehead can fail to bother to define
that "cats are animals" so that his knucklehead formal system
does not know this IS OFF-TOPIC.
Mikko offered a concrete set of axioms and made a claim about what could
be derived from those axioms. Neither cats nor animals were involved.
The point is that ∀x∃y (x⋅y = y⋅x) is undecidable in the theory which >>> he presented. Whether it is decidable in some other theory isn't
really germane to the discussion.
André
On 2026-05-13 17:40, olcott wrote:
On 5/13/2026 4:37 PM, André G. Isaak wrote:
On 2026-05-13 09:28, olcott wrote:
*The entire body of knowledge that can be expressed in language*
... is an ill-defined set which only exists in your mind. There's
over 8 billion people on earth, all of whom believe different, often
contradictory things. And, with the exception of theorems of formal
systems, there is nothing that we know with absolute certainty. Only
varying degrees of certainty, but for every given fact you won't get
a universal consensus on exactly how certain we are of that fact.
So maybe cats were never animals and this "belief"
has always been mass psychosis? In actual reality
cats were always a kind of snake?
I propose that a finite set of "atomic facts" of general
knowledge inherently exists and that no 100% concrete
counter-example can ever be found.
Until you can produce this finite set of atomic facts you're all just bluster. Here's a few statements. Which would you consider atomic facts:
– The Universe is 14 billion years old.
– The Ungulates and the Carnivores form a clade.
– Jesus Christ died for our sins.
– Nearly 70% of the mass-energy of the universe consists of dark energy.
– Anthropogenic climate change is currently occurring.
– The Earth is 6000 years old.
– Argentinosaurus is the largest land animal to ever have lived.
– Measles vaccine causes autism.
– There exists an "island of stability" where extraheavy elements with approximately 184 neutrons will have a considerably longer half-life
than that of the heaviest elements currently know.
– Turing showed that halting cannot be computed.
You keep falling back on extremely trivial examples which are non- controversial while failing to address how you would address claims of a non-trivial nature. All of the statements above are contentious, at
least in some circles, so how do you decide which statements belong to
your 'finite set of atomic facts'? If you can't explain how membership
in this set is determined, then you've got nothing.
The idea that a set which can be described using natural language automatically constitutes a valid set was one of the mistakes of naïve
set theory which you keep disparaging, and yet here you do the same thing.
Any rebuttal to this besides at least the attempt
of a 100% concrete counter-example will be dismissed
as deception.
Formal systems operate over a *fixed* set of axioms. The set of
knowledge is not fixed, but constantly changing. But the results you
are attempting to challenge (Gödels theorem, etc.) all apply to
*formal* systems based on fixed sets of axioms rather than some fluid
and vaguely defined body of knowledge.
As soon as truth theoretic semantics is utterly replaced
with proof theoretic semantics G remains true in meta-math
and becomes meaningless in PA.
Proof theoretic semantics and truth theoretic semantics are theories designed to address different classes of questions. Neither is going to replace the other.
André
On 5/13/2026 4:37 PM, André G. Isaak wrote:
On 2026-05-13 09:28, olcott wrote:
On 5/13/2026 9:38 AM, André G. Isaak wrote:
On 2026-05-13 08:20, olcott wrote:
On 5/13/2026 6:56 AM, André G. Isaak wrote:
On 2026-05-13 05:18, olcott wrote:
On 5/12/2026 10:02 PM, André G. Isaak wrote:
On 2026-05-12 07:32, olcott wrote:
On 5/12/2026 2:05 AM, Mikko wrote:
On 11/05/2026 14:44, olcott wrote:
On 5/11/2026 2:24 AM, Mikko wrote:
On 10/05/2026 22:06, olcott wrote:
We don't have the knowledge that all undecidability is >>>>>>>>>>>> merely semantic
incoherence, and can't know because we already know that >>>>>>>>>>>> there is
undecidability that is not semantic incoherence. FOr example >>>>>>>>>>>> the
axiom system
∀x (1⋅x = x)
1.5 != 5 ∴ you are wrong and I am couinting the rest as >>>>>>>>>>> gibberish
Middle dot is a commonly used mathematical operator. In this >>>>>>>>>> context
where the purpose of the operation is not specified some other >>>>>>>>>> symbols
are often used instead, like ∘ or ∙, or operands are just put >>>>>>>>>> side by
side with no operator between.
If commonly used mathematics is gibberish to you then we many >>>>>>>>>> safely
conclude that you have nothing useful to offer to the groups you >>>>>>>>>> posted to.
∀x (x⋅1 = x)
∀x∀y∀z (x⋅(y⋅z) = (x⋅y)⋅z)
∀x∃y (x⋅y = 1)
∀x∃y (y⋅x = 1)
is useful for many purposes. But there are sentences like >>>>>>>>>>>>
∀x∃y (x⋅y = y⋅x)
that are undecidable in that system. But there is notiong >>>>>>>>>>>> semantically
incoherent in that example or similar ones.
I'm curious to know how you would actually address Mikko's point >>>>>>>> here. He's pointed out the rather obvious error in your reading >>>>>>>> comprehension, but you've simply glossed over the example.
In what sense is ∀x∃y (x⋅y = y⋅x) "semantically incoherent"? >>>>>>>>
André
Decimal point versus multiplication operator?
If it is a decimal point then it is incoherent.
Obviously its nor a decimal point. He gave you the actual axioms
which define the dot operator, so there should be no dispute as to >>>>>> its meaning.
The point is that ∀x∃y (x⋅y = y⋅x) is not decidable from those >>>>>> axioms,yet it is clearly semantically coherent.
André
∀x∃y (x⋅y = y⋅x) is proven true by ∀x∀y (x⋅y = y⋅x)
which is proven true by the commutative property of multiplication.
https://people.hsc.edu/faculty-staff/blins/classes/fall18/math105/
Examples/AlgebraAxioms.pdf
But then you're introducing a new axiom which isn't part of the set
of axioms which he introduced.
My thesis:
The entire body of knowledge that can be expressed
in language can be encoded as relations between finite strings.
And how 'bout them Mets?
Therefore, you're not dealing with the same theory.
*The entire body of knowledge that can be expressed in language*
... is an ill-defined set which only exists in your mind. There's over
8 billion people on earth, all of whom believe different, often
contradictory things. And, with the exception of theorems of formal
systems, there is nothing that we know with absolute certainty. Only
varying degrees of certainty, but for every given fact you won't get a
universal consensus on exactly how certain we are of that fact.
So maybe cats were never animals and this "belief"
has always been mass psychosis? In actual reality
cats were always a kind of snake?
I propose that a finite set of "atomic facts" of general
knowledge inherently exists and that no 100% concrete
counter-example can ever be found.
Any rebuttal to this besides at least the attempt
of a 100% concrete counter-example will be dismissed
as deception.
Formal systems operate over a *fixed* set of axioms. The set of
knowledge is not fixed, but constantly changing. But the results you
are attempting to challenge (Gödels theorem, etc.) all apply to
*formal* systems based on fixed sets of axioms rather than some fluid
and vaguely defined body of knowledge.
As soon as truth theoretic semantics is utterly replaced
with proof theoretic semantics G remains true in meta-math
and becomes meaningless in PA.
Is the scope. That some knucklehead can fail to bother to define
that "cats are animals" so that his knucklehead formal system
does not know this IS OFF-TOPIC.
Mikko offered a concrete set of axioms and made a claim about what
could be derived from those axioms. Neither cats nor animals were
involved.
The point is that ∀x∃y (x⋅y = y⋅x) is undecidable in the theory which >>> he presented. Whether it is decidable in some other theory isn't
really germane to the discussion.
André
On 05/13/2026 04:40 PM, olcott wrote:
On 5/13/2026 4:37 PM, André G. Isaak wrote:
On 2026-05-13 09:28, olcott wrote:
On 5/13/2026 9:38 AM, André G. Isaak wrote:
On 2026-05-13 08:20, olcott wrote:
On 5/13/2026 6:56 AM, André G. Isaak wrote:
On 2026-05-13 05:18, olcott wrote:
On 5/12/2026 10:02 PM, André G. Isaak wrote:
On 2026-05-12 07:32, olcott wrote:
On 5/12/2026 2:05 AM, Mikko wrote:
On 11/05/2026 14:44, olcott wrote:
On 5/11/2026 2:24 AM, Mikko wrote:
On 10/05/2026 22:06, olcott wrote:
We don't have the knowledge that all undecidability is >>>>>>>>>>>>> merely semantic
incoherence, and can't know because we already know that >>>>>>>>>>>>> there is
undecidability that is not semantic incoherence. FOr example >>>>>>>>>>>>> the
axiom system
∀x (1⋅x = x)
1.5 != 5 ∴ you are wrong and I am couinting the rest as >>>>>>>>>>>> gibberish
Middle dot is a commonly used mathematical operator. In this >>>>>>>>>>> context
where the purpose of the operation is not specified some other >>>>>>>>>>> symbols
are often used instead, like ∘ or ∙, or operands are just put >>>>>>>>>>> side by
side with no operator between.
If commonly used mathematics is gibberish to you then we many >>>>>>>>>>> safely
conclude that you have nothing useful to offer to the groups you >>>>>>>>>>> posted to.
∀x (x⋅1 = x)
∀x∀y∀z (x⋅(y⋅z) = (x⋅y)⋅z)
∀x∃y (x⋅y = 1)
∀x∃y (y⋅x = 1)
is useful for many purposes. But there are sentences like >>>>>>>>>>>>>
∀x∃y (x⋅y = y⋅x)
that are undecidable in that system. But there is notiong >>>>>>>>>>>>> semantically
incoherent in that example or similar ones.
I'm curious to know how you would actually address Mikko's point >>>>>>>>> here. He's pointed out the rather obvious error in your reading >>>>>>>>> comprehension, but you've simply glossed over the example.
In what sense is ∀x∃y (x⋅y = y⋅x) "semantically incoherent"? >>>>>>>>>
André
Decimal point versus multiplication operator?
If it is a decimal point then it is incoherent.
Obviously its nor a decimal point. He gave you the actual axioms >>>>>>> which define the dot operator, so there should be no dispute as to >>>>>>> its meaning.
The point is that ∀x∃y (x⋅y = y⋅x) is not decidable from those >>>>>>> axioms,yet it is clearly semantically coherent.
André
∀x∃y (x⋅y = y⋅x) is proven true by ∀x∀y (x⋅y = y⋅x) >>>>>> which is proven true by the commutative property of multiplication. >>>>>>
https://people.hsc.edu/faculty-staff/blins/classes/fall18/math105/ >>>>>> Examples/AlgebraAxioms.pdf
But then you're introducing a new axiom which isn't part of the set
of axioms which he introduced.
My thesis:
The entire body of knowledge that can be expressed
in language can be encoded as relations between finite strings.
And how 'bout them Mets?
Therefore, you're not dealing with the same theory.
*The entire body of knowledge that can be expressed in language*
... is an ill-defined set which only exists in your mind. There's over
8 billion people on earth, all of whom believe different, often
contradictory things. And, with the exception of theorems of formal
systems, there is nothing that we know with absolute certainty. Only
varying degrees of certainty, but for every given fact you won't get a
universal consensus on exactly how certain we are of that fact.
So maybe cats were never animals and this "belief"
has always been mass psychosis? In actual reality
cats were always a kind of snake?
I propose that a finite set of "atomic facts" of general
knowledge inherently exists and that no 100% concrete
counter-example can ever be found.
Any rebuttal to this besides at least the attempt
of a 100% concrete counter-example will be dismissed
as deception.
Formal systems operate over a *fixed* set of axioms. The set of
knowledge is not fixed, but constantly changing. But the results you
are attempting to challenge (Gödels theorem, etc.) all apply to
*formal* systems based on fixed sets of axioms rather than some fluid
and vaguely defined body of knowledge.
As soon as truth theoretic semantics is utterly replaced
with proof theoretic semantics G remains true in meta-math
and becomes meaningless in PA.
which >>> he presented. Whether it is decidable in some other theoryIs the scope. That some knucklehead can fail to bother to define
that "cats are animals" so that his knucklehead formal system
does not know this IS OFF-TOPIC.
Mikko offered a concrete set of axioms and made a claim about what
could be derived from those axioms. Neither cats nor animals were
involved.
The point is that ∀x∃y (x⋅y = y⋅x) is undecidable in the theory
isn't
really germane to the discussion.
André
So, if you have a finite set of facts, then,
that's a fact, and, that's a fact, and, that's a fact,
ad infinitum: an infinite set of facts.
It's kind of like relations between physical objects
being mathematical objects being physical objects, ad infinitum,
the universe is also its own powerset of fact.
Maybe nobody cares. If your own theory of fact is satisfactory,
then, you don't need to care about other putative facts. That
said, anybody else can, and that's their own fact.
All Olcott really seems to claim is a right to be left alone,
yet he won't shut up about it and insists it's universal,
which is fallacious and faulty reasoning.
Make sure you prevent material implication from garbage-in/garbage-out
a.k.a. crazy-in/crazy-out, while you're at it, the "quasi-modal" in
the logic is perhaps the worst sort of waste-of-time in terms of
the foundations of logic or about a century's worth.
Then, matters of decide-ability and in-decide-ability involve
completeness and incompleteness: and incompleteness and independence.
Then, independence in axiomatic theories is of at least two kinds:
adding an axiom, or removing one, and about that axioms vary: expansion-of-comprehension and restriction-of-comprehension.
So, much of the accounts of axiomatics is foolish in that
it doesn't distinguish expansion-of-comprehension and the restriction-of-comprehension, or conflates them like the
retro-thesis of Russell, which is almost as hypocritical
as the retro-finitism of closed-world flat-earthers.
On 5/13/26 5:07 PM, André G. Isaak wrote:
On 2026-05-13 17:40, olcott wrote:
On 5/13/2026 4:37 PM, André G. Isaak wrote:
On 2026-05-13 09:28, olcott wrote:
*The entire body of knowledge that can be expressed in language*
... is an ill-defined set which only exists in your mind. There's
over 8 billion people on earth, all of whom believe different, often
contradictory things. And, with the exception of theorems of formal
systems, there is nothing that we know with absolute certainty. Only
varying degrees of certainty, but for every given fact you won't get
a universal consensus on exactly how certain we are of that fact.
So maybe cats were never animals and this "belief"
has always been mass psychosis? In actual reality
cats were always a kind of snake?
I propose that a finite set of "atomic facts" of general
knowledge inherently exists and that no 100% concrete
counter-example can ever be found.
Until you can produce this finite set of atomic facts you're all just
bluster. Here's a few statements. Which would you consider atomic facts:
– The Universe is 14 billion years old.
– The Ungulates and the Carnivores form a clade.
– Jesus Christ died for our sins.
– Nearly 70% of the mass-energy of the universe consists of dark energy. >>
– Anthropogenic climate change is currently occurring.
– The Earth is 6000 years old.
– Argentinosaurus is the largest land animal to ever have lived.
– Measles vaccine causes autism.
– There exists an "island of stability" where extraheavy elements with
approximately 184 neutrons will have a considerably longer half-life
than that of the heaviest elements currently know.
– Turing showed that halting cannot be computed.
actually his proof was in regards to circle-free vs circular machines,
not specifically halting ones. please do read p246 and p247 of his
paper /on computable numbers/ more carefully.
and what he showed was that it cannot be computed by a single turing machine.
no one has demonstrated any _actual_ turing machine with a halting
behavior that provably cannot be computed by _any_ machine, as such a machine would have under-specified, non-determinable semantics that then could not actually exist as a real machine, that any actual decider
would actually have to decide upon...
the theory of computing has predicated itself on a limitation that fundamentally resolves to a catch-22 type paradox that has existed since turing wrote his first paper /on computable numbers/
On 5/13/2026 9:38 AM, André G. Isaak wrote:
On 2026-05-13 08:20, olcott wrote:
On 5/13/2026 6:56 AM, André G. Isaak wrote:
On 2026-05-13 05:18, olcott wrote:
On 5/12/2026 10:02 PM, André G. Isaak wrote:
On 2026-05-12 07:32, olcott wrote:
On 5/12/2026 2:05 AM, Mikko wrote:
On 11/05/2026 14:44, olcott wrote:
On 5/11/2026 2:24 AM, Mikko wrote:
On 10/05/2026 22:06, olcott wrote:
Middle dot is a commonly used mathematical operator. In thisWe don't have the knowledge that all undecidability is merely >>>>>>>>>> semantic
incoherence, and can't know because we already know that there is >>>>>>>>>> undecidability that is not semantic incoherence. FOr example the >>>>>>>>>> axiom system
∀x (1⋅x = x)
1.5 != 5 ∴ you are wrong and I am couinting the rest as gibberish >>>>>>>>
context
where the purpose of the operation is not specified some other >>>>>>>> symbols
are often used instead, like ∘ or ∙, or operands are just put >>>>>>>> side by
side with no operator between.
If commonly used mathematics is gibberish to you then we many >>>>>>>> safely
conclude that you have nothing useful to offer to the groups you >>>>>>>> posted to.
∀x (x⋅1 = x)
∀x∀y∀z (x⋅(y⋅z) = (x⋅y)⋅z)
∀x∃y (x⋅y = 1)
∀x∃y (y⋅x = 1)
is useful for many purposes. But there are sentences like
∀x∃y (x⋅y = y⋅x)
that are undecidable in that system. But there is notiong >>>>>>>>>> semantically
incoherent in that example or similar ones.
I'm curious to know how you would actually address Mikko's point
here. He's pointed out the rather obvious error in your reading
comprehension, but you've simply glossed over the example.
In what sense is ∀x∃y (x⋅y = y⋅x) "semantically incoherent"? >>>>>>
André
Decimal point versus multiplication operator?
If it is a decimal point then it is incoherent.
Obviously its nor a decimal point. He gave you the actual axioms
which define the dot operator, so there should be no dispute as to
its meaning.
The point is that ∀x∃y (x⋅y = y⋅x) is not decidable from those >>>> axioms,yet it is clearly semantically coherent.
André
∀x∃y (x⋅y = y⋅x) is proven true by ∀x∀y (x⋅y = y⋅x)
which is proven true by the commutative property of multiplication.
https://people.hsc.edu/faculty-staff/blins/classes/fall18/math105/
Examples/AlgebraAxioms.pdf
But then you're introducing a new axiom which isn't part of the set of
axioms which he introduced.
My thesis:
The entire body of knowledge that can be expressed
in language can be encoded as relations between finite strings.
Therefore, you're not dealing with the same theory.
*The entire body of knowledge that can be expressed in language*
Is the scope. That some knucklehead can fail to bother to define
that "cats are animals" so that his knucklehead formal system
does not know this IS OFF-TOPIC.
On 5/13/2026 4:14 AM, Mikko wrote:
On 12/05/2026 16:32, olcott wrote:
On 5/12/2026 2:05 AM, Mikko wrote:
On 11/05/2026 14:44, olcott wrote:
On 5/11/2026 2:24 AM, Mikko wrote:
On 10/05/2026 22:06, olcott wrote:
On 5/10/2026 2:10 AM, Mikko wrote:
On 09/05/2026 15:13, olcott wrote:
On 5/9/2026 3:30 AM, Mikko wrote:
On 08/05/2026 19:58, olcott wrote:
On 5/8/2026 11:06 AM, dart200 wrote:
On 5/8/26 12:19 AM, Mikko wrote:
On 07/05/2026 12:00, dart200 wrote:
On 5/7/26 12:18 AM, Mikko wrote:A machine is not a "diagonal".
On 06/05/2026 22:40, dart200 wrote:the H machine defined on p247 from his paper /on
On 5/6/26 12:55 AM, Mikko wrote:it. Any use of the word before the definition is nonsense,. >>>>>>>>>>>>>
On 05/05/2026 12:28, dart200 wrote:
On 5/5/26 1:25 AM, Mikko wrote:
On 04/05/2026 10:53, dart200 wrote:
On 5/3/26 11:15 PM, Mikko wrote:
On 03/05/2026 12:09, dart200 wrote: >>>>>>>>>>>>>>>>>>>>>> On 5/3/26 12:53 AM, Mikko wrote:i can't read if u can't explain
On 02/05/2026 23:39, dart200 wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 4/19/26 10:58 AM, Richard Damon wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 4/19/26 1:21 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 4/19/2026 3:59 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 18/04/2026 15:58, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>dunno what ur saying here.
Turing proved that there are universal Turing >>>>>>>>>>>>>>>>>>>>>>> machines. An universalTuring machine halts with >>>>>>>>>>>>>>>>>>>>>>> some inputs and doesn't halt with any other >>>>>>>>>>>>>>>>>>>>>>> input. Every Turing machine that can be given the >>>>>>>>>>>>>>>>>>>>>>> same input as anUnknown truths are not elements of the body of >>>>>>>>>>>>>>>>>>>>>>>>>>>> knowledge is a semantic tautology. Did you >>>>>>>>>>>>>>>>>>>>>>>>>>>> thinkNo, but that measn that for some sentences X >>>>>>>>>>>>>>>>>>>>>>>>>>> True(X) is unknown and there >>>>>>>>>>>>>>>>>>>>>>>>>>> is no method to find out. >>>>>>>>>>>>>>>>>>>>>>>>>>>
that things that are unknown are known? >>>>>>>>>>>>>>>>>>>>>>>>>>>
I don't know about philosophers but >>>>>>>>>>>>>>>>>>>>>>>>>>> mathematicians and logicians don't >>>>>>>>>>>>>>>>>>>>>>>>>>> find it interesting if all you can say that >>>>>>>>>>>>>>>>>>>>>>>>>>> all knowledge is knowable >>>>>>>>>>>>>>>>>>>>>>>>>>> and everything else is not. >>>>>>>>>>>>>>>>>>>>>>>>>>>
Ross Finlayson, seemed to endlessly hedge on >>>>>>>>>>>>>>>>>>>>>>>>>> whether
or not the truth value of the Goldbach >>>>>>>>>>>>>>>>>>>>>>>>>> conjecture was
known. He seemed to think that there are >>>>>>>>>>>>>>>>>>>>>>>>>> alternative
analytical frameworks that make the question >>>>>>>>>>>>>>>>>>>>>>>>>> of whether
or not its truth value is known an ambiguous >>>>>>>>>>>>>>>>>>>>>>>>>> question.
I needed to refer to unknown truth values >>>>>>>>>>>>>>>>>>>>>>>>>> specifically
because all "undecidability" when construed >>>>>>>>>>>>>>>>>>>>>>>>>> correctly
falls into one of two categories. >>>>>>>>>>>>>>>>>>>>>>>>>> (a) Semantic incoherence
(b) Unknown truth values.
Nope.
Undecidability can not come from Semantic >>>>>>>>>>>>>>>>>>>>>>>>> Incoherence, as the definition of >>>>>>>>>>>>>>>>>>>>>>>>> Undecidability ia based on there being a >>>>>>>>>>>>>>>>>>>>>>>>> coherent answer, just not one that can be >>>>>>>>>>>>>>>>>>>>>>>>> determined by a computation.
richard richard richard, that is in-correct. >>>>>>>>>>>>>>>>>>>>>>>>
the undecidable problem turing described (as >>>>>>>>>>>>>>>>>>>>>>>> well as the basic halting problem) involves a >>>>>>>>>>>>>>>>>>>>>>>> situations that have _no_ coherent answer, not >>>>>>>>>>>>>>>>>>>>>>>> just one that can be known by not computed ... >>>>>>>>>>>>>>>>>>>>>>>
universal Turing machine either fails to accept >>>>>>>>>>>>>>>>>>>>>>> some input with which
that universal Turing machine halts or fails to >>>>>>>>>>>>>>>>>>>>>>> reject some input with
which that universal Turing macnie does not halt. >>>>>>>>>>>>>>>>>>>>>>
There is a way to find out if you can read. >>>>>>>>>>>>>>>>>>>>
I can't explain the art of reading Common Language. >>>>>>>>>>>>>>>>>>>
It is impossible to have a Turing machine that >>>>>>>>>>>>>>>>>>> computes a number thatyes, but then he argues it's impossible to compute >>>>>>>>>>>>>>>>>>>> the diagonal because of the paradox that ensues when >>>>>>>>>>>>>>>>>>>> naively running the classifier on the diagonal itself >>>>>>>>>>>>>>>>>>> inturing hypothesized a diagonal computation that >>>>>>>>>>>>>>>>>>>>>> tries to put the Nth digit from the Nth circle- >>>>>>>>>>>>>>>>>>>>>> free machine as the Nth digit on this diagonal >>>>>>>>>>>>>>>>>>>>>> across all circle- free machine...
That is possible because there nither the machines >>>>>>>>>>>>>>>>>>>>> nor digit positions
are more numerous than natural numbers. >>>>>>>>>>>>>>>>>>>>
no Turing machine can compute. But you can compute it >>>>>>>>>>>>>>>>>>> if you can use
all (infinitely many) Turing machines.
no you can't.
Hard to test as I han't infinite many Turing machines. >>>>>>>>>>>>>>>>> But it is
u don't need to test it, you can't define a total >>>>>>>>>>>>>>>> dovetailing machine to compute turing's diagonal, >>>>>>>>>>>>>>> You should not say anything about the diagonal before you >>>>>>>>>>>>>>> have defined
computable numbers/
the machine supposes to compute the "turing's diagonal" >>>>>>>>>>>> across circle- free sequences, otherwise labeled as β' in >>>>>>>>>>>> the paper, defined at the bottom of p246
Anything that any machine can possibly compute can
be computed by applying a finite set of finite string
transformation rules to a finite set of finite strings.
Everything else is simply out-of-scope for computation
like making a silk purse from a sow's ear.
That "everything else" includes many thigns that would be >>>>>>>>>> useful to
know. In particular, whether some useful function can be
computed is
in that "everything else".
Like the truth value of: "This sentence is not true"
that has no truth value.
I don't think knowing the truth value of that would be useful. >>>>>>>> At least
not for any important purpose.
Knowing that all undecidability is merely semantic
incoherence enables:
"true on the basis of meaning expressed in language"
to be reliably computable for the entire body of knowledge.
We don't have the knowledge that all undecidability is merely
semantic
incoherence, and can't know because we already know that there is
undecidability that is not semantic incoherence. FOr example the
axiom system
∀x (1⋅x = x)
1.5 != 5 ∴ you are wrong and I am couinting the rest as gibberish
Middle dot is a commonly used mathematical operator. In this context
where the purpose of the operation is not specified some other symbols >>>> are often used instead, like ∘ or ∙, or operands are just put side by >>>> side with no operator between.
If commonly used mathematics is gibberish to you then we many safely
conclude that you have nothing useful to offer to the groups you
posted to.
∀x (x⋅1 = x)
∀x∀y∀z (x⋅(y⋅z) = (x⋅y)⋅z)
∀x∃y (x⋅y = 1)
∀x∃y (y⋅x = 1)
is useful for many purposes. But there are sentences like
∀x∃y (x⋅y = y⋅x)
that are undecidable in that system. But there is notiong
semantically
incoherent in that example or similar ones.
The truth about climate change and election fraud could
be computed.
Not without real world information.
Yes, so what?
So the biggest problem is not how to compute but how to get and verify >>>> the relevant real world infomration.
A set of "atomic facts" does exist. We only nee to write> them all down.
THat is a lot of work that can never be completed.
It can be completed with sufficient automation.
The place to start would be published textbooks.
How long does it take to read all texbooks published in one year?
IDK, an LLM might do this in five minutes.
Then peer reviewed papers.
Now long does it take to read all reviewed papers published in one year?
Then published newspaper articles.
How long does it take to read all newspaper articles publised in one
year?
An LLM might read everything ever published in one year.
And what to do with the "atomic facts" that conflict each other?
All knowledge that can be expressed in language would
include the exact (x,y,z) coordinates of every atom of your
body relative to the exact center of the Earth every millisecond.
Because this degree of detail is not physically implementable
to implement my system we exclude most specific details. It
is a system of general knowledge of about 200 petabytes.
Of course you may postulate that
the climate is immutable or that there was massimbe undetected fraud >>>>>> in the last or some earlier election but that is not what the word >>>>>> "knowledge" means.
The key elements of election fraud are two things:
(a) There was no actual evidence of election fraud
that could have possibly changed the results.
The key element of elction fraud is to find a vulnerability in the
election procedure.
There has only been 1620 total documented cases in the USA
in the last 30 years. Every investigation into fraud by
audits found a few more votes against Trump than prior to
the audit. Each of the 60 election fraud cases Trump lost.
He lost because his lawyers could not tell the wild stories
that he was telling the public without getting themselves
convicted of perjury.
These these fact were unconvincing seems to prove that
his supporters are in a cult.
But not that there were no fraud performed skillfully enough to avoid
detection. What was found was only small unintentional errors that
nobody tried to hide.
Likewise there is no perfect logical proof that
can possibly exist that five minutes ago ever existed.
It may also be the case that all of reality is entirely
fictional.
Within the possibly false assumption that reality is
not fictional and five minutes ago did exist then
Trump is merely copying Hitler's big lie about election
fraud is as certain as certain can possibly be.
On 13/05/2026 14:32, olcott wrote:
On 5/13/2026 4:14 AM, Mikko wrote:
On 12/05/2026 16:32, olcott wrote:
On 5/12/2026 2:05 AM, Mikko wrote:
On 11/05/2026 14:44, olcott wrote:
On 5/11/2026 2:24 AM, Mikko wrote:Middle dot is a commonly used mathematical operator. In this context >>>>> where the purpose of the operation is not specified some other symbols >>>>> are often used instead, like ∘ or ∙, or operands are just put side by >>>>> side with no operator between.
On 10/05/2026 22:06, olcott wrote:
On 5/10/2026 2:10 AM, Mikko wrote:
On 09/05/2026 15:13, olcott wrote:
On 5/9/2026 3:30 AM, Mikko wrote:
On 08/05/2026 19:58, olcott wrote:
On 5/8/2026 11:06 AM, dart200 wrote:
On 5/8/26 12:19 AM, Mikko wrote:
On 07/05/2026 12:00, dart200 wrote:
On 5/7/26 12:18 AM, Mikko wrote:A machine is not a "diagonal".
On 06/05/2026 22:40, dart200 wrote:the H machine defined on p247 from his paper /on >>>>>>>>>>>>>>> computable numbers/
On 5/6/26 12:55 AM, Mikko wrote:it. Any use of the word before the definition is nonsense,. >>>>>>>>>>>>>>
On 05/05/2026 12:28, dart200 wrote:
On 5/5/26 1:25 AM, Mikko wrote:
On 04/05/2026 10:53, dart200 wrote:
On 5/3/26 11:15 PM, Mikko wrote:
On 03/05/2026 12:09, dart200 wrote: >>>>>>>>>>>>>>>>>>>>>>> On 5/3/26 12:53 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 02/05/2026 23:39, dart200 wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 4/19/26 10:58 AM, Richard Damon wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 4/19/26 1:21 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 4/19/2026 3:59 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 18/04/2026 15:58, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>i can't read if u can't explain
dunno what ur saying here.Turing proved that there are universal Turing >>>>>>>>>>>>>>>>>>>>>>>> machines. An universalTuring machine halts with >>>>>>>>>>>>>>>>>>>>>>>> some inputs and doesn't halt with any other >>>>>>>>>>>>>>>>>>>>>>>> input. Every Turing machine that can be given >>>>>>>>>>>>>>>>>>>>>>>> the same input as anrichard richard richard, that is in-correct. >>>>>>>>>>>>>>>>>>>>>>>>>Unknown truths are not elements of the body of >>>>>>>>>>>>>>>>>>>>>>>>>>>>> knowledge is a semantic tautology. Did you >>>>>>>>>>>>>>>>>>>>>>>>>>>>> thinkNo, but that measn that for some sentences X >>>>>>>>>>>>>>>>>>>>>>>>>>>> True(X) is unknown and there >>>>>>>>>>>>>>>>>>>>>>>>>>>> is no method to find out. >>>>>>>>>>>>>>>>>>>>>>>>>>>>
that things that are unknown are known? >>>>>>>>>>>>>>>>>>>>>>>>>>>>
I don't know about philosophers but >>>>>>>>>>>>>>>>>>>>>>>>>>>> mathematicians and logicians don't >>>>>>>>>>>>>>>>>>>>>>>>>>>> find it interesting if all you can say that >>>>>>>>>>>>>>>>>>>>>>>>>>>> all knowledge is knowable >>>>>>>>>>>>>>>>>>>>>>>>>>>> and everything else is not. >>>>>>>>>>>>>>>>>>>>>>>>>>>>
Ross Finlayson, seemed to endlessly hedge on >>>>>>>>>>>>>>>>>>>>>>>>>>> whether
or not the truth value of the Goldbach >>>>>>>>>>>>>>>>>>>>>>>>>>> conjecture was
known. He seemed to think that there are >>>>>>>>>>>>>>>>>>>>>>>>>>> alternative
analytical frameworks that make the question >>>>>>>>>>>>>>>>>>>>>>>>>>> of whether
or not its truth value is known an ambiguous >>>>>>>>>>>>>>>>>>>>>>>>>>> question.
I needed to refer to unknown truth values >>>>>>>>>>>>>>>>>>>>>>>>>>> specifically
because all "undecidability" when construed >>>>>>>>>>>>>>>>>>>>>>>>>>> correctly
falls into one of two categories. >>>>>>>>>>>>>>>>>>>>>>>>>>> (a) Semantic incoherence >>>>>>>>>>>>>>>>>>>>>>>>>>> (b) Unknown truth values. >>>>>>>>>>>>>>>>>>>>>>>>>>>
Nope.
Undecidability can not come from Semantic >>>>>>>>>>>>>>>>>>>>>>>>>> Incoherence, as the definition of >>>>>>>>>>>>>>>>>>>>>>>>>> Undecidability ia based on there being a >>>>>>>>>>>>>>>>>>>>>>>>>> coherent answer, just not one that can be >>>>>>>>>>>>>>>>>>>>>>>>>> determined by a computation. >>>>>>>>>>>>>>>>>>>>>>>>>
the undecidable problem turing described (as >>>>>>>>>>>>>>>>>>>>>>>>> well as the basic halting problem) involves a >>>>>>>>>>>>>>>>>>>>>>>>> situations that have _no_ coherent answer, not >>>>>>>>>>>>>>>>>>>>>>>>> just one that can be known by not computed ... >>>>>>>>>>>>>>>>>>>>>>>>
universal Turing machine either fails to accept >>>>>>>>>>>>>>>>>>>>>>>> some input with which
that universal Turing machine halts or fails to >>>>>>>>>>>>>>>>>>>>>>>> reject some input with
which that universal Turing macnie does not halt. >>>>>>>>>>>>>>>>>>>>>>>
There is a way to find out if you can read. >>>>>>>>>>>>>>>>>>>>>
I can't explain the art of reading Common Language. >>>>>>>>>>>>>>>>>>>>
inyes, but then he argues it's impossible to compute >>>>>>>>>>>>>>>>>>>>> the diagonal because of the paradox that ensues >>>>>>>>>>>>>>>>>>>>> when naively running the classifier on the diagonal >>>>>>>>>>>>>>>>>>>>> itselfturing hypothesized a diagonal computation that >>>>>>>>>>>>>>>>>>>>>>> tries to put the Nth digit from the Nth circle- >>>>>>>>>>>>>>>>>>>>>>> free machine as the Nth digit on this diagonal >>>>>>>>>>>>>>>>>>>>>>> across all circle- free machine... >>>>>>>>>>>>>>>>>>>>>>That is possible because there nither the machines >>>>>>>>>>>>>>>>>>>>>> nor digit positions
are more numerous than natural numbers. >>>>>>>>>>>>>>>>>>>>>
It is impossible to have a Turing machine that >>>>>>>>>>>>>>>>>>>> computes a number that
no Turing machine can compute. But you can compute >>>>>>>>>>>>>>>>>>>> it if you can use
all (infinitely many) Turing machines.
no you can't.
Hard to test as I han't infinite many Turing machines. >>>>>>>>>>>>>>>>>> But it is
u don't need to test it, you can't define a total >>>>>>>>>>>>>>>>> dovetailing machine to compute turing's diagonal, >>>>>>>>>>>>>>>> You should not say anything about the diagonal before >>>>>>>>>>>>>>>> you have defined
the machine supposes to compute the "turing's diagonal" >>>>>>>>>>>>> across circle- free sequences, otherwise labeled as β' in >>>>>>>>>>>>> the paper, defined at the bottom of p246
Anything that any machine can possibly compute can
be computed by applying a finite set of finite string
transformation rules to a finite set of finite strings. >>>>>>>>>>>>
Everything else is simply out-of-scope for computation >>>>>>>>>>>> like making a silk purse from a sow's ear.
That "everything else" includes many thigns that would be >>>>>>>>>>> useful to
know. In particular, whether some useful function can be >>>>>>>>>>> computed is
in that "everything else".
Like the truth value of: "This sentence is not true"
that has no truth value.
I don't think knowing the truth value of that would be useful. >>>>>>>>> At least
not for any important purpose.
Knowing that all undecidability is merely semantic
incoherence enables:
"true on the basis of meaning expressed in language"
to be reliably computable for the entire body of knowledge.
We don't have the knowledge that all undecidability is merely
semantic
incoherence, and can't know because we already know that there is >>>>>>> undecidability that is not semantic incoherence. FOr example the >>>>>>> axiom system
∀x (1⋅x = x)
1.5 != 5 ∴ you are wrong and I am couinting the rest as gibberish >>>>>
If commonly used mathematics is gibberish to you then we many safely >>>>> conclude that you have nothing useful to offer to the groups you
posted to.
∀x (x⋅1 = x)
∀x∀y∀z (x⋅(y⋅z) = (x⋅y)⋅z)
∀x∃y (x⋅y = 1)
∀x∃y (y⋅x = 1)
is useful for many purposes. But there are sentences like
∀x∃y (x⋅y = y⋅x)
that are undecidable in that system. But there is notiong
semantically
incoherent in that example or similar ones.
The truth about climate change and election fraud could
be computed.
Not without real world information.
Yes, so what?
So the biggest problem is not how to compute but how to get and verify >>>>> the relevant real world infomration.
A set of "atomic facts" does exist. We only nee to write> them all
down.
THat is a lot of work that can never be completed.
It can be completed with sufficient automation.
No, it can't. It is not completed before it contains all material that
will be published.
The place to start would be published textbooks.
How long does it take to read all texbooks published in one year?
IDK, an LLM might do this in five minutes.
No, because in that time it cannot access all of the material. And
it takes time to extract atomic facts and to store them into a big
database.
Then peer reviewed papers.
Now long does it take to read all reviewed papers published in one year? >>>
Then published newspaper articles.
How long does it take to read all newspaper articles publised in one
year?
An LLM might read everything ever published in one year.
During that year more is publised.
And what to do with the "atomic facts" that conflict each other?
All knowledge that can be expressed in language would
include the exact (x,y,z) coordinates of every atom of your
body relative to the exact center of the Earth every millisecond.
Because this degree of detail is not physically implementable
to implement my system we exclude most specific details. It
is a system of general knowledge of about 200 petabytes.
Of course you may postulate that
the climate is immutable or that there was massimbe undetected fraud >>>>>>> in the last or some earlier election but that is not what the word >>>>>>> "knowledge" means.
The key elements of election fraud are two things:
(a) There was no actual evidence of election fraud
that could have possibly changed the results.
The key element of elction fraud is to find a vulnerability in the
election procedure.
There has only been 1620 total documented cases in the USA
in the last 30 years. Every investigation into fraud by
audits found a few more votes against Trump than prior to
the audit. Each of the 60 election fraud cases Trump lost.
He lost because his lawyers could not tell the wild stories
that he was telling the public without getting themselves
convicted of perjury.
These these fact were unconvincing seems to prove that
his supporters are in a cult.
But not that there were no fraud performed skillfully enough to avoid
detection. What was found was only small unintentional errors that
nobody tried to hide.
Likewise there is no perfect logical proof that
can possibly exist that five minutes ago ever existed.
It may also be the case that all of reality is entirely
fictional.
That is right. But that is not relevant to our understanding of the
assumed processes that given the world the form it has now or that
we can expect it to have in the near future. Perhaps the world is
just God's thought but if it is it seems to be a coherent thought.
Within the possibly false assumption that reality is
not fictional and five minutes ago did exist then
Trump is merely copying Hitler's big lie about election
fraud is as certain as certain can possibly be.
When did Hitler claim anything about an election fraud?
On 13/05/2026 18:28, olcott wrote:
On 5/13/2026 9:38 AM, André G. Isaak wrote:
On 2026-05-13 08:20, olcott wrote:
On 5/13/2026 6:56 AM, André G. Isaak wrote:
On 2026-05-13 05:18, olcott wrote:
On 5/12/2026 10:02 PM, André G. Isaak wrote:
On 2026-05-12 07:32, olcott wrote:
On 5/12/2026 2:05 AM, Mikko wrote:
On 11/05/2026 14:44, olcott wrote:
On 5/11/2026 2:24 AM, Mikko wrote:
On 10/05/2026 22:06, olcott wrote:
Middle dot is a commonly used mathematical operator. In this >>>>>>>>> contextWe don't have the knowledge that all undecidability is merely >>>>>>>>>>> semantic
incoherence, and can't know because we already know that >>>>>>>>>>> there is
undecidability that is not semantic incoherence. FOr example the >>>>>>>>>>> axiom system
∀x (1⋅x = x)
1.5 != 5 ∴ you are wrong and I am couinting the rest as gibberish >>>>>>>>>
where the purpose of the operation is not specified some other >>>>>>>>> symbols
are often used instead, like ∘ or ∙, or operands are just put >>>>>>>>> side by
side with no operator between.
If commonly used mathematics is gibberish to you then we many >>>>>>>>> safely
conclude that you have nothing useful to offer to the groups you >>>>>>>>> posted to.
∀x (x⋅1 = x)
∀x∀y∀z (x⋅(y⋅z) = (x⋅y)⋅z)
∀x∃y (x⋅y = 1)
∀x∃y (y⋅x = 1)
is useful for many purposes. But there are sentences like >>>>>>>>>>>
∀x∃y (x⋅y = y⋅x)
that are undecidable in that system. But there is notiong >>>>>>>>>>> semantically
incoherent in that example or similar ones.
I'm curious to know how you would actually address Mikko's point >>>>>>> here. He's pointed out the rather obvious error in your reading >>>>>>> comprehension, but you've simply glossed over the example.
In what sense is ∀x∃y (x⋅y = y⋅x) "semantically incoherent"? >>>>>>>
André
Decimal point versus multiplication operator?
If it is a decimal point then it is incoherent.
Obviously its nor a decimal point. He gave you the actual axioms
which define the dot operator, so there should be no dispute as to
its meaning.
The point is that ∀x∃y (x⋅y = y⋅x) is not decidable from those >>>>> axioms,yet it is clearly semantically coherent.
André
∀x∃y (x⋅y = y⋅x) is proven true by ∀x∀y (x⋅y = y⋅x)
which is proven true by the commutative property of multiplication.
https://people.hsc.edu/faculty-staff/blins/classes/fall18/math105/
Examples/AlgebraAxioms.pdf
But then you're introducing a new axiom which isn't part of the set
of axioms which he introduced.
My thesis:
The entire body of knowledge that can be expressed
in language can be encoded as relations between finite strings.
Therefore, you're not dealing with the same theory.
*The entire body of knowledge that can be expressed in language*
Is the scope. That some knucklehead can fail to bother to define
that "cats are animals" so that his knucklehead formal system
does not know this IS OFF-TOPIC.
The entire body of knowledge includes that i² = -1, j² = -1, k² = -1,
and ijk = -1. From these we can infer that ij = k and ji = -k and
that ij ≠ ji, at least when we are talking about Hamilton's quaternions.
On 5/13/2026 9:51 PM, Ross Finlayson wrote:
On 05/13/2026 04:40 PM, olcott wrote:
On 5/13/2026 4:37 PM, André G. Isaak wrote:
On 2026-05-13 09:28, olcott wrote:
On 5/13/2026 9:38 AM, André G. Isaak wrote:
On 2026-05-13 08:20, olcott wrote:
On 5/13/2026 6:56 AM, André G. Isaak wrote:
On 2026-05-13 05:18, olcott wrote:
On 5/12/2026 10:02 PM, André G. Isaak wrote:
On 2026-05-12 07:32, olcott wrote:
On 5/12/2026 2:05 AM, Mikko wrote:
On 11/05/2026 14:44, olcott wrote:
On 5/11/2026 2:24 AM, Mikko wrote:
On 10/05/2026 22:06, olcott wrote:
We don't have the knowledge that all undecidability is >>>>>>>>>>>>>> merely semantic
incoherence, and can't know because we already know that >>>>>>>>>>>>>> there is
undecidability that is not semantic incoherence. FOr example >>>>>>>>>>>>>> the
axiom system
∀x (1⋅x = x)
1.5 != 5 ∴ you are wrong and I am couinting the rest as >>>>>>>>>>>>> gibberish
Middle dot is a commonly used mathematical operator. In this >>>>>>>>>>>> context
where the purpose of the operation is not specified some other >>>>>>>>>>>> symbols
are often used instead, like ∘ or ∙, or operands are just put >>>>>>>>>>>> side by
side with no operator between.
If commonly used mathematics is gibberish to you then we many >>>>>>>>>>>> safely
conclude that you have nothing useful to offer to the groups >>>>>>>>>>>> you
posted to.
∀x (x⋅1 = x)
∀x∀y∀z (x⋅(y⋅z) = (x⋅y)⋅z)
∀x∃y (x⋅y = 1)
∀x∃y (y⋅x = 1)
is useful for many purposes. But there are sentences like >>>>>>>>>>>>>>
∀x∃y (x⋅y = y⋅x)
that are undecidable in that system. But there is notiong >>>>>>>>>>>>>> semantically
incoherent in that example or similar ones.
I'm curious to know how you would actually address Mikko's point >>>>>>>>>> here. He's pointed out the rather obvious error in your reading >>>>>>>>>> comprehension, but you've simply glossed over the example. >>>>>>>>>>
In what sense is ∀x∃y (x⋅y = y⋅x) "semantically incoherent"? >>>>>>>>>>
André
Decimal point versus multiplication operator?
If it is a decimal point then it is incoherent.
Obviously its nor a decimal point. He gave you the actual axioms >>>>>>>> which define the dot operator, so there should be no dispute as to >>>>>>>> its meaning.
The point is that ∀x∃y (x⋅y = y⋅x) is not decidable from those >>>>>>>> axioms,yet it is clearly semantically coherent.
André
∀x∃y (x⋅y = y⋅x) is proven true by ∀x∀y (x⋅y = y⋅x) >>>>>>> which is proven true by the commutative property of multiplication. >>>>>>>
https://people.hsc.edu/faculty-staff/blins/classes/fall18/math105/ >>>>>>> Examples/AlgebraAxioms.pdf
But then you're introducing a new axiom which isn't part of the set >>>>>> of axioms which he introduced.
My thesis:
The entire body of knowledge that can be expressed
in language can be encoded as relations between finite strings.
And how 'bout them Mets?
Therefore, you're not dealing with the same theory.
*The entire body of knowledge that can be expressed in language*
... is an ill-defined set which only exists in your mind. There's over >>>> 8 billion people on earth, all of whom believe different, often
contradictory things. And, with the exception of theorems of formal
systems, there is nothing that we know with absolute certainty. Only
varying degrees of certainty, but for every given fact you won't get a >>>> universal consensus on exactly how certain we are of that fact.
So maybe cats were never animals and this "belief"
has always been mass psychosis? In actual reality
cats were always a kind of snake?
I propose that a finite set of "atomic facts" of general
knowledge inherently exists and that no 100% concrete
counter-example can ever be found.
Any rebuttal to this besides at least the attempt
of a 100% concrete counter-example will be dismissed
as deception.
Formal systems operate over a *fixed* set of axioms. The set of
knowledge is not fixed, but constantly changing. But the results you
are attempting to challenge (Gödels theorem, etc.) all apply to
*formal* systems based on fixed sets of axioms rather than some fluid
and vaguely defined body of knowledge.
As soon as truth theoretic semantics is utterly replaced
with proof theoretic semantics G remains true in meta-math
and becomes meaningless in PA.
which >>> he presented. Whether it is decidable in some other theoryIs the scope. That some knucklehead can fail to bother to define
that "cats are animals" so that his knucklehead formal system
does not know this IS OFF-TOPIC.
Mikko offered a concrete set of axioms and made a claim about what
could be derived from those axioms. Neither cats nor animals were
involved.
The point is that ∀x∃y (x⋅y = y⋅x) is undecidable in the theory
isn't
really germane to the discussion.
André
So, if you have a finite set of facts, then,
that's a fact, and, that's a fact, and, that's a fact,
ad infinitum: an infinite set of facts.
A finite set of "atomic facts" and a finite set of
semantic entailment relations between finite strings
can derive an infinite set of semantically correct
sentences.
It's kind of like relations between physical objects
being mathematical objects being physical objects, ad infinitum,
the universe is also its own powerset of fact.
Maybe nobody cares. If your own theory of fact is satisfactory,
then, you don't need to care about other putative facts. That
said, anybody else can, and that's their own fact.
It is required that my system encode every element of the
body of general knowledge. Some of these "atomic facts"
will be things like the current weight of evidence shows
that X seems probable, such as the Earth is 4 billion years
old.
All Olcott really seems to claim is a right to be left alone,
yet he won't shut up about it and insists it's universal,
which is fallacious and faulty reasoning.
Make sure you prevent material implication from garbage-in/garbage-out
Yes material implication is problematic.
Also disjunction introduction.
Instead of material implication we have modal necessity.
a.k.a. crazy-in/crazy-out, while you're at it, the "quasi-modal" in
the logic is perhaps the worst sort of waste-of-time in terms of
the foundations of logic or about a century's worth.
You form all of these conclusions after first becoming an
expert in proof theoretic semantics?
Then, matters of decide-ability and in-decide-ability involve
completeness and incompleteness: and incompleteness and independence.
Then, independence in axiomatic theories is of at least two kinds:
adding an axiom, or removing one, and about that axioms vary:
expansion-of-comprehension and restriction-of-comprehension.
So, much of the accounts of axiomatics is foolish in that
it doesn't distinguish expansion-of-comprehension and the
restriction-of-comprehension, or conflates them like the
retro-thesis of Russell, which is almost as hypocritical
as the retro-finitism of closed-world flat-earthers.
On 5/14/2026 2:54 AM, Mikko wrote:
On 13/05/2026 18:28, olcott wrote:
On 5/13/2026 9:38 AM, André G. Isaak wrote:
On 2026-05-13 08:20, olcott wrote:
On 5/13/2026 6:56 AM, André G. Isaak wrote:
On 2026-05-13 05:18, olcott wrote:
On 5/12/2026 10:02 PM, André G. Isaak wrote:
On 2026-05-12 07:32, olcott wrote:
On 5/12/2026 2:05 AM, Mikko wrote:
On 11/05/2026 14:44, olcott wrote:
On 5/11/2026 2:24 AM, Mikko wrote:
On 10/05/2026 22:06, olcott wrote:
We don't have the knowledge that all undecidability is >>>>>>>>>>>> merely semantic
incoherence, and can't know because we already know that >>>>>>>>>>>> there is
undecidability that is not semantic incoherence. FOr example >>>>>>>>>>>> the
axiom system
∀x (1⋅x = x)
1.5 != 5 ∴ you are wrong and I am couinting the rest as >>>>>>>>>>> gibberish
Middle dot is a commonly used mathematical operator. In this >>>>>>>>>> context
where the purpose of the operation is not specified some other >>>>>>>>>> symbols
are often used instead, like ∘ or ∙, or operands are just put >>>>>>>>>> side by
side with no operator between.
If commonly used mathematics is gibberish to you then we many >>>>>>>>>> safely
conclude that you have nothing useful to offer to the groups you >>>>>>>>>> posted to.
∀x (x⋅1 = x)
∀x∀y∀z (x⋅(y⋅z) = (x⋅y)⋅z)
∀x∃y (x⋅y = 1)
∀x∃y (y⋅x = 1)
is useful for many purposes. But there are sentences like >>>>>>>>>>>>
∀x∃y (x⋅y = y⋅x)
that are undecidable in that system. But there is notiong >>>>>>>>>>>> semantically
incoherent in that example or similar ones.
I'm curious to know how you would actually address Mikko's point >>>>>>>> here. He's pointed out the rather obvious error in your reading >>>>>>>> comprehension, but you've simply glossed over the example.
In what sense is ∀x∃y (x⋅y = y⋅x) "semantically incoherent"? >>>>>>>>
André
Decimal point versus multiplication operator?
If it is a decimal point then it is incoherent.
Obviously its nor a decimal point. He gave you the actual axioms
which define the dot operator, so there should be no dispute as to >>>>>> its meaning.
The point is that ∀x∃y (x⋅y = y⋅x) is not decidable from those >>>>>> axioms,yet it is clearly semantically coherent.
André
∀x∃y (x⋅y = y⋅x) is proven true by ∀x∀y (x⋅y = y⋅x)
which is proven true by the commutative property of multiplication.
https://people.hsc.edu/faculty-staff/blins/classes/fall18/math105/
Examples/AlgebraAxioms.pdf
But then you're introducing a new axiom which isn't part of the set
of axioms which he introduced.
My thesis:
The entire body of knowledge that can be expressed
in language can be encoded as relations between finite strings.
Therefore, you're not dealing with the same theory.
*The entire body of knowledge that can be expressed in language*
Is the scope. That some knucklehead can fail to bother to define
that "cats are animals" so that his knucklehead formal system
does not know this IS OFF-TOPIC.
The entire body of knowledge includes that i² = -1, j² = -1, k² = -1,
and ijk = -1. From these we can infer that ij = k and ji = -k and
that ij ≠ ji, at least when we are talking about Hamilton's quaternions.
i¹ = i
i² = -1
i³ = -i
The entire body of general knowledge expressed in
language includes the "atomic facts" about imaginary
numbers in a finite list and the semantic relations
between finite strings in a finite list such that
any combination of the above can be derived, no
longer a finite list.
Imaginary numbers themselves may be an incoherent notion.
In this case they would not be included in the body of
knowledge.
On 5/14/2026 3:18 AM, Mikko wrote:
On 13/05/2026 14:32, olcott wrote:
On 5/13/2026 4:14 AM, Mikko wrote:
On 12/05/2026 16:32, olcott wrote:
On 5/12/2026 2:05 AM, Mikko wrote:
On 11/05/2026 14:44, olcott wrote:
On 5/11/2026 2:24 AM, Mikko wrote:Middle dot is a commonly used mathematical operator. In this context >>>>>> where the purpose of the operation is not specified some other
On 10/05/2026 22:06, olcott wrote:
On 5/10/2026 2:10 AM, Mikko wrote:
On 09/05/2026 15:13, olcott wrote:
On 5/9/2026 3:30 AM, Mikko wrote:
On 08/05/2026 19:58, olcott wrote:
On 5/8/2026 11:06 AM, dart200 wrote:
On 5/8/26 12:19 AM, Mikko wrote:
On 07/05/2026 12:00, dart200 wrote:
On 5/7/26 12:18 AM, Mikko wrote:A machine is not a "diagonal".
On 06/05/2026 22:40, dart200 wrote:
On 5/6/26 12:55 AM, Mikko wrote:it. Any use of the word before the definition is >>>>>>>>>>>>>>>>> nonsense,.
On 05/05/2026 12:28, dart200 wrote:
On 5/5/26 1:25 AM, Mikko wrote:
On 04/05/2026 10:53, dart200 wrote: >>>>>>>>>>>>>>>>>>>>>> On 5/3/26 11:15 PM, Mikko wrote:no you can't.
On 03/05/2026 12:09, dart200 wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 5/3/26 12:53 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 02/05/2026 23:39, dart200 wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 4/19/26 10:58 AM, Richard Damon wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 4/19/26 1:21 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 4/19/2026 3:59 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 18/04/2026 15:58, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>i can't read if u can't explain
dunno what ur saying here.Turing proved that there are universal Turing >>>>>>>>>>>>>>>>>>>>>>>>> machines. An universalTuring machine halts with >>>>>>>>>>>>>>>>>>>>>>>>> some inputs and doesn't halt with any other >>>>>>>>>>>>>>>>>>>>>>>>> input. Every Turing machine that can be given >>>>>>>>>>>>>>>>>>>>>>>>> the same input as anrichard richard richard, that is in-correct. >>>>>>>>>>>>>>>>>>>>>>>>>>Unknown truths are not elements of the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> body ofNo, but that measn that for some sentences >>>>>>>>>>>>>>>>>>>>>>>>>>>>> X True(X) is unknown and there >>>>>>>>>>>>>>>>>>>>>>>>>>>>> is no method to find out. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>
knowledge is a semantic tautology. Did you >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> think
that things that are unknown are known? >>>>>>>>>>>>>>>>>>>>>>>>>>>>>
I don't know about philosophers but >>>>>>>>>>>>>>>>>>>>>>>>>>>>> mathematicians and logicians don't >>>>>>>>>>>>>>>>>>>>>>>>>>>>> find it interesting if all you can say that >>>>>>>>>>>>>>>>>>>>>>>>>>>>> all knowledge is knowable >>>>>>>>>>>>>>>>>>>>>>>>>>>>> and everything else is not. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Ross Finlayson, seemed to endlessly hedge on >>>>>>>>>>>>>>>>>>>>>>>>>>>> whether
or not the truth value of the Goldbach >>>>>>>>>>>>>>>>>>>>>>>>>>>> conjecture was
known. He seemed to think that there are >>>>>>>>>>>>>>>>>>>>>>>>>>>> alternative
analytical frameworks that make the question >>>>>>>>>>>>>>>>>>>>>>>>>>>> of whether
or not its truth value is known an ambiguous >>>>>>>>>>>>>>>>>>>>>>>>>>>> question.
I needed to refer to unknown truth values >>>>>>>>>>>>>>>>>>>>>>>>>>>> specifically
because all "undecidability" when construed >>>>>>>>>>>>>>>>>>>>>>>>>>>> correctly
falls into one of two categories. >>>>>>>>>>>>>>>>>>>>>>>>>>>> (a) Semantic incoherence >>>>>>>>>>>>>>>>>>>>>>>>>>>> (b) Unknown truth values. >>>>>>>>>>>>>>>>>>>>>>>>>>>>
Nope.
Undecidability can not come from Semantic >>>>>>>>>>>>>>>>>>>>>>>>>>> Incoherence, as the definition of >>>>>>>>>>>>>>>>>>>>>>>>>>> Undecidability ia based on there being a >>>>>>>>>>>>>>>>>>>>>>>>>>> coherent answer, just not one that can be >>>>>>>>>>>>>>>>>>>>>>>>>>> determined by a computation. >>>>>>>>>>>>>>>>>>>>>>>>>>
the undecidable problem turing described (as >>>>>>>>>>>>>>>>>>>>>>>>>> well as the basic halting problem) involves a >>>>>>>>>>>>>>>>>>>>>>>>>> situations that have _no_ coherent answer, not >>>>>>>>>>>>>>>>>>>>>>>>>> just one that can be known by not computed ... >>>>>>>>>>>>>>>>>>>>>>>>>
universal Turing machine either fails to accept >>>>>>>>>>>>>>>>>>>>>>>>> some input with which
that universal Turing machine halts or fails to >>>>>>>>>>>>>>>>>>>>>>>>> reject some input with
which that universal Turing macnie does not halt. >>>>>>>>>>>>>>>>>>>>>>>>
There is a way to find out if you can read. >>>>>>>>>>>>>>>>>>>>>>
I can't explain the art of reading Common Language. >>>>>>>>>>>>>>>>>>>>>
inyes, but then he argues it's impossible to compute >>>>>>>>>>>>>>>>>>>>>> the diagonal because of the paradox that ensues >>>>>>>>>>>>>>>>>>>>>> when naively running the classifier on the >>>>>>>>>>>>>>>>>>>>>> diagonal itselfturing hypothesized a diagonal computation that >>>>>>>>>>>>>>>>>>>>>>>> tries to put the Nth digit from the Nth circle- >>>>>>>>>>>>>>>>>>>>>>>> free machine as the Nth digit on this diagonal >>>>>>>>>>>>>>>>>>>>>>>> across all circle- free machine... >>>>>>>>>>>>>>>>>>>>>>>That is possible because there nither the >>>>>>>>>>>>>>>>>>>>>>> machines nor digit positions
are more numerous than natural numbers. >>>>>>>>>>>>>>>>>>>>>>
It is impossible to have a Turing machine that >>>>>>>>>>>>>>>>>>>>> computes a number that
no Turing machine can compute. But you can compute >>>>>>>>>>>>>>>>>>>>> it if you can use
all (infinitely many) Turing machines. >>>>>>>>>>>>>>>>>>>>
Hard to test as I han't infinite many Turing >>>>>>>>>>>>>>>>>>> machines. But it is
u don't need to test it, you can't define a total >>>>>>>>>>>>>>>>>> dovetailing machine to compute turing's diagonal, >>>>>>>>>>>>>>>>> You should not say anything about the diagonal before >>>>>>>>>>>>>>>>> you have defined
the H machine defined on p247 from his paper /on >>>>>>>>>>>>>>>> computable numbers/
the machine supposes to compute the "turing's diagonal" >>>>>>>>>>>>>> across circle- free sequences, otherwise labeled as β' in >>>>>>>>>>>>>> the paper, defined at the bottom of p246
Anything that any machine can possibly compute can
be computed by applying a finite set of finite string >>>>>>>>>>>>> transformation rules to a finite set of finite strings. >>>>>>>>>>>>>
Everything else is simply out-of-scope for computation >>>>>>>>>>>>> like making a silk purse from a sow's ear.
That "everything else" includes many thigns that would be >>>>>>>>>>>> useful to
know. In particular, whether some useful function can be >>>>>>>>>>>> computed is
in that "everything else".
Like the truth value of: "This sentence is not true"
that has no truth value.
I don't think knowing the truth value of that would be useful. >>>>>>>>>> At least
not for any important purpose.
Knowing that all undecidability is merely semantic
incoherence enables:
"true on the basis of meaning expressed in language"
to be reliably computable for the entire body of knowledge.
We don't have the knowledge that all undecidability is merely >>>>>>>> semantic
incoherence, and can't know because we already know that there is >>>>>>>> undecidability that is not semantic incoherence. FOr example the >>>>>>>> axiom system
∀x (1⋅x = x)
1.5 != 5 ∴ you are wrong and I am couinting the rest as gibberish >>>>>>
symbols
are often used instead, like ∘ or ∙, or operands are just put side by
side with no operator between.
If commonly used mathematics is gibberish to you then we many safely >>>>>> conclude that you have nothing useful to offer to the groups you
posted to.
∀x (x⋅1 = x)
∀x∀y∀z (x⋅(y⋅z) = (x⋅y)⋅z)
∀x∃y (x⋅y = 1)
∀x∃y (y⋅x = 1)
is useful for many purposes. But there are sentences like
∀x∃y (x⋅y = y⋅x)
that are undecidable in that system. But there is notiong
semantically
incoherent in that example or similar ones.
The truth about climate change and election fraud could
be computed.
Not without real world information.
Yes, so what?
So the biggest problem is not how to compute but how to get and
verify
the relevant real world infomration.
A set of "atomic facts" does exist. We only nee to write> them all
down.
THat is a lot of work that can never be completed.
It can be completed with sufficient automation.
No, it can't. It is not completed before it contains all material that
will be published.
The place to start would be published textbooks.
How long does it take to read all texbooks published in one year?
IDK, an LLM might do this in five minutes.
No, because in that time it cannot access all of the material. And
it takes time to extract atomic facts and to store them into a big
database.
LLM would have to be taught how to extract facts.
If it takes then ten times longer to extract all
the facts of a body of text they will still be done
with every textbook ever written after one year.
Then peer reviewed papers.
Now long does it take to read all reviewed papers published in one
year?
Then published newspaper articles.
How long does it take to read all newspaper articles publised in one
year?
An LLM might read everything ever published in one year.
During that year more is publised.
I may be one or two days out-of-sync far far better
than any human.
And what to do with the "atomic facts" that conflict each other?
All knowledge that can be expressed in language would
include the exact (x,y,z) coordinates of every atom of your
body relative to the exact center of the Earth every millisecond. >>>>>>> Because this degree of detail is not physically implementable
to implement my system we exclude most specific details. It
is a system of general knowledge of about 200 petabytes.
Of course you may postulate that
the climate is immutable or that there was massimbe undetected >>>>>>>> fraud
in the last or some earlier election but that is not what the word >>>>>>>> "knowledge" means.
The key elements of election fraud are two things:
(a) There was no actual evidence of election fraud
that could have possibly changed the results.
The key element of elction fraud is to find a vulnerability in the >>>>>> election procedure.
There has only been 1620 total documented cases in the USA
in the last 30 years. Every investigation into fraud by
audits found a few more votes against Trump than prior to
the audit. Each of the 60 election fraud cases Trump lost.
He lost because his lawyers could not tell the wild stories
that he was telling the public without getting themselves
convicted of perjury.
These these fact were unconvincing seems to prove that
his supporters are in a cult.
But not that there were no fraud performed skillfully enough to avoid
detection. What was found was only small unintentional errors that
nobody tried to hide.
Likewise there is no perfect logical proof that
can possibly exist that five minutes ago ever existed.
It may also be the case that all of reality is entirely
fictional.
That is right. But that is not relevant to our understanding of the
assumed processes that given the world the form it has now or that
we can expect it to have in the near future. Perhaps the world is
just God's thought but if it is it seems to be a coherent thought.
Correct, to we just encode all of this in language.
Within the possibly false assumption that reality is
not fictional and five minutes ago did exist then
Trump is merely copying Hitler's big lie about election
fraud is as certain as certain can possibly be.
When did Hitler claim anything about an election fraud?
Chapter 6 of Mein Kampf
"The receptive powers of the masses are very
restricted, and their understanding is feeble.
On the other hand, they quickly forget. Such
being the case, all effective propaganda must
be confined to a few bare essentials and those
must be expressed as far as possible in stereotyped
formulas. These slogans should be persistently
repeated until the very last individual has come
to grasp the idea that has been put forward."
Provides the details of Hitler's propaganda system. https://en.wikipedia.org/wiki/Big_lie#2020_stolen_election_claims
On 05/13/2026 08:27 PM, olcott wrote:
On 5/13/2026 9:51 PM, Ross Finlayson wrote:
On 05/13/2026 04:40 PM, olcott wrote:
On 5/13/2026 4:37 PM, André G. Isaak wrote:
On 2026-05-13 09:28, olcott wrote:
On 5/13/2026 9:38 AM, André G. Isaak wrote:
On 2026-05-13 08:20, olcott wrote:
On 5/13/2026 6:56 AM, André G. Isaak wrote:
On 2026-05-13 05:18, olcott wrote:
On 5/12/2026 10:02 PM, André G. Isaak wrote:
On 2026-05-12 07:32, olcott wrote:
On 5/12/2026 2:05 AM, Mikko wrote:
On 11/05/2026 14:44, olcott wrote:
On 5/11/2026 2:24 AM, Mikko wrote:
On 10/05/2026 22:06, olcott wrote:
We don't have the knowledge that all undecidability is >>>>>>>>>>>>>>> merely semantic
incoherence, and can't know because we already know that >>>>>>>>>>>>>>> there is
undecidability that is not semantic incoherence. FOr example >>>>>>>>>>>>>>> the
axiom system
∀x (1⋅x = x)
1.5 != 5 ∴ you are wrong and I am couinting the rest as >>>>>>>>>>>>>> gibberish
Middle dot is a commonly used mathematical operator. In this >>>>>>>>>>>>> context
where the purpose of the operation is not specified some other >>>>>>>>>>>>> symbols
are often used instead, like ∘ or ∙, or operands are just put >>>>>>>>>>>>> side by
side with no operator between.
If commonly used mathematics is gibberish to you then we many >>>>>>>>>>>>> safely
conclude that you have nothing useful to offer to the groups >>>>>>>>>>>>> you
posted to.
∀x (x⋅1 = x)
∀x∀y∀z (x⋅(y⋅z) = (x⋅y)⋅z)
∀x∃y (x⋅y = 1)
∀x∃y (y⋅x = 1)
is useful for many purposes. But there are sentences like >>>>>>>>>>>>>>>
∀x∃y (x⋅y = y⋅x)
that are undecidable in that system. But there is notiong >>>>>>>>>>>>>>> semantically
incoherent in that example or similar ones.
I'm curious to know how you would actually address Mikko's point >>>>>>>>>>> here. He's pointed out the rather obvious error in your reading >>>>>>>>>>> comprehension, but you've simply glossed over the example. >>>>>>>>>>>
In what sense is ∀x∃y (x⋅y = y⋅x) "semantically incoherent"?
André
Decimal point versus multiplication operator?
If it is a decimal point then it is incoherent.
Obviously its nor a decimal point. He gave you the actual axioms >>>>>>>>> which define the dot operator, so there should be no dispute as to >>>>>>>>> its meaning.
The point is that ∀x∃y (x⋅y = y⋅x) is not decidable from those
axioms,yet it is clearly semantically coherent.
André
∀x∃y (x⋅y = y⋅x) is proven true by ∀x∀y (x⋅y = y⋅x) >>>>>>>> which is proven true by the commutative property of multiplication. >>>>>>>>
https://people.hsc.edu/faculty-staff/blins/classes/fall18/math105/ >>>>>>>> Examples/AlgebraAxioms.pdf
But then you're introducing a new axiom which isn't part of the set >>>>>>> of axioms which he introduced.
My thesis:
The entire body of knowledge that can be expressed
in language can be encoded as relations between finite strings.
And how 'bout them Mets?
Therefore, you're not dealing with the same theory.
*The entire body of knowledge that can be expressed in language*
... is an ill-defined set which only exists in your mind. There's over >>>>> 8 billion people on earth, all of whom believe different, often
contradictory things. And, with the exception of theorems of formal
systems, there is nothing that we know with absolute certainty. Only >>>>> varying degrees of certainty, but for every given fact you won't get a >>>>> universal consensus on exactly how certain we are of that fact.
So maybe cats were never animals and this "belief"
has always been mass psychosis? In actual reality
cats were always a kind of snake?
I propose that a finite set of "atomic facts" of general
knowledge inherently exists and that no 100% concrete
counter-example can ever be found.
Any rebuttal to this besides at least the attempt
of a 100% concrete counter-example will be dismissed
as deception.
Formal systems operate over a *fixed* set of axioms. The set of
knowledge is not fixed, but constantly changing. But the results you >>>>> are attempting to challenge (Gödels theorem, etc.) all apply to
*formal* systems based on fixed sets of axioms rather than some fluid >>>>> and vaguely defined body of knowledge.
As soon as truth theoretic semantics is utterly replaced
with proof theoretic semantics G remains true in meta-math
and becomes meaningless in PA.
which >>> he presented. Whether it is decidable in some other theoryIs the scope. That some knucklehead can fail to bother to define
that "cats are animals" so that his knucklehead formal system
does not know this IS OFF-TOPIC.
Mikko offered a concrete set of axioms and made a claim about what
could be derived from those axioms. Neither cats nor animals were
involved.
The point is that ∀x∃y (x⋅y = y⋅x) is undecidable in the theory
isn't
really germane to the discussion.
André
So, if you have a finite set of facts, then,
that's a fact, and, that's a fact, and, that's a fact,
ad infinitum: an infinite set of facts.
A finite set of "atomic facts" and a finite set of
semantic entailment relations between finite strings
can derive an infinite set of semantically correct
sentences.
It's kind of like relations between physical objects
being mathematical objects being physical objects, ad infinitum,
the universe is also its own powerset of fact.
Maybe nobody cares. If your own theory of fact is satisfactory,
then, you don't need to care about other putative facts. That
said, anybody else can, and that's their own fact.
It is required that my system encode every element of the
body of general knowledge. Some of these "atomic facts"
will be things like the current weight of evidence shows
that X seems probable, such as the Earth is 4 billion years
old.
All Olcott really seems to claim is a right to be left alone,
yet he won't shut up about it and insists it's universal,
which is fallacious and faulty reasoning.
Make sure you prevent material implication from garbage-in/garbage-out
Yes material implication is problematic.
Also disjunction introduction.
Instead of material implication we have modal necessity.
a.k.a. crazy-in/crazy-out, while you're at it, the "quasi-modal" in
the logic is perhaps the worst sort of waste-of-time in terms of
the foundations of logic or about a century's worth.
You form all of these conclusions after first becoming an
expert in proof theoretic semantics?
Then, matters of decide-ability and in-decide-ability involve
completeness and incompleteness: and incompleteness and independence.
Then, independence in axiomatic theories is of at least two kinds:
adding an axiom, or removing one, and about that axioms vary:
expansion-of-comprehension and restriction-of-comprehension.
So, much of the accounts of axiomatics is foolish in that
it doesn't distinguish expansion-of-comprehension and the
restriction-of-comprehension, or conflates them like the
retro-thesis of Russell, which is almost as hypocritical
as the retro-finitism of closed-world flat-earthers.
What came first: the chicken or the egg?
Usual accounts might be that first there was a proto-chicken,
and after a course of mutation, with another proto-chicken,
resulted a chicken egg, resulting a chicken. Another account
may be that a proto-chicken evolved in its life and mutated
into a chicken.
Yet, the overall course of the question involves that
chickens come from eggs, and eggs come from chickens,
so answering the sort of question among otherwise usual
accounts of precedence, here has more than one answer.
So, from the ancient times the sorts of ideas of causes
for the causal are as of the "first principles" and as
of the "final cause". There's a rich dialectic about
causality. Today's account of logicist positivism often
makes for that both are due "science", that the principles
are a scientific theory and the causes are a scientific result.
Sowa and Smith had a "great debate" on ontology, a lot of
it is old-wrapped-as-new since the antiquarian and for
"first principles" and "final cause".
About Quine's two arguments on empiricism, here there's a third.
Anyways, any account of "fact" is unique. For example,
making an account of the temporal in the logic, has
that time-series data is attached not only to every
sort of fact its effectivity, also to every sort of
evaluation of fact, "time-series data".
Anyways, it is not so that "the entire body of fact" is finite.
Then, this is just a usual refutation of retro-finitists generally.
On 14/05/2026 18:30, olcott wrote:
On 5/14/2026 2:54 AM, Mikko wrote:
On 13/05/2026 18:28, olcott wrote:i¹ = i
On 5/13/2026 9:38 AM, André G. Isaak wrote:
On 2026-05-13 08:20, olcott wrote:
On 5/13/2026 6:56 AM, André G. Isaak wrote:
On 2026-05-13 05:18, olcott wrote:
On 5/12/2026 10:02 PM, André G. Isaak wrote:
On 2026-05-12 07:32, olcott wrote:
On 5/12/2026 2:05 AM, Mikko wrote:
On 11/05/2026 14:44, olcott wrote:
On 5/11/2026 2:24 AM, Mikko wrote:
On 10/05/2026 22:06, olcott wrote:
We don't have the knowledge that all undecidability is >>>>>>>>>>>>> merely semantic
incoherence, and can't know because we already know that >>>>>>>>>>>>> there is
undecidability that is not semantic incoherence. FOr >>>>>>>>>>>>> example the
axiom system
∀x (1⋅x = x)
1.5 != 5 ∴ you are wrong and I am couinting the rest as >>>>>>>>>>>> gibberish
Middle dot is a commonly used mathematical operator. In this >>>>>>>>>>> context
where the purpose of the operation is not specified some >>>>>>>>>>> other symbols
are often used instead, like ∘ or ∙, or operands are just put >>>>>>>>>>> side by
side with no operator between.
If commonly used mathematics is gibberish to you then we many >>>>>>>>>>> safely
conclude that you have nothing useful to offer to the groups you >>>>>>>>>>> posted to.
∀x (x⋅1 = x)
∀x∀y∀z (x⋅(y⋅z) = (x⋅y)⋅z)
∀x∃y (x⋅y = 1)
∀x∃y (y⋅x = 1)
is useful for many purposes. But there are sentences like >>>>>>>>>>>>>
∀x∃y (x⋅y = y⋅x)
that are undecidable in that system. But there is notiong >>>>>>>>>>>>> semantically
incoherent in that example or similar ones.
I'm curious to know how you would actually address Mikko's
point here. He's pointed out the rather obvious error in your >>>>>>>>> reading comprehension, but you've simply glossed over the example. >>>>>>>>>
In what sense is ∀x∃y (x⋅y = y⋅x) "semantically incoherent"? >>>>>>>>>
André
Decimal point versus multiplication operator?
If it is a decimal point then it is incoherent.
Obviously its nor a decimal point. He gave you the actual axioms >>>>>>> which define the dot operator, so there should be no dispute as >>>>>>> to its meaning.
The point is that ∀x∃y (x⋅y = y⋅x) is not decidable from those >>>>>>> axioms,yet it is clearly semantically coherent.
André
∀x∃y (x⋅y = y⋅x) is proven true by ∀x∀y (x⋅y = y⋅x) >>>>>> which is proven true by the commutative property of multiplication. >>>>>>
https://people.hsc.edu/faculty-staff/blins/classes/fall18/math105/ >>>>>> Examples/AlgebraAxioms.pdf
But then you're introducing a new axiom which isn't part of the set >>>>> of axioms which he introduced.
My thesis:
The entire body of knowledge that can be expressed
in language can be encoded as relations between finite strings.
Therefore, you're not dealing with the same theory.
*The entire body of knowledge that can be expressed in language*
Is the scope. That some knucklehead can fail to bother to define
that "cats are animals" so that his knucklehead formal system
does not know this IS OFF-TOPIC.
The entire body of knowledge includes that i² = -1, j² = -1, k² = -1, >>> and ijk = -1. From these we can infer that ij = k and ji = -k and
that ij ≠ ji, at least when we are talking about Hamilton's quaternions. >>
i² = -1
i³ = -i
The entire body of general knowledge expressed in
language includes the "atomic facts" about imaginary
numbers in a finite list and the semantic relations
between finite strings in a finite list such that
any combination of the above can be derived, no
longer a finite list.
Imaginary numbers themselves may be an incoherent notion.
In this case they would not be included in the body of
knowledge.
So a part of the body of knowledge is that multiplication is not
commutative except in restricted domains, so your above claim to
the contrary is not true.
On 14/05/2026 17:40, olcott wrote:
On 5/14/2026 3:18 AM, Mikko wrote:
On 13/05/2026 14:32, olcott wrote:
On 5/13/2026 4:14 AM, Mikko wrote:
On 12/05/2026 16:32, olcott wrote:
On 5/12/2026 2:05 AM, Mikko wrote:
On 11/05/2026 14:44, olcott wrote:
On 5/11/2026 2:24 AM, Mikko wrote:Middle dot is a commonly used mathematical operator. In this context >>>>>>> where the purpose of the operation is not specified some other
On 10/05/2026 22:06, olcott wrote:
On 5/10/2026 2:10 AM, Mikko wrote:We don't have the knowledge that all undecidability is merely >>>>>>>>> semantic
On 09/05/2026 15:13, olcott wrote:
On 5/9/2026 3:30 AM, Mikko wrote:
On 08/05/2026 19:58, olcott wrote:
On 5/8/2026 11:06 AM, dart200 wrote:
On 5/8/26 12:19 AM, Mikko wrote:
On 07/05/2026 12:00, dart200 wrote:
On 5/7/26 12:18 AM, Mikko wrote:A machine is not a "diagonal".
On 06/05/2026 22:40, dart200 wrote:
On 5/6/26 12:55 AM, Mikko wrote:it. Any use of the word before the definition is >>>>>>>>>>>>>>>>>> nonsense,.
On 05/05/2026 12:28, dart200 wrote:
On 5/5/26 1:25 AM, Mikko wrote:
On 04/05/2026 10:53, dart200 wrote: >>>>>>>>>>>>>>>>>>>>>>> On 5/3/26 11:15 PM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 03/05/2026 12:09, dart200 wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 5/3/26 12:53 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 02/05/2026 23:39, dart200 wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 4/19/26 10:58 AM, Richard Damon wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 4/19/26 1:21 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 4/19/2026 3:59 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 18/04/2026 15:58, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>no you can't.
i can't read if u can't explaindunno what ur saying here.richard richard richard, that is in-correct. >>>>>>>>>>>>>>>>>>>>>>>>>>>Unknown truths are not elements of the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> body ofNo, but that measn that for some sentences >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> X True(X) is unknown and there >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is no method to find out. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
knowledge is a semantic tautology. Did >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> you think
that things that are unknown are known? >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
I don't know about philosophers but >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> mathematicians and logicians don't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> find it interesting if all you can say >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that all knowledge is knowable >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> and everything else is not. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Ross Finlayson, seemed to endlessly hedge >>>>>>>>>>>>>>>>>>>>>>>>>>>>> on whether
or not the truth value of the Goldbach >>>>>>>>>>>>>>>>>>>>>>>>>>>>> conjecture was
known. He seemed to think that there are >>>>>>>>>>>>>>>>>>>>>>>>>>>>> alternative
analytical frameworks that make the >>>>>>>>>>>>>>>>>>>>>>>>>>>>> question of whether
or not its truth value is known an >>>>>>>>>>>>>>>>>>>>>>>>>>>>> ambiguous question.
I needed to refer to unknown truth values >>>>>>>>>>>>>>>>>>>>>>>>>>>>> specifically
because all "undecidability" when construed >>>>>>>>>>>>>>>>>>>>>>>>>>>>> correctly
falls into one of two categories. >>>>>>>>>>>>>>>>>>>>>>>>>>>>> (a) Semantic incoherence >>>>>>>>>>>>>>>>>>>>>>>>>>>>> (b) Unknown truth values. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Nope.
Undecidability can not come from Semantic >>>>>>>>>>>>>>>>>>>>>>>>>>>> Incoherence, as the definition of >>>>>>>>>>>>>>>>>>>>>>>>>>>> Undecidability ia based on there being a >>>>>>>>>>>>>>>>>>>>>>>>>>>> coherent answer, just not one that can be >>>>>>>>>>>>>>>>>>>>>>>>>>>> determined by a computation. >>>>>>>>>>>>>>>>>>>>>>>>>>>
the undecidable problem turing described (as >>>>>>>>>>>>>>>>>>>>>>>>>>> well as the basic halting problem) involves a >>>>>>>>>>>>>>>>>>>>>>>>>>> situations that have _no_ coherent answer, >>>>>>>>>>>>>>>>>>>>>>>>>>> not just one that can be known by not >>>>>>>>>>>>>>>>>>>>>>>>>>> computed ...
Turing proved that there are universal Turing >>>>>>>>>>>>>>>>>>>>>>>>>> machines. An universalTuring machine halts >>>>>>>>>>>>>>>>>>>>>>>>>> with some inputs and doesn't halt with any other >>>>>>>>>>>>>>>>>>>>>>>>>> input. Every Turing machine that can be given >>>>>>>>>>>>>>>>>>>>>>>>>> the same input as an
universal Turing machine either fails to >>>>>>>>>>>>>>>>>>>>>>>>>> accept some input with which >>>>>>>>>>>>>>>>>>>>>>>>>> that universal Turing machine halts or fails >>>>>>>>>>>>>>>>>>>>>>>>>> to reject some input with
which that universal Turing macnie does not halt. >>>>>>>>>>>>>>>>>>>>>>>>>
There is a way to find out if you can read. >>>>>>>>>>>>>>>>>>>>>>>
I can't explain the art of reading Common Language. >>>>>>>>>>>>>>>>>>>>>>
inyes, but then he argues it's impossible to >>>>>>>>>>>>>>>>>>>>>>> compute the diagonal because of the paradox that >>>>>>>>>>>>>>>>>>>>>>> ensues when naively running the classifier on the >>>>>>>>>>>>>>>>>>>>>>> diagonal itselfturing hypothesized a diagonal computation that >>>>>>>>>>>>>>>>>>>>>>>>> tries to put the Nth digit from the Nth circle- >>>>>>>>>>>>>>>>>>>>>>>>> free machine as the Nth digit on this diagonal >>>>>>>>>>>>>>>>>>>>>>>>> across all circle- free machine... >>>>>>>>>>>>>>>>>>>>>>>>That is possible because there nither the >>>>>>>>>>>>>>>>>>>>>>>> machines nor digit positions
are more numerous than natural numbers. >>>>>>>>>>>>>>>>>>>>>>>
It is impossible to have a Turing machine that >>>>>>>>>>>>>>>>>>>>>> computes a number that
no Turing machine can compute. But you can compute >>>>>>>>>>>>>>>>>>>>>> it if you can use
all (infinitely many) Turing machines. >>>>>>>>>>>>>>>>>>>>>
Hard to test as I han't infinite many Turing >>>>>>>>>>>>>>>>>>>> machines. But it is
u don't need to test it, you can't define a total >>>>>>>>>>>>>>>>>>> dovetailing machine to compute turing's diagonal, >>>>>>>>>>>>>>>>>> You should not say anything about the diagonal before >>>>>>>>>>>>>>>>>> you have defined
the H machine defined on p247 from his paper /on >>>>>>>>>>>>>>>>> computable numbers/
the machine supposes to compute the "turing's diagonal" >>>>>>>>>>>>>>> across circle- free sequences, otherwise labeled as β' in >>>>>>>>>>>>>>> the paper, defined at the bottom of p246
Anything that any machine can possibly compute can >>>>>>>>>>>>>> be computed by applying a finite set of finite string >>>>>>>>>>>>>> transformation rules to a finite set of finite strings. >>>>>>>>>>>>>>
Everything else is simply out-of-scope for computation >>>>>>>>>>>>>> like making a silk purse from a sow's ear.
That "everything else" includes many thigns that would be >>>>>>>>>>>>> useful to
know. In particular, whether some useful function can be >>>>>>>>>>>>> computed is
in that "everything else".
Like the truth value of: "This sentence is not true"
that has no truth value.
I don't think knowing the truth value of that would be
useful. At least
not for any important purpose.
Knowing that all undecidability is merely semantic
incoherence enables:
"true on the basis of meaning expressed in language"
to be reliably computable for the entire body of knowledge. >>>>>>>>>
incoherence, and can't know because we already know that there is >>>>>>>>> undecidability that is not semantic incoherence. FOr example the >>>>>>>>> axiom system
∀x (1⋅x = x)
1.5 != 5 ∴ you are wrong and I am couinting the rest as gibberish >>>>>>>
symbols
are often used instead, like ∘ or ∙, or operands are just put >>>>>>> side by
side with no operator between.
If commonly used mathematics is gibberish to you then we many safely >>>>>>> conclude that you have nothing useful to offer to the groups you >>>>>>> posted to.
∀x (x⋅1 = x)
∀x∀y∀z (x⋅(y⋅z) = (x⋅y)⋅z)
∀x∃y (x⋅y = 1)
∀x∃y (y⋅x = 1)
is useful for many purposes. But there are sentences like
∀x∃y (x⋅y = y⋅x)
that are undecidable in that system. But there is notiong
semantically
incoherent in that example or similar ones.
The truth about climate change and election fraud could
be computed.
Not without real world information.
Yes, so what?
So the biggest problem is not how to compute but how to get and >>>>>>> verify
the relevant real world infomration.
A set of "atomic facts" does exist. We only nee to write> them all >>>>>> down.
THat is a lot of work that can never be completed.
It can be completed with sufficient automation.
No, it can't. It is not completed before it contains all material that
will be published.
The place to start would be published textbooks.
How long does it take to read all texbooks published in one year?
IDK, an LLM might do this in five minutes.
No, because in that time it cannot access all of the material. And
it takes time to extract atomic facts and to store them into a big
database.
LLM would have to be taught how to extract facts.
If it takes then ten times longer to extract all
the facts of a body of text they will still be done
with every textbook ever written after one year.
Then peer reviewed papers.
Now long does it take to read all reviewed papers published in one
year?
Then published newspaper articles.
How long does it take to read all newspaper articles publised in one >>>>> year?
An LLM might read everything ever published in one year.
During that year more is publised.
I may be one or two days out-of-sync far far better
than any human.
And what to do with the "atomic facts" that conflict each other?
All knowledge that can be expressed in language would
include the exact (x,y,z) coordinates of every atom of your
body relative to the exact center of the Earth every millisecond. >>>>>>>> Because this degree of detail is not physically implementable
to implement my system we exclude most specific details. It
is a system of general knowledge of about 200 petabytes.
Of course you may postulate that
the climate is immutable or that there was massimbe undetected >>>>>>>>> fraud
in the last or some earlier election but that is not what the word >>>>>>>>> "knowledge" means.
The key elements of election fraud are two things:
(a) There was no actual evidence of election fraud
that could have possibly changed the results.
The key element of elction fraud is to find a vulnerability in the >>>>>>> election procedure.
There has only been 1620 total documented cases in the USA
in the last 30 years. Every investigation into fraud by
audits found a few more votes against Trump than prior to
the audit. Each of the 60 election fraud cases Trump lost.
He lost because his lawyers could not tell the wild stories
that he was telling the public without getting themselves
convicted of perjury.
These these fact were unconvincing seems to prove that
his supporters are in a cult.
But not that there were no fraud performed skillfully enough to avoid >>>>> detection. What was found was only small unintentional errors that
nobody tried to hide.
Likewise there is no perfect logical proof that
can possibly exist that five minutes ago ever existed.
It may also be the case that all of reality is entirely
fictional.
That is right. But that is not relevant to our understanding of the
assumed processes that given the world the form it has now or that
we can expect it to have in the near future. Perhaps the world is
just God's thought but if it is it seems to be a coherent thought.
Correct, to we just encode all of this in language.
Within the possibly false assumption that reality is
not fictional and five minutes ago did exist then
Trump is merely copying Hitler's big lie about election
fraud is as certain as certain can possibly be.
When did Hitler claim anything about an election fraud?
Chapter 6 of Mein Kampf
"The receptive powers of the masses are very
restricted, and their understanding is feeble.
On the other hand, they quickly forget. Such
being the case, all effective propaganda must
be confined to a few bare essentials and those
must be expressed as far as possible in stereotyped
formulas. These slogans should be persistently
repeated until the very last individual has come
to grasp the idea that has been put forward."
Provides the details of Hitler's propaganda system.
https://en.wikipedia.org/wiki/Big_lie#2020_stolen_election_claims
Looks like a confessison that you lied.
On 5/13/2026 10:26 PM, dart200 wrote:
On 5/13/26 5:07 PM, André G. Isaak wrote:
On 2026-05-13 17:40, olcott wrote:
On 5/13/2026 4:37 PM, André G. Isaak wrote:
On 2026-05-13 09:28, olcott wrote:
*The entire body of knowledge that can be expressed in language*
... is an ill-defined set which only exists in your mind. There's
over 8 billion people on earth, all of whom believe different,
often contradictory things. And, with the exception of theorems of
formal systems, there is nothing that we know with absolute
certainty. Only varying degrees of certainty, but for every given
fact you won't get a universal consensus on exactly how certain we
are of that fact.
So maybe cats were never animals and this "belief"
has always been mass psychosis? In actual reality
cats were always a kind of snake?
I propose that a finite set of "atomic facts" of general
knowledge inherently exists and that no 100% concrete
counter-example can ever be found.
Until you can produce this finite set of atomic facts you're all just
bluster. Here's a few statements. Which would you consider atomic facts: >>>
– The Universe is 14 billion years old.
– The Ungulates and the Carnivores form a clade.
– Jesus Christ died for our sins.
– Nearly 70% of the mass-energy of the universe consists of dark energy. >>>
– Anthropogenic climate change is currently occurring.
– The Earth is 6000 years old.
– Argentinosaurus is the largest land animal to ever have lived.
– Measles vaccine causes autism.
– There exists an "island of stability" where extraheavy elements
with approximately 184 neutrons will have a considerably longer half-
life than that of the heaviest elements currently know.
– Turing showed that halting cannot be computed.
actually his proof was in regards to circle-free vs circular machines,
not specifically halting ones. please do read p246 and p247 of his
paper /on computable numbers/ more carefully.
As with Gödel, I don't give a rat's ass about the convoluted
mess of his paper. Unless we boil these things down to their
barest possible essence they greatly exceed the capacity of
any human mind.
and what he showed was that it cannot be computed by a single turing
machine.
Only because he used a fucking dishonest trick that
proof theoretic semantics would toss out on its ass.
no one has demonstrated any _actual_ turing machine with a halting
behavior that provably cannot be computed by _any_ machine, as such a
machine would have under-specified, non-determinable semantics that
then could not actually exist as a real machine, that any actual
decider would actually have to decide upon...
the theory of computing has predicated itself on a limitation that
fundamentally resolves to a catch-22 type paradox that has existed
since turing wrote his first paper /on computable numbers/
Its essentially the same damn thing as the Liar Paradox
that mindless robot humans still have not agreed on. The
brains of most humans are hard-wired to short-circuit. To
woefully fallible humans textbooks are the word of God.
Proof theoretic semantics sees right through this crap.
On 5/13/26 8:46 PM, olcott wrote:
On 5/13/2026 10:26 PM, dart200 wrote:
On 5/13/26 5:07 PM, André G. Isaak wrote:
On 2026-05-13 17:40, olcott wrote:
On 5/13/2026 4:37 PM, André G. Isaak wrote:
On 2026-05-13 09:28, olcott wrote:
*The entire body of knowledge that can be expressed in language*
... is an ill-defined set which only exists in your mind. There's >>>>>> over 8 billion people on earth, all of whom believe different,
often contradictory things. And, with the exception of theorems of >>>>>> formal systems, there is nothing that we know with absolute
certainty. Only varying degrees of certainty, but for every given >>>>>> fact you won't get a universal consensus on exactly how certain we >>>>>> are of that fact.
So maybe cats were never animals and this "belief"
has always been mass psychosis? In actual reality
cats were always a kind of snake?
I propose that a finite set of "atomic facts" of general
knowledge inherently exists and that no 100% concrete
counter-example can ever be found.
Until you can produce this finite set of atomic facts you're all
just bluster. Here's a few statements. Which would you consider
atomic facts:
– The Universe is 14 billion years old.
– The Ungulates and the Carnivores form a clade.
– Jesus Christ died for our sins.
– Nearly 70% of the mass-energy of the universe consists of dark
energy.
– Anthropogenic climate change is currently occurring.
– The Earth is 6000 years old.
– Argentinosaurus is the largest land animal to ever have lived.
– Measles vaccine causes autism.
– There exists an "island of stability" where extraheavy elements
with approximately 184 neutrons will have a considerably longer
half- life than that of the heaviest elements currently know.
– Turing showed that halting cannot be computed.
actually his proof was in regards to circle-free vs circular
machines, not specifically halting ones. please do read p246 and p247
of his paper /on computable numbers/ more carefully.
As with Gödel, I don't give a rat's ass about the convoluted
mess of his paper. Unless we boil these things down to their
barest possible essence they greatly exceed the capacity of
any human mind.
and what he showed was that it cannot be computed by a single turing
machine.
Only because he used a fucking dishonest trick that
proof theoretic semantics would toss out on its ass.
no one has demonstrated any _actual_ turing machine with a halting
behavior that provably cannot be computed by _any_ machine, as such a
machine would have under-specified, non-determinable semantics that
then could not actually exist as a real machine, that any actual
decider would actually have to decide upon...
the theory of computing has predicated itself on a limitation that
fundamentally resolves to a catch-22 type paradox that has existed
since turing wrote his first paper /on computable numbers/
Its essentially the same damn thing as the Liar Paradox
that mindless robot humans still have not agreed on. The
brains of most humans are hard-wired to short-circuit. To
woefully fallible humans textbooks are the word of God.
Proof theoretic semantics sees right through this crap.
it just isn't polcott...
the liar's paradox is a sentence that is false, in regards to nothing.
what is it false about? who the fuck knows 🤷
godel's sentence is a truth, about nothing, that has no proof. what is
that truth?? again, who the fuck knows 🤷🤷
turing's diagonal, however, is computing an explicitly defined object.
it is trying to take the n-th digit from the n-th circle-free machine,
and constructing it into the n-th digit of a "diagonal" ... and
stumbling on the fact it never defined a digit for itself on that diagonal
On 5/15/2026 12:44 AM, Mikko wrote:
On 14/05/2026 18:30, olcott wrote:
On 5/14/2026 2:54 AM, Mikko wrote:
On 13/05/2026 18:28, olcott wrote:
On 5/13/2026 9:38 AM, André G. Isaak wrote:
On 2026-05-13 08:20, olcott wrote:
On 5/13/2026 6:56 AM, André G. Isaak wrote:
On 2026-05-13 05:18, olcott wrote:
On 5/12/2026 10:02 PM, André G. Isaak wrote:
On 2026-05-12 07:32, olcott wrote:
On 5/12/2026 2:05 AM, Mikko wrote:
On 11/05/2026 14:44, olcott wrote:
On 5/11/2026 2:24 AM, Mikko wrote:
On 10/05/2026 22:06, olcott wrote:
We don't have the knowledge that all undecidability is >>>>>>>>>>>>>> merely semantic
incoherence, and can't know because we already know that >>>>>>>>>>>>>> there is
undecidability that is not semantic incoherence. FOr >>>>>>>>>>>>>> example the
axiom system
∀x (1⋅x = x)
1.5 != 5 ∴ you are wrong and I am couinting the rest as >>>>>>>>>>>>> gibberish
Middle dot is a commonly used mathematical operator. In this >>>>>>>>>>>> context
where the purpose of the operation is not specified some >>>>>>>>>>>> other symbols
are often used instead, like ∘ or ∙, or operands are just >>>>>>>>>>>> put side by
side with no operator between.
If commonly used mathematics is gibberish to you then we >>>>>>>>>>>> many safely
conclude that you have nothing useful to offer to the groups >>>>>>>>>>>> you
posted to.
∀x (x⋅1 = x)
∀x∀y∀z (x⋅(y⋅z) = (x⋅y)⋅z)
∀x∃y (x⋅y = 1)
∀x∃y (y⋅x = 1)
is useful for many purposes. But there are sentences like >>>>>>>>>>>>>>
∀x∃y (x⋅y = y⋅x)
that are undecidable in that system. But there is notiong >>>>>>>>>>>>>> semantically
incoherent in that example or similar ones.
I'm curious to know how you would actually address Mikko's >>>>>>>>>> point here. He's pointed out the rather obvious error in your >>>>>>>>>> reading comprehension, but you've simply glossed over the >>>>>>>>>> example.
In what sense is ∀x∃y (x⋅y = y⋅x) "semantically incoherent"? >>>>>>>>>>
André
Decimal point versus multiplication operator?
If it is a decimal point then it is incoherent.
Obviously its nor a decimal point. He gave you the actual axioms >>>>>>>> which define the dot operator, so there should be no dispute as >>>>>>>> to its meaning.
The point is that ∀x∃y (x⋅y = y⋅x) is not decidable from those
axioms,yet it is clearly semantically coherent.
André
∀x∃y (x⋅y = y⋅x) is proven true by ∀x∀y (x⋅y = y⋅x) >>>>>>> which is proven true by the commutative property of multiplication. >>>>>>>
https://people.hsc.edu/faculty-staff/blins/classes/fall18/
math105/ Examples/AlgebraAxioms.pdf
But then you're introducing a new axiom which isn't part of the
set of axioms which he introduced.
My thesis:
The entire body of knowledge that can be expressed
in language can be encoded as relations between finite strings.
Therefore, you're not dealing with the same theory.
*The entire body of knowledge that can be expressed in language*
Is the scope. That some knucklehead can fail to bother to define
that "cats are animals" so that his knucklehead formal system
does not know this IS OFF-TOPIC.
The entire body of knowledge includes that i² = -1, j² = -1, k² = -1, >>>> and ijk = -1. From these we can infer that ij = k and ji = -k and
that ij ≠ ji, at least when we are talking about Hamilton's
quaternions.
i¹ = i
i² = -1
i³ = -i
The entire body of general knowledge expressed in
language includes the "atomic facts" about imaginary
numbers in a finite list and the semantic relations
between finite strings in a finite list such that
any combination of the above can be derived, no
longer a finite list.
Imaginary numbers themselves may be an incoherent notion.
In this case they would not be included in the body of
knowledge.
So a part of the body of knowledge is that multiplication is not
commutative except in restricted domains, so your above claim to
the contrary is not true.
It would be defined separately for each domain.
On 5/15/2026 12:48 AM, Mikko wrote:
On 14/05/2026 17:40, olcott wrote:
On 5/14/2026 3:18 AM, Mikko wrote:
On 13/05/2026 14:32, olcott wrote:
On 5/13/2026 4:14 AM, Mikko wrote:
On 12/05/2026 16:32, olcott wrote:
On 5/12/2026 2:05 AM, Mikko wrote:
On 11/05/2026 14:44, olcott wrote:
On 5/11/2026 2:24 AM, Mikko wrote:Middle dot is a commonly used mathematical operator. In this
On 10/05/2026 22:06, olcott wrote:
On 5/10/2026 2:10 AM, Mikko wrote:We don't have the knowledge that all undecidability is merely >>>>>>>>>> semantic
On 09/05/2026 15:13, olcott wrote:
On 5/9/2026 3:30 AM, Mikko wrote:
On 08/05/2026 19:58, olcott wrote:
On 5/8/2026 11:06 AM, dart200 wrote:
On 5/8/26 12:19 AM, Mikko wrote:
On 07/05/2026 12:00, dart200 wrote:
On 5/7/26 12:18 AM, Mikko wrote:A machine is not a "diagonal".
On 06/05/2026 22:40, dart200 wrote:
On 5/6/26 12:55 AM, Mikko wrote:it. Any use of the word before the definition is >>>>>>>>>>>>>>>>>>> nonsense,.
On 05/05/2026 12:28, dart200 wrote: >>>>>>>>>>>>>>>>>>>>>> On 5/5/26 1:25 AM, Mikko wrote:
On 04/05/2026 10:53, dart200 wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 5/3/26 11:15 PM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 03/05/2026 12:09, dart200 wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 5/3/26 12:53 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 02/05/2026 23:39, dart200 wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 4/19/26 10:58 AM, Richard Damon wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 4/19/26 1:21 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 4/19/2026 3:59 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 18/04/2026 15:58, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>no you can't.
I can't explain the art of reading Common Language. >>>>>>>>>>>>>>>>>>>>>>>i can't read if u can't explain >>>>>>>>>>>>>>>>>>>>>>>richard richard richard, that is in-correct. >>>>>>>>>>>>>>>>>>>>>>>>>>>>Unknown truths are not elements of the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> body ofNo, but that measn that for some >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> sentences X True(X) is unknown and there >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is no method to find out. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
knowledge is a semantic tautology. Did >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> you think
that things that are unknown are known? >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
I don't know about philosophers but >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> mathematicians and logicians don't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> find it interesting if all you can say >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that all knowledge is knowable >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> and everything else is not. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Ross Finlayson, seemed to endlessly hedge >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> on whether
or not the truth value of the Goldbach >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> conjecture was
known. He seemed to think that there are >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> alternative
analytical frameworks that make the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> question of whether >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> or not its truth value is known an >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> ambiguous question. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
I needed to refer to unknown truth values >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> specifically
because all "undecidability" when >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> construed correctly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> falls into one of two categories. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> (a) Semantic incoherence >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> (b) Unknown truth values. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Nope.
Undecidability can not come from Semantic >>>>>>>>>>>>>>>>>>>>>>>>>>>>> Incoherence, as the definition of >>>>>>>>>>>>>>>>>>>>>>>>>>>>> Undecidability ia based on there being a >>>>>>>>>>>>>>>>>>>>>>>>>>>>> coherent answer, just not one that can be >>>>>>>>>>>>>>>>>>>>>>>>>>>>> determined by a computation. >>>>>>>>>>>>>>>>>>>>>>>>>>>>
the undecidable problem turing described (as >>>>>>>>>>>>>>>>>>>>>>>>>>>> well as the basic halting problem) involves >>>>>>>>>>>>>>>>>>>>>>>>>>>> a situations that have _no_ coherent answer, >>>>>>>>>>>>>>>>>>>>>>>>>>>> not just one that can be known by not >>>>>>>>>>>>>>>>>>>>>>>>>>>> computed ...
Turing proved that there are universal Turing >>>>>>>>>>>>>>>>>>>>>>>>>>> machines. An universalTuring machine halts >>>>>>>>>>>>>>>>>>>>>>>>>>> with some inputs and doesn't halt with any other >>>>>>>>>>>>>>>>>>>>>>>>>>> input. Every Turing machine that can be given >>>>>>>>>>>>>>>>>>>>>>>>>>> the same input as an
universal Turing machine either fails to >>>>>>>>>>>>>>>>>>>>>>>>>>> accept some input with which >>>>>>>>>>>>>>>>>>>>>>>>>>> that universal Turing machine halts or fails >>>>>>>>>>>>>>>>>>>>>>>>>>> to reject some input with >>>>>>>>>>>>>>>>>>>>>>>>>>> which that universal Turing macnie does not >>>>>>>>>>>>>>>>>>>>>>>>>>> halt.
dunno what ur saying here.
There is a way to find out if you can read. >>>>>>>>>>>>>>>>>>>>>>>>
inyes, but then he argues it's impossible to >>>>>>>>>>>>>>>>>>>>>>>> compute the diagonal because of the paradox that >>>>>>>>>>>>>>>>>>>>>>>> ensues when naively running the classifier on >>>>>>>>>>>>>>>>>>>>>>>> the diagonal itselfturing hypothesized a diagonal computation >>>>>>>>>>>>>>>>>>>>>>>>>> that tries to put the Nth digit from the Nth >>>>>>>>>>>>>>>>>>>>>>>>>> circle- free machine as the Nth digit on this >>>>>>>>>>>>>>>>>>>>>>>>>> diagonal across all circle- free machine... >>>>>>>>>>>>>>>>>>>>>>>>>That is possible because there nither the >>>>>>>>>>>>>>>>>>>>>>>>> machines nor digit positions >>>>>>>>>>>>>>>>>>>>>>>>> are more numerous than natural numbers. >>>>>>>>>>>>>>>>>>>>>>>>
It is impossible to have a Turing machine that >>>>>>>>>>>>>>>>>>>>>>> computes a number that
no Turing machine can compute. But you can >>>>>>>>>>>>>>>>>>>>>>> compute it if you can use
all (infinitely many) Turing machines. >>>>>>>>>>>>>>>>>>>>>>
Hard to test as I han't infinite many Turing >>>>>>>>>>>>>>>>>>>>> machines. But it is
u don't need to test it, you can't define a total >>>>>>>>>>>>>>>>>>>> dovetailing machine to compute turing's diagonal, >>>>>>>>>>>>>>>>>>> You should not say anything about the diagonal before >>>>>>>>>>>>>>>>>>> you have defined
the H machine defined on p247 from his paper /on >>>>>>>>>>>>>>>>>> computable numbers/
the machine supposes to compute the "turing's diagonal" >>>>>>>>>>>>>>>> across circle- free sequences, otherwise labeled as β' >>>>>>>>>>>>>>>> in the paper, defined at the bottom of p246
Anything that any machine can possibly compute can >>>>>>>>>>>>>>> be computed by applying a finite set of finite string >>>>>>>>>>>>>>> transformation rules to a finite set of finite strings. >>>>>>>>>>>>>>>
Everything else is simply out-of-scope for computation >>>>>>>>>>>>>>> like making a silk purse from a sow's ear.
That "everything else" includes many thigns that would be >>>>>>>>>>>>>> useful to
know. In particular, whether some useful function can be >>>>>>>>>>>>>> computed is
in that "everything else".
Like the truth value of: "This sentence is not true" >>>>>>>>>>>>> that has no truth value.
I don't think knowing the truth value of that would be >>>>>>>>>>>> useful. At least
not for any important purpose.
Knowing that all undecidability is merely semantic
incoherence enables:
"true on the basis of meaning expressed in language"
to be reliably computable for the entire body of knowledge. >>>>>>>>>>
incoherence, and can't know because we already know that there is >>>>>>>>>> undecidability that is not semantic incoherence. FOr example the >>>>>>>>>> axiom system
∀x (1⋅x = x)
1.5 != 5 ∴ you are wrong and I am couinting the rest as gibberish >>>>>>>>
context
where the purpose of the operation is not specified some other >>>>>>>> symbols
are often used instead, like ∘ or ∙, or operands are just put >>>>>>>> side by
side with no operator between.
If commonly used mathematics is gibberish to you then we many >>>>>>>> safely
conclude that you have nothing useful to offer to the groups you >>>>>>>> posted to.
∀x (x⋅1 = x)
∀x∀y∀z (x⋅(y⋅z) = (x⋅y)⋅z)
∀x∃y (x⋅y = 1)
∀x∃y (y⋅x = 1)
is useful for many purposes. But there are sentences like
∀x∃y (x⋅y = y⋅x)
that are undecidable in that system. But there is notiong >>>>>>>>>> semantically
incoherent in that example or similar ones.
The truth about climate change and election fraud could
be computed.
Not without real world information.
Yes, so what?
So the biggest problem is not how to compute but how to get and >>>>>>>> verify
the relevant real world infomration.
A set of "atomic facts" does exist. We only nee to write> them
all down.
THat is a lot of work that can never be completed.
It can be completed with sufficient automation.
No, it can't. It is not completed before it contains all material that >>>> will be published.
The place to start would be published textbooks.
How long does it take to read all texbooks published in one year?
IDK, an LLM might do this in five minutes.
No, because in that time it cannot access all of the material. And
it takes time to extract atomic facts and to store them into a big
database.
LLM would have to be taught how to extract facts.
If it takes then ten times longer to extract all
the facts of a body of text they will still be done
with every textbook ever written after one year.
Then peer reviewed papers.
Now long does it take to read all reviewed papers published in one >>>>>> year?
Then published newspaper articles.
How long does it take to read all newspaper articles publised in one >>>>>> year?
An LLM might read everything ever published in one year.
During that year more is publised.
I may be one or two days out-of-sync far far better
than any human.
And what to do with the "atomic facts" that conflict each other? >>>>>>>>> All knowledge that can be expressed in language would
include the exact (x,y,z) coordinates of every atom of your
body relative to the exact center of the Earth every millisecond. >>>>>>>>> Because this degree of detail is not physically implementable >>>>>>>>> to implement my system we exclude most specific details. It
is a system of general knowledge of about 200 petabytes.
Of course you may postulate that
the climate is immutable or that there was massimbe undetected >>>>>>>>>> fraud
in the last or some earlier election but that is not what the >>>>>>>>>> word
"knowledge" means.
The key elements of election fraud are two things:
(a) There was no actual evidence of election fraud
that could have possibly changed the results.
The key element of elction fraud is to find a vulnerability in the >>>>>>>> election procedure.
There has only been 1620 total documented cases in the USA
in the last 30 years. Every investigation into fraud by
audits found a few more votes against Trump than prior to
the audit. Each of the 60 election fraud cases Trump lost.
He lost because his lawyers could not tell the wild stories
that he was telling the public without getting themselves
convicted of perjury.
These these fact were unconvincing seems to prove that
his supporters are in a cult.
But not that there were no fraud performed skillfully enough to avoid >>>>>> detection. What was found was only small unintentional errors that >>>>>> nobody tried to hide.
Likewise there is no perfect logical proof that
can possibly exist that five minutes ago ever existed.
It may also be the case that all of reality is entirely
fictional.
That is right. But that is not relevant to our understanding of the
assumed processes that given the world the form it has now or that
we can expect it to have in the near future. Perhaps the world is
just God's thought but if it is it seems to be a coherent thought.
Correct, to we just encode all of this in language.
Within the possibly false assumption that reality is
not fictional and five minutes ago did exist then
Trump is merely copying Hitler's big lie about election
fraud is as certain as certain can possibly be.
When did Hitler claim anything about an election fraud?
Chapter 6 of Mein Kampf
"The receptive powers of the masses are very
restricted, and their understanding is feeble.
On the other hand, they quickly forget. Such
being the case, all effective propaganda must
be confined to a few bare essentials and those
must be expressed as far as possible in stereotyped
formulas. These slogans should be persistently
repeated until the very last individual has come
to grasp the idea that has been put forward."
Provides the details of Hitler's propaganda system.
https://en.wikipedia.org/wiki/Big_lie#2020_stolen_election_claims
Looks like a confessison that you lied.
I did not say it as clearly as I could have said it.
Trump did exactly copy Hitler's "big lie" propaganda
system from Hitler's Chapter Six "War Propaganda"
system of Hitler's Mein Kampf in Trump's lies about
election fraud.
On 5/13/26 8:46 PM, olcott wrote:
On 5/13/2026 10:26 PM, dart200 wrote:
On 5/13/26 5:07 PM, André G. Isaak wrote:
On 2026-05-13 17:40, olcott wrote:
On 5/13/2026 4:37 PM, André G. Isaak wrote:
On 2026-05-13 09:28, olcott wrote:
*The entire body of knowledge that can be expressed in language*
... is an ill-defined set which only exists in your mind. There's >>>>>> over 8 billion people on earth, all of whom believe different,
often contradictory things. And, with the exception of theorems of >>>>>> formal systems, there is nothing that we know with absolute
certainty. Only varying degrees of certainty, but for every given >>>>>> fact you won't get a universal consensus on exactly how certain we >>>>>> are of that fact.
So maybe cats were never animals and this "belief"
has always been mass psychosis? In actual reality
cats were always a kind of snake?
I propose that a finite set of "atomic facts" of general
knowledge inherently exists and that no 100% concrete
counter-example can ever be found.
Until you can produce this finite set of atomic facts you're all
just bluster. Here's a few statements. Which would you consider
atomic facts:
– The Universe is 14 billion years old.
– The Ungulates and the Carnivores form a clade.
– Jesus Christ died for our sins.
– Nearly 70% of the mass-energy of the universe consists of dark
energy.
– Anthropogenic climate change is currently occurring.
– The Earth is 6000 years old.
– Argentinosaurus is the largest land animal to ever have lived.
– Measles vaccine causes autism.
– There exists an "island of stability" where extraheavy elements
with approximately 184 neutrons will have a considerably longer
half- life than that of the heaviest elements currently know.
– Turing showed that halting cannot be computed.
actually his proof was in regards to circle-free vs circular
machines, not specifically halting ones. please do read p246 and p247
of his paper /on computable numbers/ more carefully.
As with Gödel, I don't give a rat's ass about the convoluted
mess of his paper. Unless we boil these things down to their
barest possible essence they greatly exceed the capacity of
any human mind.
and what he showed was that it cannot be computed by a single turing
machine.
Only because he used a fucking dishonest trick that
proof theoretic semantics would toss out on its ass.
no one has demonstrated any _actual_ turing machine with a halting
behavior that provably cannot be computed by _any_ machine, as such a
machine would have under-specified, non-determinable semantics that
then could not actually exist as a real machine, that any actual
decider would actually have to decide upon...
the theory of computing has predicated itself on a limitation that
fundamentally resolves to a catch-22 type paradox that has existed
since turing wrote his first paper /on computable numbers/
Its essentially the same damn thing as the Liar Paradox
that mindless robot humans still have not agreed on. The
brains of most humans are hard-wired to short-circuit. To
woefully fallible humans textbooks are the word of God.
Proof theoretic semantics sees right through this crap.
it just isn't polcott...
the liar's paradox is a sentence that is false, in regards to nothing.
what is it false about? who the fuck knows 🤷
godel's sentence is a truth, about nothing, that has no proof. what is
that truth?? again, who the fuck knows 🤷🤷
turing's diagonal, however, is computing an explicitly defined object.
it is trying to take the n-th digit from the n-th circle-free machine,
and constructing it into the n-th digit of a "diagonal" ... and
stumbling on the fact it never defined a digit for itself on that diagonal
turing's diagonal isn't a "dishonest" trick. he legitimately got stumped
by trying to compute an explicitly defined object, and figured it
supported godel's result
On 15/05/2026 17:24, olcott wrote:
On 5/15/2026 12:44 AM, Mikko wrote:
On 14/05/2026 18:30, olcott wrote:
On 5/14/2026 2:54 AM, Mikko wrote:
On 13/05/2026 18:28, olcott wrote:
On 5/13/2026 9:38 AM, André G. Isaak wrote:
On 2026-05-13 08:20, olcott wrote:
On 5/13/2026 6:56 AM, André G. Isaak wrote:
On 2026-05-13 05:18, olcott wrote:
On 5/12/2026 10:02 PM, André G. Isaak wrote:
On 2026-05-12 07:32, olcott wrote:
On 5/12/2026 2:05 AM, Mikko wrote:
On 11/05/2026 14:44, olcott wrote:
On 5/11/2026 2:24 AM, Mikko wrote:
On 10/05/2026 22:06, olcott wrote:
We don't have the knowledge that all undecidability is >>>>>>>>>>>>>>> merely semantic
incoherence, and can't know because we already know that >>>>>>>>>>>>>>> there is
undecidability that is not semantic incoherence. FOr >>>>>>>>>>>>>>> example the
axiom system
∀x (1⋅x = x)
1.5 != 5 ∴ you are wrong and I am couinting the rest as >>>>>>>>>>>>>> gibberish
Middle dot is a commonly used mathematical operator. In >>>>>>>>>>>>> this context
where the purpose of the operation is not specified some >>>>>>>>>>>>> other symbols
are often used instead, like ∘ or ∙, or operands are just >>>>>>>>>>>>> put side by
side with no operator between.
If commonly used mathematics is gibberish to you then we >>>>>>>>>>>>> many safely
conclude that you have nothing useful to offer to the >>>>>>>>>>>>> groups you
posted to.
∀x (x⋅1 = x)
∀x∀y∀z (x⋅(y⋅z) = (x⋅y)⋅z)
∀x∃y (x⋅y = 1)
∀x∃y (y⋅x = 1)
is useful for many purposes. But there are sentences like >>>>>>>>>>>>>>>
∀x∃y (x⋅y = y⋅x)
that are undecidable in that system. But there is notiong >>>>>>>>>>>>>>> semantically
incoherent in that example or similar ones.
I'm curious to know how you would actually address Mikko's >>>>>>>>>>> point here. He's pointed out the rather obvious error in your >>>>>>>>>>> reading comprehension, but you've simply glossed over the >>>>>>>>>>> example.
In what sense is ∀x∃y (x⋅y = y⋅x) "semantically incoherent"?
André
Decimal point versus multiplication operator?
If it is a decimal point then it is incoherent.
Obviously its nor a decimal point. He gave you the actual
axioms which define the dot operator, so there should be no >>>>>>>>> dispute as to its meaning.
The point is that ∀x∃y (x⋅y = y⋅x) is not decidable from those
axioms,yet it is clearly semantically coherent.
André
∀x∃y (x⋅y = y⋅x) is proven true by ∀x∀y (x⋅y = y⋅x) >>>>>>>> which is proven true by the commutative property of multiplication. >>>>>>>>
https://people.hsc.edu/faculty-staff/blins/classes/fall18/
math105/ Examples/AlgebraAxioms.pdf
But then you're introducing a new axiom which isn't part of the >>>>>>> set of axioms which he introduced.
My thesis:
The entire body of knowledge that can be expressed
in language can be encoded as relations between finite strings.
Therefore, you're not dealing with the same theory.
*The entire body of knowledge that can be expressed in language*
Is the scope. That some knucklehead can fail to bother to define
that "cats are animals" so that his knucklehead formal system
does not know this IS OFF-TOPIC.
The entire body of knowledge includes that i² = -1, j² = -1, k² = -1, >>>>> and ijk = -1. From these we can infer that ij = k and ji = -k and
that ij ≠ ji, at least when we are talking about Hamilton's
quaternions.
i¹ = i
i² = -1
i³ = -i
The entire body of general knowledge expressed in
language includes the "atomic facts" about imaginary
numbers in a finite list and the semantic relations
between finite strings in a finite list such that
any combination of the above can be derived, no
longer a finite list.
Imaginary numbers themselves may be an incoherent notion.
In this case they would not be included in the body of
knowledge.
So a part of the body of knowledge is that multiplication is not
commutative except in restricted domains, so your above claim to
the contrary is not true.
It would be defined separately for each domain.
You claimed that all undecidability
On 15/05/2026 17:27, olcott wrote:
On 5/15/2026 12:48 AM, Mikko wrote:
On 14/05/2026 17:40, olcott wrote:
On 5/14/2026 3:18 AM, Mikko wrote:
On 13/05/2026 14:32, olcott wrote:
On 5/13/2026 4:14 AM, Mikko wrote:
On 12/05/2026 16:32, olcott wrote:
On 5/12/2026 2:05 AM, Mikko wrote:
On 11/05/2026 14:44, olcott wrote:
On 5/11/2026 2:24 AM, Mikko wrote:Middle dot is a commonly used mathematical operator. In this >>>>>>>>> context
On 10/05/2026 22:06, olcott wrote:
On 5/10/2026 2:10 AM, Mikko wrote:We don't have the knowledge that all undecidability is merely >>>>>>>>>>> semantic
On 09/05/2026 15:13, olcott wrote:
On 5/9/2026 3:30 AM, Mikko wrote:
On 08/05/2026 19:58, olcott wrote:
On 5/8/2026 11:06 AM, dart200 wrote:
On 5/8/26 12:19 AM, Mikko wrote:
On 07/05/2026 12:00, dart200 wrote:
On 5/7/26 12:18 AM, Mikko wrote:A machine is not a "diagonal".
On 06/05/2026 22:40, dart200 wrote:
On 5/6/26 12:55 AM, Mikko wrote:it. Any use of the word before the definition is >>>>>>>>>>>>>>>>>>>> nonsense,.
On 05/05/2026 12:28, dart200 wrote: >>>>>>>>>>>>>>>>>>>>>>> On 5/5/26 1:25 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 04/05/2026 10:53, dart200 wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 5/3/26 11:15 PM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 03/05/2026 12:09, dart200 wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 5/3/26 12:53 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 02/05/2026 23:39, dart200 wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 4/19/26 10:58 AM, Richard Damon wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 4/19/26 1:21 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 4/19/2026 3:59 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 18/04/2026 15:58, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
no you can't.I can't explain the art of reading Common Language. >>>>>>>>>>>>>>>>>>>>>>>>i can't read if u can't explain >>>>>>>>>>>>>>>>>>>>>>>>There is a way to find out if you can read. >>>>>>>>>>>>>>>>>>>>>>>>>Turing proved that there are universal >>>>>>>>>>>>>>>>>>>>>>>>>>>> Turing machines. An universalTuring machine >>>>>>>>>>>>>>>>>>>>>>>>>>>> halts with some inputs and doesn't halt with >>>>>>>>>>>>>>>>>>>>>>>>>>>> any otherrichard richard richard, that is in-correct. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>Unknown truths are not elements of the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> body ofNo, but that measn that for some >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> sentences X True(X) is unknown and there >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is no method to find out. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
knowledge is a semantic tautology. Did >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> you think
that things that are unknown are known? >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
I don't know about philosophers but >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> mathematicians and logicians don't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> find it interesting if all you can say >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that all knowledge is knowable >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> and everything else is not. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Ross Finlayson, seemed to endlessly hedge >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> on whether
or not the truth value of the Goldbach >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> conjecture was
known. He seemed to think that there are >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> alternative
analytical frameworks that make the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> question of whether >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> or not its truth value is known an >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> ambiguous question. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
I needed to refer to unknown truth values >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> specifically
because all "undecidability" when >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> construed correctly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> falls into one of two categories. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> (a) Semantic incoherence >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> (b) Unknown truth values. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Nope.
Undecidability can not come from Semantic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Incoherence, as the definition of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Undecidability ia based on there being a >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> coherent answer, just not one that can be >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> determined by a computation. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>
the undecidable problem turing described >>>>>>>>>>>>>>>>>>>>>>>>>>>>> (as well as the basic halting problem) >>>>>>>>>>>>>>>>>>>>>>>>>>>>> involves a situations that have _no_ >>>>>>>>>>>>>>>>>>>>>>>>>>>>> coherent answer, not just one that can be >>>>>>>>>>>>>>>>>>>>>>>>>>>>> known by not computed ... >>>>>>>>>>>>>>>>>>>>>>>>>>>>
input. Every Turing machine that can be >>>>>>>>>>>>>>>>>>>>>>>>>>>> given the same input as an >>>>>>>>>>>>>>>>>>>>>>>>>>>> universal Turing machine either fails to >>>>>>>>>>>>>>>>>>>>>>>>>>>> accept some input with which >>>>>>>>>>>>>>>>>>>>>>>>>>>> that universal Turing machine halts or fails >>>>>>>>>>>>>>>>>>>>>>>>>>>> to reject some input with >>>>>>>>>>>>>>>>>>>>>>>>>>>> which that universal Turing macnie does not >>>>>>>>>>>>>>>>>>>>>>>>>>>> halt.
dunno what ur saying here. >>>>>>>>>>>>>>>>>>>>>>>>>>
inyes, but then he argues it's impossible to >>>>>>>>>>>>>>>>>>>>>>>>> compute the diagonal because of the paradox >>>>>>>>>>>>>>>>>>>>>>>>> that ensues when naively running the classifier >>>>>>>>>>>>>>>>>>>>>>>>> on the diagonal itselfturing hypothesized a diagonal computation >>>>>>>>>>>>>>>>>>>>>>>>>>> that tries to put the Nth digit from the Nth >>>>>>>>>>>>>>>>>>>>>>>>>>> circle- free machine as the Nth digit on this >>>>>>>>>>>>>>>>>>>>>>>>>>> diagonal across all circle- free machine... >>>>>>>>>>>>>>>>>>>>>>>>>>That is possible because there nither the >>>>>>>>>>>>>>>>>>>>>>>>>> machines nor digit positions >>>>>>>>>>>>>>>>>>>>>>>>>> are more numerous than natural numbers. >>>>>>>>>>>>>>>>>>>>>>>>>
It is impossible to have a Turing machine that >>>>>>>>>>>>>>>>>>>>>>>> computes a number that
no Turing machine can compute. But you can >>>>>>>>>>>>>>>>>>>>>>>> compute it if you can use
all (infinitely many) Turing machines. >>>>>>>>>>>>>>>>>>>>>>>
Hard to test as I han't infinite many Turing >>>>>>>>>>>>>>>>>>>>>> machines. But it is
u don't need to test it, you can't define a total >>>>>>>>>>>>>>>>>>>>> dovetailing machine to compute turing's diagonal, >>>>>>>>>>>>>>>>>>>> You should not say anything about the diagonal >>>>>>>>>>>>>>>>>>>> before you have defined
the H machine defined on p247 from his paper /on >>>>>>>>>>>>>>>>>>> computable numbers/
the machine supposes to compute the "turing's diagonal" >>>>>>>>>>>>>>>>> across circle- free sequences, otherwise labeled as β' >>>>>>>>>>>>>>>>> in the paper, defined at the bottom of p246
Anything that any machine can possibly compute can >>>>>>>>>>>>>>>> be computed by applying a finite set of finite string >>>>>>>>>>>>>>>> transformation rules to a finite set of finite strings. >>>>>>>>>>>>>>>>
Everything else is simply out-of-scope for computation >>>>>>>>>>>>>>>> like making a silk purse from a sow's ear.
That "everything else" includes many thigns that would be >>>>>>>>>>>>>>> useful to
know. In particular, whether some useful function can be >>>>>>>>>>>>>>> computed is
in that "everything else".
Like the truth value of: "This sentence is not true" >>>>>>>>>>>>>> that has no truth value.
I don't think knowing the truth value of that would be >>>>>>>>>>>>> useful. At least
not for any important purpose.
Knowing that all undecidability is merely semantic
incoherence enables:
"true on the basis of meaning expressed in language"
to be reliably computable for the entire body of knowledge. >>>>>>>>>>>
incoherence, and can't know because we already know that >>>>>>>>>>> there is
undecidability that is not semantic incoherence. FOr example the >>>>>>>>>>> axiom system
∀x (1⋅x = x)
1.5 != 5 ∴ you are wrong and I am couinting the rest as gibberish >>>>>>>>>
where the purpose of the operation is not specified some other >>>>>>>>> symbols
are often used instead, like ∘ or ∙, or operands are just put >>>>>>>>> side by
side with no operator between.
If commonly used mathematics is gibberish to you then we many >>>>>>>>> safely
conclude that you have nothing useful to offer to the groups you >>>>>>>>> posted to.
∀x (x⋅1 = x)
∀x∀y∀z (x⋅(y⋅z) = (x⋅y)⋅z)
∀x∃y (x⋅y = 1)
∀x∃y (y⋅x = 1)
is useful for many purposes. But there are sentences like >>>>>>>>>>>
∀x∃y (x⋅y = y⋅x)
that are undecidable in that system. But there is notiong >>>>>>>>>>> semantically
incoherent in that example or similar ones.
The truth about climate change and election fraud could >>>>>>>>>>>> be computed.
Not without real world information.
Yes, so what?
So the biggest problem is not how to compute but how to get and >>>>>>>>> verify
the relevant real world infomration.
A set of "atomic facts" does exist. We only nee to write> them >>>>>>>> all down.
THat is a lot of work that can never be completed.
It can be completed with sufficient automation.
No, it can't. It is not completed before it contains all material that >>>>> will be published.
IDK, an LLM might do this in five minutes.The place to start would be published textbooks.
How long does it take to read all texbooks published in one year? >>>>>>
No, because in that time it cannot access all of the material. And
it takes time to extract atomic facts and to store them into a big
database.
LLM would have to be taught how to extract facts.
If it takes then ten times longer to extract all
the facts of a body of text they will still be done
with every textbook ever written after one year.
Then peer reviewed papers.
Now long does it take to read all reviewed papers published in
one year?
Then published newspaper articles.
How long does it take to read all newspaper articles publised in one >>>>>>> year?
An LLM might read everything ever published in one year.
During that year more is publised.
I may be one or two days out-of-sync far far better
than any human.
And what to do with the "atomic facts" that conflict each other? >>>>>>>>>> All knowledge that can be expressed in language would
include the exact (x,y,z) coordinates of every atom of your >>>>>>>>>> body relative to the exact center of the Earth every millisecond. >>>>>>>>>> Because this degree of detail is not physically implementable >>>>>>>>>> to implement my system we exclude most specific details. It >>>>>>>>>> is a system of general knowledge of about 200 petabytes.
Of course you may postulate that
the climate is immutable or that there was massimbe
undetected fraud
in the last or some earlier election but that is not what the >>>>>>>>>>> word
"knowledge" means.
The key elements of election fraud are two things:
(a) There was no actual evidence of election fraud
that could have possibly changed the results.
The key element of elction fraud is to find a vulnerability in the >>>>>>>>> election procedure.
There has only been 1620 total documented cases in the USA
in the last 30 years. Every investigation into fraud by
audits found a few more votes against Trump than prior to
the audit. Each of the 60 election fraud cases Trump lost.
He lost because his lawyers could not tell the wild stories
that he was telling the public without getting themselves
convicted of perjury.
These these fact were unconvincing seems to prove that
his supporters are in a cult.
But not that there were no fraud performed skillfully enough to >>>>>>> avoid
detection. What was found was only small unintentional errors that >>>>>>> nobody tried to hide.
Likewise there is no perfect logical proof that
can possibly exist that five minutes ago ever existed.
It may also be the case that all of reality is entirely
fictional.
That is right. But that is not relevant to our understanding of the
assumed processes that given the world the form it has now or that
we can expect it to have in the near future. Perhaps the world is
just God's thought but if it is it seems to be a coherent thought.
Correct, to we just encode all of this in language.
Within the possibly false assumption that reality is
not fictional and five minutes ago did exist then
Trump is merely copying Hitler's big lie about election
fraud is as certain as certain can possibly be.
When did Hitler claim anything about an election fraud?
Chapter 6 of Mein Kampf
"The receptive powers of the masses are very
restricted, and their understanding is feeble.
On the other hand, they quickly forget. Such
being the case, all effective propaganda must
be confined to a few bare essentials and those
must be expressed as far as possible in stereotyped
formulas. These slogans should be persistently
repeated until the very last individual has come
to grasp the idea that has been put forward."
Provides the details of Hitler's propaganda system.
https://en.wikipedia.org/wiki/Big_lie#2020_stolen_election_claims
Looks like a confessison that you lied.
I did not say it as clearly as I could have said it.
Trump did exactly copy Hitler's "big lie" propaganda
system from Hitler's Chapter Six "War Propaganda"
system of Hitler's Mein Kampf in Trump's lies about
election fraud.
You still don't say it as clearly as you should. Trump obviously applies
same propaganda methods as Hitler did. Why not? They worked for Hitler
and they work for Trump, too. This explains Trups claims about an
election fraud but is irrelevant to the question whether there was an election fraud and how much frauds affected the results.
On 5/13/26 8:46 PM, olcott wrote:
On 5/13/2026 10:26 PM, dart200 wrote:
On 5/13/26 5:07 PM, André G. Isaak wrote:
On 2026-05-13 17:40, olcott wrote:
On 5/13/2026 4:37 PM, André G. Isaak wrote:
On 2026-05-13 09:28, olcott wrote:
*The entire body of knowledge that can be expressed in language*
... is an ill-defined set which only exists in your mind. There's
over 8 billion people on earth, all of whom believe different,
often contradictory things. And, with the exception of theorems of >>>>>> formal systems, there is nothing that we know with absolute
certainty. Only varying degrees of certainty, but for every given
fact you won't get a universal consensus on exactly how certain we >>>>>> are of that fact.
So maybe cats were never animals and this "belief"
has always been mass psychosis? In actual reality
cats were always a kind of snake?
I propose that a finite set of "atomic facts" of general
knowledge inherently exists and that no 100% concrete
counter-example can ever be found.
Until you can produce this finite set of atomic facts you're all
just bluster. Here's a few statements. Which would you consider
atomic facts:
– The Universe is 14 billion years old.
– The Ungulates and the Carnivores form a clade.
– Jesus Christ died for our sins.
– Nearly 70% of the mass-energy of the universe consists of dark
energy.
– Anthropogenic climate change is currently occurring.
– The Earth is 6000 years old.
– Argentinosaurus is the largest land animal to ever have lived.
– Measles vaccine causes autism.
– There exists an "island of stability" where extraheavy elements
with approximately 184 neutrons will have a considerably longer
half- life than that of the heaviest elements currently know.
– Turing showed that halting cannot be computed.
actually his proof was in regards to circle-free vs circular
machines, not specifically halting ones. please do read p246 and p247
of his paper /on computable numbers/ more carefully.
As with Gödel, I don't give a rat's ass about the convoluted
mess of his paper. Unless we boil these things down to their
barest possible essence they greatly exceed the capacity of
any human mind.
and what he showed was that it cannot be computed by a single turing
machine.
Only because he used a fucking dishonest trick that
proof theoretic semantics would toss out on its ass.
no one has demonstrated any _actual_ turing machine with a halting
behavior that provably cannot be computed by _any_ machine, as such a
machine would have under-specified, non-determinable semantics that
then could not actually exist as a real machine, that any actual
decider would actually have to decide upon...
the theory of computing has predicated itself on a limitation that
fundamentally resolves to a catch-22 type paradox that has existed
since turing wrote his first paper /on computable numbers/
Its essentially the same damn thing as the Liar Paradox
that mindless robot humans still have not agreed on. The
brains of most humans are hard-wired to short-circuit. To
woefully fallible humans textbooks are the word of God.
Proof theoretic semantics sees right through this crap.
it just isn't polcott...
the liar's paradox is a sentence that is false, in regards to nothing.
what is it false about? who the fuck knows 🤷
godel's sentence is a truth, about nothing, that has no proof. what is
that truth?? again, who the fuck knows 🤷🤷
turing's diagonal, however, is computing an explicitly defined object.
it is trying to take the n-th digit from the n-th circle-free machine,
and constructing it into the n-th digit of a "diagonal" ... and
stumbling on the fact it never defined a digit for itself on that diagonal
turing's diagonal isn't a "dishonest" trick. he legitimately got stumped
by trying to compute an explicitly defined object, and figured it
supported godel's result
On 05/15/2026 11:45 PM, dart200 wrote:
On 5/13/26 8:46 PM, olcott wrote:
On 5/13/2026 10:26 PM, dart200 wrote:
On 5/13/26 5:07 PM, André G. Isaak wrote:
On 2026-05-13 17:40, olcott wrote:
On 5/13/2026 4:37 PM, André G. Isaak wrote:
On 2026-05-13 09:28, olcott wrote:
*The entire body of knowledge that can be expressed in language* >>>>>>>... is an ill-defined set which only exists in your mind. There's >>>>>>> over 8 billion people on earth, all of whom believe different,
often contradictory things. And, with the exception of theorems of >>>>>>> formal systems, there is nothing that we know with absolute
certainty. Only varying degrees of certainty, but for every given >>>>>>> fact you won't get a universal consensus on exactly how certain we >>>>>>> are of that fact.
So maybe cats were never animals and this "belief"
has always been mass psychosis? In actual reality
cats were always a kind of snake?
I propose that a finite set of "atomic facts" of general
knowledge inherently exists and that no 100% concrete
counter-example can ever be found.
Until you can produce this finite set of atomic facts you're all
just bluster. Here's a few statements. Which would you consider
atomic facts:
– The Universe is 14 billion years old.
– The Ungulates and the Carnivores form a clade.
– Jesus Christ died for our sins.
– Nearly 70% of the mass-energy of the universe consists of dark
energy.
– Anthropogenic climate change is currently occurring.
– The Earth is 6000 years old.
– Argentinosaurus is the largest land animal to ever have lived.
– Measles vaccine causes autism.
– There exists an "island of stability" where extraheavy elements
with approximately 184 neutrons will have a considerably longer
half- life than that of the heaviest elements currently know.
– Turing showed that halting cannot be computed.
actually his proof was in regards to circle-free vs circular
machines, not specifically halting ones. please do read p246 and p247
of his paper /on computable numbers/ more carefully.
As with Gödel, I don't give a rat's ass about the convoluted
mess of his paper. Unless we boil these things down to their
barest possible essence they greatly exceed the capacity of
any human mind.
and what he showed was that it cannot be computed by a single turing
machine.
Only because he used a fucking dishonest trick that
proof theoretic semantics would toss out on its ass.
no one has demonstrated any _actual_ turing machine with a halting
behavior that provably cannot be computed by _any_ machine, as such a
machine would have under-specified, non-determinable semantics that
then could not actually exist as a real machine, that any actual
decider would actually have to decide upon...
the theory of computing has predicated itself on a limitation that
fundamentally resolves to a catch-22 type paradox that has existed
since turing wrote his first paper /on computable numbers/
Its essentially the same damn thing as the Liar Paradox
that mindless robot humans still have not agreed on. The
brains of most humans are hard-wired to short-circuit. To
woefully fallible humans textbooks are the word of God.
Proof theoretic semantics sees right through this crap.
it just isn't polcott...
the liar's paradox is a sentence that is false, in regards to nothing.
what is it false about? who the fuck knows 🤷
godel's sentence is a truth, about nothing, that has no proof. what is
that truth?? again, who the fuck knows 🤷🤷
turing's diagonal, however, is computing an explicitly defined object.
it is trying to take the n-th digit from the n-th circle-free machine,
and constructing it into the n-th digit of a "diagonal" ... and
stumbling on the fact it never defined a digit for itself on that
diagonal
turing's diagonal isn't a "dishonest" trick. he legitimately got stumped
by trying to compute an explicitly defined object, and figured it
supported godel's result
Ever heard of Yaroslav Sergeyev?
How about Simon Stevin?
You must have heard of Zeno.
Then, I imagine you remember geometry and the compass and edge,
and about classical constructions.
So, if you add an Archimedean spiral to compass and edge,
all of a sudden the "angle-trisection" and "squaring the
circle" and "doubling the cube" are constructible, since
it's a new elementary object that happens to fulfill
making it so that these otherwise "impossible" constructions
are not impossible any-more.
Have you heard of Ruffini-Abel and the insolvability of
the quintic? It presumes a limited set of elementary
functions, it doesn't say the quintic doesn't have
solutions, only as among some usual elementary functions.
So, Turing didn't have a "Zeno machine" architecture,
while it's figured that nature in its continuity
solves Turing problems all the time.
Then, mathematical idea of the infinite make for that
number theorists like Erdos make constructions that
disagree, about the laws of large numbers and limits
and the inductive limit (beyond classical constructions),
the "infinite" limit and the "continuum" limit, make
for things in mathematics that are called "emergence"
after "convergence" since "convergence" would never arrive.
Anyways people can look to Mirimanoff who points out
that an infinitely-many would have an infinitely-grand,
and then take Goedel's theorem and point out that
that's the first obvious thing to Goedel's missing
sentence to be, "extra-ordinary".
It's obvious, or "duh".
On 05/16/2026 07:58 AM, Ross Finlayson wrote:
On 05/15/2026 11:45 PM, dart200 wrote:
On 5/13/26 8:46 PM, olcott wrote:
On 5/13/2026 10:26 PM, dart200 wrote:
On 5/13/26 5:07 PM, André G. Isaak wrote:
On 2026-05-13 17:40, olcott wrote:
On 5/13/2026 4:37 PM, André G. Isaak wrote:
On 2026-05-13 09:28, olcott wrote:
*The entire body of knowledge that can be expressed in language* >>>>>>>>... is an ill-defined set which only exists in your mind. There's >>>>>>>> over 8 billion people on earth, all of whom believe different, >>>>>>>> often contradictory things. And, with the exception of theorems of >>>>>>>> formal systems, there is nothing that we know with absolute
certainty. Only varying degrees of certainty, but for every given >>>>>>>> fact you won't get a universal consensus on exactly how certain we >>>>>>>> are of that fact.
So maybe cats were never animals and this "belief"
has always been mass psychosis? In actual reality
cats were always a kind of snake?
I propose that a finite set of "atomic facts" of general
knowledge inherently exists and that no 100% concrete
counter-example can ever be found.
Until you can produce this finite set of atomic facts you're all
just bluster. Here's a few statements. Which would you consider
atomic facts:
– The Universe is 14 billion years old.
– The Ungulates and the Carnivores form a clade.
– Jesus Christ died for our sins.
– Nearly 70% of the mass-energy of the universe consists of dark >>>>>> energy.
– Anthropogenic climate change is currently occurring.
– The Earth is 6000 years old.
– Argentinosaurus is the largest land animal to ever have lived. >>>>>>
– Measles vaccine causes autism.
– There exists an "island of stability" where extraheavy elements >>>>>> with approximately 184 neutrons will have a considerably longer
half- life than that of the heaviest elements currently know.
– Turing showed that halting cannot be computed.
actually his proof was in regards to circle-free vs circular
machines, not specifically halting ones. please do read p246 and p247 >>>>> of his paper /on computable numbers/ more carefully.
As with Gödel, I don't give a rat's ass about the convoluted
mess of his paper. Unless we boil these things down to their
barest possible essence they greatly exceed the capacity of
any human mind.
and what he showed was that it cannot be computed by a single turing >>>>> machine.
Only because he used a fucking dishonest trick that
proof theoretic semantics would toss out on its ass.
no one has demonstrated any _actual_ turing machine with a halting
behavior that provably cannot be computed by _any_ machine, as such a >>>>> machine would have under-specified, non-determinable semantics that
then could not actually exist as a real machine, that any actual
decider would actually have to decide upon...
the theory of computing has predicated itself on a limitation that
fundamentally resolves to a catch-22 type paradox that has existed
since turing wrote his first paper /on computable numbers/
Its essentially the same damn thing as the Liar Paradox
that mindless robot humans still have not agreed on. The
brains of most humans are hard-wired to short-circuit. To
woefully fallible humans textbooks are the word of God.
Proof theoretic semantics sees right through this crap.
it just isn't polcott...
the liar's paradox is a sentence that is false, in regards to nothing.
what is it false about? who the fuck knows 🤷
godel's sentence is a truth, about nothing, that has no proof. what is
that truth?? again, who the fuck knows 🤷🤷
turing's diagonal, however, is computing an explicitly defined object.
it is trying to take the n-th digit from the n-th circle-free machine,
and constructing it into the n-th digit of a "diagonal" ... and
stumbling on the fact it never defined a digit for itself on that
diagonal
turing's diagonal isn't a "dishonest" trick. he legitimately got stumped >>> by trying to compute an explicitly defined object, and figured it
supported godel's result
Ever heard of Yaroslav Sergeyev?
How about Simon Stevin?
You must have heard of Zeno.
Then, I imagine you remember geometry and the compass and edge,
and about classical constructions.
So, if you add an Archimedean spiral to compass and edge,
all of a sudden the "angle-trisection" and "squaring the
circle" and "doubling the cube" are constructible, since
it's a new elementary object that happens to fulfill
making it so that these otherwise "impossible" constructions
are not impossible any-more.
Have you heard of Ruffini-Abel and the insolvability of
the quintic? It presumes a limited set of elementary
functions, it doesn't say the quintic doesn't have
solutions, only as among some usual elementary functions.
So, Turing didn't have a "Zeno machine" architecture,
while it's figured that nature in its continuity
solves Turing problems all the time.
Then, mathematical idea of the infinite make for that
number theorists like Erdos make constructions that
disagree, about the laws of large numbers and limits
and the inductive limit (beyond classical constructions),
the "infinite" limit and the "continuum" limit, make
for things in mathematics that are called "emergence"
after "convergence" since "convergence" would never arrive.
Anyways people can look to Mirimanoff who points out
that an infinitely-many would have an infinitely-grand,
and then take Goedel's theorem and point out that
that's the first obvious thing to Goedel's missing
sentence to be, "extra-ordinary".
It's obvious, or "duh".
And, "The Liar" is false about _nothing_ yet itself.
It's like, in a world where there is no 'but', only 'yet',
that "the Liar", is the only "but".
That "there is no but: only yet", is the idea that instead
of excluded-middle being universal, since it isn't and
instead only defines a class of propositions that happen
to be binary predicates, instead that the temporal modal
relevance logic keeps "yet" as proper.
"There are IFs, there are ANDs, ...,
don't really need any BUTs, ..., yet".
'Yet': it's kind of like 'that', and is implicit anywhere.
Yet that yet that yet that yet that yet that it is so:
that that that that that it is so.
Ross Finlayson wrote:
On 05/16/2026 07:58 AM, Ross Finlayson wrote:I find that 'except' paired with 'yet' covers every instance of 'but.'
On 05/15/2026 11:45 PM, dart200 wrote:
On 5/13/26 8:46 PM, olcott wrote:
On 5/13/2026 10:26 PM, dart200 wrote:
On 5/13/26 5:07 PM, André G. Isaak wrote:
On 2026-05-13 17:40, olcott wrote:
On 5/13/2026 4:37 PM, André G. Isaak wrote:
On 2026-05-13 09:28, olcott wrote:
*The entire body of knowledge that can be expressed in language* >>>>>>>>>... is an ill-defined set which only exists in your mind. There's >>>>>>>>> over 8 billion people on earth, all of whom believe different, >>>>>>>>> often contradictory things. And, with the exception of theorems of >>>>>>>>> formal systems, there is nothing that we know with absolute
certainty. Only varying degrees of certainty, but for every given >>>>>>>>> fact you won't get a universal consensus on exactly how certain we >>>>>>>>> are of that fact.
So maybe cats were never animals and this "belief"
has always been mass psychosis? In actual reality
cats were always a kind of snake?
I propose that a finite set of "atomic facts" of general
knowledge inherently exists and that no 100% concrete
counter-example can ever be found.
Until you can produce this finite set of atomic facts you're all >>>>>>> just bluster. Here's a few statements. Which would you consider
atomic facts:
– The Universe is 14 billion years old.
– The Ungulates and the Carnivores form a clade.
– Jesus Christ died for our sins.
– Nearly 70% of the mass-energy of the universe consists of dark >>>>>>> energy.
– Anthropogenic climate change is currently occurring.
– The Earth is 6000 years old.
– Argentinosaurus is the largest land animal to ever have lived. >>>>>>>
– Measles vaccine causes autism.
– There exists an "island of stability" where extraheavy elements >>>>>>> with approximately 184 neutrons will have a considerably longer
half- life than that of the heaviest elements currently know.
– Turing showed that halting cannot be computed.
actually his proof was in regards to circle-free vs circular
machines, not specifically halting ones. please do read p246 and p247 >>>>>> of his paper /on computable numbers/ more carefully.
As with Gödel, I don't give a rat's ass about the convoluted
mess of his paper. Unless we boil these things down to their
barest possible essence they greatly exceed the capacity of
any human mind.
and what he showed was that it cannot be computed by a single turing >>>>>> machine.
Only because he used a fucking dishonest trick that
proof theoretic semantics would toss out on its ass.
no one has demonstrated any _actual_ turing machine with a halting >>>>>> behavior that provably cannot be computed by _any_ machine, as such a >>>>>> machine would have under-specified, non-determinable semantics that >>>>>> then could not actually exist as a real machine, that any actual
decider would actually have to decide upon...
the theory of computing has predicated itself on a limitation that >>>>>> fundamentally resolves to a catch-22 type paradox that has existed >>>>>> since turing wrote his first paper /on computable numbers/
Its essentially the same damn thing as the Liar Paradox
that mindless robot humans still have not agreed on. The
brains of most humans are hard-wired to short-circuit. To
woefully fallible humans textbooks are the word of God.
Proof theoretic semantics sees right through this crap.
it just isn't polcott...
the liar's paradox is a sentence that is false, in regards to nothing. >>>> what is it false about? who the fuck knows 🤷
godel's sentence is a truth, about nothing, that has no proof. what is >>>> that truth?? again, who the fuck knows 🤷🤷
turing's diagonal, however, is computing an explicitly defined object. >>>> it is trying to take the n-th digit from the n-th circle-free machine, >>>> and constructing it into the n-th digit of a "diagonal" ... and
stumbling on the fact it never defined a digit for itself on that
diagonal
turing's diagonal isn't a "dishonest" trick. he legitimately got
stumped
by trying to compute an explicitly defined object, and figured it
supported godel's result
Ever heard of Yaroslav Sergeyev?
How about Simon Stevin?
You must have heard of Zeno.
Then, I imagine you remember geometry and the compass and edge,
and about classical constructions.
So, if you add an Archimedean spiral to compass and edge,
all of a sudden the "angle-trisection" and "squaring the
circle" and "doubling the cube" are constructible, since
it's a new elementary object that happens to fulfill
making it so that these otherwise "impossible" constructions
are not impossible any-more.
Have you heard of Ruffini-Abel and the insolvability of
the quintic? It presumes a limited set of elementary
functions, it doesn't say the quintic doesn't have
solutions, only as among some usual elementary functions.
So, Turing didn't have a "Zeno machine" architecture,
while it's figured that nature in its continuity
solves Turing problems all the time.
Then, mathematical idea of the infinite make for that
number theorists like Erdos make constructions that
disagree, about the laws of large numbers and limits
and the inductive limit (beyond classical constructions),
the "infinite" limit and the "continuum" limit, make
for things in mathematics that are called "emergence"
after "convergence" since "convergence" would never arrive.
Anyways people can look to Mirimanoff who points out
that an infinitely-many would have an infinitely-grand,
and then take Goedel's theorem and point out that
that's the first obvious thing to Goedel's missing
sentence to be, "extra-ordinary".
It's obvious, or "duh".
And, "The Liar" is false about _nothing_ yet itself.
It's like, in a world where there is no 'but', only 'yet',
that "the Liar", is the only "but".
That "there is no but: only yet", is the idea that instead
of excluded-middle being universal, since it isn't and
instead only defines a class of propositions that happen
to be binary predicates, instead that the temporal modal
relevance logic keeps "yet" as proper.
"There are IFs, there are ANDs, ...,
don't really need any BUTs, ..., yet".
'Yet': it's kind of like 'that', and is implicit anywhere.
Yet that yet that yet that yet that yet that it is so:
that that that that that it is so.
If you can find an exception to this, please show me.
On 05/16/2026 08:37 AM, phoenix wrote:
Ross Finlayson wrote:
On 05/16/2026 07:58 AM, Ross Finlayson wrote:I find that 'except' paired with 'yet' covers every instance of 'but.'
On 05/15/2026 11:45 PM, dart200 wrote:
On 5/13/26 8:46 PM, olcott wrote:
On 5/13/2026 10:26 PM, dart200 wrote:
On 5/13/26 5:07 PM, André G. Isaak wrote:
On 2026-05-13 17:40, olcott wrote:
On 5/13/2026 4:37 PM, André G. Isaak wrote:
On 2026-05-13 09:28, olcott wrote:
*The entire body of knowledge that can be expressed in language* >>>>>>>>>>... is an ill-defined set which only exists in your mind. There's >>>>>>>>>> over 8 billion people on earth, all of whom believe different, >>>>>>>>>> often contradictory things. And, with the exception of
theorems of
formal systems, there is nothing that we know with absolute >>>>>>>>>> certainty. Only varying degrees of certainty, but for every given >>>>>>>>>> fact you won't get a universal consensus on exactly how
certain we
are of that fact.
So maybe cats were never animals and this "belief"
has always been mass psychosis? In actual reality
cats were always a kind of snake?
I propose that a finite set of "atomic facts" of general
knowledge inherently exists and that no 100% concrete
counter-example can ever be found.
Until you can produce this finite set of atomic facts you're all >>>>>>>> just bluster. Here's a few statements. Which would you consider >>>>>>>> atomic facts:
– The Universe is 14 billion years old.
– The Ungulates and the Carnivores form a clade.
– Jesus Christ died for our sins.
– Nearly 70% of the mass-energy of the universe consists of dark >>>>>>>> energy.
– Anthropogenic climate change is currently occurring.
– The Earth is 6000 years old.
– Argentinosaurus is the largest land animal to ever have lived. >>>>>>>>
– Measles vaccine causes autism.
– There exists an "island of stability" where extraheavy elements >>>>>>>> with approximately 184 neutrons will have a considerably longer >>>>>>>> half- life than that of the heaviest elements currently know.
– Turing showed that halting cannot be computed.
actually his proof was in regards to circle-free vs circular
machines, not specifically halting ones. please do read p246 and >>>>>>> p247
of his paper /on computable numbers/ more carefully.
As with Gödel, I don't give a rat's ass about the convoluted
mess of his paper. Unless we boil these things down to their
barest possible essence they greatly exceed the capacity of
any human mind.
and what he showed was that it cannot be computed by a single turing >>>>>>> machine.
Only because he used a fucking dishonest trick that
proof theoretic semantics would toss out on its ass.
no one has demonstrated any _actual_ turing machine with a halting >>>>>>> behavior that provably cannot be computed by _any_ machine, as
such a
machine would have under-specified, non-determinable semantics that >>>>>>> then could not actually exist as a real machine, that any actual >>>>>>> decider would actually have to decide upon...
the theory of computing has predicated itself on a limitation that >>>>>>> fundamentally resolves to a catch-22 type paradox that has existed >>>>>>> since turing wrote his first paper /on computable numbers/
Its essentially the same damn thing as the Liar Paradox
that mindless robot humans still have not agreed on. The
brains of most humans are hard-wired to short-circuit. To
woefully fallible humans textbooks are the word of God.
Proof theoretic semantics sees right through this crap.
it just isn't polcott...
the liar's paradox is a sentence that is false, in regards to nothing. >>>>> what is it false about? who the fuck knows 🤷
godel's sentence is a truth, about nothing, that has no proof. what is >>>>> that truth?? again, who the fuck knows 🤷🤷
turing's diagonal, however, is computing an explicitly defined object. >>>>> it is trying to take the n-th digit from the n-th circle-free machine, >>>>> and constructing it into the n-th digit of a "diagonal" ... and
stumbling on the fact it never defined a digit for itself on that
diagonal
turing's diagonal isn't a "dishonest" trick. he legitimately got
stumped
by trying to compute an explicitly defined object, and figured it
supported godel's result
Ever heard of Yaroslav Sergeyev?
How about Simon Stevin?
You must have heard of Zeno.
Then, I imagine you remember geometry and the compass and edge,
and about classical constructions.
So, if you add an Archimedean spiral to compass and edge,
all of a sudden the "angle-trisection" and "squaring the
circle" and "doubling the cube" are constructible, since
it's a new elementary object that happens to fulfill
making it so that these otherwise "impossible" constructions
are not impossible any-more.
Have you heard of Ruffini-Abel and the insolvability of
the quintic? It presumes a limited set of elementary
functions, it doesn't say the quintic doesn't have
solutions, only as among some usual elementary functions.
So, Turing didn't have a "Zeno machine" architecture,
while it's figured that nature in its continuity
solves Turing problems all the time.
Then, mathematical idea of the infinite make for that
number theorists like Erdos make constructions that
disagree, about the laws of large numbers and limits
and the inductive limit (beyond classical constructions),
the "infinite" limit and the "continuum" limit, make
for things in mathematics that are called "emergence"
after "convergence" since "convergence" would never arrive.
Anyways people can look to Mirimanoff who points out
that an infinitely-many would have an infinitely-grand,
and then take Goedel's theorem and point out that
that's the first obvious thing to Goedel's missing
sentence to be, "extra-ordinary".
It's obvious, or "duh".
And, "The Liar" is false about _nothing_ yet itself.
It's like, in a world where there is no 'but', only 'yet',
that "the Liar", is the only "but".
That "there is no but: only yet", is the idea that instead
of excluded-middle being universal, since it isn't and
instead only defines a class of propositions that happen
to be binary predicates, instead that the temporal modal
relevance logic keeps "yet" as proper.
"There are IFs, there are ANDs, ...,
don't really need any BUTs, ..., yet".
'Yet': it's kind of like 'that', and is implicit anywhere.
Yet that yet that yet that yet that yet that it is so:
that that that that that it is so.
If you can find an exception to this, please show me.
Perhaps most striking is that "yet" and "but" often could stand
in for each other in the simple posing or positing of contraries,
similarly "but not" and "yet not",
yet "not but" and "not yet" make for entirely opposite sorts
of suppositions (or suppositiones since Occam), then as with
regards to, "yet but" as alike "not but" and "but yet" as
alike either "yet" or "but".
So, for introducing terms like "multi-valued" or "multi-valent"
logic, or, the temporal, for time-series data, has it that
"yet" is overall stronger, more expressive and not less un-ambiguous.
Then, for an account where a truly classical logic is
_not_ the quasi-modal, and that "there is no material implication,
only direct implication", then there is that "yet" instead of
"but" also makes for the usual account of "assume" that instead
of "this but that (but this but that ..., fail)" is for along
the lines of "this yet that: these".
Anyways I've been using always 'yet' and never 'but'
for quite some years, and, not missing anything.
"... but but but but ..." -> contradiction
"... yet yet yet yet ..." -> contingency
So, usual accounts of proof-by-contradiction are
by themselves merely partial and half of accounts,
of truly classical Chrysippean Aristotlean logic,
that today is called "modal temporal relevance logic",
and may include the multi-valent, and has _all_ the
expressive and decisive power of logic, where,
for example, that 'but' has not.
"The "inductive" is very much like the "empirical",
and "deduction" isn't only about "elimination".
"There is no but: only yet", reflects that the
modal and temporally modal relevance logic is
not about contradictions, instead change.
The very idea of a Principle of Contradiction
instead of a Principle of Inversion leads to
a very simple obstinacy and fallacies like
those of, "material implication", that aren't so.
Then a principle of inversion can help arrive
at a Principle of Sufficient Reason: yet a
more "Principle of Sufficient, and Thorough, Reason".
The analytical bridges for abduction about the
deduction about the impasses of induction, help
make for the "classical superclassical" reason
usually attributes to Zeno with the most, "paradoxes",
that there are none or that there is one a paradox,
make for a, "wider, fuller dialectic", what makes
for why "axiomless natural deduction" arrives at
being the only true theory of Truth, capital Truth.
Then, that requires a bit of a complete ontological
commitment, yet at least it's true so won't be wrong. " - 5/31/2025
"Well, the "paradoxes" of mathematical logic have kind of
been "decided" one way, the existence of an ordinary inductive
set, yet, that doesn't always make sense, since, it's stipulated
that that's so, and there's no right to do that, except in a theory.
Induction then carries out into the limit, yet it results being
entirely timid about, after an "inductive limit", some,
"infinite limit", about some, "continuum limit".
Now, everybody knows cases for induction, what's so and
so for the next is so for any iteration. Yet, in the limit, there
are cases where induction fails. Besides things like convergence
laws of mathematics, that sometimes don't hold, like Stirling's
formula for factorial and various laws of convergence, then
a graphical example is the yin-yang ad infinitum. A circle has
a constant coefficient relating its cirumference and diameter,
it's pi. So, two half circles whose diameter are the radii of
the outer diameter, have the same sum diameter, so they
have the same sum circumference. Yet, in the limit, those
go to zero, and the sum of the flat line in the limit, is only
1, or 2, and not pi. So, induction fails, as an example. Then
the most usual classical example is the Heap or Sorites,
how many grains is a heap and this sort thing, and how many
grains less than a heap is no longer a heap and this sort of thing.
Then, the most direct example about the discrete and continuous
is about points and lines, that dividing lines doesn't make a point
and combining points doesn't make a line, yet it's another axiom
in today's usual axiomatic descriptive set theory that after making
models of integers and rationals it's axiomatized the least-upper-bound property thusly that lines are point-sets, then that uncountability
sits right there and that's said to be "The foundations of mathematics".
So anyways: sometimes induction fails.
Then, it takes a wider, fuller, dialectical account of the
deductive, than what is a one-side partial account of
the inductive, to make thorough sense.
So, things like the branching or halting problems,
well, these have the baggage of having ordinals and
cardinals together, about an inductive set, which is
about ordinals (i.e., that inductive cases are serial,
besides the fact that a separate apparatus, may
count them).
It's not even necessarily a fact that there's a standard
model of integers at all, only bounded if unbounded fragments
and actually infinite extensions.
Some have P(halts) around zero,
some have P(halts) around one,
some have P(halts) as about .85,
some have P(halts) as 1/2."
Ross Finlayson wrote:
On 05/16/2026 08:37 AM, phoenix wrote:
Ross Finlayson wrote:
On 05/16/2026 07:58 AM, Ross Finlayson wrote:I find that 'except' paired with 'yet' covers every instance of 'but.'
On 05/15/2026 11:45 PM, dart200 wrote:
On 5/13/26 8:46 PM, olcott wrote:
On 5/13/2026 10:26 PM, dart200 wrote:
On 5/13/26 5:07 PM, André G. Isaak wrote:
On 2026-05-13 17:40, olcott wrote:
On 5/13/2026 4:37 PM, André G. Isaak wrote:
On 2026-05-13 09:28, olcott wrote:
*The entire body of knowledge that can be expressed in >>>>>>>>>>>> language*
... is an ill-defined set which only exists in your mind. >>>>>>>>>>> There's
over 8 billion people on earth, all of whom believe different, >>>>>>>>>>> often contradictory things. And, with the exception of
theorems of
formal systems, there is nothing that we know with absolute >>>>>>>>>>> certainty. Only varying degrees of certainty, but for every >>>>>>>>>>> given
fact you won't get a universal consensus on exactly how
certain we
are of that fact.
So maybe cats were never animals and this "belief"
has always been mass psychosis? In actual reality
cats were always a kind of snake?
I propose that a finite set of "atomic facts" of general
knowledge inherently exists and that no 100% concrete
counter-example can ever be found.
Until you can produce this finite set of atomic facts you're all >>>>>>>>> just bluster. Here's a few statements. Which would you consider >>>>>>>>> atomic facts:
– The Universe is 14 billion years old.
– The Ungulates and the Carnivores form a clade.
– Jesus Christ died for our sins.
– Nearly 70% of the mass-energy of the universe consists of dark >>>>>>>>> energy.
– Anthropogenic climate change is currently occurring.
– The Earth is 6000 years old.
– Argentinosaurus is the largest land animal to ever have lived. >>>>>>>>>
– Measles vaccine causes autism.
– There exists an "island of stability" where extraheavy elements >>>>>>>>> with approximately 184 neutrons will have a considerably longer >>>>>>>>> half- life than that of the heaviest elements currently know. >>>>>>>>>
– Turing showed that halting cannot be computed.
actually his proof was in regards to circle-free vs circular
machines, not specifically halting ones. please do read p246 and >>>>>>>> p247
of his paper /on computable numbers/ more carefully.
As with Gödel, I don't give a rat's ass about the convoluted
mess of his paper. Unless we boil these things down to their
barest possible essence they greatly exceed the capacity of
any human mind.
and what he showed was that it cannot be computed by a single
turing
machine.
Only because he used a fucking dishonest trick that
proof theoretic semantics would toss out on its ass.
no one has demonstrated any _actual_ turing machine with a halting >>>>>>>> behavior that provably cannot be computed by _any_ machine, as >>>>>>>> such a
machine would have under-specified, non-determinable semantics that >>>>>>>> then could not actually exist as a real machine, that any actual >>>>>>>> decider would actually have to decide upon...
the theory of computing has predicated itself on a limitation that >>>>>>>> fundamentally resolves to a catch-22 type paradox that has existed >>>>>>>> since turing wrote his first paper /on computable numbers/
Its essentially the same damn thing as the Liar Paradox
that mindless robot humans still have not agreed on. The
brains of most humans are hard-wired to short-circuit. To
woefully fallible humans textbooks are the word of God.
Proof theoretic semantics sees right through this crap.
it just isn't polcott...
the liar's paradox is a sentence that is false, in regards to
nothing.
what is it false about? who the fuck knows 🤷
godel's sentence is a truth, about nothing, that has no proof.
what is
that truth?? again, who the fuck knows 🤷🤷
turing's diagonal, however, is computing an explicitly defined
object.
it is trying to take the n-th digit from the n-th circle-free
machine,
and constructing it into the n-th digit of a "diagonal" ... and
stumbling on the fact it never defined a digit for itself on that
diagonal
turing's diagonal isn't a "dishonest" trick. he legitimately got
stumped
by trying to compute an explicitly defined object, and figured it
supported godel's result
Ever heard of Yaroslav Sergeyev?
How about Simon Stevin?
You must have heard of Zeno.
Then, I imagine you remember geometry and the compass and edge,
and about classical constructions.
So, if you add an Archimedean spiral to compass and edge,
all of a sudden the "angle-trisection" and "squaring the
circle" and "doubling the cube" are constructible, since
it's a new elementary object that happens to fulfill
making it so that these otherwise "impossible" constructions
are not impossible any-more.
Have you heard of Ruffini-Abel and the insolvability of
the quintic? It presumes a limited set of elementary
functions, it doesn't say the quintic doesn't have
solutions, only as among some usual elementary functions.
So, Turing didn't have a "Zeno machine" architecture,
while it's figured that nature in its continuity
solves Turing problems all the time.
Then, mathematical idea of the infinite make for that
number theorists like Erdos make constructions that
disagree, about the laws of large numbers and limits
and the inductive limit (beyond classical constructions),
the "infinite" limit and the "continuum" limit, make
for things in mathematics that are called "emergence"
after "convergence" since "convergence" would never arrive.
Anyways people can look to Mirimanoff who points out
that an infinitely-many would have an infinitely-grand,
and then take Goedel's theorem and point out that
that's the first obvious thing to Goedel's missing
sentence to be, "extra-ordinary".
It's obvious, or "duh".
And, "The Liar" is false about _nothing_ yet itself.
It's like, in a world where there is no 'but', only 'yet',
that "the Liar", is the only "but".
That "there is no but: only yet", is the idea that instead
of excluded-middle being universal, since it isn't and
instead only defines a class of propositions that happen
to be binary predicates, instead that the temporal modal
relevance logic keeps "yet" as proper.
"There are IFs, there are ANDs, ...,
don't really need any BUTs, ..., yet".
'Yet': it's kind of like 'that', and is implicit anywhere.
Yet that yet that yet that yet that yet that it is so:
that that that that that it is so.
If you can find an exception to this, please show me.
Perhaps most striking is that "yet" and "but" often could stand
in for each other in the simple posing or positing of contraries,
similarly "but not" and "yet not",
yet "not but" and "not yet" make for entirely opposite sorts
of suppositions (or suppositiones since Occam), then as with
regards to, "yet but" as alike "not but" and "but yet" as
alike either "yet" or "but".
So, for introducing terms like "multi-valued" or "multi-valent"
logic, or, the temporal, for time-series data, has it that
"yet" is overall stronger, more expressive and not less un-ambiguous.
Then, for an account where a truly classical logic is
_not_ the quasi-modal, and that "there is no material implication,
only direct implication", then there is that "yet" instead of
"but" also makes for the usual account of "assume" that instead
of "this but that (but this but that ..., fail)" is for along
the lines of "this yet that: these".
Anyways I've been using always 'yet' and never 'but'
for quite some years, and, not missing anything.
"... but but but but ..." -> contradiction
"... yet yet yet yet ..." -> contingency
So, usual accounts of proof-by-contradiction are
by themselves merely partial and half of accounts,
of truly classical Chrysippean Aristotlean logic,
that today is called "modal temporal relevance logic",
and may include the multi-valent, and has _all_ the
expressive and decisive power of logic, where,
for example, that 'but' has not.
"The "inductive" is very much like the "empirical",
and "deduction" isn't only about "elimination".
"There is no but: only yet", reflects that the
modal and temporally modal relevance logic is
not about contradictions, instead change.
The very idea of a Principle of Contradiction
instead of a Principle of Inversion leads to
a very simple obstinacy and fallacies like
those of, "material implication", that aren't so.
Then a principle of inversion can help arrive
at a Principle of Sufficient Reason: yet a
more "Principle of Sufficient, and Thorough, Reason".
The analytical bridges for abduction about the
deduction about the impasses of induction, help
make for the "classical superclassical" reason
usually attributes to Zeno with the most, "paradoxes",
that there are none or that there is one a paradox,
make for a, "wider, fuller dialectic", what makes
for why "axiomless natural deduction" arrives at
being the only true theory of Truth, capital Truth.
Then, that requires a bit of a complete ontological
commitment, yet at least it's true so won't be wrong. " - 5/31/2025
"Well, the "paradoxes" of mathematical logic have kind of
been "decided" one way, the existence of an ordinary inductive
set, yet, that doesn't always make sense, since, it's stipulated
that that's so, and there's no right to do that, except in a theory.
Induction then carries out into the limit, yet it results being
entirely timid about, after an "inductive limit", some,
"infinite limit", about some, "continuum limit".
Now, everybody knows cases for induction, what's so and
so for the next is so for any iteration. Yet, in the limit, there
are cases where induction fails. Besides things like convergence
laws of mathematics, that sometimes don't hold, like Stirling's
formula for factorial and various laws of convergence, then
a graphical example is the yin-yang ad infinitum. A circle has
a constant coefficient relating its cirumference and diameter,
it's pi. So, two half circles whose diameter are the radii of
the outer diameter, have the same sum diameter, so they
have the same sum circumference. Yet, in the limit, those
go to zero, and the sum of the flat line in the limit, is only
1, or 2, and not pi. So, induction fails, as an example. Then
the most usual classical example is the Heap or Sorites,
how many grains is a heap and this sort thing, and how many
grains less than a heap is no longer a heap and this sort of thing.
Then, the most direct example about the discrete and continuous
is about points and lines, that dividing lines doesn't make a point
and combining points doesn't make a line, yet it's another axiom
in today's usual axiomatic descriptive set theory that after making
models of integers and rationals it's axiomatized the least-upper-bound
property thusly that lines are point-sets, then that uncountability
sits right there and that's said to be "The foundations of mathematics".
So anyways: sometimes induction fails.
Then, it takes a wider, fuller, dialectical account of the
deductive, than what is a one-side partial account of
the inductive, to make thorough sense.
So, things like the branching or halting problems,
well, these have the baggage of having ordinals and
cardinals together, about an inductive set, which is
about ordinals (i.e., that inductive cases are serial,
besides the fact that a separate apparatus, may
count them).
It's not even necessarily a fact that there's a standard
model of integers at all, only bounded if unbounded fragments
and actually infinite extensions.
Some have P(halts) around zero,
some have P(halts) around one,
some have P(halts) as about .85,
some have P(halts) as 1/2."
Except that this is English, and we don't necessarily apply 1/2 to
'except' and 1/2 to 'yet'. I contend that in some cases either would be applicable, amounting to a modicum of overlap, which means that the sum
of 'except' and 'yet' is likely to be greater than 1.
Speaking figuratively, of course.
Ross Finlayson wrote:
On 05/16/2026 07:58 AM, Ross Finlayson wrote:I find that 'except' paired with 'yet' covers every instance of 'but.'
On 05/15/2026 11:45 PM, dart200 wrote:
On 5/13/26 8:46 PM, olcott wrote:
On 5/13/2026 10:26 PM, dart200 wrote:
On 5/13/26 5:07 PM, André G. Isaak wrote:
On 2026-05-13 17:40, olcott wrote:
On 5/13/2026 4:37 PM, André G. Isaak wrote:
On 2026-05-13 09:28, olcott wrote:
*The entire body of knowledge that can be expressed in language* >>>>>>>>>... is an ill-defined set which only exists in your mind. There's >>>>>>>>> over 8 billion people on earth, all of whom believe different, >>>>>>>>> often contradictory things. And, with the exception of theorems of >>>>>>>>> formal systems, there is nothing that we know with absolute
certainty. Only varying degrees of certainty, but for every given >>>>>>>>> fact you won't get a universal consensus on exactly how certain we >>>>>>>>> are of that fact.
So maybe cats were never animals and this "belief"
has always been mass psychosis? In actual reality
cats were always a kind of snake?
I propose that a finite set of "atomic facts" of general
knowledge inherently exists and that no 100% concrete
counter-example can ever be found.
Until you can produce this finite set of atomic facts you're all >>>>>>> just bluster. Here's a few statements. Which would you consider
atomic facts:
– The Universe is 14 billion years old.
– The Ungulates and the Carnivores form a clade.
– Jesus Christ died for our sins.
– Nearly 70% of the mass-energy of the universe consists of dark >>>>>>> energy.
– Anthropogenic climate change is currently occurring.
– The Earth is 6000 years old.
– Argentinosaurus is the largest land animal to ever have lived. >>>>>>>
– Measles vaccine causes autism.
– There exists an "island of stability" where extraheavy elements >>>>>>> with approximately 184 neutrons will have a considerably longer
half- life than that of the heaviest elements currently know.
– Turing showed that halting cannot be computed.
actually his proof was in regards to circle-free vs circular
machines, not specifically halting ones. please do read p246 and p247 >>>>>> of his paper /on computable numbers/ more carefully.
As with Gödel, I don't give a rat's ass about the convoluted
mess of his paper. Unless we boil these things down to their
barest possible essence they greatly exceed the capacity of
any human mind.
and what he showed was that it cannot be computed by a single turing >>>>>> machine.
Only because he used a fucking dishonest trick that
proof theoretic semantics would toss out on its ass.
no one has demonstrated any _actual_ turing machine with a halting >>>>>> behavior that provably cannot be computed by _any_ machine, as such a >>>>>> machine would have under-specified, non-determinable semantics that >>>>>> then could not actually exist as a real machine, that any actual
decider would actually have to decide upon...
the theory of computing has predicated itself on a limitation that >>>>>> fundamentally resolves to a catch-22 type paradox that has existed >>>>>> since turing wrote his first paper /on computable numbers/
Its essentially the same damn thing as the Liar Paradox
that mindless robot humans still have not agreed on. The
brains of most humans are hard-wired to short-circuit. To
woefully fallible humans textbooks are the word of God.
Proof theoretic semantics sees right through this crap.
it just isn't polcott...
the liar's paradox is a sentence that is false, in regards to nothing. >>>> what is it false about? who the fuck knows 🤷
godel's sentence is a truth, about nothing, that has no proof. what is >>>> that truth?? again, who the fuck knows 🤷🤷
turing's diagonal, however, is computing an explicitly defined object. >>>> it is trying to take the n-th digit from the n-th circle-free machine, >>>> and constructing it into the n-th digit of a "diagonal" ... and
stumbling on the fact it never defined a digit for itself on that
diagonal
turing's diagonal isn't a "dishonest" trick. he legitimately got
stumped
by trying to compute an explicitly defined object, and figured it
supported godel's result
Ever heard of Yaroslav Sergeyev?
How about Simon Stevin?
You must have heard of Zeno.
Then, I imagine you remember geometry and the compass and edge,
and about classical constructions.
So, if you add an Archimedean spiral to compass and edge,
all of a sudden the "angle-trisection" and "squaring the
circle" and "doubling the cube" are constructible, since
it's a new elementary object that happens to fulfill
making it so that these otherwise "impossible" constructions
are not impossible any-more.
Have you heard of Ruffini-Abel and the insolvability of
the quintic? It presumes a limited set of elementary
functions, it doesn't say the quintic doesn't have
solutions, only as among some usual elementary functions.
So, Turing didn't have a "Zeno machine" architecture,
while it's figured that nature in its continuity
solves Turing problems all the time.
Then, mathematical idea of the infinite make for that
number theorists like Erdos make constructions that
disagree, about the laws of large numbers and limits
and the inductive limit (beyond classical constructions),
the "infinite" limit and the "continuum" limit, make
for things in mathematics that are called "emergence"
after "convergence" since "convergence" would never arrive.
Anyways people can look to Mirimanoff who points out
that an infinitely-many would have an infinitely-grand,
and then take Goedel's theorem and point out that
that's the first obvious thing to Goedel's missing
sentence to be, "extra-ordinary".
It's obvious, or "duh".
And, "The Liar" is false about _nothing_ yet itself.
It's like, in a world where there is no 'but', only 'yet',
that "the Liar", is the only "but".
That "there is no but: only yet", is the idea that instead
of excluded-middle being universal, since it isn't and
instead only defines a class of propositions that happen
to be binary predicates, instead that the temporal modal
relevance logic keeps "yet" as proper.
"There are IFs, there are ANDs, ...,
don't really need any BUTs, ..., yet".
'Yet': it's kind of like 'that', and is implicit anywhere.
Yet that yet that yet that yet that yet that it is so:
that that that that that it is so.
If you can find an exception to this, please show me.
Or maybe a different tarot, "the star" because you have such aI find that 'except' paired with 'yet' covers every instance of 'but.'
Yet that yet that yet that yet that yet that it is so:
that that that that that it is so.
If you can find an exception to this, please show me.
On 5/16/2026 4:15 AM, Mikko wrote:That the set of axioms
On 15/05/2026 17:24, olcott wrote:
On 5/15/2026 12:44 AM, Mikko wrote:
On 14/05/2026 18:30, olcott wrote:
On 5/14/2026 2:54 AM, Mikko wrote:
On 13/05/2026 18:28, olcott wrote:
On 5/13/2026 9:38 AM, André G. Isaak wrote:
On 2026-05-13 08:20, olcott wrote:
On 5/13/2026 6:56 AM, André G. Isaak wrote:
On 2026-05-13 05:18, olcott wrote:
On 5/12/2026 10:02 PM, André G. Isaak wrote:
On 2026-05-12 07:32, olcott wrote:
On 5/12/2026 2:05 AM, Mikko wrote:
On 11/05/2026 14:44, olcott wrote:
On 5/11/2026 2:24 AM, Mikko wrote:
On 10/05/2026 22:06, olcott wrote:
We don't have the knowledge that all undecidability is >>>>>>>>>>>>>>>> merely semantic
incoherence, and can't know because we already know that >>>>>>>>>>>>>>>> there is
undecidability that is not semantic incoherence. FOr >>>>>>>>>>>>>>>> example the
axiom system
∀x (1⋅x = x)
1.5 != 5 ∴ you are wrong and I am couinting the rest as >>>>>>>>>>>>>>> gibberish
Middle dot is a commonly used mathematical operator. In >>>>>>>>>>>>>> this context
where the purpose of the operation is not specified some >>>>>>>>>>>>>> other symbols
are often used instead, like ∘ or ∙, or operands are just >>>>>>>>>>>>>> put side by
side with no operator between.
If commonly used mathematics is gibberish to you then we >>>>>>>>>>>>>> many safely
conclude that you have nothing useful to offer to the >>>>>>>>>>>>>> groups you
posted to.
∀x (x⋅1 = x)
∀x∀y∀z (x⋅(y⋅z) = (x⋅y)⋅z)
∀x∃y (x⋅y = 1)
∀x∃y (y⋅x = 1)
is useful for many purposes. But there are sentences like >>>>>>>>>>>>>>>>
∀x∃y (x⋅y = y⋅x)
that are undecidable in that system. But there is >>>>>>>>>>>>>>>> notiong semantically
incoherent in that example or similar ones.
I'm curious to know how you would actually address Mikko's >>>>>>>>>>>> point here. He's pointed out the rather obvious error in >>>>>>>>>>>> your reading comprehension, but you've simply glossed over >>>>>>>>>>>> the example.
In what sense is ∀x∃y (x⋅y = y⋅x) "semantically incoherent"?
André
Decimal point versus multiplication operator?
If it is a decimal point then it is incoherent.
Obviously its nor a decimal point. He gave you the actual >>>>>>>>>> axioms which define the dot operator, so there should be no >>>>>>>>>> dispute as to its meaning.
The point is that ∀x∃y (x⋅y = y⋅x) is not decidable from those
axioms,yet it is clearly semantically coherent.
André
∀x∃y (x⋅y = y⋅x) is proven true by ∀x∀y (x⋅y = y⋅x) >>>>>>>>> which is proven true by the commutative property of
multiplication.
https://people.hsc.edu/faculty-staff/blins/classes/fall18/
math105/ Examples/AlgebraAxioms.pdf
But then you're introducing a new axiom which isn't part of the >>>>>>>> set of axioms which he introduced.
My thesis:
The entire body of knowledge that can be expressed
in language can be encoded as relations between finite strings.
Therefore, you're not dealing with the same theory.
*The entire body of knowledge that can be expressed in language* >>>>>>> Is the scope. That some knucklehead can fail to bother to define >>>>>>> that "cats are animals" so that his knucklehead formal system
does not know this IS OFF-TOPIC.
The entire body of knowledge includes that i² = -1, j² = -1, k² = -1, >>>>>> and ijk = -1. From these we can infer that ij = k and ji = -k and
that ij ≠ ji, at least when we are talking about Hamilton's
quaternions.
i¹ = i
i² = -1
i³ = -i
The entire body of general knowledge expressed in
language includes the "atomic facts" about imaginary
numbers in a finite list and the semantic relations
between finite strings in a finite list such that
any combination of the above can be derived, no
longer a finite list.
Imaginary numbers themselves may be an incoherent notion.
In this case they would not be included in the body of
knowledge.
So a part of the body of knowledge is that multiplication is not
commutative except in restricted domains, so your above claim to
the contrary is not true.
It would be defined separately for each domain.
You claimed that all undecidability
Within the body of knowledge that can be expressed in
language. is merely semantic incoherence
∀x (x⋅1 = x)
∀x∀y∀z (x⋅(y⋅z) = (x⋅y)⋅z)
∀x∃y (x⋅y = 1)
∀x∃y (y⋅x = 1)
On 5/16/2026 4:24 AM, Mikko wrote:
On 15/05/2026 17:27, olcott wrote:
On 5/15/2026 12:48 AM, Mikko wrote:
On 14/05/2026 17:40, olcott wrote:
On 5/14/2026 3:18 AM, Mikko wrote:
On 13/05/2026 14:32, olcott wrote:
On 5/13/2026 4:14 AM, Mikko wrote:
On 12/05/2026 16:32, olcott wrote:
On 5/12/2026 2:05 AM, Mikko wrote:
On 11/05/2026 14:44, olcott wrote:
On 5/11/2026 2:24 AM, Mikko wrote:
On 10/05/2026 22:06, olcott wrote:
On 5/10/2026 2:10 AM, Mikko wrote:We don't have the knowledge that all undecidability is >>>>>>>>>>>> merely semantic
On 09/05/2026 15:13, olcott wrote:
On 5/9/2026 3:30 AM, Mikko wrote:
On 08/05/2026 19:58, olcott wrote:
On 5/8/2026 11:06 AM, dart200 wrote:
On 5/8/26 12:19 AM, Mikko wrote:Anything that any machine can possibly compute can >>>>>>>>>>>>>>>>> be computed by applying a finite set of finite string >>>>>>>>>>>>>>>>> transformation rules to a finite set of finite strings. >>>>>>>>>>>>>>>>>
On 07/05/2026 12:00, dart200 wrote:
On 5/7/26 12:18 AM, Mikko wrote:A machine is not a "diagonal".
On 06/05/2026 22:40, dart200 wrote: >>>>>>>>>>>>>>>>>>>>>> On 5/6/26 12:55 AM, Mikko wrote:
it. Any use of the word before the definition is >>>>>>>>>>>>>>>>>>>>> nonsense,.On 05/05/2026 12:28, dart200 wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 5/5/26 1:25 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 04/05/2026 10:53, dart200 wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 5/3/26 11:15 PM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 03/05/2026 12:09, dart200 wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 5/3/26 12:53 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 02/05/2026 23:39, dart200 wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 4/19/26 10:58 AM, Richard Damon wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 4/19/26 1:21 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 4/19/2026 3:59 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 18/04/2026 15:58, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
no you can't.I can't explain the art of reading Common >>>>>>>>>>>>>>>>>>>>>>>>> Language.i can't read if u can't explain >>>>>>>>>>>>>>>>>>>>>>>>>There is a way to find out if you can read. >>>>>>>>>>>>>>>>>>>>>>>>>>Turing proved that there are universal >>>>>>>>>>>>>>>>>>>>>>>>>>>>> Turing machines. An universalTuring machine >>>>>>>>>>>>>>>>>>>>>>>>>>>>> halts with some inputs and doesn't halt >>>>>>>>>>>>>>>>>>>>>>>>>>>>> with any otherrichard richard richard, that is in-correct. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>Unknown truths are not elements of the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> body ofNo, but that measn that for some >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> sentences X True(X) is unknown and there >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is no method to find out. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
knowledge is a semantic tautology. Did >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> you think
that things that are unknown are known? >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
I don't know about philosophers but >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> mathematicians and logicians don't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> find it interesting if all you can say >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that all knowledge is knowable >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> and everything else is not. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Ross Finlayson, seemed to endlessly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> hedge on whether >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> or not the truth value of the Goldbach >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> conjecture was >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> known. He seemed to think that there are >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> alternative
analytical frameworks that make the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> question of whether >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> or not its truth value is known an >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> ambiguous question. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
I needed to refer to unknown truth >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> values specifically >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> because all "undecidability" when >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> construed correctly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> falls into one of two categories. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> (a) Semantic incoherence >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> (b) Unknown truth values. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Nope.
Undecidability can not come from Semantic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Incoherence, as the definition of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Undecidability ia based on there being a >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> coherent answer, just not one that can be >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> determined by a computation. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
the undecidable problem turing described >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> (as well as the basic halting problem) >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> involves a situations that have _no_ >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> coherent answer, not just one that can be >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> known by not computed ... >>>>>>>>>>>>>>>>>>>>>>>>>>>>>
input. Every Turing machine that can be >>>>>>>>>>>>>>>>>>>>>>>>>>>>> given the same input as an >>>>>>>>>>>>>>>>>>>>>>>>>>>>> universal Turing machine either fails to >>>>>>>>>>>>>>>>>>>>>>>>>>>>> accept some input with which >>>>>>>>>>>>>>>>>>>>>>>>>>>>> that universal Turing machine halts or >>>>>>>>>>>>>>>>>>>>>>>>>>>>> fails to reject some input with >>>>>>>>>>>>>>>>>>>>>>>>>>>>> which that universal Turing macnie does not >>>>>>>>>>>>>>>>>>>>>>>>>>>>> halt.
dunno what ur saying here. >>>>>>>>>>>>>>>>>>>>>>>>>>>
It is impossible to have a Turing machine that >>>>>>>>>>>>>>>>>>>>>>>>> computes a number thatyes, but then he argues it's impossible to >>>>>>>>>>>>>>>>>>>>>>>>>> compute the diagonal because of the paradox >>>>>>>>>>>>>>>>>>>>>>>>>> that ensues when naively running the >>>>>>>>>>>>>>>>>>>>>>>>>> classifier on the diagonal itself >>>>>>>>>>>>>>>>>>>>>>>>> inturing hypothesized a diagonal computation >>>>>>>>>>>>>>>>>>>>>>>>>>>> that tries to put the Nth digit from the Nth >>>>>>>>>>>>>>>>>>>>>>>>>>>> circle- free machine as the Nth digit on >>>>>>>>>>>>>>>>>>>>>>>>>>>> this diagonal across all circle- free >>>>>>>>>>>>>>>>>>>>>>>>>>>> machine...
That is possible because there nither the >>>>>>>>>>>>>>>>>>>>>>>>>>> machines nor digit positions >>>>>>>>>>>>>>>>>>>>>>>>>>> are more numerous than natural numbers. >>>>>>>>>>>>>>>>>>>>>>>>>>
no Turing machine can compute. But you can >>>>>>>>>>>>>>>>>>>>>>>>> compute it if you can use
all (infinitely many) Turing machines. >>>>>>>>>>>>>>>>>>>>>>>>
Hard to test as I han't infinite many Turing >>>>>>>>>>>>>>>>>>>>>>> machines. But it is
u don't need to test it, you can't define a total >>>>>>>>>>>>>>>>>>>>>> dovetailing machine to compute turing's diagonal, >>>>>>>>>>>>>>>>>>>>> You should not say anything about the diagonal >>>>>>>>>>>>>>>>>>>>> before you have defined
the H machine defined on p247 from his paper /on >>>>>>>>>>>>>>>>>>>> computable numbers/
the machine supposes to compute the "turing's >>>>>>>>>>>>>>>>>> diagonal" across circle- free sequences, otherwise >>>>>>>>>>>>>>>>>> labeled as β' in the paper, defined at the bottom of p246 >>>>>>>>>>>>>>>>>
Everything else is simply out-of-scope for computation >>>>>>>>>>>>>>>>> like making a silk purse from a sow's ear.
That "everything else" includes many thigns that would >>>>>>>>>>>>>>>> be useful to
know. In particular, whether some useful function can be >>>>>>>>>>>>>>>> computed is
in that "everything else".
Like the truth value of: "This sentence is not true" >>>>>>>>>>>>>>> that has no truth value.
I don't think knowing the truth value of that would be >>>>>>>>>>>>>> useful. At least
not for any important purpose.
Knowing that all undecidability is merely semantic
incoherence enables:
"true on the basis of meaning expressed in language" >>>>>>>>>>>>> to be reliably computable for the entire body of knowledge. >>>>>>>>>>>>
incoherence, and can't know because we already know that >>>>>>>>>>>> there is
undecidability that is not semantic incoherence. FOr example >>>>>>>>>>>> the
axiom system
∀x (1⋅x = x)
1.5 != 5 ∴ you are wrong and I am couinting the rest as >>>>>>>>>>> gibberish
Middle dot is a commonly used mathematical operator. In this >>>>>>>>>> context
where the purpose of the operation is not specified some other >>>>>>>>>> symbols
are often used instead, like ∘ or ∙, or operands are just put >>>>>>>>>> side by
side with no operator between.
If commonly used mathematics is gibberish to you then we many >>>>>>>>>> safely
conclude that you have nothing useful to offer to the groups you >>>>>>>>>> posted to.
∀x (x⋅1 = x)
∀x∀y∀z (x⋅(y⋅z) = (x⋅y)⋅z)
∀x∃y (x⋅y = 1)
∀x∃y (y⋅x = 1)
is useful for many purposes. But there are sentences like >>>>>>>>>>>>
∀x∃y (x⋅y = y⋅x)
that are undecidable in that system. But there is notiong >>>>>>>>>>>> semantically
incoherent in that example or similar ones.
The truth about climate change and election fraud could >>>>>>>>>>>>> be computed.
Not without real world information.
Yes, so what?
So the biggest problem is not how to compute but how to get >>>>>>>>>> and verify
the relevant real world infomration.
A set of "atomic facts" does exist. We only nee to write> them >>>>>>>>> all down.
THat is a lot of work that can never be completed.
It can be completed with sufficient automation.
No, it can't. It is not completed before it contains all material >>>>>> that
will be published.
IDK, an LLM might do this in five minutes.The place to start would be published textbooks.
How long does it take to read all texbooks published in one year? >>>>>>>
No, because in that time it cannot access all of the material. And >>>>>> it takes time to extract atomic facts and to store them into a big >>>>>> database.
LLM would have to be taught how to extract facts.
If it takes then ten times longer to extract all
the facts of a body of text they will still be done
with every textbook ever written after one year.
Then peer reviewed papers.
Now long does it take to read all reviewed papers published in >>>>>>>> one year?
Then published newspaper articles.
How long does it take to read all newspaper articles publised in >>>>>>>> one
year?
An LLM might read everything ever published in one year.
During that year more is publised.
I may be one or two days out-of-sync far far better
than any human.
And what to do with the "atomic facts" that conflict each other? >>>>>>>>>>> All knowledge that can be expressed in language would
include the exact (x,y,z) coordinates of every atom of your >>>>>>>>>>> body relative to the exact center of the Earth every
millisecond.
Because this degree of detail is not physically implementable >>>>>>>>>>> to implement my system we exclude most specific details. It >>>>>>>>>>> is a system of general knowledge of about 200 petabytes. >>>>>>>>>>>
Of course you may postulate that
the climate is immutable or that there was massimbe
undetected fraud
in the last or some earlier election but that is not what >>>>>>>>>>>> the word
"knowledge" means.
The key elements of election fraud are two things:
(a) There was no actual evidence of election fraud
that could have possibly changed the results.
The key element of elction fraud is to find a vulnerability in >>>>>>>>>> the
election procedure.
There has only been 1620 total documented cases in the USA
in the last 30 years. Every investigation into fraud by
audits found a few more votes against Trump than prior to
the audit. Each of the 60 election fraud cases Trump lost.
He lost because his lawyers could not tell the wild stories
that he was telling the public without getting themselves
convicted of perjury.
These these fact were unconvincing seems to prove that
his supporters are in a cult.
But not that there were no fraud performed skillfully enough to >>>>>>>> avoid
detection. What was found was only small unintentional errors that >>>>>>>> nobody tried to hide.
Likewise there is no perfect logical proof that
can possibly exist that five minutes ago ever existed.
It may also be the case that all of reality is entirely
fictional.
That is right. But that is not relevant to our understanding of the >>>>>> assumed processes that given the world the form it has now or that >>>>>> we can expect it to have in the near future. Perhaps the world is
just God's thought but if it is it seems to be a coherent thought. >>>>>>
Correct, to we just encode all of this in language.
Within the possibly false assumption that reality is
not fictional and five minutes ago did exist then
Trump is merely copying Hitler's big lie about election
fraud is as certain as certain can possibly be.
When did Hitler claim anything about an election fraud?
Chapter 6 of Mein Kampf
"The receptive powers of the masses are very
restricted, and their understanding is feeble.
On the other hand, they quickly forget. Such
being the case, all effective propaganda must
be confined to a few bare essentials and those
must be expressed as far as possible in stereotyped
formulas. These slogans should be persistently
repeated until the very last individual has come
to grasp the idea that has been put forward."
Provides the details of Hitler's propaganda system.
https://en.wikipedia.org/wiki/Big_lie#2020_stolen_election_claims
Looks like a confessison that you lied.
I did not say it as clearly as I could have said it.
Trump did exactly copy Hitler's "big lie" propaganda
system from Hitler's Chapter Six "War Propaganda"
system of Hitler's Mein Kampf in Trump's lies about
election fraud.
You still don't say it as clearly as you should. Trump obviously applies
same propaganda methods as Hitler did. Why not? They worked for Hitler
and they work for Trump, too. This explains Trups claims about an
election fraud but is irrelevant to the question whether there was an
election fraud and how much frauds affected the results.
There is no evidence of election fraud
and there is
much evidence that Trump is lying about election fraud
using Hilter's own system of lies therefore rational
minds would conclude that the evidence supports Trump
is lying about election fraud though fascist methods.
On 16/05/2026 13:16, olcott wrote:
On 5/16/2026 4:24 AM, Mikko wrote:
On 15/05/2026 17:27, olcott wrote:
On 5/15/2026 12:48 AM, Mikko wrote:
On 14/05/2026 17:40, olcott wrote:
On 5/14/2026 3:18 AM, Mikko wrote:
On 13/05/2026 14:32, olcott wrote:
On 5/13/2026 4:14 AM, Mikko wrote:
On 12/05/2026 16:32, olcott wrote:
On 5/12/2026 2:05 AM, Mikko wrote:
On 11/05/2026 14:44, olcott wrote:
On 5/11/2026 2:24 AM, Mikko wrote:
On 10/05/2026 22:06, olcott wrote:
On 5/10/2026 2:10 AM, Mikko wrote:We don't have the knowledge that all undecidability is >>>>>>>>>>>>> merely semantic
On 09/05/2026 15:13, olcott wrote:
On 5/9/2026 3:30 AM, Mikko wrote:
On 08/05/2026 19:58, olcott wrote:
On 5/8/2026 11:06 AM, dart200 wrote:
On 5/8/26 12:19 AM, Mikko wrote:
On 07/05/2026 12:00, dart200 wrote:
On 5/7/26 12:18 AM, Mikko wrote:A machine is not a "diagonal".
On 06/05/2026 22:40, dart200 wrote: >>>>>>>>>>>>>>>>>>>>>>> On 5/6/26 12:55 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 05/05/2026 12:28, dart200 wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 5/5/26 1:25 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 04/05/2026 10:53, dart200 wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 5/3/26 11:15 PM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 03/05/2026 12:09, dart200 wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 5/3/26 12:53 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 02/05/2026 23:39, dart200 wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 4/19/26 10:58 AM, Richard Damon wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 4/19/26 1:21 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 4/19/2026 3:59 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 18/04/2026 15:58, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
it. Any use of the word before the definition is >>>>>>>>>>>>>>>>>>>>>> nonsense,.no you can't.I can't explain the art of reading Common >>>>>>>>>>>>>>>>>>>>>>>>>> Language.i can't read if u can't explain >>>>>>>>>>>>>>>>>>>>>>>>>>There is a way to find out if you can read. >>>>>>>>>>>>>>>>>>>>>>>>>>>Turing proved that there are universal >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Turing machines. An universalTuring >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> machine halts with some inputs and doesn't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> halt with any other >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> input. Every Turing machine that can be >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> given the same input as an >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> universal Turing machine either fails to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> accept some input with which >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that universal Turing machine halts or >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> fails to reject some input with >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> which that universal Turing macnie does >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> not halt.richard richard richard, that is in-correct. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>Unknown truths are not elements of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the body of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> knowledge is a semantic tautology. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Did you think >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that things that are unknown are known? >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>No, but that measn that for some >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> sentences X True(X) is unknown and there >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is no method to find out. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
I don't know about philosophers but >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> mathematicians and logicians don't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> find it interesting if all you can say >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that all knowledge is knowable >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> and everything else is not. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Ross Finlayson, seemed to endlessly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> hedge on whether >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> or not the truth value of the Goldbach >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> conjecture was >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> known. He seemed to think that there >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> are alternative >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> analytical frameworks that make the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> question of whether >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> or not its truth value is known an >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> ambiguous question. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
I needed to refer to unknown truth >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> values specifically >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> because all "undecidability" when >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> construed correctly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> falls into one of two categories. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> (a) Semantic incoherence >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> (b) Unknown truth values. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Nope.
Undecidability can not come from >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Semantic Incoherence, as the definition >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of Undecidability ia based on there >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> being a coherent answer, just not one >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that can be determined by a computation. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
the undecidable problem turing described >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> (as well as the basic halting problem) >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> involves a situations that have _no_ >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> coherent answer, not just one that can be >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> known by not computed ... >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
dunno what ur saying here. >>>>>>>>>>>>>>>>>>>>>>>>>>>>
It is impossible to have a Turing machine that >>>>>>>>>>>>>>>>>>>>>>>>>> computes a number thatyes, but then he argues it's impossible to >>>>>>>>>>>>>>>>>>>>>>>>>>> compute the diagonal because of the paradox >>>>>>>>>>>>>>>>>>>>>>>>>>> that ensues when naively running the >>>>>>>>>>>>>>>>>>>>>>>>>>> classifier on the diagonal itself >>>>>>>>>>>>>>>>>>>>>>>>>> inturing hypothesized a diagonal computation >>>>>>>>>>>>>>>>>>>>>>>>>>>>> that tries to put the Nth digit from the >>>>>>>>>>>>>>>>>>>>>>>>>>>>> Nth circle- free machine as the Nth digit >>>>>>>>>>>>>>>>>>>>>>>>>>>>> on this diagonal across all circle- free >>>>>>>>>>>>>>>>>>>>>>>>>>>>> machine...
That is possible because there nither the >>>>>>>>>>>>>>>>>>>>>>>>>>>> machines nor digit positions >>>>>>>>>>>>>>>>>>>>>>>>>>>> are more numerous than natural numbers. >>>>>>>>>>>>>>>>>>>>>>>>>>>
no Turing machine can compute. But you can >>>>>>>>>>>>>>>>>>>>>>>>>> compute it if you can use
all (infinitely many) Turing machines. >>>>>>>>>>>>>>>>>>>>>>>>>
Hard to test as I han't infinite many Turing >>>>>>>>>>>>>>>>>>>>>>>> machines. But it is
u don't need to test it, you can't define a total >>>>>>>>>>>>>>>>>>>>>>> dovetailing machine to compute turing's diagonal, >>>>>>>>>>>>>>>>>>>>>> You should not say anything about the diagonal >>>>>>>>>>>>>>>>>>>>>> before you have defined
the H machine defined on p247 from his paper /on >>>>>>>>>>>>>>>>>>>>> computable numbers/
the machine supposes to compute the "turing's >>>>>>>>>>>>>>>>>>> diagonal" across circle- free sequences, otherwise >>>>>>>>>>>>>>>>>>> labeled as β' in the paper, defined at the bottom of >>>>>>>>>>>>>>>>>>> p246
Anything that any machine can possibly compute can >>>>>>>>>>>>>>>>>> be computed by applying a finite set of finite string >>>>>>>>>>>>>>>>>> transformation rules to a finite set of finite strings. >>>>>>>>>>>>>>>>>>
Everything else is simply out-of-scope for computation >>>>>>>>>>>>>>>>>> like making a silk purse from a sow's ear.
That "everything else" includes many thigns that would >>>>>>>>>>>>>>>>> be useful to
know. In particular, whether some useful function can >>>>>>>>>>>>>>>>> be computed is
in that "everything else".
Like the truth value of: "This sentence is not true" >>>>>>>>>>>>>>>> that has no truth value.
I don't think knowing the truth value of that would be >>>>>>>>>>>>>>> useful. At least
not for any important purpose.
Knowing that all undecidability is merely semantic >>>>>>>>>>>>>> incoherence enables:
"true on the basis of meaning expressed in language" >>>>>>>>>>>>>> to be reliably computable for the entire body of knowledge. >>>>>>>>>>>>>
incoherence, and can't know because we already know that >>>>>>>>>>>>> there is
undecidability that is not semantic incoherence. FOr >>>>>>>>>>>>> example the
axiom system
∀x (1⋅x = x)
1.5 != 5 ∴ you are wrong and I am couinting the rest as >>>>>>>>>>>> gibberish
Middle dot is a commonly used mathematical operator. In this >>>>>>>>>>> context
where the purpose of the operation is not specified some >>>>>>>>>>> other symbols
are often used instead, like ∘ or ∙, or operands are just put >>>>>>>>>>> side by
side with no operator between.
If commonly used mathematics is gibberish to you then we many >>>>>>>>>>> safely
conclude that you have nothing useful to offer to the groups you >>>>>>>>>>> posted to.
∀x (x⋅1 = x)
∀x∀y∀z (x⋅(y⋅z) = (x⋅y)⋅z)
∀x∃y (x⋅y = 1)
∀x∃y (y⋅x = 1)
is useful for many purposes. But there are sentences like >>>>>>>>>>>>>
∀x∃y (x⋅y = y⋅x)
that are undecidable in that system. But there is notiong >>>>>>>>>>>>> semantically
incoherent in that example or similar ones.
The truth about climate change and election fraud could >>>>>>>>>>>>>> be computed.
Not without real world information.
Yes, so what?
So the biggest problem is not how to compute but how to get >>>>>>>>>>> and verify
the relevant real world infomration.
A set of "atomic facts" does exist. We only nee to write> them >>>>>>>>>> all down.
THat is a lot of work that can never be completed.
It can be completed with sufficient automation.
No, it can't. It is not completed before it contains all material >>>>>>> that
will be published.
IDK, an LLM might do this in five minutes.The place to start would be published textbooks.
How long does it take to read all texbooks published in one year? >>>>>>>>
No, because in that time it cannot access all of the material. And >>>>>>> it takes time to extract atomic facts and to store them into a big >>>>>>> database.
LLM would have to be taught how to extract facts.
If it takes then ten times longer to extract all
the facts of a body of text they will still be done
with every textbook ever written after one year.
Then peer reviewed papers.
Now long does it take to read all reviewed papers published in >>>>>>>>> one year?
Then published newspaper articles.
How long does it take to read all newspaper articles publised >>>>>>>>> in one
year?
An LLM might read everything ever published in one year.
During that year more is publised.
I may be one or two days out-of-sync far far better
than any human.
And what to do with the "atomic facts" that conflict each other? >>>>>>>>>>>> All knowledge that can be expressed in language would
include the exact (x,y,z) coordinates of every atom of your >>>>>>>>>>>> body relative to the exact center of the Earth every
millisecond.
Because this degree of detail is not physically implementable >>>>>>>>>>>> to implement my system we exclude most specific details. It >>>>>>>>>>>> is a system of general knowledge of about 200 petabytes. >>>>>>>>>>>>
Of course you may postulate that
the climate is immutable or that there was massimbe >>>>>>>>>>>>> undetected fraud
in the last or some earlier election but that is not what >>>>>>>>>>>>> the word
"knowledge" means.
The key elements of election fraud are two things:
(a) There was no actual evidence of election fraud
that could have possibly changed the results.
The key element of elction fraud is to find a vulnerability >>>>>>>>>>> in the
election procedure.
There has only been 1620 total documented cases in the USA >>>>>>>>>> in the last 30 years. Every investigation into fraud by
audits found a few more votes against Trump than prior to
the audit. Each of the 60 election fraud cases Trump lost. >>>>>>>>>> He lost because his lawyers could not tell the wild stories >>>>>>>>>> that he was telling the public without getting themselves
convicted of perjury.
These these fact were unconvincing seems to prove that
his supporters are in a cult.
But not that there were no fraud performed skillfully enough to >>>>>>>>> avoid
detection. What was found was only small unintentional errors that >>>>>>>>> nobody tried to hide.
Likewise there is no perfect logical proof that
can possibly exist that five minutes ago ever existed.
It may also be the case that all of reality is entirely
fictional.
That is right. But that is not relevant to our understanding of the >>>>>>> assumed processes that given the world the form it has now or that >>>>>>> we can expect it to have in the near future. Perhaps the world is >>>>>>> just God's thought but if it is it seems to be a coherent thought. >>>>>>>
Correct, to we just encode all of this in language.
Within the possibly false assumption that reality is
not fictional and five minutes ago did exist then
Trump is merely copying Hitler's big lie about election
fraud is as certain as certain can possibly be.
When did Hitler claim anything about an election fraud?
Chapter 6 of Mein Kampf
"The receptive powers of the masses are very
restricted, and their understanding is feeble.
On the other hand, they quickly forget. Such
being the case, all effective propaganda must
be confined to a few bare essentials and those
must be expressed as far as possible in stereotyped
formulas. These slogans should be persistently
repeated until the very last individual has come
to grasp the idea that has been put forward."
Provides the details of Hitler's propaganda system.
https://en.wikipedia.org/wiki/Big_lie#2020_stolen_election_claims
Looks like a confessison that you lied.
I did not say it as clearly as I could have said it.
Trump did exactly copy Hitler's "big lie" propaganda
system from Hitler's Chapter Six "War Propaganda"
system of Hitler's Mein Kampf in Trump's lies about
election fraud.
You still don't say it as clearly as you should. Trump obviously applies >>> same propaganda methods as Hitler did. Why not? They worked for Hitler
and they work for Trump, too. This explains Trups claims about an
election fraud but is irrelevant to the question whether there was an
election fraud and how much frauds affected the results.
There is no evidence of election fraud
So you say but can't prove.
and there is
much evidence that Trump is lying about election fraud
using Hilter's own system of lies therefore rational
minds would conclude that the evidence supports Trump
is lying about election fraud though fascist methods.
Irrelevant to the question whether there was an undetected election
fraud. Trump obviously can't know about the fraud if it is undetected.
Chris M. Thomasson wrote:
Or maybe a different tarot, "the star" because you have such aI find that 'except' paired with 'yet' covers every instance of
Yet that yet that yet that yet that yet that it is so:
that that that that that it is so.
'but.' If you can find an exception to this, please show me.
fascination with me?
On 5/16/2026 2:30 PM, phoenix wrote:
Chris M. Thomasson wrote:
Or maybe a different tarot, "the star" because you have such aI find that 'except' paired with 'yet' covers every instance of
Yet that yet that yet that yet that yet that it is so:
that that that that that it is so.
'but.' If you can find an exception to this, please show me.
fascination with me?
I think you are a sock puppet for olcott.
Chris M. Thomasson wrote:
On 5/16/2026 2:30 PM, phoenix wrote:
Chris M. Thomasson wrote:
Or maybe a different tarot, "the star" because you have such aI find that 'except' paired with 'yet' covers every instance of
Yet that yet that yet that yet that yet that it is so:
that that that that that it is so.
'but.' If you can find an exception to this, please show me.
fascination with me?
I think you are a sock puppet for olcott.
I know you think that, but I don't see any motivation on my part to
disabuse you of the notion. Why not play into it and further befuddle
you? If it were the case that I were not olcott, that is.
On 5/17/2026 2:21 PM, phoenix wrote:
Chris M. Thomasson wrote:
On 5/16/2026 2:30 PM, phoenix wrote:
Chris M. Thomasson wrote:
Or maybe a different tarot, "the star" because you have such aI find that 'except' paired with 'yet' covers every instance of
Yet that yet that yet that yet that yet that it is so:
that that that that that it is so.
'but.' If you can find an exception to this, please show me.
fascination with me?
I think you are a sock puppet for olcott.
I know you think that, but I don't see any motivation on my part to
disabuse you of the notion. Why not play into it and further befuddle
you? If it were the case that I were not olcott, that is.
Ask your self what his halting decider would say... Look in the mirror?
On 05/17/2026 02:46 PM, Chris M. Thomasson wrote:
On 5/17/2026 2:21 PM, phoenix wrote:
Chris M. Thomasson wrote:
On 5/16/2026 2:30 PM, phoenix wrote:
Chris M. Thomasson wrote:
Or maybe a different tarot, "the star" because you have such aI find that 'except' paired with 'yet' covers every instance of
Yet that yet that yet that yet that yet that it is so:
that that that that that it is so.
'but.' If you can find an exception to this, please show me.
fascination with me?
I think you are a sock puppet for olcott.
I know you think that, but I don't see any motivation on my part to
disabuse you of the notion. Why not play into it and further befuddle
you? If it were the case that I were not olcott, that is.
Ask your self what his halting decider would say... Look in the mirror?
One of the problems of environments of the unmoderated and pseudonymous
sort is that there are all kinds of trolls. There are plain rage-bait
and flamer trolls, looky-loos and non-sequitur types, then, also all
sorts of anti-trolls, and these and those.
Then, for example, for something like "it's a free country", then
when I see stuff like either
"smell the new normal, you're living in a dictatorship",
or,
"suffer the children, so your social media and phone get hacked",
then either way the idea of being aware ("woke" wasn't a word
and I'd imagine it would be "awoke" or "woken", or, "woke" will do),
and caring (although, you know, not _too_ caring), that trolls
and repeti-bots on "social" media are anti-social.
So, it's fair that people get wary of trolls, and, begin to suspect
trolls in the likely places, and learn to make a troll-filter,
and basically a skeptical if not cynical outlook on the world today,
that there are trolls and trolls, and sometimes it's easiest to
ignore them away.
Then, there are cranks, ....
The crank is one of the easiest sorts of identities to mimic,
give it a howler fallacy it won't let go and the plain obstinance
combined with the stubbornness along with the sort of plain
unwarranted persistence, then it's not always easy to tell the
difference between cranks and trolls, though often it is,
and between persons and bots, though often it is.
'Murica.
Then, about the thread, the idea is that it's great if these
long-running mostly-empty tit-for-tat nonsense threads get
hijacked by passers-by then into discussions about the issues
at hand, like about the many, many things to do with the
"mathematics" of continuity and infinity, since, despite
the idea of some retro-finitists that their world is a
dot, and not even like AP a giant plutonium atom, there's
much to be done to bring real infinite and continuity into
mathematics, then for physics and so on.
So, new blood (or fresh meat) writing on the thread so
it's not just an echo-chamber of trolls and anti-trolls
which is one big troll, is not necessarily a bad thing.
On 05/17/2026 05:10 PM, Ross Finlayson wrote:
On 05/17/2026 02:46 PM, Chris M. Thomasson wrote:
On 5/17/2026 2:21 PM, phoenix wrote:
Chris M. Thomasson wrote:
On 5/16/2026 2:30 PM, phoenix wrote:
Chris M. Thomasson wrote:
Or maybe a different tarot, "the star" because you have such aI find that 'except' paired with 'yet' covers every instance of >>>>>>>> 'but.' If you can find an exception to this, please show me.
Yet that yet that yet that yet that yet that it is so:
that that that that that it is so.
fascination with me?
I think you are a sock puppet for olcott.
I know you think that, but I don't see any motivation on my part to
disabuse you of the notion. Why not play into it and further befuddle
you? If it were the case that I were not olcott, that is.
Ask your self what his halting decider would say... Look in the mirror?
One of the problems of environments of the unmoderated and pseudonymous
sort is that there are all kinds of trolls. There are plain rage-bait
and flamer trolls, looky-loos and non-sequitur types, then, also all
sorts of anti-trolls, and these and those.
Then, for example, for something like "it's a free country", then
when I see stuff like either
"smell the new normal, you're living in a dictatorship",
or,
"suffer the children, so your social media and phone get hacked",
then either way the idea of being aware ("woke" wasn't a word
and I'd imagine it would be "awoke" or "woken", or, "woke" will do),
and caring (although, you know, not _too_ caring), that trolls
and repeti-bots on "social" media are anti-social.
So, it's fair that people get wary of trolls, and, begin to suspect
trolls in the likely places, and learn to make a troll-filter,
and basically a skeptical if not cynical outlook on the world today,
that there are trolls and trolls, and sometimes it's easiest to
ignore them away.
Then, there are cranks, ....
The crank is one of the easiest sorts of identities to mimic,
give it a howler fallacy it won't let go and the plain obstinance
combined with the stubbornness along with the sort of plain
unwarranted persistence, then it's not always easy to tell the
difference between cranks and trolls, though often it is,
and between persons and bots, though often it is.
'Murica.
Then, about the thread, the idea is that it's great if these
long-running mostly-empty tit-for-tat nonsense threads get
hijacked by passers-by then into discussions about the issues
at hand, like about the many, many things to do with the
"mathematics" of continuity and infinity, since, despite
the idea of some retro-finitists that their world is a
dot, and not even like AP a giant plutonium atom, there's
much to be done to bring real infinite and continuity into
mathematics, then for physics and so on.
So, new blood (or fresh meat) writing on the thread so
it's not just an echo-chamber of trolls and anti-trolls
which is one big troll, is not necessarily a bad thing.
I enjoy CMT's usual spontaneous cheerful enthusiasm,
though as a perceived bot itself when it once-a-year
cites its prompter, then though the affected anxiety
pronation reminds me of too many lessons learned like
not to smell fear or flinch or beg or impose or presume
or assume or judge or telepathically scan or lurk or
menace or make gossip or berate or scoff.
About cranks then, there's something about a crank I admire,
not so much the being wrong part yet the dream, having the
dreams, I'm all for people having the dream when it's not
frustrating or threatening other people's dreams.
So, as I usually enough put it, "retro-finitist crankety
trolls can step off and get bent".
I'm not a fan of any "new" normal, we already have plain
old "normal normal".
On 5/17/2026 5:24 PM, Ross Finlayson wrote:
On 05/17/2026 05:10 PM, Ross Finlayson wrote:
On 05/17/2026 02:46 PM, Chris M. Thomasson wrote:
On 5/17/2026 2:21 PM, phoenix wrote:
Chris M. Thomasson wrote:
On 5/16/2026 2:30 PM, phoenix wrote:
Chris M. Thomasson wrote:
Or maybe a different tarot, "the star" because you have such aI find that 'except' paired with 'yet' covers every instance of >>>>>>>>> 'but.' If you can find an exception to this, please show me. >>>>>>>>>
Yet that yet that yet that yet that yet that it is so:
that that that that that it is so.
fascination with me?
I think you are a sock puppet for olcott.
I know you think that, but I don't see any motivation on my part to
disabuse you of the notion. Why not play into it and further befuddle >>>>> you? If it were the case that I were not olcott, that is.
Ask your self what his halting decider would say... Look in the mirror? >>>
One of the problems of environments of the unmoderated and pseudonymous
sort is that there are all kinds of trolls. There are plain rage-bait
and flamer trolls, looky-loos and non-sequitur types, then, also all
sorts of anti-trolls, and these and those.
Then, for example, for something like "it's a free country", then
when I see stuff like either
"smell the new normal, you're living in a dictatorship",
or,
"suffer the children, so your social media and phone get hacked",
then either way the idea of being aware ("woke" wasn't a word
and I'd imagine it would be "awoke" or "woken", or, "woke" will do),
and caring (although, you know, not _too_ caring), that trolls
and repeti-bots on "social" media are anti-social.
So, it's fair that people get wary of trolls, and, begin to suspect
trolls in the likely places, and learn to make a troll-filter,
and basically a skeptical if not cynical outlook on the world today,
that there are trolls and trolls, and sometimes it's easiest to
ignore them away.
Then, there are cranks, ....
The crank is one of the easiest sorts of identities to mimic,
give it a howler fallacy it won't let go and the plain obstinance
combined with the stubbornness along with the sort of plain
unwarranted persistence, then it's not always easy to tell the
difference between cranks and trolls, though often it is,
and between persons and bots, though often it is.
'Murica.
Then, about the thread, the idea is that it's great if these
long-running mostly-empty tit-for-tat nonsense threads get
hijacked by passers-by then into discussions about the issues
at hand, like about the many, many things to do with the
"mathematics" of continuity and infinity, since, despite
the idea of some retro-finitists that their world is a
dot, and not even like AP a giant plutonium atom, there's
much to be done to bring real infinite and continuity into
mathematics, then for physics and so on.
So, new blood (or fresh meat) writing on the thread so
it's not just an echo-chamber of trolls and anti-trolls
which is one big troll, is not necessarily a bad thing.
I enjoy CMT's usual spontaneous cheerful enthusiasm,
though as a perceived bot itself when it once-a-year
cites its prompter, then though the affected anxiety
pronation reminds me of too many lessons learned like
not to smell fear or flinch or beg or impose or presume
or assume or judge or telepathically scan or lurk or
menace or make gossip or berate or scoff.
Fwiw, check out these funny halt deciders... They only halt when all possible paths are hit. If you think about its kind of akin to olcotts
DD. i simply hijack its result. Here is a version that uses random
numbers for the fuzzer:
In applesoft basic for fun. ;^D
You can run these here:
https://www.calormen.com/jsbasic/
_____________________________
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
1010 PRINT "FIN... All paths hit."
1020 PRINT "NON_HALT P0 = "; P0
1030 PRINT "HALT P1 = "; P1
_____________________________
Here is one that requires input from a user:
_____________________________
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 INPUT "Shall DD halt or not? " ; A$
110 REM 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
_____________________________
It only halts when all paths have been hit.
About cranks then, there's something about a crank I admire,
not so much the being wrong part yet the dream, having the
dreams, I'm all for people having the dream when it's not
frustrating or threatening other people's dreams.
So, as I usually enough put it, "retro-finitist crankety
trolls can step off and get bent".
I'm not a fan of any "new" normal, we already have plain
old "normal normal".
On 5/16/2026 2:30 PM, phoenix wrote:
Chris M. Thomasson wrote:
Or maybe a different tarot, "the star" because you have such aI find that 'except' paired with 'yet' covers every instance of
Yet that yet that yet that yet that yet that it is so:
that that that that that it is so.
'but.' If you can find an exception to this, please show me.
fascination with me?
I think you are a sock puppet for olcott.
On 5/17/2026 8:46 PM, Chris M. Thomasson wrote:
On 5/17/2026 5:24 PM, Ross Finlayson wrote:
On 05/17/2026 05:10 PM, Ross Finlayson wrote:
On 05/17/2026 02:46 PM, Chris M. Thomasson wrote:
On 5/17/2026 2:21 PM, phoenix wrote:
Chris M. Thomasson wrote:
On 5/16/2026 2:30 PM, phoenix wrote:
Chris M. Thomasson wrote:
Or maybe a different tarot, "the star" because you have such a >>>>>>>> fascination with me?I find that 'except' paired with 'yet' covers every instance of >>>>>>>>>> 'but.' If you can find an exception to this, please show me. >>>>>>>>>>
Yet that yet that yet that yet that yet that it is so:
that that that that that it is so.
I think you are a sock puppet for olcott.
I know you think that, but I don't see any motivation on my part to >>>>>> disabuse you of the notion. Why not play into it and further befuddle >>>>>> you? If it were the case that I were not olcott, that is.
Ask your self what his halting decider would say... Look in the
mirror?
One of the problems of environments of the unmoderated and pseudonymous >>>> sort is that there are all kinds of trolls. There are plain rage-bait
and flamer trolls, looky-loos and non-sequitur types, then, also all
sorts of anti-trolls, and these and those.
Then, for example, for something like "it's a free country", then
when I see stuff like either
"smell the new normal, you're living in a dictatorship",
or,
"suffer the children, so your social media and phone get hacked",
then either way the idea of being aware ("woke" wasn't a word
and I'd imagine it would be "awoke" or "woken", or, "woke" will do),
and caring (although, you know, not _too_ caring), that trolls
and repeti-bots on "social" media are anti-social.
So, it's fair that people get wary of trolls, and, begin to suspect
trolls in the likely places, and learn to make a troll-filter,
and basically a skeptical if not cynical outlook on the world today,
that there are trolls and trolls, and sometimes it's easiest to
ignore them away.
Then, there are cranks, ....
The crank is one of the easiest sorts of identities to mimic,
give it a howler fallacy it won't let go and the plain obstinance
combined with the stubbornness along with the sort of plain
unwarranted persistence, then it's not always easy to tell the
difference between cranks and trolls, though often it is,
and between persons and bots, though often it is.
'Murica.
Then, about the thread, the idea is that it's great if these
long-running mostly-empty tit-for-tat nonsense threads get
hijacked by passers-by then into discussions about the issues
at hand, like about the many, many things to do with the
"mathematics" of continuity and infinity, since, despite
the idea of some retro-finitists that their world is a
dot, and not even like AP a giant plutonium atom, there's
much to be done to bring real infinite and continuity into
mathematics, then for physics and so on.
So, new blood (or fresh meat) writing on the thread so
it's not just an echo-chamber of trolls and anti-trolls
which is one big troll, is not necessarily a bad thing.
I enjoy CMT's usual spontaneous cheerful enthusiasm,
though as a perceived bot itself when it once-a-year
cites its prompter, then though the affected anxiety
pronation reminds me of too many lessons learned like
not to smell fear or flinch or beg or impose or presume
or assume or judge or telepathically scan or lurk or
menace or make gossip or berate or scoff.
Fwiw, check out these funny halt deciders... They only halt when all
possible paths are hit. If you think about its kind of akin to olcotts
DD. i simply hijack its result. Here is a version that uses random
numbers for the fuzzer:
In applesoft basic for fun. ;^D
You can run these here:
https://www.calormen.com/jsbasic/
_____________________________
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
1010 PRINT "FIN... All paths hit."
1020 PRINT "NON_HALT P0 = "; P0
1030 PRINT "HALT P1 = "; P1
_____________________________
Here is one that requires input from a user:
_____________________________
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 INPUT "Shall DD halt or not? " ; A$
110 REM 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
^^^^^^^^^^^^
_____________________________
God damn it forgot to add in line 1000 onward! Shit happens:
1000
1010 PRINT "FIN... All paths hit."
1020 PRINT "NON_HALT P0 = "; P0
1030 PRINT "HALT P1 = "; P1
Corrected user input one:
_______________
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 INPUT "Shall DD halt or not? " ; A$
110 REM 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
1010 PRINT "FIN... All paths hit."
1020 PRINT "NON_HALT P0 = "; P0
1030 PRINT "HALT P1 = "; P1
_______________
Sorry about that shit!
It only halts when all paths have been hit.
About cranks then, there's something about a crank I admire,
not so much the being wrong part yet the dream, having the
dreams, I'm all for people having the dream when it's not
frustrating or threatening other people's dreams.
So, as I usually enough put it, "retro-finitist crankety
trolls can step off and get bent".
I'm not a fan of any "new" normal, we already have plain
old "normal normal".
On 05/17/2026 08:48 PM, Chris M. Thomasson wrote:
On 5/17/2026 8:46 PM, Chris M. Thomasson wrote:
On 5/17/2026 5:24 PM, Ross Finlayson wrote:
On 05/17/2026 05:10 PM, Ross Finlayson wrote:
On 05/17/2026 02:46 PM, Chris M. Thomasson wrote:
On 5/17/2026 2:21 PM, phoenix wrote:
Chris M. Thomasson wrote:
On 5/16/2026 2:30 PM, phoenix wrote:
Chris M. Thomasson wrote:
Or maybe a different tarot, "the star" because you have such a >>>>>>>>> fascination with me?I find that 'except' paired with 'yet' covers every instance of >>>>>>>>>>> 'but.' If you can find an exception to this, please show me. >>>>>>>>>>>
Yet that yet that yet that yet that yet that it is so: >>>>>>>>>>>> that that that that that it is so.
I think you are a sock puppet for olcott.
I know you think that, but I don't see any motivation on my part to >>>>>>> disabuse you of the notion. Why not play into it and further
befuddle
you? If it were the case that I were not olcott, that is.
Ask your self what his halting decider would say... Look in the
mirror?
One of the problems of environments of the unmoderated and
pseudonymous
sort is that there are all kinds of trolls. There are plain rage-bait >>>>> and flamer trolls, looky-loos and non-sequitur types, then, also all >>>>> sorts of anti-trolls, and these and those.
Then, for example, for something like "it's a free country", then
when I see stuff like either
"smell the new normal, you're living in a dictatorship",
or,
"suffer the children, so your social media and phone get hacked",
then either way the idea of being aware ("woke" wasn't a word
and I'd imagine it would be "awoke" or "woken", or, "woke" will do), >>>>> and caring (although, you know, not _too_ caring), that trolls
and repeti-bots on "social" media are anti-social.
So, it's fair that people get wary of trolls, and, begin to suspect
trolls in the likely places, and learn to make a troll-filter,
and basically a skeptical if not cynical outlook on the world today, >>>>> that there are trolls and trolls, and sometimes it's easiest to
ignore them away.
Then, there are cranks, ....
The crank is one of the easiest sorts of identities to mimic,
give it a howler fallacy it won't let go and the plain obstinance
combined with the stubbornness along with the sort of plain
unwarranted persistence, then it's not always easy to tell the
difference between cranks and trolls, though often it is,
and between persons and bots, though often it is.
'Murica.
Then, about the thread, the idea is that it's great if these
long-running mostly-empty tit-for-tat nonsense threads get
hijacked by passers-by then into discussions about the issues
at hand, like about the many, many things to do with the
"mathematics" of continuity and infinity, since, despite
the idea of some retro-finitists that their world is a
dot, and not even like AP a giant plutonium atom, there's
much to be done to bring real infinite and continuity into
mathematics, then for physics and so on.
So, new blood (or fresh meat) writing on the thread so
it's not just an echo-chamber of trolls and anti-trolls
which is one big troll, is not necessarily a bad thing.
I enjoy CMT's usual spontaneous cheerful enthusiasm,
though as a perceived bot itself when it once-a-year
cites its prompter, then though the affected anxiety
pronation reminds me of too many lessons learned like
not to smell fear or flinch or beg or impose or presume
or assume or judge or telepathically scan or lurk or
menace or make gossip or berate or scoff.
Fwiw, check out these funny halt deciders... They only halt when all
possible paths are hit. If you think about its kind of akin to olcotts
DD. i simply hijack its result. Here is a version that uses random
numbers for the fuzzer:
In applesoft basic for fun. ;^D
You can run these here:
https://www.calormen.com/jsbasic/
_____________________________
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
1010 PRINT "FIN... All paths hit."
1020 PRINT "NON_HALT P0 = "; P0
1030 PRINT "HALT P1 = "; P1
_____________________________
Here is one that requires input from a user:
_____________________________
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 INPUT "Shall DD halt or not? " ; A$
110 REM 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
^^^^^^^^^^^^
_____________________________
God damn it forgot to add in line 1000 onward! Shit happens:
1000
1010 PRINT "FIN... All paths hit."
1020 PRINT "NON_HALT P0 = "; P0
1030 PRINT "HALT P1 = "; P1
Corrected user input one:
_______________
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 INPUT "Shall DD halt or not? " ; A$
110 REM 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
1010 PRINT "FIN... All paths hit."
1020 PRINT "NON_HALT P0 = "; P0
1030 PRINT "HALT P1 = "; P1
_______________
Sorry about that shit!
It only halts when all paths have been hit.
About cranks then, there's something about a crank I admire,
not so much the being wrong part yet the dream, having the
dreams, I'm all for people having the dream when it's not
frustrating or threatening other people's dreams.
So, as I usually enough put it, "retro-finitist crankety
trolls can step off and get bent".
I'm not a fan of any "new" normal, we already have plain
old "normal normal".
Hm.
There are at least three accounts of programs whether they halt.
A) almost-all programs halt
B) almost-all programs don't halt
C) half of programs halt
On 5/18/2026 10:14 AM, Ross Finlayson wrote:
On 05/17/2026 08:48 PM, Chris M. Thomasson wrote:How can a man as smart as you get this so incorrectly?
On 5/17/2026 8:46 PM, Chris M. Thomasson wrote:
On 5/17/2026 5:24 PM, Ross Finlayson wrote:
On 05/17/2026 05:10 PM, Ross Finlayson wrote:
On 05/17/2026 02:46 PM, Chris M. Thomasson wrote:
On 5/17/2026 2:21 PM, phoenix wrote:
Chris M. Thomasson wrote:
On 5/16/2026 2:30 PM, phoenix wrote:
Chris M. Thomasson wrote:
Or maybe a different tarot, "the star" because you have such a >>>>>>>>>> fascination with me?I find that 'except' paired with 'yet' covers every instance of >>>>>>>>>>>> 'but.' If you can find an exception to this, please show me. >>>>>>>>>>>>
Yet that yet that yet that yet that yet that it is so: >>>>>>>>>>>>> that that that that that it is so.
I think you are a sock puppet for olcott.
I know you think that, but I don't see any motivation on my part to >>>>>>>> disabuse you of the notion. Why not play into it and further
befuddle
you? If it were the case that I were not olcott, that is.
Ask your self what his halting decider would say... Look in the
mirror?
One of the problems of environments of the unmoderated and
pseudonymous
sort is that there are all kinds of trolls. There are plain rage-bait >>>>>> and flamer trolls, looky-loos and non-sequitur types, then, also all >>>>>> sorts of anti-trolls, and these and those.
Then, for example, for something like "it's a free country", then
when I see stuff like either
"smell the new normal, you're living in a dictatorship",
or,
"suffer the children, so your social media and phone get hacked",
then either way the idea of being aware ("woke" wasn't a word
and I'd imagine it would be "awoke" or "woken", or, "woke" will do), >>>>>> and caring (although, you know, not _too_ caring), that trolls
and repeti-bots on "social" media are anti-social.
So, it's fair that people get wary of trolls, and, begin to suspect >>>>>> trolls in the likely places, and learn to make a troll-filter,
and basically a skeptical if not cynical outlook on the world today, >>>>>> that there are trolls and trolls, and sometimes it's easiest to
ignore them away.
Then, there are cranks, ....
The crank is one of the easiest sorts of identities to mimic,
give it a howler fallacy it won't let go and the plain obstinance
combined with the stubbornness along with the sort of plain
unwarranted persistence, then it's not always easy to tell the
difference between cranks and trolls, though often it is,
and between persons and bots, though often it is.
'Murica.
Then, about the thread, the idea is that it's great if these
long-running mostly-empty tit-for-tat nonsense threads get
hijacked by passers-by then into discussions about the issues
at hand, like about the many, many things to do with the
"mathematics" of continuity and infinity, since, despite
the idea of some retro-finitists that their world is a
dot, and not even like AP a giant plutonium atom, there's
much to be done to bring real infinite and continuity into
mathematics, then for physics and so on.
So, new blood (or fresh meat) writing on the thread so
it's not just an echo-chamber of trolls and anti-trolls
which is one big troll, is not necessarily a bad thing.
I enjoy CMT's usual spontaneous cheerful enthusiasm,
though as a perceived bot itself when it once-a-year
cites its prompter, then though the affected anxiety
pronation reminds me of too many lessons learned like
not to smell fear or flinch or beg or impose or presume
or assume or judge or telepathically scan or lurk or
menace or make gossip or berate or scoff.
Fwiw, check out these funny halt deciders... They only halt when all
possible paths are hit. If you think about its kind of akin to olcotts >>>> DD. i simply hijack its result. Here is a version that uses random
numbers for the fuzzer:
In applesoft basic for fun. ;^D
You can run these here:
https://www.calormen.com/jsbasic/
_____________________________
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
1010 PRINT "FIN... All paths hit."
1020 PRINT "NON_HALT P0 = "; P0
1030 PRINT "HALT P1 = "; P1
_____________________________
Here is one that requires input from a user:
_____________________________
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 INPUT "Shall DD halt or not? " ; A$
110 REM 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
^^^^^^^^^^^^
_____________________________
God damn it forgot to add in line 1000 onward! Shit happens:
1000
1010 PRINT "FIN... All paths hit."
1020 PRINT "NON_HALT P0 = "; P0
1030 PRINT "HALT P1 = "; P1
Corrected user input one:
_______________
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 INPUT "Shall DD halt or not? " ; A$
110 REM 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
1010 PRINT "FIN... All paths hit."
1020 PRINT "NON_HALT P0 = "; P0
1030 PRINT "HALT P1 = "; P1
_______________
Sorry about that shit!
It only halts when all paths have been hit.
About cranks then, there's something about a crank I admire,
not so much the being wrong part yet the dream, having the
dreams, I'm all for people having the dream when it's not
frustrating or threatening other people's dreams.
So, as I usually enough put it, "retro-finitist crankety
trolls can step off and get bent".
I'm not a fan of any "new" normal, we already have plain
old "normal normal".
Hm.
There are at least three accounts of programs whether they halt.
A) almost-all programs halt
B) almost-all programs don't halt
C) half of programs halt
The number of programs that halt is between 0 and 100%
excluding the endpoints.
On 5/18/2026 10:14 AM, Ross Finlayson wrote:
On 05/17/2026 08:48 PM, Chris M. Thomasson wrote:How can a man as smart as you get this so incorrectly?
On 5/17/2026 8:46 PM, Chris M. Thomasson wrote:
On 5/17/2026 5:24 PM, Ross Finlayson wrote:
On 05/17/2026 05:10 PM, Ross Finlayson wrote:
On 05/17/2026 02:46 PM, Chris M. Thomasson wrote:
On 5/17/2026 2:21 PM, phoenix wrote:
Chris M. Thomasson wrote:
On 5/16/2026 2:30 PM, phoenix wrote:
Chris M. Thomasson wrote:
Or maybe a different tarot, "the star" because you have such a >>>>>>>>>> fascination with me?I find that 'except' paired with 'yet' covers every instance of >>>>>>>>>>>> 'but.' If you can find an exception to this, please show me. >>>>>>>>>>>>
Yet that yet that yet that yet that yet that it is so: >>>>>>>>>>>>> that that that that that it is so.
I think you are a sock puppet for olcott.
I know you think that, but I don't see any motivation on my part to >>>>>>>> disabuse you of the notion. Why not play into it and further
befuddle
you? If it were the case that I were not olcott, that is.
Ask your self what his halting decider would say... Look in the
mirror?
One of the problems of environments of the unmoderated and
pseudonymous
sort is that there are all kinds of trolls. There are plain rage-bait >>>>>> and flamer trolls, looky-loos and non-sequitur types, then, also all >>>>>> sorts of anti-trolls, and these and those.
Then, for example, for something like "it's a free country", then
when I see stuff like either
"smell the new normal, you're living in a dictatorship",
or,
"suffer the children, so your social media and phone get hacked",
then either way the idea of being aware ("woke" wasn't a word
and I'd imagine it would be "awoke" or "woken", or, "woke" will do), >>>>>> and caring (although, you know, not _too_ caring), that trolls
and repeti-bots on "social" media are anti-social.
So, it's fair that people get wary of trolls, and, begin to suspect >>>>>> trolls in the likely places, and learn to make a troll-filter,
and basically a skeptical if not cynical outlook on the world today, >>>>>> that there are trolls and trolls, and sometimes it's easiest to
ignore them away.
Then, there are cranks, ....
The crank is one of the easiest sorts of identities to mimic,
give it a howler fallacy it won't let go and the plain obstinance
combined with the stubbornness along with the sort of plain
unwarranted persistence, then it's not always easy to tell the
difference between cranks and trolls, though often it is,
and between persons and bots, though often it is.
'Murica.
Then, about the thread, the idea is that it's great if these
long-running mostly-empty tit-for-tat nonsense threads get
hijacked by passers-by then into discussions about the issues
at hand, like about the many, many things to do with the
"mathematics" of continuity and infinity, since, despite
the idea of some retro-finitists that their world is a
dot, and not even like AP a giant plutonium atom, there's
much to be done to bring real infinite and continuity into
mathematics, then for physics and so on.
So, new blood (or fresh meat) writing on the thread so
it's not just an echo-chamber of trolls and anti-trolls
which is one big troll, is not necessarily a bad thing.
I enjoy CMT's usual spontaneous cheerful enthusiasm,
though as a perceived bot itself when it once-a-year
cites its prompter, then though the affected anxiety
pronation reminds me of too many lessons learned like
not to smell fear or flinch or beg or impose or presume
or assume or judge or telepathically scan or lurk or
menace or make gossip or berate or scoff.
Fwiw, check out these funny halt deciders... They only halt when all
possible paths are hit. If you think about its kind of akin to olcotts >>>> DD. i simply hijack its result. Here is a version that uses random
numbers for the fuzzer:
In applesoft basic for fun. ;^D
You can run these here:
https://www.calormen.com/jsbasic/
_____________________________
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
1010 PRINT "FIN... All paths hit."
1020 PRINT "NON_HALT P0 = "; P0
1030 PRINT "HALT P1 = "; P1
_____________________________
Here is one that requires input from a user:
_____________________________
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 INPUT "Shall DD halt or not? " ; A$
110 REM 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
^^^^^^^^^^^^
_____________________________
God damn it forgot to add in line 1000 onward! Shit happens:
1000
1010 PRINT "FIN... All paths hit."
1020 PRINT "NON_HALT P0 = "; P0
1030 PRINT "HALT P1 = "; P1
Corrected user input one:
_______________
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 INPUT "Shall DD halt or not? " ; A$
110 REM 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
1010 PRINT "FIN... All paths hit."
1020 PRINT "NON_HALT P0 = "; P0
1030 PRINT "HALT P1 = "; P1
_______________
Sorry about that shit!
It only halts when all paths have been hit.
About cranks then, there's something about a crank I admire,
not so much the being wrong part yet the dream, having the
dreams, I'm all for people having the dream when it's not
frustrating or threatening other people's dreams.
So, as I usually enough put it, "retro-finitist crankety
trolls can step off and get bent".
I'm not a fan of any "new" normal, we already have plain
old "normal normal".
Hm.
There are at least three accounts of programs whether they halt.
A) almost-all programs halt
B) almost-all programs don't halt
C) half of programs halt
The number of programs that halt is between 0 and 100%
excluding the endpoints.
On 17/05/2026 23:22, Chris M. Thomasson wrote:
On 5/16/2026 2:30 PM, phoenix wrote:
Chris M. Thomasson wrote:
Or maybe a different tarot, "the star" because you have such aI find that 'except' paired with 'yet' covers every instance of
Yet that yet that yet that yet that yet that it is so:
that that that that that it is so.
'but.' If you can find an exception to this, please show me.
fascination with me?
I think you are a sock puppet for olcott.
Unlikely. Phoenix writes like someone who can think.
On 05/17/2026 08:48 PM, Chris M. Thomasson wrote:
On 5/17/2026 8:46 PM, Chris M. Thomasson wrote:
On 5/17/2026 5:24 PM, Ross Finlayson wrote:
On 05/17/2026 05:10 PM, Ross Finlayson wrote:
On 05/17/2026 02:46 PM, Chris M. Thomasson wrote:
On 5/17/2026 2:21 PM, phoenix wrote:
Chris M. Thomasson wrote:
On 5/16/2026 2:30 PM, phoenix wrote:
Chris M. Thomasson wrote:
Or maybe a different tarot, "the star" because you have such a >>>>>>>>> fascination with me?I find that 'except' paired with 'yet' covers every instance of >>>>>>>>>>> 'but.' If you can find an exception to this, please show me. >>>>>>>>>>>
Yet that yet that yet that yet that yet that it is so: >>>>>>>>>>>> that that that that that it is so.
I think you are a sock puppet for olcott.
I know you think that, but I don't see any motivation on my part to >>>>>>> disabuse you of the notion. Why not play into it and further
befuddle
you? If it were the case that I were not olcott, that is.
Ask your self what his halting decider would say... Look in the
mirror?
One of the problems of environments of the unmoderated and
pseudonymous
sort is that there are all kinds of trolls. There are plain rage-bait >>>>> and flamer trolls, looky-loos and non-sequitur types, then, also all >>>>> sorts of anti-trolls, and these and those.
Then, for example, for something like "it's a free country", then
when I see stuff like either
"smell the new normal, you're living in a dictatorship",
or,
"suffer the children, so your social media and phone get hacked",
then either way the idea of being aware ("woke" wasn't a word
and I'd imagine it would be "awoke" or "woken", or, "woke" will do), >>>>> and caring (although, you know, not _too_ caring), that trolls
and repeti-bots on "social" media are anti-social.
So, it's fair that people get wary of trolls, and, begin to suspect
trolls in the likely places, and learn to make a troll-filter,
and basically a skeptical if not cynical outlook on the world today, >>>>> that there are trolls and trolls, and sometimes it's easiest to
ignore them away.
Then, there are cranks, ....
The crank is one of the easiest sorts of identities to mimic,
give it a howler fallacy it won't let go and the plain obstinance
combined with the stubbornness along with the sort of plain
unwarranted persistence, then it's not always easy to tell the
difference between cranks and trolls, though often it is,
and between persons and bots, though often it is.
'Murica.
Then, about the thread, the idea is that it's great if these
long-running mostly-empty tit-for-tat nonsense threads get
hijacked by passers-by then into discussions about the issues
at hand, like about the many, many things to do with the
"mathematics" of continuity and infinity, since, despite
the idea of some retro-finitists that their world is a
dot, and not even like AP a giant plutonium atom, there's
much to be done to bring real infinite and continuity into
mathematics, then for physics and so on.
So, new blood (or fresh meat) writing on the thread so
it's not just an echo-chamber of trolls and anti-trolls
which is one big troll, is not necessarily a bad thing.
I enjoy CMT's usual spontaneous cheerful enthusiasm,
though as a perceived bot itself when it once-a-year
cites its prompter, then though the affected anxiety
pronation reminds me of too many lessons learned like
not to smell fear or flinch or beg or impose or presume
or assume or judge or telepathically scan or lurk or
menace or make gossip or berate or scoff.
Fwiw, check out these funny halt deciders... They only halt when all
possible paths are hit. If you think about its kind of akin to olcotts
DD. i simply hijack its result. Here is a version that uses random
numbers for the fuzzer:
In applesoft basic for fun. ;^D
You can run these here:
https://www.calormen.com/jsbasic/
_____________________________
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
1010 PRINT "FIN... All paths hit."
1020 PRINT "NON_HALT P0 = "; P0
1030 PRINT "HALT P1 = "; P1
_____________________________
Here is one that requires input from a user:
_____________________________
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 INPUT "Shall DD halt or not? " ; A$
110 REM 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
^^^^^^^^^^^^
_____________________________
God damn it forgot to add in line 1000 onward! Shit happens:
1000
1010 PRINT "FIN... All paths hit."
1020 PRINT "NON_HALT P0 = "; P0
1030 PRINT "HALT P1 = "; P1
Corrected user input one:
_______________
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 INPUT "Shall DD halt or not? " ; A$
110 REM 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
1010 PRINT "FIN... All paths hit."
1020 PRINT "NON_HALT P0 = "; P0
1030 PRINT "HALT P1 = "; P1
_______________
Sorry about that shit!
It only halts when all paths have been hit.
About cranks then, there's something about a crank I admire,
not so much the being wrong part yet the dream, having the
dreams, I'm all for people having the dream when it's not
frustrating or threatening other people's dreams.
So, as I usually enough put it, "retro-finitist crankety
trolls can step off and get bent".
I'm not a fan of any "new" normal, we already have plain
old "normal normal".
Hm.
There are at least three accounts of programs whether they halt.
A) almost-all programs halt
B) almost-all programs don't halt
C) half of programs halt
Then, a usual account "there doesn't exist a halt decider"
has the usual opposite account "any program has another
program in static analysis that determines whether it halts".
The entire notion of "static analysis" finds whether programs
halt on given inputs, or for example, enter loops, those being
eliminable also and loopingly-halts.
Then, Gregory Chaitin's account of P(Halts) or "Omega" is
about 0.85+. Well, what's special about that. It's basically
as from counting arguments and probability theory the usual
idea that that's 1+ standard deviation away from 50/50.
Anyways, here there are:
A) three models of continuous domains (line-reals, field-reals,
signal-reals)
B) three models of Cantor space (square, sparse, signal)
C) three models of natural infinities (fragments, extensions, standard)
D) three probabilistic limit theorems (uniformizing, central, polar)
So, these are the sorts of things that get involved
that a conscientious mathematician needs to know
else they are retro-finitist crankety-trolls.
When talking about "infinity" and "continuity",
or "totals" and "completions".
On 5/18/2026 8:14 AM, Ross Finlayson wrote:
On 05/17/2026 08:48 PM, Chris M. Thomasson wrote:
On 5/17/2026 8:46 PM, Chris M. Thomasson wrote:
On 5/17/2026 5:24 PM, Ross Finlayson wrote:
On 05/17/2026 05:10 PM, Ross Finlayson wrote:
On 05/17/2026 02:46 PM, Chris M. Thomasson wrote:
On 5/17/2026 2:21 PM, phoenix wrote:
Chris M. Thomasson wrote:
On 5/16/2026 2:30 PM, phoenix wrote:
Chris M. Thomasson wrote:
Or maybe a different tarot, "the star" because you have such a >>>>>>>>>> fascination with me?I find that 'except' paired with 'yet' covers every instance of >>>>>>>>>>>> 'but.' If you can find an exception to this, please show me. >>>>>>>>>>>>
Yet that yet that yet that yet that yet that it is so: >>>>>>>>>>>>> that that that that that it is so.
I think you are a sock puppet for olcott.
I know you think that, but I don't see any motivation on my part to >>>>>>>> disabuse you of the notion. Why not play into it and further
befuddle
you? If it were the case that I were not olcott, that is.
Ask your self what his halting decider would say... Look in the
mirror?
One of the problems of environments of the unmoderated and
pseudonymous
sort is that there are all kinds of trolls. There are plain rage-bait >>>>>> and flamer trolls, looky-loos and non-sequitur types, then, also all >>>>>> sorts of anti-trolls, and these and those.
Then, for example, for something like "it's a free country", then
when I see stuff like either
"smell the new normal, you're living in a dictatorship",
or,
"suffer the children, so your social media and phone get hacked",
then either way the idea of being aware ("woke" wasn't a word
and I'd imagine it would be "awoke" or "woken", or, "woke" will do), >>>>>> and caring (although, you know, not _too_ caring), that trolls
and repeti-bots on "social" media are anti-social.
So, it's fair that people get wary of trolls, and, begin to suspect >>>>>> trolls in the likely places, and learn to make a troll-filter,
and basically a skeptical if not cynical outlook on the world today, >>>>>> that there are trolls and trolls, and sometimes it's easiest to
ignore them away.
Then, there are cranks, ....
The crank is one of the easiest sorts of identities to mimic,
give it a howler fallacy it won't let go and the plain obstinance
combined with the stubbornness along with the sort of plain
unwarranted persistence, then it's not always easy to tell the
difference between cranks and trolls, though often it is,
and between persons and bots, though often it is.
'Murica.
Then, about the thread, the idea is that it's great if these
long-running mostly-empty tit-for-tat nonsense threads get
hijacked by passers-by then into discussions about the issues
at hand, like about the many, many things to do with the
"mathematics" of continuity and infinity, since, despite
the idea of some retro-finitists that their world is a
dot, and not even like AP a giant plutonium atom, there's
much to be done to bring real infinite and continuity into
mathematics, then for physics and so on.
So, new blood (or fresh meat) writing on the thread so
it's not just an echo-chamber of trolls and anti-trolls
which is one big troll, is not necessarily a bad thing.
I enjoy CMT's usual spontaneous cheerful enthusiasm,
though as a perceived bot itself when it once-a-year
cites its prompter, then though the affected anxiety
pronation reminds me of too many lessons learned like
not to smell fear or flinch or beg or impose or presume
or assume or judge or telepathically scan or lurk or
menace or make gossip or berate or scoff.
Fwiw, check out these funny halt deciders... They only halt when all
possible paths are hit. If you think about its kind of akin to olcotts >>>> DD. i simply hijack its result. Here is a version that uses random
numbers for the fuzzer:
In applesoft basic for fun. ;^D
You can run these here:
https://www.calormen.com/jsbasic/
_____________________________
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
1010 PRINT "FIN... All paths hit."
1020 PRINT "NON_HALT P0 = "; P0
1030 PRINT "HALT P1 = "; P1
_____________________________
Here is one that requires input from a user:
_____________________________
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 INPUT "Shall DD halt or not? " ; A$
110 REM 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
^^^^^^^^^^^^
_____________________________
God damn it forgot to add in line 1000 onward! Shit happens:
1000
1010 PRINT "FIN... All paths hit."
1020 PRINT "NON_HALT P0 = "; P0
1030 PRINT "HALT P1 = "; P1
Corrected user input one:
_______________
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 INPUT "Shall DD halt or not? " ; A$
110 REM 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
1010 PRINT "FIN... All paths hit."
1020 PRINT "NON_HALT P0 = "; P0
1030 PRINT "HALT P1 = "; P1
_______________
Sorry about that shit!
It only halts when all paths have been hit.
About cranks then, there's something about a crank I admire,
not so much the being wrong part yet the dream, having the
dreams, I'm all for people having the dream when it's not
frustrating or threatening other people's dreams.
So, as I usually enough put it, "retro-finitist crankety
trolls can step off and get bent".
I'm not a fan of any "new" normal, we already have plain
old "normal normal".
Hm.
There are at least three accounts of programs whether they halt.
A) almost-all programs halt
B) almost-all programs don't halt
C) half of programs halt
Then, a usual account "there doesn't exist a halt decider"
has the usual opposite account "any program has another
program in static analysis that determines whether it halts".
The entire notion of "static analysis" finds whether programs
halt on given inputs, or for example, enter loops, those being
eliminable also and loopingly-halts.
Then, Gregory Chaitin's account of P(Halts) or "Omega" is
about 0.85+. Well, what's special about that. It's basically
as from counting arguments and probability theory the usual
idea that that's 1+ standard deviation away from 50/50.
Anyways, here there are:
A) three models of continuous domains (line-reals, field-reals,
signal-reals)
B) three models of Cantor space (square, sparse, signal)
C) three models of natural infinities (fragments, extensions, standard)
D) three probabilistic limit theorems (uniformizing, central, polar)
So, these are the sorts of things that get involved
that a conscientious mathematician needs to know
else they are retro-finitist crankety-trolls.
When talking about "infinity" and "continuity",
or "totals" and "completions".
Three paths using a random fuzzer:
____________________________
1 HOME
5 PRINT "ct_dr_fuzz v3 lol. ;^)"
6 P0 = 0 : P1 = 0 : P2 = 0
10 REM Fuzzer... three branches baby!
20 A$ = "NOPE!"
30 R = RND(1)
40 IF R < 0.333 THEN A$ = "YES"
45 IF R >= 0.333 AND R < 0.666 THEN A$ = "MAYBE"
100 REM INPUT "Shall DD halt or not? " ; A$
110 PRINT "Shall DD halt or not? "; A$
200 IF A$ = "YES" GOTO 666
300 IF A$ = "MAYBE" GOTO 777
400 REM Else = NOPE (non-halting)
410 P0 = P0 + 1
420 PRINT "NON_HALT P0 = "; P0
430 GOTO 900
666 PRINT "OK! (halts)"
667 P1 = P1 + 1
668 PRINT "HALT P1 = "; P1
669 GOTO 900
777 PRINT "hmmm... (undecidable)"
778 P2 = P2 + 1
779 PRINT "MAYBE P2 = "; P2
900 IF P0 > 0 AND P1 > 0 AND P2 > 0 GOTO 1000
910 GOTO 10
1000 PRINT: PRINT "FIN... ALL THREE PATHS HIT!"
1010 PRINT "NON_HALT P0 = "; P0
1020 PRINT "HALT P1 = "; P1
1030 PRINT "MAYBE P2 = "; P2
1040 PRINT "Static analysis BTFO'd once again."
____________________________
lol!
On 05/18/2026 09:03 AM, olcott wrote:
On 5/18/2026 10:14 AM, Ross Finlayson wrote:
On 05/17/2026 08:48 PM, Chris M. Thomasson wrote:How can a man as smart as you get this so incorrectly?
On 5/17/2026 8:46 PM, Chris M. Thomasson wrote:
On 5/17/2026 5:24 PM, Ross Finlayson wrote:
On 05/17/2026 05:10 PM, Ross Finlayson wrote:
On 05/17/2026 02:46 PM, Chris M. Thomasson wrote:
On 5/17/2026 2:21 PM, phoenix wrote:
Chris M. Thomasson wrote:
On 5/16/2026 2:30 PM, phoenix wrote:
Chris M. Thomasson wrote:
Or maybe a different tarot, "the star" because you have such a >>>>>>>>>>> fascination with me?I find that 'except' paired with 'yet' covers every >>>>>>>>>>>>> instance of
Yet that yet that yet that yet that yet that it is so: >>>>>>>>>>>>>> that that that that that it is so.
'but.' If you can find an exception to this, please show me. >>>>>>>>>>>>>
I think you are a sock puppet for olcott.
I know you think that, but I don't see any motivation on my >>>>>>>>> part to
disabuse you of the notion. Why not play into it and further >>>>>>>>> befuddle
you? If it were the case that I were not olcott, that is.
Ask your self what his halting decider would say... Look in the >>>>>>>> mirror?
One of the problems of environments of the unmoderated and
pseudonymous
sort is that there are all kinds of trolls. There are plain rage- >>>>>>> bait
and flamer trolls, looky-loos and non-sequitur types, then, also all >>>>>>> sorts of anti-trolls, and these and those.
Then, for example, for something like "it's a free country", then >>>>>>> when I see stuff like either
"smell the new normal, you're living in a dictatorship",
or,
"suffer the children, so your social media and phone get hacked", >>>>>>> then either way the idea of being aware ("woke" wasn't a word
and I'd imagine it would be "awoke" or "woken", or, "woke" will do), >>>>>>> and caring (although, you know, not _too_ caring), that trolls
and repeti-bots on "social" media are anti-social.
So, it's fair that people get wary of trolls, and, begin to suspect >>>>>>> trolls in the likely places, and learn to make a troll-filter,
and basically a skeptical if not cynical outlook on the world today, >>>>>>> that there are trolls and trolls, and sometimes it's easiest to
ignore them away.
Then, there are cranks, ....
The crank is one of the easiest sorts of identities to mimic,
give it a howler fallacy it won't let go and the plain obstinance >>>>>>> combined with the stubbornness along with the sort of plain
unwarranted persistence, then it's not always easy to tell the
difference between cranks and trolls, though often it is,
and between persons and bots, though often it is.
'Murica.
Then, about the thread, the idea is that it's great if these
long-running mostly-empty tit-for-tat nonsense threads get
hijacked by passers-by then into discussions about the issues
at hand, like about the many, many things to do with the
"mathematics" of continuity and infinity, since, despite
the idea of some retro-finitists that their world is a
dot, and not even like AP a giant plutonium atom, there's
much to be done to bring real infinite and continuity into
mathematics, then for physics and so on.
So, new blood (or fresh meat) writing on the thread so
it's not just an echo-chamber of trolls and anti-trolls
which is one big troll, is not necessarily a bad thing.
I enjoy CMT's usual spontaneous cheerful enthusiasm,
though as a perceived bot itself when it once-a-year
cites its prompter, then though the affected anxiety
pronation reminds me of too many lessons learned like
not to smell fear or flinch or beg or impose or presume
or assume or judge or telepathically scan or lurk or
menace or make gossip or berate or scoff.
Fwiw, check out these funny halt deciders... They only halt when all >>>>> possible paths are hit. If you think about its kind of akin to olcotts >>>>> DD. i simply hijack its result. Here is a version that uses random
numbers for the fuzzer:
In applesoft basic for fun. ;^D
You can run these here:
https://www.calormen.com/jsbasic/
_____________________________
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
1010 PRINT "FIN... All paths hit."
1020 PRINT "NON_HALT P0 = "; P0
1030 PRINT "HALT P1 = "; P1
_____________________________
Here is one that requires input from a user:
_____________________________
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 INPUT "Shall DD halt or not? " ; A$
110 REM 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
^^^^^^^^^^^^
_____________________________
God damn it forgot to add in line 1000 onward! Shit happens:
1000
1010 PRINT "FIN... All paths hit."
1020 PRINT "NON_HALT P0 = "; P0
1030 PRINT "HALT P1 = "; P1
Corrected user input one:
_______________
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 INPUT "Shall DD halt or not? " ; A$
110 REM 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
1010 PRINT "FIN... All paths hit."
1020 PRINT "NON_HALT P0 = "; P0
1030 PRINT "HALT P1 = "; P1
_______________
Sorry about that shit!
It only halts when all paths have been hit.
About cranks then, there's something about a crank I admire,
not so much the being wrong part yet the dream, having the
dreams, I'm all for people having the dream when it's not
frustrating or threatening other people's dreams.
So, as I usually enough put it, "retro-finitist crankety
trolls can step off and get bent".
I'm not a fan of any "new" normal, we already have plain
old "normal normal".
Hm.
There are at least three accounts of programs whether they halt.
A) almost-all programs halt
B) almost-all programs don't halt
C) half of programs halt
The number of programs that halt is between 0 and 100%
excluding the endpoints.
https://arxiv.org/abs/math/0611740
"The Halting Probability Omega: Irreducible Complexity in Pure
Mathematics", G. Chaitin
"Gödel himself did not think that his theorem showed that mathematics
has limitations. In several essays he made it clear that he believed
that mathematicians could eventually settle any significant question by
using their mathematical intuition, their ability to directly perceive
the Platonic world of mathematical ideas, and by inventing or
discovering new concepts and new axioms, new principles.
Furthermore, I share Enriques’s faith in intuition. I think that
excessive formalism and abstraction is killing mathematics. In my
opinion math papers shouldn’t attempt to replace all words by formulas, instead they should be like literary essays, they should attempt to
explain and convince.
So let me tell you the story of metamathematics, of how mathematicians
have tried to use mathematical methods to study the power and the
limitations of math itself. It’s a fairly dramatic story; in a previous
era it might have been the subject of epic poems, of Iliads and Odysseys
of verse. I’ll start with David Hilbert."
"In my opinion this is a fundamental step forward in the philosophy of mathematics because it makes incompleteness seem much more concrete and
much more natural. It’s almost a problem in physics, it’s about a machine, you just ask whether or not it’s going to eventually stop, and
it turns out there’s no way, no general way, to answer that question.
Let me emphasize that if a program does halt, we can eventually discover that. The problem, an extremely deep one, is to show that a program will never halt if this is in fact so. One can settle many special cases,
even an infinity of them, but no finite set of axioms can enable you to settle all possible cases."
Hm, " ... no finite set of axioms ...", ..., how about "no axioms".
"The real numbers are the simplest thing in the world geometrically,
they are just points on a line. But arithmetically, as individuals, real numbers are actually rather unreal. Turing’s 1936 uncomputable real is
just the tip of the iceberg, the problem is a lot more serious than that."
Here the iota-values are points _in_ a line, field-reals _on_ a line,
and signal-reals _about_ and _around_ a line.
So, Chaitin doesn't even have three models of continuous domains,
or "repleteness", of concepts like Lebnitz' principle of perfection
and Hilbert's postulate of continuity.
Mathematics really _does_ define continuity:
and there are at least three models of continuous domains.
So, say you want to sample a real number from [0,1] the interval
at uniform random, and all you have is a fair coin that
gives samples from {0, 1} the set.
So, you start flipping coins and marking the result to make
a sequence of 0's and 1's. Each coin toss _refines_ the
sample.
Yet, each coin toss also _begins_ a new sample. So, to sample
one real number, the super-task results sampling infinitely-many
real numbers.
So, the probability of the first sample being a rational value
is, according to the law of large numbers the law of small numbers,
small, and arbitrarily and infinitesimally small. In theories
that are Pythagorean it's almost-all rationals, while in theories
that are Cantorian it's almost-all transcendentals.
Yet, if a sample arrives at a rational, the repeating character
of rationals means that thusly the _one_ sample of a rational
number is automatically _infinitely-many_ samples of rational
numbers.
So, it makes sense to consider that the probability of sampling
a rational number from [0,1] is about 0.5.
This isn't Pythagorean by itself, and isn't Cantorian by itself.
It's them together according to accounts of paradox-free reason,
not "non-classical logics where we ignore contradiction",
which is _hypocrisy_ and furthermore _fallacious_,
since "infinity" and "continuity" are "absolute" and "replete".
"Let’s start with Borel’s know-it-all number, but now let’s use the Nth binary digit to tell us whether or not the Nth computer program ever
halts. So now Borel’s number is an oracle for the halting problem. For example, there is a bit which tells us whether or not the Riemann
hypothesis is true, for that is equivalent to the statement that a
program that systematically searches for zeros of the zeta function that
are in the wrong place, never halts.
It turns out that this number, which I’ll call Turing’s number even though it does not occur in Turing’s paper, is wasting bits, it is
actually highly redundant. We don’t really need N bits to answer N cases
of the halting problem, a much smaller number of bits will do. Why?
Well, consider some large number N of cases of the halting problem, some large number N of individual programs for which we want to know whether
or not each one halts. Is this really N bits of mathematical
information? No, the answers are not independent, they are highly
correlated. How? Well, in order to answer N cases of the halting
problem, we don’t really need to know each individual answer; it
suffices to know how many of these N programs will eventually halt. Once
we know this number, which is only about log_2 N
bits of information, we can run the N programs in parallel until exactly
this number of them halt, and then we know that none of the remaining programs will ever halt. And log_2 N is much, much less than N for all sufficiently large N. In other words, Turing’s number isn’t the best possible oracle for the halting problem. It is highly redundant, it uses
far too many bits.
Using essentially this idea, we can get the best possible oracle number
for the halting problem; that is the halting probability Ω, which has no redundancy, none at all.
So, now that there's readily equipped a notion of uniform sampling
that results "oracle numbers", always _infinitely-many_ just to get one,
then Chaitin's quote is equipped some context that makes
quite a fresh reading.
This goes for all y'all.
On 5/18/2026 11:44 AM, Ross Finlayson wrote:
On 05/18/2026 09:03 AM, olcott wrote:
On 5/18/2026 10:14 AM, Ross Finlayson wrote:
On 05/17/2026 08:48 PM, Chris M. Thomasson wrote:How can a man as smart as you get this so incorrectly?
On 5/17/2026 8:46 PM, Chris M. Thomasson wrote:
On 5/17/2026 5:24 PM, Ross Finlayson wrote:
On 05/17/2026 05:10 PM, Ross Finlayson wrote:
On 05/17/2026 02:46 PM, Chris M. Thomasson wrote:
On 5/17/2026 2:21 PM, phoenix wrote:
Chris M. Thomasson wrote:
On 5/16/2026 2:30 PM, phoenix wrote:
Chris M. Thomasson wrote:
Or maybe a different tarot, "the star" because you have such a >>>>>>>>>>>> fascination with me?I find that 'except' paired with 'yet' covers every >>>>>>>>>>>>>> instance of
Yet that yet that yet that yet that yet that it is so: >>>>>>>>>>>>>>> that that that that that it is so.
'but.' If you can find an exception to this, please show me. >>>>>>>>>>>>>>
I think you are a sock puppet for olcott.
I know you think that, but I don't see any motivation on my >>>>>>>>>> part to
disabuse you of the notion. Why not play into it and further >>>>>>>>>> befuddle
you? If it were the case that I were not olcott, that is.
Ask your self what his halting decider would say... Look in the >>>>>>>>> mirror?
One of the problems of environments of the unmoderated and
pseudonymous
sort is that there are all kinds of trolls. There are plain
rage- bait
and flamer trolls, looky-loos and non-sequitur types, then, also >>>>>>>> all
sorts of anti-trolls, and these and those.
Then, for example, for something like "it's a free country", then >>>>>>>> when I see stuff like either
"smell the new normal, you're living in a dictatorship",
or,
"suffer the children, so your social media and phone get hacked", >>>>>>>> then either way the idea of being aware ("woke" wasn't a word
and I'd imagine it would be "awoke" or "woken", or, "woke" will >>>>>>>> do),
and caring (although, you know, not _too_ caring), that trolls >>>>>>>> and repeti-bots on "social" media are anti-social.
So, it's fair that people get wary of trolls, and, begin to suspect >>>>>>>> trolls in the likely places, and learn to make a troll-filter, >>>>>>>> and basically a skeptical if not cynical outlook on the world
today,
that there are trolls and trolls, and sometimes it's easiest to >>>>>>>> ignore them away.
Then, there are cranks, ....
The crank is one of the easiest sorts of identities to mimic,
give it a howler fallacy it won't let go and the plain obstinance >>>>>>>> combined with the stubbornness along with the sort of plain
unwarranted persistence, then it's not always easy to tell the >>>>>>>> difference between cranks and trolls, though often it is,
and between persons and bots, though often it is.
'Murica.
Then, about the thread, the idea is that it's great if these
long-running mostly-empty tit-for-tat nonsense threads get
hijacked by passers-by then into discussions about the issues
at hand, like about the many, many things to do with the
"mathematics" of continuity and infinity, since, despite
the idea of some retro-finitists that their world is a
dot, and not even like AP a giant plutonium atom, there's
much to be done to bring real infinite and continuity into
mathematics, then for physics and so on.
So, new blood (or fresh meat) writing on the thread so
it's not just an echo-chamber of trolls and anti-trolls
which is one big troll, is not necessarily a bad thing.
I enjoy CMT's usual spontaneous cheerful enthusiasm,
though as a perceived bot itself when it once-a-year
cites its prompter, then though the affected anxiety
pronation reminds me of too many lessons learned like
not to smell fear or flinch or beg or impose or presume
or assume or judge or telepathically scan or lurk or
menace or make gossip or berate or scoff.
Fwiw, check out these funny halt deciders... They only halt when all >>>>>> possible paths are hit. If you think about its kind of akin to
olcotts
DD. i simply hijack its result. Here is a version that uses random >>>>>> numbers for the fuzzer:
In applesoft basic for fun. ;^D
You can run these here:
https://www.calormen.com/jsbasic/
_____________________________
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
1010 PRINT "FIN... All paths hit."
1020 PRINT "NON_HALT P0 = "; P0
1030 PRINT "HALT P1 = "; P1
_____________________________
Here is one that requires input from a user:
_____________________________
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 INPUT "Shall DD halt or not? " ; A$
110 REM 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
^^^^^^^^^^^^
_____________________________
God damn it forgot to add in line 1000 onward! Shit happens:
1000
1010 PRINT "FIN... All paths hit."
1020 PRINT "NON_HALT P0 = "; P0
1030 PRINT "HALT P1 = "; P1
Corrected user input one:
_______________
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 INPUT "Shall DD halt or not? " ; A$
110 REM 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
1010 PRINT "FIN... All paths hit."
1020 PRINT "NON_HALT P0 = "; P0
1030 PRINT "HALT P1 = "; P1
_______________
Sorry about that shit!
It only halts when all paths have been hit.
About cranks then, there's something about a crank I admire,
not so much the being wrong part yet the dream, having the
dreams, I'm all for people having the dream when it's not
frustrating or threatening other people's dreams.
So, as I usually enough put it, "retro-finitist crankety
trolls can step off and get bent".
I'm not a fan of any "new" normal, we already have plain
old "normal normal".
Hm.
There are at least three accounts of programs whether they halt.
A) almost-all programs halt
B) almost-all programs don't halt
C) half of programs halt
The number of programs that halt is between 0 and 100%
excluding the endpoints.
https://arxiv.org/abs/math/0611740
"The Halting Probability Omega: Irreducible Complexity in Pure
Mathematics", G. Chaitin
"Gödel himself did not think that his theorem showed that mathematics
has limitations. In several essays he made it clear that he believed
that mathematicians could eventually settle any significant question by
using their mathematical intuition, their ability to directly perceive
the Platonic world of mathematical ideas, and by inventing or
discovering new concepts and new axioms, new principles.
Furthermore, I share Enriques’s faith in intuition. I think that
excessive formalism and abstraction is killing mathematics. In my
opinion math papers shouldn’t attempt to replace all words by formulas,
instead they should be like literary essays, they should attempt to
explain and convince.
Extending Dag Prawitz's Theory of Grounds while remaining
directly within the realm of proof theoretic Semantics then
G simply becomes ungrounded in PA and grounded in meta-math.
It has taken PTS quite a few decades, all the way up to 2012
to catch up with what Wittgenstein said decades earlier:
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's
system' means: the opposite has been proved in Russell's
system. https://www.liarparadox.org/Wittgenstein.pdf
So let me tell you the story of metamathematics, of how mathematicians
have tried to use mathematical methods to study the power and the
limitations of math itself. It’s a fairly dramatic story; in a previous
era it might have been the subject of epic poems, of Iliads and Odysseys
of verse. I’ll start with David Hilbert."
"In my opinion this is a fundamental step forward in the philosophy of
mathematics because it makes incompleteness seem much more concrete and
much more natural. It’s almost a problem in physics, it’s about a
machine, you just ask whether or not it’s going to eventually stop, and
it turns out there’s no way, no general way, to answer that question.
Let me emphasize that if a program does halt, we can eventually discover
that. The problem, an extremely deep one, is to show that a program will
never halt if this is in fact so. One can settle many special cases,
even an infinity of them, but no finite set of axioms can enable you to
settle all possible cases."
Hm, " ... no finite set of axioms ...", ..., how about "no axioms".
"The real numbers are the simplest thing in the world geometrically,
they are just points on a line. But arithmetically, as individuals, real
numbers are actually rather unreal. Turing’s 1936 uncomputable real is
just the tip of the iceberg, the problem is a lot more serious than
that."
Here the iota-values are points _in_ a line, field-reals _on_ a line,
and signal-reals _about_ and _around_ a line.
So, Chaitin doesn't even have three models of continuous domains,
or "repleteness", of concepts like Lebnitz' principle of perfection
and Hilbert's postulate of continuity.
Mathematics really _does_ define continuity:
and there are at least three models of continuous domains.
So, say you want to sample a real number from [0,1] the interval
at uniform random, and all you have is a fair coin that
gives samples from {0, 1} the set.
So, you start flipping coins and marking the result to make
a sequence of 0's and 1's. Each coin toss _refines_ the
sample.
Yet, each coin toss also _begins_ a new sample. So, to sample
one real number, the super-task results sampling infinitely-many
real numbers.
So, the probability of the first sample being a rational value
is, according to the law of large numbers the law of small numbers,
small, and arbitrarily and infinitesimally small. In theories
that are Pythagorean it's almost-all rationals, while in theories
that are Cantorian it's almost-all transcendentals.
Yet, if a sample arrives at a rational, the repeating character
of rationals means that thusly the _one_ sample of a rational
number is automatically _infinitely-many_ samples of rational
numbers.
So, it makes sense to consider that the probability of sampling
a rational number from [0,1] is about 0.5.
This isn't Pythagorean by itself, and isn't Cantorian by itself.
It's them together according to accounts of paradox-free reason,
not "non-classical logics where we ignore contradiction",
which is _hypocrisy_ and furthermore _fallacious_,
since "infinity" and "continuity" are "absolute" and "replete".
"Let’s start with Borel’s know-it-all number, but now let’s use the Nth
binary digit to tell us whether or not the Nth computer program ever
halts. So now Borel’s number is an oracle for the halting problem. For
example, there is a bit which tells us whether or not the Riemann
hypothesis is true, for that is equivalent to the statement that a
program that systematically searches for zeros of the zeta function that
are in the wrong place, never halts.
It turns out that this number, which I’ll call Turing’s number even
though it does not occur in Turing’s paper, is wasting bits, it is
actually highly redundant. We don’t really need N bits to answer N cases >> of the halting problem, a much smaller number of bits will do. Why?
Well, consider some large number N of cases of the halting problem, some
large number N of individual programs for which we want to know whether
or not each one halts. Is this really N bits of mathematical
information? No, the answers are not independent, they are highly
correlated. How? Well, in order to answer N cases of the halting
problem, we don’t really need to know each individual answer; it
suffices to know how many of these N programs will eventually halt. Once
we know this number, which is only about log_2 N
bits of information, we can run the N programs in parallel until exactly
this number of them halt, and then we know that none of the remaining
programs will ever halt. And log_2 N is much, much less than N for all
sufficiently large N. In other words, Turing’s number isn’t the best
possible oracle for the halting problem. It is highly redundant, it uses
far too many bits.
Using essentially this idea, we can get the best possible oracle number
for the halting problem; that is the halting probability Ω, which has no
redundancy, none at all.
So, now that there's readily equipped a notion of uniform sampling
that results "oracle numbers", always _infinitely-many_ just to get one,
then Chaitin's quote is equipped some context that makes
quite a fresh reading.
This goes for all y'all.
On 05/21/2026 06:02 AM, olcott wrote:
On 5/18/2026 11:44 AM, Ross Finlayson wrote:
On 05/18/2026 09:03 AM, olcott wrote:
On 5/18/2026 10:14 AM, Ross Finlayson wrote:
On 05/17/2026 08:48 PM, Chris M. Thomasson wrote:How can a man as smart as you get this so incorrectly?
On 5/17/2026 8:46 PM, Chris M. Thomasson wrote:
On 5/17/2026 5:24 PM, Ross Finlayson wrote:
On 05/17/2026 05:10 PM, Ross Finlayson wrote:
On 05/17/2026 02:46 PM, Chris M. Thomasson wrote:
On 5/17/2026 2:21 PM, phoenix wrote:
Chris M. Thomasson wrote:
On 5/16/2026 2:30 PM, phoenix wrote:
Chris M. Thomasson wrote:
Or maybe a different tarot, "the star" because you have such a >>>>>>>>>>>>> fascination with me?I find that 'except' paired with 'yet' covers every >>>>>>>>>>>>>>> instance of
Yet that yet that yet that yet that yet that it is so: >>>>>>>>>>>>>>>> that that that that that it is so.
'but.' If you can find an exception to this, please show me. >>>>>>>>>>>>>>>
I think you are a sock puppet for olcott.
I know you think that, but I don't see any motivation on my >>>>>>>>>>> part to
disabuse you of the notion. Why not play into it and further >>>>>>>>>>> befuddle
you? If it were the case that I were not olcott, that is. >>>>>>>>>>>
Ask your self what his halting decider would say... Look in the >>>>>>>>>> mirror?
One of the problems of environments of the unmoderated and
pseudonymous
sort is that there are all kinds of trolls. There are plain
rage- bait
and flamer trolls, looky-loos and non-sequitur types, then, also >>>>>>>>> all
sorts of anti-trolls, and these and those.
Then, for example, for something like "it's a free country", then >>>>>>>>> when I see stuff like either
"smell the new normal, you're living in a dictatorship",
or,
"suffer the children, so your social media and phone get hacked", >>>>>>>>> then either way the idea of being aware ("woke" wasn't a word >>>>>>>>> and I'd imagine it would be "awoke" or "woken", or, "woke" will >>>>>>>>> do),
and caring (although, you know, not _too_ caring), that trolls >>>>>>>>> and repeti-bots on "social" media are anti-social.
So, it's fair that people get wary of trolls, and, begin to >>>>>>>>> suspect
trolls in the likely places, and learn to make a troll-filter, >>>>>>>>> and basically a skeptical if not cynical outlook on the world >>>>>>>>> today,
that there are trolls and trolls, and sometimes it's easiest to >>>>>>>>> ignore them away.
Then, there are cranks, ....
The crank is one of the easiest sorts of identities to mimic, >>>>>>>>> give it a howler fallacy it won't let go and the plain obstinance >>>>>>>>> combined with the stubbornness along with the sort of plain
unwarranted persistence, then it's not always easy to tell the >>>>>>>>> difference between cranks and trolls, though often it is,
and between persons and bots, though often it is.
'Murica.
Then, about the thread, the idea is that it's great if these >>>>>>>>> long-running mostly-empty tit-for-tat nonsense threads get
hijacked by passers-by then into discussions about the issues >>>>>>>>> at hand, like about the many, many things to do with the
"mathematics" of continuity and infinity, since, despite
the idea of some retro-finitists that their world is a
dot, and not even like AP a giant plutonium atom, there's
much to be done to bring real infinite and continuity into
mathematics, then for physics and so on.
So, new blood (or fresh meat) writing on the thread so
it's not just an echo-chamber of trolls and anti-trolls
which is one big troll, is not necessarily a bad thing.
I enjoy CMT's usual spontaneous cheerful enthusiasm,
though as a perceived bot itself when it once-a-year
cites its prompter, then though the affected anxiety
pronation reminds me of too many lessons learned like
not to smell fear or flinch or beg or impose or presume
or assume or judge or telepathically scan or lurk or
menace or make gossip or berate or scoff.
Fwiw, check out these funny halt deciders... They only halt when all >>>>>>> possible paths are hit. If you think about its kind of akin to
olcotts
DD. i simply hijack its result. Here is a version that uses random >>>>>>> numbers for the fuzzer:
In applesoft basic for fun. ;^D
You can run these here:
https://www.calormen.com/jsbasic/
_____________________________
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
1010 PRINT "FIN... All paths hit."
1020 PRINT "NON_HALT P0 = "; P0
1030 PRINT "HALT P1 = "; P1
_____________________________
Here is one that requires input from a user:
_____________________________
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 INPUT "Shall DD halt or not? " ; A$
110 REM 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
^^^^^^^^^^^^
_____________________________
God damn it forgot to add in line 1000 onward! Shit happens:
1000
1010 PRINT "FIN... All paths hit."
1020 PRINT "NON_HALT P0 = "; P0
1030 PRINT "HALT P1 = "; P1
Corrected user input one:
_______________
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 INPUT "Shall DD halt or not? " ; A$
110 REM 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
1010 PRINT "FIN... All paths hit."
1020 PRINT "NON_HALT P0 = "; P0
1030 PRINT "HALT P1 = "; P1
_______________
Sorry about that shit!
It only halts when all paths have been hit.
About cranks then, there's something about a crank I admire,
not so much the being wrong part yet the dream, having the
dreams, I'm all for people having the dream when it's not
frustrating or threatening other people's dreams.
So, as I usually enough put it, "retro-finitist crankety
trolls can step off and get bent".
I'm not a fan of any "new" normal, we already have plain
old "normal normal".
Hm.
There are at least three accounts of programs whether they halt.
A) almost-all programs halt
B) almost-all programs don't halt
C) half of programs halt
The number of programs that halt is between 0 and 100%
excluding the endpoints.
https://arxiv.org/abs/math/0611740
"The Halting Probability Omega: Irreducible Complexity in Pure
Mathematics", G. Chaitin
"Gödel himself did not think that his theorem showed that mathematics
has limitations. In several essays he made it clear that he believed
that mathematicians could eventually settle any significant question by
using their mathematical intuition, their ability to directly perceive
the Platonic world of mathematical ideas, and by inventing or
discovering new concepts and new axioms, new principles.
Furthermore, I share Enriques’s faith in intuition. I think that
excessive formalism and abstraction is killing mathematics. In my
opinion math papers shouldn’t attempt to replace all words by formulas, >>> instead they should be like literary essays, they should attempt to
explain and convince.
Extending Dag Prawitz's Theory of Grounds while remaining
directly within the realm of proof theoretic Semantics then
G simply becomes ungrounded in PA and grounded in meta-math.
It has taken PTS quite a few decades, all the way up to 2012
to catch up with what Wittgenstein said decades earlier:
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's
system' means: the opposite has been proved in Russell's
system. https://www.liarparadox.org/Wittgenstein.pdf
So let me tell you the story of metamathematics, of how mathematicians
have tried to use mathematical methods to study the power and the
limitations of math itself. It’s a fairly dramatic story; in a previous >>> era it might have been the subject of epic poems, of Iliads and Odysseys >>> of verse. I’ll start with David Hilbert."
"In my opinion this is a fundamental step forward in the philosophy of
mathematics because it makes incompleteness seem much more concrete and
much more natural. It’s almost a problem in physics, it’s about a
machine, you just ask whether or not it’s going to eventually stop, and >>> it turns out there’s no way, no general way, to answer that question.
Let me emphasize that if a program does halt, we can eventually discover >>> that. The problem, an extremely deep one, is to show that a program will >>> never halt if this is in fact so. One can settle many special cases,
even an infinity of them, but no finite set of axioms can enable you to
settle all possible cases."
Hm, " ... no finite set of axioms ...", ..., how about "no axioms".
"The real numbers are the simplest thing in the world geometrically,
they are just points on a line. But arithmetically, as individuals, real >>> numbers are actually rather unreal. Turing’s 1936 uncomputable real is >>> just the tip of the iceberg, the problem is a lot more serious than
that."
Here the iota-values are points _in_ a line, field-reals _on_ a line,
and signal-reals _about_ and _around_ a line.
So, Chaitin doesn't even have three models of continuous domains,
or "repleteness", of concepts like Lebnitz' principle of perfection
and Hilbert's postulate of continuity.
Mathematics really _does_ define continuity:
and there are at least three models of continuous domains.
So, say you want to sample a real number from [0,1] the interval
at uniform random, and all you have is a fair coin that
gives samples from {0, 1} the set.
So, you start flipping coins and marking the result to make
a sequence of 0's and 1's. Each coin toss _refines_ the
sample.
Yet, each coin toss also _begins_ a new sample. So, to sample
one real number, the super-task results sampling infinitely-many
real numbers.
So, the probability of the first sample being a rational value
is, according to the law of large numbers the law of small numbers,
small, and arbitrarily and infinitesimally small. In theories
that are Pythagorean it's almost-all rationals, while in theories
that are Cantorian it's almost-all transcendentals.
Yet, if a sample arrives at a rational, the repeating character
of rationals means that thusly the _one_ sample of a rational
number is automatically _infinitely-many_ samples of rational
numbers.
So, it makes sense to consider that the probability of sampling
a rational number from [0,1] is about 0.5.
This isn't Pythagorean by itself, and isn't Cantorian by itself.
It's them together according to accounts of paradox-free reason,
not "non-classical logics where we ignore contradiction",
which is _hypocrisy_ and furthermore _fallacious_,
since "infinity" and "continuity" are "absolute" and "replete".
"Let’s start with Borel’s know-it-all number, but now let’s use the Nth
binary digit to tell us whether or not the Nth computer program ever
halts. So now Borel’s number is an oracle for the halting problem. For >>> example, there is a bit which tells us whether or not the Riemann
hypothesis is true, for that is equivalent to the statement that a
program that systematically searches for zeros of the zeta function that >>> are in the wrong place, never halts.
It turns out that this number, which I’ll call Turing’s number even
though it does not occur in Turing’s paper, is wasting bits, it is
actually highly redundant. We don’t really need N bits to answer N cases >>> of the halting problem, a much smaller number of bits will do. Why?
Well, consider some large number N of cases of the halting problem, some >>> large number N of individual programs for which we want to know whether
or not each one halts. Is this really N bits of mathematical
information? No, the answers are not independent, they are highly
correlated. How? Well, in order to answer N cases of the halting
problem, we don’t really need to know each individual answer; it
suffices to know how many of these N programs will eventually halt. Once >>> we know this number, which is only about log_2 N
bits of information, we can run the N programs in parallel until exactly >>> this number of them halt, and then we know that none of the remaining
programs will ever halt. And log_2 N is much, much less than N for all
sufficiently large N. In other words, Turing’s number isn’t the best >>> possible oracle for the halting problem. It is highly redundant, it uses >>> far too many bits.
Using essentially this idea, we can get the best possible oracle number
for the halting problem; that is the halting probability Ω, which has no >>> redundancy, none at all.
So, now that there's readily equipped a notion of uniform sampling
that results "oracle numbers", always _infinitely-many_ just to get one, >>> then Chaitin's quote is equipped some context that makes
quite a fresh reading.
This goes for all y'all.
Actually, thousands of years before Russell or Tarski claimed that
"truth is whatever I, Lord Russell or Tsar Tarski, say that agrees
with myself", the notion that mathematical truth is _discovered_ not _invented_ was "the truth", then that structural realism and realist structuralism make for an account with both an idealistic and an
analytical tradition, keeping science for itself as a strengthened
analytical position and the idealistic getting equipped with mental
senses of the faculties of reason about logic and mathematics (and
infinity and continuity) so that Kant is satisfied that "1 + 1 = 2".
Then, Wittgenstein is just a cad, and while it's respected
his right to say "I, wild Wittgenstein, say that you can't say
that you say anything at all", it's ignored as saying jack squat.
Natural reasoners can simply arrive at grounds for reason after
axiomless natural deduction making for logic, geometry, number theory,
with infinity and continuity, and so on. Then formalisms follow as
after perspectival accounts of restriction-of-comprehension given a
thorough account of expansion-of-comprehension.
Plato could be proud.
On 05/21/2026 06:02 AM, olcott wrote:
On 5/18/2026 11:44 AM, Ross Finlayson wrote:
On 05/18/2026 09:03 AM, olcott wrote:
On 5/18/2026 10:14 AM, Ross Finlayson wrote:
On 05/17/2026 08:48 PM, Chris M. Thomasson wrote:How can a man as smart as you get this so incorrectly?
On 5/17/2026 8:46 PM, Chris M. Thomasson wrote:
On 5/17/2026 5:24 PM, Ross Finlayson wrote:
On 05/17/2026 05:10 PM, Ross Finlayson wrote:
On 05/17/2026 02:46 PM, Chris M. Thomasson wrote:
On 5/17/2026 2:21 PM, phoenix wrote:
Chris M. Thomasson wrote:
On 5/16/2026 2:30 PM, phoenix wrote:
Chris M. Thomasson wrote:
Or maybe a different tarot, "the star" because you have such a >>>>>>>>>>>>> fascination with me?I find that 'except' paired with 'yet' covers every >>>>>>>>>>>>>>> instance of
Yet that yet that yet that yet that yet that it is so: >>>>>>>>>>>>>>>> that that that that that it is so.
'but.' If you can find an exception to this, please show me. >>>>>>>>>>>>>>>
I think you are a sock puppet for olcott.
I know you think that, but I don't see any motivation on my >>>>>>>>>>> part to
disabuse you of the notion. Why not play into it and further >>>>>>>>>>> befuddle
you? If it were the case that I were not olcott, that is. >>>>>>>>>>>
Ask your self what his halting decider would say... Look in the >>>>>>>>>> mirror?
One of the problems of environments of the unmoderated and
pseudonymous
sort is that there are all kinds of trolls. There are plain
rage- bait
and flamer trolls, looky-loos and non-sequitur types, then, also >>>>>>>>> all
sorts of anti-trolls, and these and those.
Then, for example, for something like "it's a free country", then >>>>>>>>> when I see stuff like either
"smell the new normal, you're living in a dictatorship",
or,
"suffer the children, so your social media and phone get hacked", >>>>>>>>> then either way the idea of being aware ("woke" wasn't a word >>>>>>>>> and I'd imagine it would be "awoke" or "woken", or, "woke" will >>>>>>>>> do),
and caring (although, you know, not _too_ caring), that trolls >>>>>>>>> and repeti-bots on "social" media are anti-social.
So, it's fair that people get wary of trolls, and, begin to >>>>>>>>> suspect
trolls in the likely places, and learn to make a troll-filter, >>>>>>>>> and basically a skeptical if not cynical outlook on the world >>>>>>>>> today,
that there are trolls and trolls, and sometimes it's easiest to >>>>>>>>> ignore them away.
Then, there are cranks, ....
The crank is one of the easiest sorts of identities to mimic, >>>>>>>>> give it a howler fallacy it won't let go and the plain obstinance >>>>>>>>> combined with the stubbornness along with the sort of plain
unwarranted persistence, then it's not always easy to tell the >>>>>>>>> difference between cranks and trolls, though often it is,
and between persons and bots, though often it is.
'Murica.
Then, about the thread, the idea is that it's great if these >>>>>>>>> long-running mostly-empty tit-for-tat nonsense threads get
hijacked by passers-by then into discussions about the issues >>>>>>>>> at hand, like about the many, many things to do with the
"mathematics" of continuity and infinity, since, despite
the idea of some retro-finitists that their world is a
dot, and not even like AP a giant plutonium atom, there's
much to be done to bring real infinite and continuity into
mathematics, then for physics and so on.
So, new blood (or fresh meat) writing on the thread so
it's not just an echo-chamber of trolls and anti-trolls
which is one big troll, is not necessarily a bad thing.
I enjoy CMT's usual spontaneous cheerful enthusiasm,
though as a perceived bot itself when it once-a-year
cites its prompter, then though the affected anxiety
pronation reminds me of too many lessons learned like
not to smell fear or flinch or beg or impose or presume
or assume or judge or telepathically scan or lurk or
menace or make gossip or berate or scoff.
Fwiw, check out these funny halt deciders... They only halt when all >>>>>>> possible paths are hit. If you think about its kind of akin to
olcotts
DD. i simply hijack its result. Here is a version that uses random >>>>>>> numbers for the fuzzer:
In applesoft basic for fun. ;^D
You can run these here:
https://www.calormen.com/jsbasic/
_____________________________
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
1010 PRINT "FIN... All paths hit."
1020 PRINT "NON_HALT P0 = "; P0
1030 PRINT "HALT P1 = "; P1
_____________________________
Here is one that requires input from a user:
_____________________________
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 INPUT "Shall DD halt or not? " ; A$
110 REM 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
^^^^^^^^^^^^
_____________________________
God damn it forgot to add in line 1000 onward! Shit happens:
1000
1010 PRINT "FIN... All paths hit."
1020 PRINT "NON_HALT P0 = "; P0
1030 PRINT "HALT P1 = "; P1
Corrected user input one:
_______________
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 INPUT "Shall DD halt or not? " ; A$
110 REM 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
1010 PRINT "FIN... All paths hit."
1020 PRINT "NON_HALT P0 = "; P0
1030 PRINT "HALT P1 = "; P1
_______________
Sorry about that shit!
It only halts when all paths have been hit.
About cranks then, there's something about a crank I admire,
not so much the being wrong part yet the dream, having the
dreams, I'm all for people having the dream when it's not
frustrating or threatening other people's dreams.
So, as I usually enough put it, "retro-finitist crankety
trolls can step off and get bent".
I'm not a fan of any "new" normal, we already have plain
old "normal normal".
Hm.
There are at least three accounts of programs whether they halt.
A) almost-all programs halt
B) almost-all programs don't halt
C) half of programs halt
The number of programs that halt is between 0 and 100%
excluding the endpoints.
https://arxiv.org/abs/math/0611740
"The Halting Probability Omega: Irreducible Complexity in Pure
Mathematics", G. Chaitin
"Gödel himself did not think that his theorem showed that mathematics
has limitations. In several essays he made it clear that he believed
that mathematicians could eventually settle any significant question by
using their mathematical intuition, their ability to directly perceive
the Platonic world of mathematical ideas, and by inventing or
discovering new concepts and new axioms, new principles.
Furthermore, I share Enriques’s faith in intuition. I think that
excessive formalism and abstraction is killing mathematics. In my
opinion math papers shouldn’t attempt to replace all words by formulas, >>> instead they should be like literary essays, they should attempt to
explain and convince.
Extending Dag Prawitz's Theory of Grounds while remaining
directly within the realm of proof theoretic Semantics then
G simply becomes ungrounded in PA and grounded in meta-math.
It has taken PTS quite a few decades, all the way up to 2012
to catch up with what Wittgenstein said decades earlier:
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's
system' means: the opposite has been proved in Russell's
system. https://www.liarparadox.org/Wittgenstein.pdf
So let me tell you the story of metamathematics, of how mathematicians
have tried to use mathematical methods to study the power and the
limitations of math itself. It’s a fairly dramatic story; in a previous >>> era it might have been the subject of epic poems, of Iliads and Odysseys >>> of verse. I’ll start with David Hilbert."
"In my opinion this is a fundamental step forward in the philosophy of
mathematics because it makes incompleteness seem much more concrete and
much more natural. It’s almost a problem in physics, it’s about a
machine, you just ask whether or not it’s going to eventually stop, and >>> it turns out there’s no way, no general way, to answer that question.
Let me emphasize that if a program does halt, we can eventually discover >>> that. The problem, an extremely deep one, is to show that a program will >>> never halt if this is in fact so. One can settle many special cases,
even an infinity of them, but no finite set of axioms can enable you to
settle all possible cases."
Hm, " ... no finite set of axioms ...", ..., how about "no axioms".
"The real numbers are the simplest thing in the world geometrically,
they are just points on a line. But arithmetically, as individuals, real >>> numbers are actually rather unreal. Turing’s 1936 uncomputable real is >>> just the tip of the iceberg, the problem is a lot more serious than
that."
Here the iota-values are points _in_ a line, field-reals _on_ a line,
and signal-reals _about_ and _around_ a line.
So, Chaitin doesn't even have three models of continuous domains,
or "repleteness", of concepts like Lebnitz' principle of perfection
and Hilbert's postulate of continuity.
Mathematics really _does_ define continuity:
and there are at least three models of continuous domains.
So, say you want to sample a real number from [0,1] the interval
at uniform random, and all you have is a fair coin that
gives samples from {0, 1} the set.
So, you start flipping coins and marking the result to make
a sequence of 0's and 1's. Each coin toss _refines_ the
sample.
Yet, each coin toss also _begins_ a new sample. So, to sample
one real number, the super-task results sampling infinitely-many
real numbers.
So, the probability of the first sample being a rational value
is, according to the law of large numbers the law of small numbers,
small, and arbitrarily and infinitesimally small. In theories
that are Pythagorean it's almost-all rationals, while in theories
that are Cantorian it's almost-all transcendentals.
Yet, if a sample arrives at a rational, the repeating character
of rationals means that thusly the _one_ sample of a rational
number is automatically _infinitely-many_ samples of rational
numbers.
So, it makes sense to consider that the probability of sampling
a rational number from [0,1] is about 0.5.
This isn't Pythagorean by itself, and isn't Cantorian by itself.
It's them together according to accounts of paradox-free reason,
not "non-classical logics where we ignore contradiction",
which is _hypocrisy_ and furthermore _fallacious_,
since "infinity" and "continuity" are "absolute" and "replete".
"Let’s start with Borel’s know-it-all number, but now let’s use the Nth
binary digit to tell us whether or not the Nth computer program ever
halts. So now Borel’s number is an oracle for the halting problem. For >>> example, there is a bit which tells us whether or not the Riemann
hypothesis is true, for that is equivalent to the statement that a
program that systematically searches for zeros of the zeta function that >>> are in the wrong place, never halts.
It turns out that this number, which I’ll call Turing’s number even
though it does not occur in Turing’s paper, is wasting bits, it is
actually highly redundant. We don’t really need N bits to answer N cases >>> of the halting problem, a much smaller number of bits will do. Why?
Well, consider some large number N of cases of the halting problem, some >>> large number N of individual programs for which we want to know whether
or not each one halts. Is this really N bits of mathematical
information? No, the answers are not independent, they are highly
correlated. How? Well, in order to answer N cases of the halting
problem, we don’t really need to know each individual answer; it
suffices to know how many of these N programs will eventually halt. Once >>> we know this number, which is only about log_2 N
bits of information, we can run the N programs in parallel until exactly >>> this number of them halt, and then we know that none of the remaining
programs will ever halt. And log_2 N is much, much less than N for all
sufficiently large N. In other words, Turing’s number isn’t the best >>> possible oracle for the halting problem. It is highly redundant, it uses >>> far too many bits.
Using essentially this idea, we can get the best possible oracle number
for the halting problem; that is the halting probability Ω, which has no >>> redundancy, none at all.
So, now that there's readily equipped a notion of uniform sampling
that results "oracle numbers", always _infinitely-many_ just to get one, >>> then Chaitin's quote is equipped some context that makes
quite a fresh reading.
This goes for all y'all.
Actually, thousands of years before Russell or Tarski claimed that
"truth is whatever I, Lord Russell or Tsar Tarski, say that agrees
with myself", the notion that mathematical truth is _discovered_ not _invented_ was "the truth", then that structural realism and realist structuralism make for an account with both an idealistic and an
analytical tradition, keeping science for itself as a strengthened
analytical position and the idealistic getting equipped with mental
senses of the faculties of reason about logic and mathematics (and
infinity and continuity) so that Kant is satisfied that "1 + 1 = 2".
Then, Wittgenstein is just a cad, and while it's respected
his right to say "I, wild Wittgenstein, say that you can't say
that you say anything at all", it's ignored as saying jack squat.
Natural reasoners can simply arrive at grounds for reason after
axiomless natural deduction making for logic, geometry, number theory,
with infinity and continuity, and so on. Then formalisms follow as
after perspectival accounts of restriction-of-comprehension given a
thorough account of expansion-of-comprehension.
Plato could be proud.
On 5/21/26 9:54 AM, Ross Finlayson wrote:
On 05/21/2026 06:02 AM, olcott wrote:
On 5/18/2026 11:44 AM, Ross Finlayson wrote:
On 05/18/2026 09:03 AM, olcott wrote:
On 5/18/2026 10:14 AM, Ross Finlayson wrote:
On 05/17/2026 08:48 PM, Chris M. Thomasson wrote:How can a man as smart as you get this so incorrectly?
On 5/17/2026 8:46 PM, Chris M. Thomasson wrote:
On 5/17/2026 5:24 PM, Ross Finlayson wrote:
On 05/17/2026 05:10 PM, Ross Finlayson wrote:
On 05/17/2026 02:46 PM, Chris M. Thomasson wrote:
On 5/17/2026 2:21 PM, phoenix wrote:
Chris M. Thomasson wrote:
On 5/16/2026 2:30 PM, phoenix wrote:
Chris M. Thomasson wrote:
Or maybe a different tarot, "the star" because you have >>>>>>>>>>>>>> such aI find that 'except' paired with 'yet' covers every >>>>>>>>>>>>>>>> instance of
Yet that yet that yet that yet that yet that it is so: >>>>>>>>>>>>>>>>> that that that that that it is so.
'but.' If you can find an exception to this, please show >>>>>>>>>>>>>>>> me.
fascination with me?
I think you are a sock puppet for olcott.
I know you think that, but I don't see any motivation on my >>>>>>>>>>>> part to
disabuse you of the notion. Why not play into it and further >>>>>>>>>>>> befuddle
you? If it were the case that I were not olcott, that is. >>>>>>>>>>>>
Ask your self what his halting decider would say... Look in the >>>>>>>>>>> mirror?
One of the problems of environments of the unmoderated and >>>>>>>>>> pseudonymous
sort is that there are all kinds of trolls. There are plain >>>>>>>>>> rage- bait
and flamer trolls, looky-loos and non-sequitur types, then, also >>>>>>>>>> all
sorts of anti-trolls, and these and those.
Then, for example, for something like "it's a free country", then >>>>>>>>>> when I see stuff like either
"smell the new normal, you're living in a dictatorship",
or,
"suffer the children, so your social media and phone get hacked", >>>>>>>>>> then either way the idea of being aware ("woke" wasn't a word >>>>>>>>>> and I'd imagine it would be "awoke" or "woken", or, "woke" will >>>>>>>>>> do),
and caring (although, you know, not _too_ caring), that trolls >>>>>>>>>> and repeti-bots on "social" media are anti-social.
So, it's fair that people get wary of trolls, and, begin to >>>>>>>>>> suspect
trolls in the likely places, and learn to make a troll-filter, >>>>>>>>>> and basically a skeptical if not cynical outlook on the world >>>>>>>>>> today,
that there are trolls and trolls, and sometimes it's easiest to >>>>>>>>>> ignore them away.
Then, there are cranks, ....
The crank is one of the easiest sorts of identities to mimic, >>>>>>>>>> give it a howler fallacy it won't let go and the plain obstinance >>>>>>>>>> combined with the stubbornness along with the sort of plain >>>>>>>>>> unwarranted persistence, then it's not always easy to tell the >>>>>>>>>> difference between cranks and trolls, though often it is,
and between persons and bots, though often it is.
'Murica.
Then, about the thread, the idea is that it's great if these >>>>>>>>>> long-running mostly-empty tit-for-tat nonsense threads get >>>>>>>>>> hijacked by passers-by then into discussions about the issues >>>>>>>>>> at hand, like about the many, many things to do with the
"mathematics" of continuity and infinity, since, despite
the idea of some retro-finitists that their world is a
dot, and not even like AP a giant plutonium atom, there's
much to be done to bring real infinite and continuity into >>>>>>>>>> mathematics, then for physics and so on.
So, new blood (or fresh meat) writing on the thread so
it's not just an echo-chamber of trolls and anti-trolls
which is one big troll, is not necessarily a bad thing.
I enjoy CMT's usual spontaneous cheerful enthusiasm,
though as a perceived bot itself when it once-a-year
cites its prompter, then though the affected anxiety
pronation reminds me of too many lessons learned like
not to smell fear or flinch or beg or impose or presume
or assume or judge or telepathically scan or lurk or
menace or make gossip or berate or scoff.
Fwiw, check out these funny halt deciders... They only halt when >>>>>>>> all
possible paths are hit. If you think about its kind of akin to >>>>>>>> olcotts
DD. i simply hijack its result. Here is a version that uses random >>>>>>>> numbers for the fuzzer:
In applesoft basic for fun. ;^D
You can run these here:
https://www.calormen.com/jsbasic/
_____________________________
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
1010 PRINT "FIN... All paths hit."
1020 PRINT "NON_HALT P0 = "; P0
1030 PRINT "HALT P1 = "; P1
_____________________________
Here is one that requires input from a user:
_____________________________
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 INPUT "Shall DD halt or not? " ; A$
110 REM 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
^^^^^^^^^^^^
_____________________________
God damn it forgot to add in line 1000 onward! Shit happens:
1000
1010 PRINT "FIN... All paths hit."
1020 PRINT "NON_HALT P0 = "; P0
1030 PRINT "HALT P1 = "; P1
Corrected user input one:
_______________
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 INPUT "Shall DD halt or not? " ; A$
110 REM 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
1010 PRINT "FIN... All paths hit."
1020 PRINT "NON_HALT P0 = "; P0
1030 PRINT "HALT P1 = "; P1
_______________
Sorry about that shit!
It only halts when all paths have been hit.
About cranks then, there's something about a crank I admire, >>>>>>>>> not so much the being wrong part yet the dream, having the
dreams, I'm all for people having the dream when it's not
frustrating or threatening other people's dreams.
So, as I usually enough put it, "retro-finitist crankety
trolls can step off and get bent".
I'm not a fan of any "new" normal, we already have plain
old "normal normal".
Hm.
There are at least three accounts of programs whether they halt.
A) almost-all programs halt
B) almost-all programs don't halt
C) half of programs halt
The number of programs that halt is between 0 and 100%
excluding the endpoints.
https://arxiv.org/abs/math/0611740
"The Halting Probability Omega: Irreducible Complexity in Pure
Mathematics", G. Chaitin
"Gödel himself did not think that his theorem showed that mathematics >>>> has limitations. In several essays he made it clear that he believed
that mathematicians could eventually settle any significant question by >>>> using their mathematical intuition, their ability to directly perceive >>>> the Platonic world of mathematical ideas, and by inventing or
discovering new concepts and new axioms, new principles.
Furthermore, I share Enriques’s faith in intuition. I think that
excessive formalism and abstraction is killing mathematics. In my
opinion math papers shouldn’t attempt to replace all words by formulas, >>>> instead they should be like literary essays, they should attempt to
explain and convince.
Extending Dag Prawitz's Theory of Grounds while remaining
directly within the realm of proof theoretic Semantics then
G simply becomes ungrounded in PA and grounded in meta-math.
It has taken PTS quite a few decades, all the way up to 2012
to catch up with what Wittgenstein said decades earlier:
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's
system' means: the opposite has been proved in Russell's
system. https://www.liarparadox.org/Wittgenstein.pdf
So let me tell you the story of metamathematics, of how mathematicians >>>> have tried to use mathematical methods to study the power and the
limitations of math itself. It’s a fairly dramatic story; in a previous >>>> era it might have been the subject of epic poems, of Iliads and
Odysseys
of verse. I’ll start with David Hilbert."
"In my opinion this is a fundamental step forward in the philosophy of >>>> mathematics because it makes incompleteness seem much more concrete and >>>> much more natural. It’s almost a problem in physics, it’s about a
machine, you just ask whether or not it’s going to eventually stop, and >>>> it turns out there’s no way, no general way, to answer that question. >>>> Let me emphasize that if a program does halt, we can eventually
discover
that. The problem, an extremely deep one, is to show that a program
will
never halt if this is in fact so. One can settle many special cases,
even an infinity of them, but no finite set of axioms can enable you to >>>> settle all possible cases."
Hm, " ... no finite set of axioms ...", ..., how about "no axioms".
"The real numbers are the simplest thing in the world geometrically,
they are just points on a line. But arithmetically, as individuals,
real
numbers are actually rather unreal. Turing’s 1936 uncomputable real is >>>> just the tip of the iceberg, the problem is a lot more serious than
that."
Here the iota-values are points _in_ a line, field-reals _on_ a line,
and signal-reals _about_ and _around_ a line.
So, Chaitin doesn't even have three models of continuous domains,
or "repleteness", of concepts like Lebnitz' principle of perfection
and Hilbert's postulate of continuity.
Mathematics really _does_ define continuity:
and there are at least three models of continuous domains.
So, say you want to sample a real number from [0,1] the interval
at uniform random, and all you have is a fair coin that
gives samples from {0, 1} the set.
So, you start flipping coins and marking the result to make
a sequence of 0's and 1's. Each coin toss _refines_ the
sample.
Yet, each coin toss also _begins_ a new sample. So, to sample
one real number, the super-task results sampling infinitely-many
real numbers.
So, the probability of the first sample being a rational value
is, according to the law of large numbers the law of small numbers,
small, and arbitrarily and infinitesimally small. In theories
that are Pythagorean it's almost-all rationals, while in theories
that are Cantorian it's almost-all transcendentals.
Yet, if a sample arrives at a rational, the repeating character
of rationals means that thusly the _one_ sample of a rational
number is automatically _infinitely-many_ samples of rational
numbers.
So, it makes sense to consider that the probability of sampling
a rational number from [0,1] is about 0.5.
This isn't Pythagorean by itself, and isn't Cantorian by itself.
It's them together according to accounts of paradox-free reason,
not "non-classical logics where we ignore contradiction",
which is _hypocrisy_ and furthermore _fallacious_,
since "infinity" and "continuity" are "absolute" and "replete".
"Let’s start with Borel’s know-it-all number, but now let’s use the Nth
binary digit to tell us whether or not the Nth computer program ever
halts. So now Borel’s number is an oracle for the halting problem. For >>>> example, there is a bit which tells us whether or not the Riemann
hypothesis is true, for that is equivalent to the statement that a
program that systematically searches for zeros of the zeta function
that
are in the wrong place, never halts.
It turns out that this number, which I’ll call Turing’s number even >>>> though it does not occur in Turing’s paper, is wasting bits, it is
actually highly redundant. We don’t really need N bits to answer N
cases
of the halting problem, a much smaller number of bits will do. Why?
Well, consider some large number N of cases of the halting problem,
some
large number N of individual programs for which we want to know whether >>>> or not each one halts. Is this really N bits of mathematical
information? No, the answers are not independent, they are highly
correlated. How? Well, in order to answer N cases of the halting
problem, we don’t really need to know each individual answer; it
suffices to know how many of these N programs will eventually halt.
Once
we know this number, which is only about log_2 N
bits of information, we can run the N programs in parallel until
exactly
this number of them halt, and then we know that none of the remaining
programs will ever halt. And log_2 N is much, much less than N for all >>>> sufficiently large N. In other words, Turing’s number isn’t the best >>>> possible oracle for the halting problem. It is highly redundant, it
uses
far too many bits.
Using essentially this idea, we can get the best possible oracle number >>>> for the halting problem; that is the halting probability Ω, which
has no
redundancy, none at all.
So, now that there's readily equipped a notion of uniform sampling
that results "oracle numbers", always _infinitely-many_ just to get
one,
then Chaitin's quote is equipped some context that makes
quite a fresh reading.
This goes for all y'all.
Actually, thousands of years before Russell or Tarski claimed that
"truth is whatever I, Lord Russell or Tsar Tarski, say that agrees
with myself", the notion that mathematical truth is _discovered_ not
_invented_ was "the truth", then that structural realism and realist
structuralism make for an account with both an idealistic and an
analytical tradition, keeping science for itself as a strengthened
analytical position and the idealistic getting equipped with mental
senses of the faculties of reason about logic and mathematics (and
infinity and continuity) so that Kant is satisfied that "1 + 1 = 2".
Then, Wittgenstein is just a cad, and while it's respected
his right to say "I, wild Wittgenstein, say that you can't say
that you say anything at all", it's ignored as saying jack squat.
Natural reasoners can simply arrive at grounds for reason after
axiomless natural deduction making for logic, geometry, number theory,
with infinity and continuity, and so on. Then formalisms follow as
after perspectival accounts of restriction-of-comprehension given a
thorough account of expansion-of-comprehension.
Plato could be proud.
hey ross what group are you commenting from?
On 05/21/2026 11:14 AM, dart200 wrote:
On 5/21/26 9:54 AM, Ross Finlayson wrote:
On 05/21/2026 06:02 AM, olcott wrote:
On 5/18/2026 11:44 AM, Ross Finlayson wrote:
On 05/18/2026 09:03 AM, olcott wrote:
On 5/18/2026 10:14 AM, Ross Finlayson wrote:
On 05/17/2026 08:48 PM, Chris M. Thomasson wrote:How can a man as smart as you get this so incorrectly?
On 5/17/2026 8:46 PM, Chris M. Thomasson wrote:
On 5/17/2026 5:24 PM, Ross Finlayson wrote:
On 05/17/2026 05:10 PM, Ross Finlayson wrote:
On 05/17/2026 02:46 PM, Chris M. Thomasson wrote:
On 5/17/2026 2:21 PM, phoenix wrote:
Chris M. Thomasson wrote:
On 5/16/2026 2:30 PM, phoenix wrote:
Chris M. Thomasson wrote:
Or maybe a different tarot, "the star" because you have >>>>>>>>>>>>>>> such aI find that 'except' paired with 'yet' covers every >>>>>>>>>>>>>>>>> instance of
Yet that yet that yet that yet that yet that it is so: >>>>>>>>>>>>>>>>>> that that that that that it is so.
'but.' If you can find an exception to this, please show >>>>>>>>>>>>>>>>> me.
fascination with me?
I think you are a sock puppet for olcott.
I know you think that, but I don't see any motivation on my >>>>>>>>>>>>> part to
disabuse you of the notion. Why not play into it and further >>>>>>>>>>>>> befuddle
you? If it were the case that I were not olcott, that is. >>>>>>>>>>>>>
Ask your self what his halting decider would say... Look in the >>>>>>>>>>>> mirror?
One of the problems of environments of the unmoderated and >>>>>>>>>>> pseudonymous
sort is that there are all kinds of trolls. There are plain >>>>>>>>>>> rage- bait
and flamer trolls, looky-loos and non-sequitur types, then, also >>>>>>>>>>> all
sorts of anti-trolls, and these and those.
Then, for example, for something like "it's a free country", >>>>>>>>>>> then
when I see stuff like either
"smell the new normal, you're living in a dictatorship", >>>>>>>>>>> or,
"suffer the children, so your social media and phone get >>>>>>>>>>> hacked",
then either way the idea of being aware ("woke" wasn't a word >>>>>>>>>>> and I'd imagine it would be "awoke" or "woken", or, "woke" will >>>>>>>>>>> do),
and caring (although, you know, not _too_ caring), that trolls >>>>>>>>>>> and repeti-bots on "social" media are anti-social.
So, it's fair that people get wary of trolls, and, begin to >>>>>>>>>>> suspect
trolls in the likely places, and learn to make a troll-filter, >>>>>>>>>>> and basically a skeptical if not cynical outlook on the world >>>>>>>>>>> today,
that there are trolls and trolls, and sometimes it's easiest to >>>>>>>>>>> ignore them away.
Then, there are cranks, ....
The crank is one of the easiest sorts of identities to mimic, >>>>>>>>>>> give it a howler fallacy it won't let go and the plain
obstinance
combined with the stubbornness along with the sort of plain >>>>>>>>>>> unwarranted persistence, then it's not always easy to tell the >>>>>>>>>>> difference between cranks and trolls, though often it is, >>>>>>>>>>> and between persons and bots, though often it is.
'Murica.
Then, about the thread, the idea is that it's great if these >>>>>>>>>>> long-running mostly-empty tit-for-tat nonsense threads get >>>>>>>>>>> hijacked by passers-by then into discussions about the issues >>>>>>>>>>> at hand, like about the many, many things to do with the >>>>>>>>>>> "mathematics" of continuity and infinity, since, despite >>>>>>>>>>> the idea of some retro-finitists that their world is a
dot, and not even like AP a giant plutonium atom, there's >>>>>>>>>>> much to be done to bring real infinite and continuity into >>>>>>>>>>> mathematics, then for physics and so on.
So, new blood (or fresh meat) writing on the thread so
it's not just an echo-chamber of trolls and anti-trolls
which is one big troll, is not necessarily a bad thing.
I enjoy CMT's usual spontaneous cheerful enthusiasm,
though as a perceived bot itself when it once-a-year
cites its prompter, then though the affected anxiety
pronation reminds me of too many lessons learned like
not to smell fear or flinch or beg or impose or presume
or assume or judge or telepathically scan or lurk or
menace or make gossip or berate or scoff.
Fwiw, check out these funny halt deciders... They only halt when >>>>>>>>> all
possible paths are hit. If you think about its kind of akin to >>>>>>>>> olcotts
DD. i simply hijack its result. Here is a version that uses random >>>>>>>>> numbers for the fuzzer:
In applesoft basic for fun. ;^D
You can run these here:
https://www.calormen.com/jsbasic/
_____________________________
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
1010 PRINT "FIN... All paths hit."
1020 PRINT "NON_HALT P0 = "; P0
1030 PRINT "HALT P1 = "; P1
_____________________________
Here is one that requires input from a user:
_____________________________
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 INPUT "Shall DD halt or not? " ; A$
110 REM 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
^^^^^^^^^^^^
_____________________________
God damn it forgot to add in line 1000 onward! Shit happens:
1000
1010 PRINT "FIN... All paths hit."
1020 PRINT "NON_HALT P0 = "; P0
1030 PRINT "HALT P1 = "; P1
Corrected user input one:
_______________
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 INPUT "Shall DD halt or not? " ; A$
110 REM 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
1010 PRINT "FIN... All paths hit."
1020 PRINT "NON_HALT P0 = "; P0
1030 PRINT "HALT P1 = "; P1
_______________
Sorry about that shit!
It only halts when all paths have been hit.
About cranks then, there's something about a crank I admire, >>>>>>>>>> not so much the being wrong part yet the dream, having the >>>>>>>>>> dreams, I'm all for people having the dream when it's not
frustrating or threatening other people's dreams.
So, as I usually enough put it, "retro-finitist crankety
trolls can step off and get bent".
I'm not a fan of any "new" normal, we already have plain
old "normal normal".
Hm.
There are at least three accounts of programs whether they halt. >>>>>>>
A) almost-all programs halt
B) almost-all programs don't halt
C) half of programs halt
The number of programs that halt is between 0 and 100%
excluding the endpoints.
https://arxiv.org/abs/math/0611740
"The Halting Probability Omega: Irreducible Complexity in Pure
Mathematics", G. Chaitin
"Gödel himself did not think that his theorem showed that mathematics >>>>> has limitations. In several essays he made it clear that he believed >>>>> that mathematicians could eventually settle any significant
question by
using their mathematical intuition, their ability to directly perceive >>>>> the Platonic world of mathematical ideas, and by inventing or
discovering new concepts and new axioms, new principles.
Furthermore, I share Enriques’s faith in intuition. I think that
excessive formalism and abstraction is killing mathematics. In my
opinion math papers shouldn’t attempt to replace all words by
formulas,
instead they should be like literary essays, they should attempt to
explain and convince.
Extending Dag Prawitz's Theory of Grounds while remaining
directly within the realm of proof theoretic Semantics then
G simply becomes ungrounded in PA and grounded in meta-math.
It has taken PTS quite a few decades, all the way up to 2012
to catch up with what Wittgenstein said decades earlier:
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's
system' means: the opposite has been proved in Russell's
system. https://www.liarparadox.org/Wittgenstein.pdf
So let me tell you the story of metamathematics, of how mathematicians >>>>> have tried to use mathematical methods to study the power and the
limitations of math itself. It’s a fairly dramatic story; in a
previous
era it might have been the subject of epic poems, of Iliads and
Odysseys
of verse. I’ll start with David Hilbert."
"In my opinion this is a fundamental step forward in the philosophy of >>>>> mathematics because it makes incompleteness seem much more concrete >>>>> and
much more natural. It’s almost a problem in physics, it’s about a >>>>> machine, you just ask whether or not it’s going to eventually stop, >>>>> and
it turns out there’s no way, no general way, to answer that question. >>>>> Let me emphasize that if a program does halt, we can eventually
discover
that. The problem, an extremely deep one, is to show that a program
will
never halt if this is in fact so. One can settle many special cases, >>>>> even an infinity of them, but no finite set of axioms can enable
you to
settle all possible cases."
Hm, " ... no finite set of axioms ...", ..., how about "no axioms".
"The real numbers are the simplest thing in the world geometrically, >>>>> they are just points on a line. But arithmetically, as individuals,
real
numbers are actually rather unreal. Turing’s 1936 uncomputable real is >>>>> just the tip of the iceberg, the problem is a lot more serious than
that."
Here the iota-values are points _in_ a line, field-reals _on_ a line, >>>>> and signal-reals _about_ and _around_ a line.
So, Chaitin doesn't even have three models of continuous domains,
or "repleteness", of concepts like Lebnitz' principle of perfection
and Hilbert's postulate of continuity.
Mathematics really _does_ define continuity:
and there are at least three models of continuous domains.
So, say you want to sample a real number from [0,1] the interval
at uniform random, and all you have is a fair coin that
gives samples from {0, 1} the set.
So, you start flipping coins and marking the result to make
a sequence of 0's and 1's. Each coin toss _refines_ the
sample.
Yet, each coin toss also _begins_ a new sample. So, to sample
one real number, the super-task results sampling infinitely-many
real numbers.
So, the probability of the first sample being a rational value
is, according to the law of large numbers the law of small numbers,
small, and arbitrarily and infinitesimally small. In theories
that are Pythagorean it's almost-all rationals, while in theories
that are Cantorian it's almost-all transcendentals.
Yet, if a sample arrives at a rational, the repeating character
of rationals means that thusly the _one_ sample of a rational
number is automatically _infinitely-many_ samples of rational
numbers.
So, it makes sense to consider that the probability of sampling
a rational number from [0,1] is about 0.5.
This isn't Pythagorean by itself, and isn't Cantorian by itself.
It's them together according to accounts of paradox-free reason,
not "non-classical logics where we ignore contradiction",
which is _hypocrisy_ and furthermore _fallacious_,
since "infinity" and "continuity" are "absolute" and "replete".
"Let’s start with Borel’s know-it-all number, but now let’s use the
Nth
binary digit to tell us whether or not the Nth computer program ever >>>>> halts. So now Borel’s number is an oracle for the halting problem. For >>>>> example, there is a bit which tells us whether or not the Riemann
hypothesis is true, for that is equivalent to the statement that a
program that systematically searches for zeros of the zeta function
that
are in the wrong place, never halts.
It turns out that this number, which I’ll call Turing’s number even >>>>> though it does not occur in Turing’s paper, is wasting bits, it is >>>>> actually highly redundant. We don’t really need N bits to answer N >>>>> cases
of the halting problem, a much smaller number of bits will do. Why?
Well, consider some large number N of cases of the halting problem,
some
large number N of individual programs for which we want to know
whether
or not each one halts. Is this really N bits of mathematical
information? No, the answers are not independent, they are highly
correlated. How? Well, in order to answer N cases of the halting
problem, we don’t really need to know each individual answer; it
suffices to know how many of these N programs will eventually halt.
Once
we know this number, which is only about log_2 N
bits of information, we can run the N programs in parallel until
exactly
this number of them halt, and then we know that none of the remaining >>>>> programs will ever halt. And log_2 N is much, much less than N for all >>>>> sufficiently large N. In other words, Turing’s number isn’t the best >>>>> possible oracle for the halting problem. It is highly redundant, it
uses
far too many bits.
Using essentially this idea, we can get the best possible oracle
number
for the halting problem; that is the halting probability Ω, which
has no
redundancy, none at all.
So, now that there's readily equipped a notion of uniform sampling
that results "oracle numbers", always _infinitely-many_ just to get
one,
then Chaitin's quote is equipped some context that makes
quite a fresh reading.
This goes for all y'all.
Actually, thousands of years before Russell or Tarski claimed that
"truth is whatever I, Lord Russell or Tsar Tarski, say that agrees
with myself", the notion that mathematical truth is _discovered_ not
_invented_ was "the truth", then that structural realism and realist
structuralism make for an account with both an idealistic and an
analytical tradition, keeping science for itself as a strengthened
analytical position and the idealistic getting equipped with mental
senses of the faculties of reason about logic and mathematics (and
infinity and continuity) so that Kant is satisfied that "1 + 1 = 2".
Then, Wittgenstein is just a cad, and while it's respected
his right to say "I, wild Wittgenstein, say that you can't say
that you say anything at all", it's ignored as saying jack squat.
Natural reasoners can simply arrive at grounds for reason after
axiomless natural deduction making for logic, geometry, number theory,
with infinity and continuity, and so on. Then formalisms follow as
after perspectival accounts of restriction-of-comprehension given a
thorough account of expansion-of-comprehension.
Plato could be proud.
hey ross what group are you commenting from?
I usually read sci.math and sci.logic, and sometimes comp.ai.philosophy,
not so much comp.theory, though,
here there's a general idea that "Zeno machines"
are a model of computation vis-a-vis usual accounts
after Turing machines or Frege's concept-script or
MiX or stack machines or Harvard/vonNeumann or
finite-state-machines the automata.
For decades and since I formalized a few key aspects
of models of continuous domains, nobody tells me I'm
wrong anymore since I'm not wrong, or rather,
the mathematics isn't wrong.
Arriving at that though involves of a bit of a
thorough account of theory for reason, which
here is a paleo-classical post-modern account.
Anyways "olcott" is just the latest spam troll
in a sense - then that it doesn't much matter
whether it was standard accounts or non-standard accounts
or plain retro-finitist crankety troll accounts,
I can offer a sound criticism to any.
On 5/21/2026 7:45 PM, Ross Finlayson wrote:
On 05/21/2026 11:14 AM, dart200 wrote:
On 5/21/26 9:54 AM, Ross Finlayson wrote:
On 05/21/2026 06:02 AM, olcott wrote:
On 5/18/2026 11:44 AM, Ross Finlayson wrote:
On 05/18/2026 09:03 AM, olcott wrote:
On 5/18/2026 10:14 AM, Ross Finlayson wrote:
On 05/17/2026 08:48 PM, Chris M. Thomasson wrote:How can a man as smart as you get this so incorrectly?
On 5/17/2026 8:46 PM, Chris M. Thomasson wrote:
On 5/17/2026 5:24 PM, Ross Finlayson wrote:
On 05/17/2026 05:10 PM, Ross Finlayson wrote:
On 05/17/2026 02:46 PM, Chris M. Thomasson wrote:
On 5/17/2026 2:21 PM, phoenix wrote:
Chris M. Thomasson wrote:
On 5/16/2026 2:30 PM, phoenix wrote:
Chris M. Thomasson wrote:
Or maybe a different tarot, "the star" because you have >>>>>>>>>>>>>>>> such aI find that 'except' paired with 'yet' covers every >>>>>>>>>>>>>>>>>> instance of
Yet that yet that yet that yet that yet that it is so: >>>>>>>>>>>>>>>>>>> that that that that that it is so.
'but.' If you can find an exception to this, please show >>>>>>>>>>>>>>>>>> me.
fascination with me?
I think you are a sock puppet for olcott.
I know you think that, but I don't see any motivation on my >>>>>>>>>>>>>> part to
disabuse you of the notion. Why not play into it and further >>>>>>>>>>>>>> befuddle
you? If it were the case that I were not olcott, that is. >>>>>>>>>>>>>>
Ask your self what his halting decider would say... Look in >>>>>>>>>>>>> the
mirror?
One of the problems of environments of the unmoderated and >>>>>>>>>>>> pseudonymous
sort is that there are all kinds of trolls. There are plain >>>>>>>>>>>> rage- bait
and flamer trolls, looky-loos and non-sequitur types, then, >>>>>>>>>>>> also
all
sorts of anti-trolls, and these and those.
Then, for example, for something like "it's a free country", >>>>>>>>>>>> then
when I see stuff like either
"smell the new normal, you're living in a dictatorship", >>>>>>>>>>>> or,
"suffer the children, so your social media and phone get >>>>>>>>>>>> hacked",
then either way the idea of being aware ("woke" wasn't a word >>>>>>>>>>>> and I'd imagine it would be "awoke" or "woken", or, "woke" will >>>>>>>>>>>> do),
and caring (although, you know, not _too_ caring), that trolls >>>>>>>>>>>> and repeti-bots on "social" media are anti-social.
So, it's fair that people get wary of trolls, and, begin to >>>>>>>>>>>> suspect
trolls in the likely places, and learn to make a troll-filter, >>>>>>>>>>>> and basically a skeptical if not cynical outlook on the world >>>>>>>>>>>> today,
that there are trolls and trolls, and sometimes it's easiest to >>>>>>>>>>>> ignore them away.
Then, there are cranks, ....
The crank is one of the easiest sorts of identities to mimic, >>>>>>>>>>>> give it a howler fallacy it won't let go and the plain >>>>>>>>>>>> obstinance
combined with the stubbornness along with the sort of plain >>>>>>>>>>>> unwarranted persistence, then it's not always easy to tell the >>>>>>>>>>>> difference between cranks and trolls, though often it is, >>>>>>>>>>>> and between persons and bots, though often it is.
'Murica.
Then, about the thread, the idea is that it's great if these >>>>>>>>>>>> long-running mostly-empty tit-for-tat nonsense threads get >>>>>>>>>>>> hijacked by passers-by then into discussions about the issues >>>>>>>>>>>> at hand, like about the many, many things to do with the >>>>>>>>>>>> "mathematics" of continuity and infinity, since, despite >>>>>>>>>>>> the idea of some retro-finitists that their world is a >>>>>>>>>>>> dot, and not even like AP a giant plutonium atom, there's >>>>>>>>>>>> much to be done to bring real infinite and continuity into >>>>>>>>>>>> mathematics, then for physics and so on.
So, new blood (or fresh meat) writing on the thread so >>>>>>>>>>>> it's not just an echo-chamber of trolls and anti-trolls >>>>>>>>>>>> which is one big troll, is not necessarily a bad thing. >>>>>>>>>>>>
I enjoy CMT's usual spontaneous cheerful enthusiasm,
though as a perceived bot itself when it once-a-year
cites its prompter, then though the affected anxiety
pronation reminds me of too many lessons learned like
not to smell fear or flinch or beg or impose or presume
or assume or judge or telepathically scan or lurk or
menace or make gossip or berate or scoff.
Fwiw, check out these funny halt deciders... They only halt when >>>>>>>>>> all
possible paths are hit. If you think about its kind of akin to >>>>>>>>>> olcotts
DD. i simply hijack its result. Here is a version that uses >>>>>>>>>> random
numbers for the fuzzer:
In applesoft basic for fun. ;^D
You can run these here:
https://www.calormen.com/jsbasic/
_____________________________
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
1010 PRINT "FIN... All paths hit."
1020 PRINT "NON_HALT P0 = "; P0
1030 PRINT "HALT P1 = "; P1
_____________________________
Here is one that requires input from a user:
_____________________________
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 INPUT "Shall DD halt or not? " ; A$
110 REM 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
^^^^^^^^^^^^
_____________________________
God damn it forgot to add in line 1000 onward! Shit happens: >>>>>>>>>
1000
1010 PRINT "FIN... All paths hit."
1020 PRINT "NON_HALT P0 = "; P0
1030 PRINT "HALT P1 = "; P1
Corrected user input one:
_______________
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 INPUT "Shall DD halt or not? " ; A$
110 REM 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
1010 PRINT "FIN... All paths hit."
1020 PRINT "NON_HALT P0 = "; P0
1030 PRINT "HALT P1 = "; P1
_______________
Sorry about that shit!
It only halts when all paths have been hit.
About cranks then, there's something about a crank I admire, >>>>>>>>>>> not so much the being wrong part yet the dream, having the >>>>>>>>>>> dreams, I'm all for people having the dream when it's not >>>>>>>>>>> frustrating or threatening other people's dreams.
So, as I usually enough put it, "retro-finitist crankety >>>>>>>>>>> trolls can step off and get bent".
I'm not a fan of any "new" normal, we already have plain >>>>>>>>>>> old "normal normal".
Hm.
There are at least three accounts of programs whether they halt. >>>>>>>>
A) almost-all programs halt
B) almost-all programs don't halt
C) half of programs halt
The number of programs that halt is between 0 and 100%
excluding the endpoints.
https://arxiv.org/abs/math/0611740
"The Halting Probability Omega: Irreducible Complexity in Pure
Mathematics", G. Chaitin
"Gödel himself did not think that his theorem showed that mathematics >>>>>> has limitations. In several essays he made it clear that he believed >>>>>> that mathematicians could eventually settle any significant
question by
using their mathematical intuition, their ability to directly
perceive
the Platonic world of mathematical ideas, and by inventing or
discovering new concepts and new axioms, new principles.
Furthermore, I share Enriques’s faith in intuition. I think that >>>>>> excessive formalism and abstraction is killing mathematics. In my
opinion math papers shouldn’t attempt to replace all words by
formulas,
instead they should be like literary essays, they should attempt to >>>>>> explain and convince.
Extending Dag Prawitz's Theory of Grounds while remaining
directly within the realm of proof theoretic Semantics then
G simply becomes ungrounded in PA and grounded in meta-math.
It has taken PTS quite a few decades, all the way up to 2012
to catch up with what Wittgenstein said decades earlier:
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's
system' means: the opposite has been proved in Russell's
system. https://www.liarparadox.org/Wittgenstein.pdf
So let me tell you the story of metamathematics, of how
mathematicians
have tried to use mathematical methods to study the power and the
limitations of math itself. It’s a fairly dramatic story; in a
previous
era it might have been the subject of epic poems, of Iliads and
Odysseys
of verse. I’ll start with David Hilbert."
"In my opinion this is a fundamental step forward in the
philosophy of
mathematics because it makes incompleteness seem much more
concrete and
much more natural. It’s almost a problem in physics, it’s about a >>>>>> machine, you just ask whether or not it’s going to eventually
stop, and
it turns out there’s no way, no general way, to answer that question. >>>>>> Let me emphasize that if a program does halt, we can eventually
discover
that. The problem, an extremely deep one, is to show that a program >>>>>> will
never halt if this is in fact so. One can settle many special cases, >>>>>> even an infinity of them, but no finite set of axioms can enable
you to
settle all possible cases."
Hm, " ... no finite set of axioms ...", ..., how about "no axioms". >>>>>>
"The real numbers are the simplest thing in the world geometrically, >>>>>> they are just points on a line. But arithmetically, as individuals, >>>>>> real
numbers are actually rather unreal. Turing’s 1936 uncomputable
real is
just the tip of the iceberg, the problem is a lot more serious than >>>>>> that."
Here the iota-values are points _in_ a line, field-reals _on_ a line, >>>>>> and signal-reals _about_ and _around_ a line.
So, Chaitin doesn't even have three models of continuous domains,
or "repleteness", of concepts like Lebnitz' principle of perfection >>>>>> and Hilbert's postulate of continuity.
Mathematics really _does_ define continuity:
and there are at least three models of continuous domains.
So, say you want to sample a real number from [0,1] the interval
at uniform random, and all you have is a fair coin that
gives samples from {0, 1} the set.
So, you start flipping coins and marking the result to make
a sequence of 0's and 1's. Each coin toss _refines_ the
sample.
Yet, each coin toss also _begins_ a new sample. So, to sample
one real number, the super-task results sampling infinitely-many
real numbers.
So, the probability of the first sample being a rational value
is, according to the law of large numbers the law of small numbers, >>>>>> small, and arbitrarily and infinitesimally small. In theories
that are Pythagorean it's almost-all rationals, while in theories
that are Cantorian it's almost-all transcendentals.
Yet, if a sample arrives at a rational, the repeating character
of rationals means that thusly the _one_ sample of a rational
number is automatically _infinitely-many_ samples of rational
numbers.
So, it makes sense to consider that the probability of sampling
a rational number from [0,1] is about 0.5.
This isn't Pythagorean by itself, and isn't Cantorian by itself.
It's them together according to accounts of paradox-free reason,
not "non-classical logics where we ignore contradiction",
which is _hypocrisy_ and furthermore _fallacious_,
since "infinity" and "continuity" are "absolute" and "replete".
"Let’s start with Borel’s know-it-all number, but now let’s use >>>>>> the Nth
binary digit to tell us whether or not the Nth computer program ever >>>>>> halts. So now Borel’s number is an oracle for the halting problem. >>>>>> For
example, there is a bit which tells us whether or not the Riemann
hypothesis is true, for that is equivalent to the statement that a >>>>>> program that systematically searches for zeros of the zeta function >>>>>> that
are in the wrong place, never halts.
It turns out that this number, which I’ll call Turing’s number even >>>>>> though it does not occur in Turing’s paper, is wasting bits, it is >>>>>> actually highly redundant. We don’t really need N bits to answer N >>>>>> cases
of the halting problem, a much smaller number of bits will do. Why? >>>>>>
Well, consider some large number N of cases of the halting problem, >>>>>> some
large number N of individual programs for which we want to know
whether
or not each one halts. Is this really N bits of mathematical
information? No, the answers are not independent, they are highly
correlated. How? Well, in order to answer N cases of the halting
problem, we don’t really need to know each individual answer; it >>>>>> suffices to know how many of these N programs will eventually halt. >>>>>> Once
we know this number, which is only about log_2 N
bits of information, we can run the N programs in parallel until
exactly
this number of them halt, and then we know that none of the remaining >>>>>> programs will ever halt. And log_2 N is much, much less than N for >>>>>> all
sufficiently large N. In other words, Turing’s number isn’t the best >>>>>> possible oracle for the halting problem. It is highly redundant, it >>>>>> uses
far too many bits.
Using essentially this idea, we can get the best possible oracle
number
for the halting problem; that is the halting probability Ω, which >>>>>> has no
redundancy, none at all.
So, now that there's readily equipped a notion of uniform sampling >>>>>> that results "oracle numbers", always _infinitely-many_ just to get >>>>>> one,
then Chaitin's quote is equipped some context that makes
quite a fresh reading.
This goes for all y'all.
Actually, thousands of years before Russell or Tarski claimed that
"truth is whatever I, Lord Russell or Tsar Tarski, say that agrees
with myself", the notion that mathematical truth is _discovered_ not
_invented_ was "the truth", then that structural realism and realist
structuralism make for an account with both an idealistic and an
analytical tradition, keeping science for itself as a strengthened
analytical position and the idealistic getting equipped with mental
senses of the faculties of reason about logic and mathematics (and
infinity and continuity) so that Kant is satisfied that "1 + 1 = 2".
Then, Wittgenstein is just a cad, and while it's respected
his right to say "I, wild Wittgenstein, say that you can't say
that you say anything at all", it's ignored as saying jack squat.
Natural reasoners can simply arrive at grounds for reason after
axiomless natural deduction making for logic, geometry, number theory, >>>> with infinity and continuity, and so on. Then formalisms follow as
after perspectival accounts of restriction-of-comprehension given a
thorough account of expansion-of-comprehension.
Plato could be proud.
hey ross what group are you commenting from?
I usually read sci.math and sci.logic, and sometimes comp.ai.philosophy,
not so much comp.theory, though,
here there's a general idea that "Zeno machines"
are a model of computation vis-a-vis usual accounts
after Turing machines or Frege's concept-script or
MiX or stack machines or Harvard/vonNeumann or
finite-state-machines the automata.
For decades and since I formalized a few key aspects
of models of continuous domains, nobody tells me I'm
wrong anymore since I'm not wrong, or rather,
the mathematics isn't wrong.
Arriving at that though involves of a bit of a
thorough account of theory for reason, which
here is a paleo-classical post-modern account.
Anyways "olcott" is just the latest spam troll
in a sense - then that it doesn't much matter
whether it was standard accounts or non-standard accounts
or plain retro-finitist crankety troll accounts,
I can offer a sound criticism to any.
Infinity does not actually count at all for the
crucial things of the world such as the survival
of the species and the health of the planet.
On the other hand my inter-linked finite semantic
tautologies (or something like them) are required
for dividing truth from dangerous lies.
You seem to be coming off as a mere pseudo-intellectual
in that you judge people instead of the soundness of
their ideas.
If nothing grounds an expression of language in a
truth value then (well duh) it remains ungrounded
in a truth value.
On 05/21/2026 08:34 PM, olcott wrote:
On 5/21/2026 7:45 PM, Ross Finlayson wrote:
On 05/21/2026 11:14 AM, dart200 wrote:
On 5/21/26 9:54 AM, Ross Finlayson wrote:
On 05/21/2026 06:02 AM, olcott wrote:
On 5/18/2026 11:44 AM, Ross Finlayson wrote:
On 05/18/2026 09:03 AM, olcott wrote:
On 5/18/2026 10:14 AM, Ross Finlayson wrote:
On 05/17/2026 08:48 PM, Chris M. Thomasson wrote:How can a man as smart as you get this so incorrectly?
On 5/17/2026 8:46 PM, Chris M. Thomasson wrote:
On 5/17/2026 5:24 PM, Ross Finlayson wrote:
On 05/17/2026 05:10 PM, Ross Finlayson wrote:
On 05/17/2026 02:46 PM, Chris M. Thomasson wrote:
On 5/17/2026 2:21 PM, phoenix wrote:
Chris M. Thomasson wrote:
On 5/16/2026 2:30 PM, phoenix wrote:
Chris M. Thomasson wrote:
Or maybe a different tarot, "the star" because you have >>>>>>>>>>>>>>>>> such aI find that 'except' paired with 'yet' covers every >>>>>>>>>>>>>>>>>>> instance of
Yet that yet that yet that yet that yet that it is so: >>>>>>>>>>>>>>>>>>>> that that that that that it is so.
'but.' If you can find an exception to this, please show >>>>>>>>>>>>>>>>>>> me.
fascination with me?
I think you are a sock puppet for olcott.
I know you think that, but I don't see any motivation on my >>>>>>>>>>>>>>> part to
disabuse you of the notion. Why not play into it and further >>>>>>>>>>>>>>> befuddle
you? If it were the case that I were not olcott, that is. >>>>>>>>>>>>>>>
Ask your self what his halting decider would say... Look in >>>>>>>>>>>>>> the
mirror?
One of the problems of environments of the unmoderated and >>>>>>>>>>>>> pseudonymous
sort is that there are all kinds of trolls. There are plain >>>>>>>>>>>>> rage- bait
and flamer trolls, looky-loos and non-sequitur types, then, >>>>>>>>>>>>> also
all
sorts of anti-trolls, and these and those.
Then, for example, for something like "it's a free country", >>>>>>>>>>>>> then
when I see stuff like either
"smell the new normal, you're living in a dictatorship", >>>>>>>>>>>>> or,
"suffer the children, so your social media and phone get >>>>>>>>>>>>> hacked",
then either way the idea of being aware ("woke" wasn't a word >>>>>>>>>>>>> and I'd imagine it would be "awoke" or "woken", or, "woke" >>>>>>>>>>>>> will
do),
and caring (although, you know, not _too_ caring), that trolls >>>>>>>>>>>>> and repeti-bots on "social" media are anti-social.
So, it's fair that people get wary of trolls, and, begin to >>>>>>>>>>>>> suspect
trolls in the likely places, and learn to make a troll-filter, >>>>>>>>>>>>> and basically a skeptical if not cynical outlook on the world >>>>>>>>>>>>> today,
that there are trolls and trolls, and sometimes it's >>>>>>>>>>>>> easiest to
ignore them away.
Then, there are cranks, ....
The crank is one of the easiest sorts of identities to mimic, >>>>>>>>>>>>> give it a howler fallacy it won't let go and the plain >>>>>>>>>>>>> obstinance
combined with the stubbornness along with the sort of plain >>>>>>>>>>>>> unwarranted persistence, then it's not always easy to tell the >>>>>>>>>>>>> difference between cranks and trolls, though often it is, >>>>>>>>>>>>> and between persons and bots, though often it is.
'Murica.
Then, about the thread, the idea is that it's great if these >>>>>>>>>>>>> long-running mostly-empty tit-for-tat nonsense threads get >>>>>>>>>>>>> hijacked by passers-by then into discussions about the issues >>>>>>>>>>>>> at hand, like about the many, many things to do with the >>>>>>>>>>>>> "mathematics" of continuity and infinity, since, despite >>>>>>>>>>>>> the idea of some retro-finitists that their world is a >>>>>>>>>>>>> dot, and not even like AP a giant plutonium atom, there's >>>>>>>>>>>>> much to be done to bring real infinite and continuity into >>>>>>>>>>>>> mathematics, then for physics and so on.
So, new blood (or fresh meat) writing on the thread so >>>>>>>>>>>>> it's not just an echo-chamber of trolls and anti-trolls >>>>>>>>>>>>> which is one big troll, is not necessarily a bad thing. >>>>>>>>>>>>>
I enjoy CMT's usual spontaneous cheerful enthusiasm,
though as a perceived bot itself when it once-a-year
cites its prompter, then though the affected anxiety
pronation reminds me of too many lessons learned like
not to smell fear or flinch or beg or impose or presume >>>>>>>>>>>> or assume or judge or telepathically scan or lurk or
menace or make gossip or berate or scoff.
Fwiw, check out these funny halt deciders... They only halt when >>>>>>>>>>> all
possible paths are hit. If you think about its kind of akin to >>>>>>>>>>> olcotts
DD. i simply hijack its result. Here is a version that uses >>>>>>>>>>> random
numbers for the fuzzer:
In applesoft basic for fun. ;^D
You can run these here:
https://www.calormen.com/jsbasic/
_____________________________
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
1010 PRINT "FIN... All paths hit."
1020 PRINT "NON_HALT P0 = "; P0
1030 PRINT "HALT P1 = "; P1
_____________________________
Here is one that requires input from a user:
_____________________________
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 INPUT "Shall DD halt or not? " ; A$
110 REM 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
^^^^^^^^^^^^
_____________________________
God damn it forgot to add in line 1000 onward! Shit happens: >>>>>>>>>>
1000
1010 PRINT "FIN... All paths hit."
1020 PRINT "NON_HALT P0 = "; P0
1030 PRINT "HALT P1 = "; P1
Corrected user input one:
_______________
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 INPUT "Shall DD halt or not? " ; A$
110 REM 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
1010 PRINT "FIN... All paths hit."
1020 PRINT "NON_HALT P0 = "; P0
1030 PRINT "HALT P1 = "; P1
_______________
Sorry about that shit!
It only halts when all paths have been hit.
About cranks then, there's something about a crank I admire, >>>>>>>>>>>> not so much the being wrong part yet the dream, having the >>>>>>>>>>>> dreams, I'm all for people having the dream when it's not >>>>>>>>>>>> frustrating or threatening other people's dreams.
So, as I usually enough put it, "retro-finitist crankety >>>>>>>>>>>> trolls can step off and get bent".
I'm not a fan of any "new" normal, we already have plain >>>>>>>>>>>> old "normal normal".
Hm.
There are at least three accounts of programs whether they halt. >>>>>>>>>
A) almost-all programs halt
B) almost-all programs don't halt
C) half of programs halt
The number of programs that halt is between 0 and 100%
excluding the endpoints.
https://arxiv.org/abs/math/0611740
"The Halting Probability Omega: Irreducible Complexity in Pure
Mathematics", G. Chaitin
"Gödel himself did not think that his theorem showed that
mathematics
has limitations. In several essays he made it clear that he believed >>>>>>> that mathematicians could eventually settle any significant
question by
using their mathematical intuition, their ability to directly
perceive
the Platonic world of mathematical ideas, and by inventing or
discovering new concepts and new axioms, new principles.
Furthermore, I share Enriques’s faith in intuition. I think that >>>>>>> excessive formalism and abstraction is killing mathematics. In my >>>>>>> opinion math papers shouldn’t attempt to replace all words by
formulas,
instead they should be like literary essays, they should attempt to >>>>>>> explain and convince.
Extending Dag Prawitz's Theory of Grounds while remaining
directly within the realm of proof theoretic Semantics then
G simply becomes ungrounded in PA and grounded in meta-math.
It has taken PTS quite a few decades, all the way up to 2012
to catch up with what Wittgenstein said decades earlier:
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's
system' means: the opposite has been proved in Russell's
system. https://www.liarparadox.org/Wittgenstein.pdf
So let me tell you the story of metamathematics, of how
mathematicians
have tried to use mathematical methods to study the power and the >>>>>>> limitations of math itself. It’s a fairly dramatic story; in a >>>>>>> previous
era it might have been the subject of epic poems, of Iliads and
Odysseys
of verse. I’ll start with David Hilbert."
"In my opinion this is a fundamental step forward in the
philosophy of
mathematics because it makes incompleteness seem much more
concrete and
much more natural. It’s almost a problem in physics, it’s about a >>>>>>> machine, you just ask whether or not it’s going to eventually
stop, and
it turns out there’s no way, no general way, to answer that
question.
Let me emphasize that if a program does halt, we can eventually
discover
that. The problem, an extremely deep one, is to show that a program >>>>>>> will
never halt if this is in fact so. One can settle many special cases, >>>>>>> even an infinity of them, but no finite set of axioms can enable >>>>>>> you to
settle all possible cases."
Hm, " ... no finite set of axioms ...", ..., how about "no axioms". >>>>>>>
"The real numbers are the simplest thing in the world geometrically, >>>>>>> they are just points on a line. But arithmetically, as individuals, >>>>>>> real
numbers are actually rather unreal. Turing’s 1936 uncomputable >>>>>>> real is
just the tip of the iceberg, the problem is a lot more serious than >>>>>>> that."
Here the iota-values are points _in_ a line, field-reals _on_ a
line,
and signal-reals _about_ and _around_ a line.
So, Chaitin doesn't even have three models of continuous domains, >>>>>>> or "repleteness", of concepts like Lebnitz' principle of perfection >>>>>>> and Hilbert's postulate of continuity.
Mathematics really _does_ define continuity:
and there are at least three models of continuous domains.
So, say you want to sample a real number from [0,1] the interval >>>>>>> at uniform random, and all you have is a fair coin that
gives samples from {0, 1} the set.
So, you start flipping coins and marking the result to make
a sequence of 0's and 1's. Each coin toss _refines_ the
sample.
Yet, each coin toss also _begins_ a new sample. So, to sample
one real number, the super-task results sampling infinitely-many >>>>>>> real numbers.
So, the probability of the first sample being a rational value
is, according to the law of large numbers the law of small numbers, >>>>>>> small, and arbitrarily and infinitesimally small. In theories
that are Pythagorean it's almost-all rationals, while in theories >>>>>>> that are Cantorian it's almost-all transcendentals.
Yet, if a sample arrives at a rational, the repeating character
of rationals means that thusly the _one_ sample of a rational
number is automatically _infinitely-many_ samples of rational
numbers.
So, it makes sense to consider that the probability of sampling
a rational number from [0,1] is about 0.5.
This isn't Pythagorean by itself, and isn't Cantorian by itself. >>>>>>> It's them together according to accounts of paradox-free reason, >>>>>>> not "non-classical logics where we ignore contradiction",
which is _hypocrisy_ and furthermore _fallacious_,
since "infinity" and "continuity" are "absolute" and "replete".
"Let’s start with Borel’s know-it-all number, but now let’s use >>>>>>> the Nth
binary digit to tell us whether or not the Nth computer program ever >>>>>>> halts. So now Borel’s number is an oracle for the halting problem. >>>>>>> For
example, there is a bit which tells us whether or not the Riemann >>>>>>> hypothesis is true, for that is equivalent to the statement that a >>>>>>> program that systematically searches for zeros of the zeta function >>>>>>> that
are in the wrong place, never halts.
It turns out that this number, which I’ll call Turing’s number even >>>>>>> though it does not occur in Turing’s paper, is wasting bits, it is >>>>>>> actually highly redundant. We don’t really need N bits to answer N >>>>>>> cases
of the halting problem, a much smaller number of bits will do. Why? >>>>>>>
Well, consider some large number N of cases of the halting problem, >>>>>>> some
large number N of individual programs for which we want to know
whether
or not each one halts. Is this really N bits of mathematical
information? No, the answers are not independent, they are highly >>>>>>> correlated. How? Well, in order to answer N cases of the halting >>>>>>> problem, we don’t really need to know each individual answer; it >>>>>>> suffices to know how many of these N programs will eventually halt. >>>>>>> Once
we know this number, which is only about log_2 N
bits of information, we can run the N programs in parallel until >>>>>>> exactly
this number of them halt, and then we know that none of the
remaining
programs will ever halt. And log_2 N is much, much less than N for >>>>>>> all
sufficiently large N. In other words, Turing’s number isn’t the best
possible oracle for the halting problem. It is highly redundant, it >>>>>>> uses
far too many bits.
Using essentially this idea, we can get the best possible oracle >>>>>>> number
for the halting problem; that is the halting probability Ω, which >>>>>>> has no
redundancy, none at all.
So, now that there's readily equipped a notion of uniform sampling >>>>>>> that results "oracle numbers", always _infinitely-many_ just to get >>>>>>> one,
then Chaitin's quote is equipped some context that makes
quite a fresh reading.
This goes for all y'all.
Actually, thousands of years before Russell or Tarski claimed that
"truth is whatever I, Lord Russell or Tsar Tarski, say that agrees
with myself", the notion that mathematical truth is _discovered_ not >>>>> _invented_ was "the truth", then that structural realism and realist >>>>> structuralism make for an account with both an idealistic and an
analytical tradition, keeping science for itself as a strengthened
analytical position and the idealistic getting equipped with mental
senses of the faculties of reason about logic and mathematics (and
infinity and continuity) so that Kant is satisfied that "1 + 1 = 2". >>>>>
Then, Wittgenstein is just a cad, and while it's respected
his right to say "I, wild Wittgenstein, say that you can't say
that you say anything at all", it's ignored as saying jack squat.
Natural reasoners can simply arrive at grounds for reason after
axiomless natural deduction making for logic, geometry, number theory, >>>>> with infinity and continuity, and so on. Then formalisms follow as
after perspectival accounts of restriction-of-comprehension given a
thorough account of expansion-of-comprehension.
Plato could be proud.
hey ross what group are you commenting from?
I usually read sci.math and sci.logic, and sometimes comp.ai.philosophy, >>> not so much comp.theory, though,
here there's a general idea that "Zeno machines"
are a model of computation vis-a-vis usual accounts
after Turing machines or Frege's concept-script or
MiX or stack machines or Harvard/vonNeumann or
finite-state-machines the automata.
For decades and since I formalized a few key aspects
of models of continuous domains, nobody tells me I'm
wrong anymore since I'm not wrong, or rather,
the mathematics isn't wrong.
Arriving at that though involves of a bit of a
thorough account of theory for reason, which
here is a paleo-classical post-modern account.
Anyways "olcott" is just the latest spam troll
in a sense - then that it doesn't much matter
whether it was standard accounts or non-standard accounts
or plain retro-finitist crankety troll accounts,
I can offer a sound criticism to any.
Infinity does not actually count at all for the
crucial things of the world such as the survival
of the species and the health of the planet.
On the other hand my inter-linked finite semantic
tautologies (or something like them) are required
for dividing truth from dangerous lies.
You seem to be coming off as a mere pseudo-intellectual
in that you judge people instead of the soundness of
their ideas.
If nothing grounds an expression of language in a
truth value then (well duh) it remains ungrounded
in a truth value.
Infinity disagrees.
There are results due infinitary reasoning simply not available
to finitary reasoning. The Dirac delta function, if you've
ever heard of that, of course is ubiquitous in physics, signal
theory, differential analysis, Fourier-style analysis, and so
on, and its width is _infinitesimal_ and its height is _infinite_
and it's integrable and has area _one_.
Similarly, the perfect results of the calculus are not so
for _any_ _finite_ difference, only "in the limit" and
for the _infinitesimal_ _differential_, simply not being
so for any _finite_ difference.
There are results, furthermore, in the analysis that simply
_belie_, make false, not only any non-infinite limit, also
any _finite_ initial approximation, that even approximations
fail, not merely having a "nominally non-zero error",
actually that there error bound is the same as the approximation,
with regards to numerical methods and other usual accounts of
finite-element analysis.
Then, even better, there are doubling spaces and doubling measures,
and halving spaces and halving measures, and pi-ratio spaces,
that make accounts of equi-decomposability, that _since the
time of Zeno_, that not only the usual account of the ant's march
and iterative halves their sum equaling one the geometric series,
the bee's flights that are actually _double_, _and_, there already
exist in many derivations in physics these "spurious" factors,
that _really_ have an explanation.
So, for many matters of convergence, then emergence, and the
many counter-examples of convergence according to the law of
small numbers as "the" law of large numbers, instead has that
_infinity_ is _real_ and _necessary_ for _continuity_.
And what you have there "grounding in a truth value" that you
make your mind, is known since antiquity to be _ungrounded_
itself, and instead of making a first-class science of it,
as conscientious scientists may, you, sir, are an idiot.
Can't have finite without infinite. Otherwise you got few,
that people the usual third word for numbers in primitive
societies "one, two, a few, ..., too many to count".
There are my hundeds hours low-key lectures in my video channel,
suitable for inobtrusive background noise of the mathematically
(and physically) enriching variety.
Read some Ernst Cassirer and get back to yourself.
On 05/21/2026 11:14 AM, dart200 wrote:
On 5/21/26 9:54 AM, Ross Finlayson wrote:
On 05/21/2026 06:02 AM, olcott wrote:
On 5/18/2026 11:44 AM, Ross Finlayson wrote:
On 05/18/2026 09:03 AM, olcott wrote:
On 5/18/2026 10:14 AM, Ross Finlayson wrote:
On 05/17/2026 08:48 PM, Chris M. Thomasson wrote:How can a man as smart as you get this so incorrectly?
On 5/17/2026 8:46 PM, Chris M. Thomasson wrote:
On 5/17/2026 5:24 PM, Ross Finlayson wrote:
On 05/17/2026 05:10 PM, Ross Finlayson wrote:
On 05/17/2026 02:46 PM, Chris M. Thomasson wrote:
On 5/17/2026 2:21 PM, phoenix wrote:
Chris M. Thomasson wrote:
On 5/16/2026 2:30 PM, phoenix wrote:
Chris M. Thomasson wrote:
Or maybe a different tarot, "the star" because you have >>>>>>>>>>>>>>> such aI find that 'except' paired with 'yet' covers every >>>>>>>>>>>>>>>>> instance of
Yet that yet that yet that yet that yet that it is so: >>>>>>>>>>>>>>>>>> that that that that that it is so.
'but.' If you can find an exception to this, please show >>>>>>>>>>>>>>>>> me.
fascination with me?
I think you are a sock puppet for olcott.
I know you think that, but I don't see any motivation on my >>>>>>>>>>>>> part to
disabuse you of the notion. Why not play into it and further >>>>>>>>>>>>> befuddle
you? If it were the case that I were not olcott, that is. >>>>>>>>>>>>>
Ask your self what his halting decider would say... Look in the >>>>>>>>>>>> mirror?
One of the problems of environments of the unmoderated and >>>>>>>>>>> pseudonymous
sort is that there are all kinds of trolls. There are plain >>>>>>>>>>> rage- bait
and flamer trolls, looky-loos and non-sequitur types, then, also >>>>>>>>>>> all
sorts of anti-trolls, and these and those.
Then, for example, for something like "it's a free country", >>>>>>>>>>> then
when I see stuff like either
"smell the new normal, you're living in a dictatorship", >>>>>>>>>>> or,
"suffer the children, so your social media and phone get >>>>>>>>>>> hacked",
then either way the idea of being aware ("woke" wasn't a word >>>>>>>>>>> and I'd imagine it would be "awoke" or "woken", or, "woke" will >>>>>>>>>>> do),
and caring (although, you know, not _too_ caring), that trolls >>>>>>>>>>> and repeti-bots on "social" media are anti-social.
So, it's fair that people get wary of trolls, and, begin to >>>>>>>>>>> suspect
trolls in the likely places, and learn to make a troll-filter, >>>>>>>>>>> and basically a skeptical if not cynical outlook on the world >>>>>>>>>>> today,
that there are trolls and trolls, and sometimes it's easiest to >>>>>>>>>>> ignore them away.
Then, there are cranks, ....
The crank is one of the easiest sorts of identities to mimic, >>>>>>>>>>> give it a howler fallacy it won't let go and the plain
obstinance
combined with the stubbornness along with the sort of plain >>>>>>>>>>> unwarranted persistence, then it's not always easy to tell the >>>>>>>>>>> difference between cranks and trolls, though often it is, >>>>>>>>>>> and between persons and bots, though often it is.
'Murica.
Then, about the thread, the idea is that it's great if these >>>>>>>>>>> long-running mostly-empty tit-for-tat nonsense threads get >>>>>>>>>>> hijacked by passers-by then into discussions about the issues >>>>>>>>>>> at hand, like about the many, many things to do with the >>>>>>>>>>> "mathematics" of continuity and infinity, since, despite >>>>>>>>>>> the idea of some retro-finitists that their world is a
dot, and not even like AP a giant plutonium atom, there's >>>>>>>>>>> much to be done to bring real infinite and continuity into >>>>>>>>>>> mathematics, then for physics and so on.
So, new blood (or fresh meat) writing on the thread so
it's not just an echo-chamber of trolls and anti-trolls
which is one big troll, is not necessarily a bad thing.
I enjoy CMT's usual spontaneous cheerful enthusiasm,
though as a perceived bot itself when it once-a-year
cites its prompter, then though the affected anxiety
pronation reminds me of too many lessons learned like
not to smell fear or flinch or beg or impose or presume
or assume or judge or telepathically scan or lurk or
menace or make gossip or berate or scoff.
Fwiw, check out these funny halt deciders... They only halt when >>>>>>>>> all
possible paths are hit. If you think about its kind of akin to >>>>>>>>> olcotts
DD. i simply hijack its result. Here is a version that uses random >>>>>>>>> numbers for the fuzzer:
In applesoft basic for fun. ;^D
You can run these here:
https://www.calormen.com/jsbasic/
_____________________________
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
1010 PRINT "FIN... All paths hit."
1020 PRINT "NON_HALT P0 = "; P0
1030 PRINT "HALT P1 = "; P1
_____________________________
Here is one that requires input from a user:
_____________________________
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 INPUT "Shall DD halt or not? " ; A$
110 REM 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
^^^^^^^^^^^^
_____________________________
God damn it forgot to add in line 1000 onward! Shit happens:
1000
1010 PRINT "FIN... All paths hit."
1020 PRINT "NON_HALT P0 = "; P0
1030 PRINT "HALT P1 = "; P1
Corrected user input one:
_______________
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 INPUT "Shall DD halt or not? " ; A$
110 REM 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
1010 PRINT "FIN... All paths hit."
1020 PRINT "NON_HALT P0 = "; P0
1030 PRINT "HALT P1 = "; P1
_______________
Sorry about that shit!
It only halts when all paths have been hit.
About cranks then, there's something about a crank I admire, >>>>>>>>>> not so much the being wrong part yet the dream, having the >>>>>>>>>> dreams, I'm all for people having the dream when it's not
frustrating or threatening other people's dreams.
So, as I usually enough put it, "retro-finitist crankety
trolls can step off and get bent".
I'm not a fan of any "new" normal, we already have plain
old "normal normal".
Hm.
There are at least three accounts of programs whether they halt. >>>>>>>
A) almost-all programs halt
B) almost-all programs don't halt
C) half of programs halt
The number of programs that halt is between 0 and 100%
excluding the endpoints.
https://arxiv.org/abs/math/0611740
"The Halting Probability Omega: Irreducible Complexity in Pure
Mathematics", G. Chaitin
"Gödel himself did not think that his theorem showed that mathematics >>>>> has limitations. In several essays he made it clear that he believed >>>>> that mathematicians could eventually settle any significant
question by
using their mathematical intuition, their ability to directly perceive >>>>> the Platonic world of mathematical ideas, and by inventing or
discovering new concepts and new axioms, new principles.
Furthermore, I share Enriques’s faith in intuition. I think that
excessive formalism and abstraction is killing mathematics. In my
opinion math papers shouldn’t attempt to replace all words by
formulas,
instead they should be like literary essays, they should attempt to
explain and convince.
Extending Dag Prawitz's Theory of Grounds while remaining
directly within the realm of proof theoretic Semantics then
G simply becomes ungrounded in PA and grounded in meta-math.
It has taken PTS quite a few decades, all the way up to 2012
to catch up with what Wittgenstein said decades earlier:
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's
system' means: the opposite has been proved in Russell's
system. https://www.liarparadox.org/Wittgenstein.pdf
So let me tell you the story of metamathematics, of how mathematicians >>>>> have tried to use mathematical methods to study the power and the
limitations of math itself. It’s a fairly dramatic story; in a
previous
era it might have been the subject of epic poems, of Iliads and
Odysseys
of verse. I’ll start with David Hilbert."
"In my opinion this is a fundamental step forward in the philosophy of >>>>> mathematics because it makes incompleteness seem much more concrete >>>>> and
much more natural. It’s almost a problem in physics, it’s about a >>>>> machine, you just ask whether or not it’s going to eventually stop, >>>>> and
it turns out there’s no way, no general way, to answer that question. >>>>> Let me emphasize that if a program does halt, we can eventually
discover
that. The problem, an extremely deep one, is to show that a program
will
never halt if this is in fact so. One can settle many special cases, >>>>> even an infinity of them, but no finite set of axioms can enable
you to
settle all possible cases."
Hm, " ... no finite set of axioms ...", ..., how about "no axioms".
"The real numbers are the simplest thing in the world geometrically, >>>>> they are just points on a line. But arithmetically, as individuals,
real
numbers are actually rather unreal. Turing’s 1936 uncomputable real is >>>>> just the tip of the iceberg, the problem is a lot more serious than
that."
Here the iota-values are points _in_ a line, field-reals _on_ a line, >>>>> and signal-reals _about_ and _around_ a line.
So, Chaitin doesn't even have three models of continuous domains,
or "repleteness", of concepts like Lebnitz' principle of perfection
and Hilbert's postulate of continuity.
Mathematics really _does_ define continuity:
and there are at least three models of continuous domains.
So, say you want to sample a real number from [0,1] the interval
at uniform random, and all you have is a fair coin that
gives samples from {0, 1} the set.
So, you start flipping coins and marking the result to make
a sequence of 0's and 1's. Each coin toss _refines_ the
sample.
Yet, each coin toss also _begins_ a new sample. So, to sample
one real number, the super-task results sampling infinitely-many
real numbers.
So, the probability of the first sample being a rational value
is, according to the law of large numbers the law of small numbers,
small, and arbitrarily and infinitesimally small. In theories
that are Pythagorean it's almost-all rationals, while in theories
that are Cantorian it's almost-all transcendentals.
Yet, if a sample arrives at a rational, the repeating character
of rationals means that thusly the _one_ sample of a rational
number is automatically _infinitely-many_ samples of rational
numbers.
So, it makes sense to consider that the probability of sampling
a rational number from [0,1] is about 0.5.
This isn't Pythagorean by itself, and isn't Cantorian by itself.
It's them together according to accounts of paradox-free reason,
not "non-classical logics where we ignore contradiction",
which is _hypocrisy_ and furthermore _fallacious_,
since "infinity" and "continuity" are "absolute" and "replete".
"Let’s start with Borel’s know-it-all number, but now let’s use the
Nth
binary digit to tell us whether or not the Nth computer program ever >>>>> halts. So now Borel’s number is an oracle for the halting problem. For >>>>> example, there is a bit which tells us whether or not the Riemann
hypothesis is true, for that is equivalent to the statement that a
program that systematically searches for zeros of the zeta function
that
are in the wrong place, never halts.
It turns out that this number, which I’ll call Turing’s number even >>>>> though it does not occur in Turing’s paper, is wasting bits, it is >>>>> actually highly redundant. We don’t really need N bits to answer N >>>>> cases
of the halting problem, a much smaller number of bits will do. Why?
Well, consider some large number N of cases of the halting problem,
some
large number N of individual programs for which we want to know
whether
or not each one halts. Is this really N bits of mathematical
information? No, the answers are not independent, they are highly
correlated. How? Well, in order to answer N cases of the halting
problem, we don’t really need to know each individual answer; it
suffices to know how many of these N programs will eventually halt.
Once
we know this number, which is only about log_2 N
bits of information, we can run the N programs in parallel until
exactly
this number of them halt, and then we know that none of the remaining >>>>> programs will ever halt. And log_2 N is much, much less than N for all >>>>> sufficiently large N. In other words, Turing’s number isn’t the best >>>>> possible oracle for the halting problem. It is highly redundant, it
uses
far too many bits.
Using essentially this idea, we can get the best possible oracle
number
for the halting problem; that is the halting probability Ω, which
has no
redundancy, none at all.
So, now that there's readily equipped a notion of uniform sampling
that results "oracle numbers", always _infinitely-many_ just to get
one,
then Chaitin's quote is equipped some context that makes
quite a fresh reading.
This goes for all y'all.
Actually, thousands of years before Russell or Tarski claimed that
"truth is whatever I, Lord Russell or Tsar Tarski, say that agrees
with myself", the notion that mathematical truth is _discovered_ not
_invented_ was "the truth", then that structural realism and realist
structuralism make for an account with both an idealistic and an
analytical tradition, keeping science for itself as a strengthened
analytical position and the idealistic getting equipped with mental
senses of the faculties of reason about logic and mathematics (and
infinity and continuity) so that Kant is satisfied that "1 + 1 = 2".
Then, Wittgenstein is just a cad, and while it's respected
his right to say "I, wild Wittgenstein, say that you can't say
that you say anything at all", it's ignored as saying jack squat.
Natural reasoners can simply arrive at grounds for reason after
axiomless natural deduction making for logic, geometry, number theory,
with infinity and continuity, and so on. Then formalisms follow as
after perspectival accounts of restriction-of-comprehension given a
thorough account of expansion-of-comprehension.
Plato could be proud.
hey ross what group are you commenting from?
I usually read sci.math and sci.logic, and sometimes comp.ai.philosophy,
not so much comp.theory, though,
here there's a general idea that "Zeno machines"
are a model of computation vis-a-vis usual accounts
after Turing machines or Frege's concept-script or
MiX or stack machines or Harvard/vonNeumann or
finite-state-machines the automata.
For decades and since I formalized a few key aspects
of models of continuous domains, nobody tells me I'm
wrong anymore since I'm not wrong, or rather,
the mathematics isn't wrong.
Arriving at that though involves of a bit of a
thorough account of theory for reason, which
here is a paleo-classical post-modern account.
Anyways "olcott" is just the latest spam troll
in a sense - then that it doesn't much matter
whether it was standard accounts or non-standard accounts
or plain retro-finitist crankety troll accounts,
I can offer a sound criticism to any.
On 05/21/2026 08:34 PM, olcott wrote:
On 5/21/2026 7:45 PM, Ross Finlayson wrote:
On 05/21/2026 11:14 AM, dart200 wrote:
On 5/21/26 9:54 AM, Ross Finlayson wrote:
On 05/21/2026 06:02 AM, olcott wrote:
On 5/18/2026 11:44 AM, Ross Finlayson wrote:
On 05/18/2026 09:03 AM, olcott wrote:
On 5/18/2026 10:14 AM, Ross Finlayson wrote:
On 05/17/2026 08:48 PM, Chris M. Thomasson wrote:How can a man as smart as you get this so incorrectly?
On 5/17/2026 8:46 PM, Chris M. Thomasson wrote:
On 5/17/2026 5:24 PM, Ross Finlayson wrote:
On 05/17/2026 05:10 PM, Ross Finlayson wrote:
On 05/17/2026 02:46 PM, Chris M. Thomasson wrote:
On 5/17/2026 2:21 PM, phoenix wrote:
Chris M. Thomasson wrote:
On 5/16/2026 2:30 PM, phoenix wrote:
Chris M. Thomasson wrote:
Or maybe a different tarot, "the star" because you have >>>>>>>>>>>>>>>>> such aI find that 'except' paired with 'yet' covers every >>>>>>>>>>>>>>>>>>> instance of
Yet that yet that yet that yet that yet that it is so: >>>>>>>>>>>>>>>>>>>> that that that that that it is so.
'but.' If you can find an exception to this, please show >>>>>>>>>>>>>>>>>>> me.
fascination with me?
I think you are a sock puppet for olcott.
I know you think that, but I don't see any motivation on my >>>>>>>>>>>>>>> part to
disabuse you of the notion. Why not play into it and further >>>>>>>>>>>>>>> befuddle
you? If it were the case that I were not olcott, that is. >>>>>>>>>>>>>>>
Ask your self what his halting decider would say... Look in >>>>>>>>>>>>>> the
mirror?
One of the problems of environments of the unmoderated and >>>>>>>>>>>>> pseudonymous
sort is that there are all kinds of trolls. There are plain >>>>>>>>>>>>> rage- bait
and flamer trolls, looky-loos and non-sequitur types, then, >>>>>>>>>>>>> also
all
sorts of anti-trolls, and these and those.
Then, for example, for something like "it's a free country", >>>>>>>>>>>>> then
when I see stuff like either
"smell the new normal, you're living in a dictatorship", >>>>>>>>>>>>> or,
"suffer the children, so your social media and phone get >>>>>>>>>>>>> hacked",
then either way the idea of being aware ("woke" wasn't a word >>>>>>>>>>>>> and I'd imagine it would be "awoke" or "woken", or, "woke" >>>>>>>>>>>>> will
do),
and caring (although, you know, not _too_ caring), that trolls >>>>>>>>>>>>> and repeti-bots on "social" media are anti-social.
So, it's fair that people get wary of trolls, and, begin to >>>>>>>>>>>>> suspect
trolls in the likely places, and learn to make a troll-filter, >>>>>>>>>>>>> and basically a skeptical if not cynical outlook on the world >>>>>>>>>>>>> today,
that there are trolls and trolls, and sometimes it's >>>>>>>>>>>>> easiest to
ignore them away.
Then, there are cranks, ....
The crank is one of the easiest sorts of identities to mimic, >>>>>>>>>>>>> give it a howler fallacy it won't let go and the plain >>>>>>>>>>>>> obstinance
combined with the stubbornness along with the sort of plain >>>>>>>>>>>>> unwarranted persistence, then it's not always easy to tell the >>>>>>>>>>>>> difference between cranks and trolls, though often it is, >>>>>>>>>>>>> and between persons and bots, though often it is.
'Murica.
Then, about the thread, the idea is that it's great if these >>>>>>>>>>>>> long-running mostly-empty tit-for-tat nonsense threads get >>>>>>>>>>>>> hijacked by passers-by then into discussions about the issues >>>>>>>>>>>>> at hand, like about the many, many things to do with the >>>>>>>>>>>>> "mathematics" of continuity and infinity, since, despite >>>>>>>>>>>>> the idea of some retro-finitists that their world is a >>>>>>>>>>>>> dot, and not even like AP a giant plutonium atom, there's >>>>>>>>>>>>> much to be done to bring real infinite and continuity into >>>>>>>>>>>>> mathematics, then for physics and so on.
So, new blood (or fresh meat) writing on the thread so >>>>>>>>>>>>> it's not just an echo-chamber of trolls and anti-trolls >>>>>>>>>>>>> which is one big troll, is not necessarily a bad thing. >>>>>>>>>>>>>
I enjoy CMT's usual spontaneous cheerful enthusiasm,
though as a perceived bot itself when it once-a-year
cites its prompter, then though the affected anxiety
pronation reminds me of too many lessons learned like
not to smell fear or flinch or beg or impose or presume >>>>>>>>>>>> or assume or judge or telepathically scan or lurk or
menace or make gossip or berate or scoff.
Fwiw, check out these funny halt deciders... They only halt when >>>>>>>>>>> all
possible paths are hit. If you think about its kind of akin to >>>>>>>>>>> olcotts
DD. i simply hijack its result. Here is a version that uses >>>>>>>>>>> random
numbers for the fuzzer:
In applesoft basic for fun. ;^D
You can run these here:
https://www.calormen.com/jsbasic/
_____________________________
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
1010 PRINT "FIN... All paths hit."
1020 PRINT "NON_HALT P0 = "; P0
1030 PRINT "HALT P1 = "; P1
_____________________________
Here is one that requires input from a user:
_____________________________
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 INPUT "Shall DD halt or not? " ; A$
110 REM 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
^^^^^^^^^^^^
_____________________________
God damn it forgot to add in line 1000 onward! Shit happens: >>>>>>>>>>
1000
1010 PRINT "FIN... All paths hit."
1020 PRINT "NON_HALT P0 = "; P0
1030 PRINT "HALT P1 = "; P1
Corrected user input one:
_______________
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 INPUT "Shall DD halt or not? " ; A$
110 REM 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
1010 PRINT "FIN... All paths hit."
1020 PRINT "NON_HALT P0 = "; P0
1030 PRINT "HALT P1 = "; P1
_______________
Sorry about that shit!
It only halts when all paths have been hit.
About cranks then, there's something about a crank I admire, >>>>>>>>>>>> not so much the being wrong part yet the dream, having the >>>>>>>>>>>> dreams, I'm all for people having the dream when it's not >>>>>>>>>>>> frustrating or threatening other people's dreams.
So, as I usually enough put it, "retro-finitist crankety >>>>>>>>>>>> trolls can step off and get bent".
I'm not a fan of any "new" normal, we already have plain >>>>>>>>>>>> old "normal normal".
Hm.
There are at least three accounts of programs whether they halt. >>>>>>>>>
A) almost-all programs halt
B) almost-all programs don't halt
C) half of programs halt
The number of programs that halt is between 0 and 100%
excluding the endpoints.
https://arxiv.org/abs/math/0611740
"The Halting Probability Omega: Irreducible Complexity in Pure
Mathematics", G. Chaitin
"Gödel himself did not think that his theorem showed that
mathematics
has limitations. In several essays he made it clear that he believed >>>>>>> that mathematicians could eventually settle any significant
question by
using their mathematical intuition, their ability to directly
perceive
the Platonic world of mathematical ideas, and by inventing or
discovering new concepts and new axioms, new principles.
Furthermore, I share Enriques’s faith in intuition. I think that >>>>>>> excessive formalism and abstraction is killing mathematics. In my >>>>>>> opinion math papers shouldn’t attempt to replace all words by
formulas,
instead they should be like literary essays, they should attempt to >>>>>>> explain and convince.
Extending Dag Prawitz's Theory of Grounds while remaining
directly within the realm of proof theoretic Semantics then
G simply becomes ungrounded in PA and grounded in meta-math.
It has taken PTS quite a few decades, all the way up to 2012
to catch up with what Wittgenstein said decades earlier:
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's
system' means: the opposite has been proved in Russell's
system. https://www.liarparadox.org/Wittgenstein.pdf
So let me tell you the story of metamathematics, of how
mathematicians
have tried to use mathematical methods to study the power and the >>>>>>> limitations of math itself. It’s a fairly dramatic story; in a >>>>>>> previous
era it might have been the subject of epic poems, of Iliads and
Odysseys
of verse. I’ll start with David Hilbert."
"In my opinion this is a fundamental step forward in the
philosophy of
mathematics because it makes incompleteness seem much more
concrete and
much more natural. It’s almost a problem in physics, it’s about a >>>>>>> machine, you just ask whether or not it’s going to eventually
stop, and
it turns out there’s no way, no general way, to answer that
question.
Let me emphasize that if a program does halt, we can eventually
discover
that. The problem, an extremely deep one, is to show that a program >>>>>>> will
never halt if this is in fact so. One can settle many special cases, >>>>>>> even an infinity of them, but no finite set of axioms can enable >>>>>>> you to
settle all possible cases."
Hm, " ... no finite set of axioms ...", ..., how about "no axioms". >>>>>>>
"The real numbers are the simplest thing in the world geometrically, >>>>>>> they are just points on a line. But arithmetically, as individuals, >>>>>>> real
numbers are actually rather unreal. Turing’s 1936 uncomputable >>>>>>> real is
just the tip of the iceberg, the problem is a lot more serious than >>>>>>> that."
Here the iota-values are points _in_ a line, field-reals _on_ a >>>>>>> line,
and signal-reals _about_ and _around_ a line.
So, Chaitin doesn't even have three models of continuous domains, >>>>>>> or "repleteness", of concepts like Lebnitz' principle of perfection >>>>>>> and Hilbert's postulate of continuity.
Mathematics really _does_ define continuity:
and there are at least three models of continuous domains.
So, say you want to sample a real number from [0,1] the interval >>>>>>> at uniform random, and all you have is a fair coin that
gives samples from {0, 1} the set.
So, you start flipping coins and marking the result to make
a sequence of 0's and 1's. Each coin toss _refines_ the
sample.
Yet, each coin toss also _begins_ a new sample. So, to sample
one real number, the super-task results sampling infinitely-many >>>>>>> real numbers.
So, the probability of the first sample being a rational value
is, according to the law of large numbers the law of small numbers, >>>>>>> small, and arbitrarily and infinitesimally small. In theories
that are Pythagorean it's almost-all rationals, while in theories >>>>>>> that are Cantorian it's almost-all transcendentals.
Yet, if a sample arrives at a rational, the repeating character
of rationals means that thusly the _one_ sample of a rational
number is automatically _infinitely-many_ samples of rational
numbers.
So, it makes sense to consider that the probability of sampling
a rational number from [0,1] is about 0.5.
This isn't Pythagorean by itself, and isn't Cantorian by itself. >>>>>>> It's them together according to accounts of paradox-free reason, >>>>>>> not "non-classical logics where we ignore contradiction",
which is _hypocrisy_ and furthermore _fallacious_,
since "infinity" and "continuity" are "absolute" and "replete".
"Let’s start with Borel’s know-it-all number, but now let’s use >>>>>>> the Nth
binary digit to tell us whether or not the Nth computer program ever >>>>>>> halts. So now Borel’s number is an oracle for the halting problem. >>>>>>> For
example, there is a bit which tells us whether or not the Riemann >>>>>>> hypothesis is true, for that is equivalent to the statement that a >>>>>>> program that systematically searches for zeros of the zeta function >>>>>>> that
are in the wrong place, never halts.
It turns out that this number, which I’ll call Turing’s number even >>>>>>> though it does not occur in Turing’s paper, is wasting bits, it is >>>>>>> actually highly redundant. We don’t really need N bits to answer N >>>>>>> cases
of the halting problem, a much smaller number of bits will do. Why? >>>>>>>
Well, consider some large number N of cases of the halting problem, >>>>>>> some
large number N of individual programs for which we want to know
whether
or not each one halts. Is this really N bits of mathematical
information? No, the answers are not independent, they are highly >>>>>>> correlated. How? Well, in order to answer N cases of the halting >>>>>>> problem, we don’t really need to know each individual answer; it >>>>>>> suffices to know how many of these N programs will eventually halt. >>>>>>> Once
we know this number, which is only about log_2 N
bits of information, we can run the N programs in parallel until >>>>>>> exactly
this number of them halt, and then we know that none of the
remaining
programs will ever halt. And log_2 N is much, much less than N for >>>>>>> all
sufficiently large N. In other words, Turing’s number isn’t the best
possible oracle for the halting problem. It is highly redundant, it >>>>>>> uses
far too many bits.
Using essentially this idea, we can get the best possible oracle >>>>>>> number
for the halting problem; that is the halting probability Ω, which >>>>>>> has no
redundancy, none at all.
So, now that there's readily equipped a notion of uniform sampling >>>>>>> that results "oracle numbers", always _infinitely-many_ just to get >>>>>>> one,
then Chaitin's quote is equipped some context that makes
quite a fresh reading.
This goes for all y'all.
Actually, thousands of years before Russell or Tarski claimed that
"truth is whatever I, Lord Russell or Tsar Tarski, say that agrees
with myself", the notion that mathematical truth is _discovered_ not >>>>> _invented_ was "the truth", then that structural realism and realist >>>>> structuralism make for an account with both an idealistic and an
analytical tradition, keeping science for itself as a strengthened
analytical position and the idealistic getting equipped with mental
senses of the faculties of reason about logic and mathematics (and
infinity and continuity) so that Kant is satisfied that "1 + 1 = 2". >>>>>
Then, Wittgenstein is just a cad, and while it's respected
his right to say "I, wild Wittgenstein, say that you can't say
that you say anything at all", it's ignored as saying jack squat.
Natural reasoners can simply arrive at grounds for reason after
axiomless natural deduction making for logic, geometry, number theory, >>>>> with infinity and continuity, and so on. Then formalisms follow as
after perspectival accounts of restriction-of-comprehension given a
thorough account of expansion-of-comprehension.
Plato could be proud.
hey ross what group are you commenting from?
I usually read sci.math and sci.logic, and sometimes comp.ai.philosophy, >>> not so much comp.theory, though,
here there's a general idea that "Zeno machines"
are a model of computation vis-a-vis usual accounts
after Turing machines or Frege's concept-script or
MiX or stack machines or Harvard/vonNeumann or
finite-state-machines the automata.
For decades and since I formalized a few key aspects
of models of continuous domains, nobody tells me I'm
wrong anymore since I'm not wrong, or rather,
the mathematics isn't wrong.
Arriving at that though involves of a bit of a
thorough account of theory for reason, which
here is a paleo-classical post-modern account.
Anyways "olcott" is just the latest spam troll
in a sense - then that it doesn't much matter
whether it was standard accounts or non-standard accounts
or plain retro-finitist crankety troll accounts,
I can offer a sound criticism to any.
Infinity does not actually count at all for the
crucial things of the world such as the survival
of the species and the health of the planet.
On the other hand my inter-linked finite semantic
tautologies (or something like them) are required
for dividing truth from dangerous lies.
You seem to be coming off as a mere pseudo-intellectual
in that you judge people instead of the soundness of
their ideas.
If nothing grounds an expression of language in a
truth value then (well duh) it remains ungrounded
in a truth value.
Infinity disagrees.
There are results due infinitary reasoning simply not available
to finitary reasoning.
The Dirac delta function, if you've
ever heard of that, of course is ubiquitous in physics, signal
theory, differential analysis, Fourier-style analysis, and so
on, and its width is _infinitesimal_ and its height is _infinite_
and it's integrable and has area _one_.
Similarly, the perfect results of the calculus are not so
for _any_ _finite_ difference, only "in the limit" and
for the _infinitesimal_ _differential_, simply not being
so for any _finite_ difference.
There are results, furthermore, in the analysis that simply
_belie_, make false, not only any non-infinite limit, also
any _finite_ initial approximation, that even approximations
fail, not merely having a "nominally non-zero error",
actually that there error bound is the same as the approximation,
with regards to numerical methods and other usual accounts of
finite-element analysis.
Then, even better, there are doubling spaces and doubling measures,
and halving spaces and halving measures, and pi-ratio spaces,
that make accounts of equi-decomposability, that _since the
time of Zeno_, that not only the usual account of the ant's march
and iterative halves their sum equaling one the geometric series,
the bee's flights that are actually _double_, _and_, there already
exist in many derivations in physics these "spurious" factors,
that _really_ have an explanation.
So, for many matters of convergence, then emergence, and the
many counter-examples of convergence according to the law of
small numbers as "the" law of large numbers, instead has that
_infinity_ is _real_ and _necessary_ for _continuity_.
And what you have there "grounding in a truth value" that you
make your mind, is known since antiquity to be _ungrounded_
itself, and instead of making a first-class science of it,
as conscientious scientists may, you, sir, are an idiot.
Can't have finite without infinite. Otherwise you got few,
that people the usual third word for numbers in primitive
societies "one, two, a few, ..., too many to count".
There are my hundeds hours low-key lectures in my video channel,
suitable for inobtrusive background noise of the mathematically
(and physically) enriching variety.
Read some Ernst Cassirer and get back to yourself.
On 05/21/2026 08:34 PM, olcott wrote:
On 5/21/2026 7:45 PM, Ross Finlayson wrote:
On 05/21/2026 11:14 AM, dart200 wrote:
On 5/21/26 9:54 AM, Ross Finlayson wrote:
On 05/21/2026 06:02 AM, olcott wrote:
On 5/18/2026 11:44 AM, Ross Finlayson wrote:
On 05/18/2026 09:03 AM, olcott wrote:
On 5/18/2026 10:14 AM, Ross Finlayson wrote:
On 05/17/2026 08:48 PM, Chris M. Thomasson wrote:How can a man as smart as you get this so incorrectly?
On 5/17/2026 8:46 PM, Chris M. Thomasson wrote:
On 5/17/2026 5:24 PM, Ross Finlayson wrote:
On 05/17/2026 05:10 PM, Ross Finlayson wrote:
On 05/17/2026 02:46 PM, Chris M. Thomasson wrote:
On 5/17/2026 2:21 PM, phoenix wrote:
Chris M. Thomasson wrote:
On 5/16/2026 2:30 PM, phoenix wrote:
Chris M. Thomasson wrote:
Or maybe a different tarot, "the star" because you have >>>>>>>>>>>>>>>>> such aI find that 'except' paired with 'yet' covers every >>>>>>>>>>>>>>>>>>> instance of
Yet that yet that yet that yet that yet that it is so: >>>>>>>>>>>>>>>>>>>> that that that that that it is so.
'but.' If you can find an exception to this, please show >>>>>>>>>>>>>>>>>>> me.
fascination with me?
I think you are a sock puppet for olcott.
I know you think that, but I don't see any motivation on my >>>>>>>>>>>>>>> part to
disabuse you of the notion. Why not play into it and further >>>>>>>>>>>>>>> befuddle
you? If it were the case that I were not olcott, that is. >>>>>>>>>>>>>>>
Ask your self what his halting decider would say... Look in >>>>>>>>>>>>>> the
mirror?
One of the problems of environments of the unmoderated and >>>>>>>>>>>>> pseudonymous
sort is that there are all kinds of trolls. There are plain >>>>>>>>>>>>> rage- bait
and flamer trolls, looky-loos and non-sequitur types, then, >>>>>>>>>>>>> also
all
sorts of anti-trolls, and these and those.
Then, for example, for something like "it's a free country", >>>>>>>>>>>>> then
when I see stuff like either
"smell the new normal, you're living in a dictatorship", >>>>>>>>>>>>> or,
"suffer the children, so your social media and phone get >>>>>>>>>>>>> hacked",
then either way the idea of being aware ("woke" wasn't a word >>>>>>>>>>>>> and I'd imagine it would be "awoke" or "woken", or, "woke" >>>>>>>>>>>>> will
do),
and caring (although, you know, not _too_ caring), that trolls >>>>>>>>>>>>> and repeti-bots on "social" media are anti-social.
So, it's fair that people get wary of trolls, and, begin to >>>>>>>>>>>>> suspect
trolls in the likely places, and learn to make a troll-filter, >>>>>>>>>>>>> and basically a skeptical if not cynical outlook on the world >>>>>>>>>>>>> today,
that there are trolls and trolls, and sometimes it's >>>>>>>>>>>>> easiest to
ignore them away.
Then, there are cranks, ....
The crank is one of the easiest sorts of identities to mimic, >>>>>>>>>>>>> give it a howler fallacy it won't let go and the plain >>>>>>>>>>>>> obstinance
combined with the stubbornness along with the sort of plain >>>>>>>>>>>>> unwarranted persistence, then it's not always easy to tell the >>>>>>>>>>>>> difference between cranks and trolls, though often it is, >>>>>>>>>>>>> and between persons and bots, though often it is.
'Murica.
Then, about the thread, the idea is that it's great if these >>>>>>>>>>>>> long-running mostly-empty tit-for-tat nonsense threads get >>>>>>>>>>>>> hijacked by passers-by then into discussions about the issues >>>>>>>>>>>>> at hand, like about the many, many things to do with the >>>>>>>>>>>>> "mathematics" of continuity and infinity, since, despite >>>>>>>>>>>>> the idea of some retro-finitists that their world is a >>>>>>>>>>>>> dot, and not even like AP a giant plutonium atom, there's >>>>>>>>>>>>> much to be done to bring real infinite and continuity into >>>>>>>>>>>>> mathematics, then for physics and so on.
So, new blood (or fresh meat) writing on the thread so >>>>>>>>>>>>> it's not just an echo-chamber of trolls and anti-trolls >>>>>>>>>>>>> which is one big troll, is not necessarily a bad thing. >>>>>>>>>>>>>
I enjoy CMT's usual spontaneous cheerful enthusiasm,
though as a perceived bot itself when it once-a-year
cites its prompter, then though the affected anxiety
pronation reminds me of too many lessons learned like
not to smell fear or flinch or beg or impose or presume >>>>>>>>>>>> or assume or judge or telepathically scan or lurk or
menace or make gossip or berate or scoff.
Fwiw, check out these funny halt deciders... They only halt when >>>>>>>>>>> all
possible paths are hit. If you think about its kind of akin to >>>>>>>>>>> olcotts
DD. i simply hijack its result. Here is a version that uses >>>>>>>>>>> random
numbers for the fuzzer:
In applesoft basic for fun. ;^D
You can run these here:
https://www.calormen.com/jsbasic/
_____________________________
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
1010 PRINT "FIN... All paths hit."
1020 PRINT "NON_HALT P0 = "; P0
1030 PRINT "HALT P1 = "; P1
_____________________________
Here is one that requires input from a user:
_____________________________
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 INPUT "Shall DD halt or not? " ; A$
110 REM 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
^^^^^^^^^^^^
_____________________________
God damn it forgot to add in line 1000 onward! Shit happens: >>>>>>>>>>
1000
1010 PRINT "FIN... All paths hit."
1020 PRINT "NON_HALT P0 = "; P0
1030 PRINT "HALT P1 = "; P1
Corrected user input one:
_______________
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 INPUT "Shall DD halt or not? " ; A$
110 REM 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
1010 PRINT "FIN... All paths hit."
1020 PRINT "NON_HALT P0 = "; P0
1030 PRINT "HALT P1 = "; P1
_______________
Sorry about that shit!
It only halts when all paths have been hit.
About cranks then, there's something about a crank I admire, >>>>>>>>>>>> not so much the being wrong part yet the dream, having the >>>>>>>>>>>> dreams, I'm all for people having the dream when it's not >>>>>>>>>>>> frustrating or threatening other people's dreams.
So, as I usually enough put it, "retro-finitist crankety >>>>>>>>>>>> trolls can step off and get bent".
I'm not a fan of any "new" normal, we already have plain >>>>>>>>>>>> old "normal normal".
Hm.
There are at least three accounts of programs whether they halt. >>>>>>>>>
A) almost-all programs halt
B) almost-all programs don't halt
C) half of programs halt
The number of programs that halt is between 0 and 100%
excluding the endpoints.
https://arxiv.org/abs/math/0611740
"The Halting Probability Omega: Irreducible Complexity in Pure
Mathematics", G. Chaitin
"Gödel himself did not think that his theorem showed that
mathematics
has limitations. In several essays he made it clear that he believed >>>>>>> that mathematicians could eventually settle any significant
question by
using their mathematical intuition, their ability to directly
perceive
the Platonic world of mathematical ideas, and by inventing or
discovering new concepts and new axioms, new principles.
Furthermore, I share Enriques’s faith in intuition. I think that >>>>>>> excessive formalism and abstraction is killing mathematics. In my >>>>>>> opinion math papers shouldn’t attempt to replace all words by
formulas,
instead they should be like literary essays, they should attempt to >>>>>>> explain and convince.
Extending Dag Prawitz's Theory of Grounds while remaining
directly within the realm of proof theoretic Semantics then
G simply becomes ungrounded in PA and grounded in meta-math.
It has taken PTS quite a few decades, all the way up to 2012
to catch up with what Wittgenstein said decades earlier:
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's
system' means: the opposite has been proved in Russell's
system. https://www.liarparadox.org/Wittgenstein.pdf
So let me tell you the story of metamathematics, of how
mathematicians
have tried to use mathematical methods to study the power and the >>>>>>> limitations of math itself. It’s a fairly dramatic story; in a >>>>>>> previous
era it might have been the subject of epic poems, of Iliads and
Odysseys
of verse. I’ll start with David Hilbert."
"In my opinion this is a fundamental step forward in the
philosophy of
mathematics because it makes incompleteness seem much more
concrete and
much more natural. It’s almost a problem in physics, it’s about a >>>>>>> machine, you just ask whether or not it’s going to eventually
stop, and
it turns out there’s no way, no general way, to answer that
question.
Let me emphasize that if a program does halt, we can eventually
discover
that. The problem, an extremely deep one, is to show that a program >>>>>>> will
never halt if this is in fact so. One can settle many special cases, >>>>>>> even an infinity of them, but no finite set of axioms can enable >>>>>>> you to
settle all possible cases."
Hm, " ... no finite set of axioms ...", ..., how about "no axioms". >>>>>>>
"The real numbers are the simplest thing in the world geometrically, >>>>>>> they are just points on a line. But arithmetically, as individuals, >>>>>>> real
numbers are actually rather unreal. Turing’s 1936 uncomputable >>>>>>> real is
just the tip of the iceberg, the problem is a lot more serious than >>>>>>> that."
Here the iota-values are points _in_ a line, field-reals _on_ a >>>>>>> line,
and signal-reals _about_ and _around_ a line.
So, Chaitin doesn't even have three models of continuous domains, >>>>>>> or "repleteness", of concepts like Lebnitz' principle of perfection >>>>>>> and Hilbert's postulate of continuity.
Mathematics really _does_ define continuity:
and there are at least three models of continuous domains.
So, say you want to sample a real number from [0,1] the interval >>>>>>> at uniform random, and all you have is a fair coin that
gives samples from {0, 1} the set.
So, you start flipping coins and marking the result to make
a sequence of 0's and 1's. Each coin toss _refines_ the
sample.
Yet, each coin toss also _begins_ a new sample. So, to sample
one real number, the super-task results sampling infinitely-many >>>>>>> real numbers.
So, the probability of the first sample being a rational value
is, according to the law of large numbers the law of small numbers, >>>>>>> small, and arbitrarily and infinitesimally small. In theories
that are Pythagorean it's almost-all rationals, while in theories >>>>>>> that are Cantorian it's almost-all transcendentals.
Yet, if a sample arrives at a rational, the repeating character
of rationals means that thusly the _one_ sample of a rational
number is automatically _infinitely-many_ samples of rational
numbers.
So, it makes sense to consider that the probability of sampling
a rational number from [0,1] is about 0.5.
This isn't Pythagorean by itself, and isn't Cantorian by itself. >>>>>>> It's them together according to accounts of paradox-free reason, >>>>>>> not "non-classical logics where we ignore contradiction",
which is _hypocrisy_ and furthermore _fallacious_,
since "infinity" and "continuity" are "absolute" and "replete".
"Let’s start with Borel’s know-it-all number, but now let’s use >>>>>>> the Nth
binary digit to tell us whether or not the Nth computer program ever >>>>>>> halts. So now Borel’s number is an oracle for the halting problem. >>>>>>> For
example, there is a bit which tells us whether or not the Riemann >>>>>>> hypothesis is true, for that is equivalent to the statement that a >>>>>>> program that systematically searches for zeros of the zeta function >>>>>>> that
are in the wrong place, never halts.
It turns out that this number, which I’ll call Turing’s number even >>>>>>> though it does not occur in Turing’s paper, is wasting bits, it is >>>>>>> actually highly redundant. We don’t really need N bits to answer N >>>>>>> cases
of the halting problem, a much smaller number of bits will do. Why? >>>>>>>
Well, consider some large number N of cases of the halting problem, >>>>>>> some
large number N of individual programs for which we want to know
whether
or not each one halts. Is this really N bits of mathematical
information? No, the answers are not independent, they are highly >>>>>>> correlated. How? Well, in order to answer N cases of the halting >>>>>>> problem, we don’t really need to know each individual answer; it >>>>>>> suffices to know how many of these N programs will eventually halt. >>>>>>> Once
we know this number, which is only about log_2 N
bits of information, we can run the N programs in parallel until >>>>>>> exactly
this number of them halt, and then we know that none of the
remaining
programs will ever halt. And log_2 N is much, much less than N for >>>>>>> all
sufficiently large N. In other words, Turing’s number isn’t the best
possible oracle for the halting problem. It is highly redundant, it >>>>>>> uses
far too many bits.
Using essentially this idea, we can get the best possible oracle >>>>>>> number
for the halting problem; that is the halting probability Ω, which >>>>>>> has no
redundancy, none at all.
So, now that there's readily equipped a notion of uniform sampling >>>>>>> that results "oracle numbers", always _infinitely-many_ just to get >>>>>>> one,
then Chaitin's quote is equipped some context that makes
quite a fresh reading.
This goes for all y'all.
Actually, thousands of years before Russell or Tarski claimed that
"truth is whatever I, Lord Russell or Tsar Tarski, say that agrees
with myself", the notion that mathematical truth is _discovered_ not >>>>> _invented_ was "the truth", then that structural realism and realist >>>>> structuralism make for an account with both an idealistic and an
analytical tradition, keeping science for itself as a strengthened
analytical position and the idealistic getting equipped with mental
senses of the faculties of reason about logic and mathematics (and
infinity and continuity) so that Kant is satisfied that "1 + 1 = 2". >>>>>
Then, Wittgenstein is just a cad, and while it's respected
his right to say "I, wild Wittgenstein, say that you can't say
that you say anything at all", it's ignored as saying jack squat.
Natural reasoners can simply arrive at grounds for reason after
axiomless natural deduction making for logic, geometry, number theory, >>>>> with infinity and continuity, and so on. Then formalisms follow as
after perspectival accounts of restriction-of-comprehension given a
thorough account of expansion-of-comprehension.
Plato could be proud.
hey ross what group are you commenting from?
I usually read sci.math and sci.logic, and sometimes comp.ai.philosophy, >>> not so much comp.theory, though,
here there's a general idea that "Zeno machines"
are a model of computation vis-a-vis usual accounts
after Turing machines or Frege's concept-script or
MiX or stack machines or Harvard/vonNeumann or
finite-state-machines the automata.
For decades and since I formalized a few key aspects
of models of continuous domains, nobody tells me I'm
wrong anymore since I'm not wrong, or rather,
the mathematics isn't wrong.
Arriving at that though involves of a bit of a
thorough account of theory for reason, which
here is a paleo-classical post-modern account.
Anyways "olcott" is just the latest spam troll
in a sense - then that it doesn't much matter
whether it was standard accounts or non-standard accounts
or plain retro-finitist crankety troll accounts,
I can offer a sound criticism to any.
Infinity does not actually count at all for the
crucial things of the world such as the survival
of the species and the health of the planet.
On the other hand my inter-linked finite semantic
tautologies (or something like them) are required
for dividing truth from dangerous lies.
You seem to be coming off as a mere pseudo-intellectual
in that you judge people instead of the soundness of
their ideas.
If nothing grounds an expression of language in a
truth value then (well duh) it remains ungrounded
in a truth value.
Infinity disagrees.
There are results due infinitary reasoning simply not available
to finitary reasoning. The Dirac delta function, if you've
ever heard of that, of course is ubiquitous in physics, signal
theory, differential analysis, Fourier-style analysis, and so
on, and its width is _infinitesimal_ and its height is _infinite_
and it's integrable and has area _one_.
Similarly, the perfect results of the calculus are not so
for _any_ _finite_ difference, only "in the limit" and
for the _infinitesimal_ _differential_, simply not being
so for any _finite_ difference.
There are results, furthermore, in the analysis that simply
_belie_, make false, not only any non-infinite limit, also
any _finite_ initial approximation, that even approximations
fail, not merely having a "nominally non-zero error",
actually that there error bound is the same as the approximation,
with regards to numerical methods and other usual accounts of
finite-element analysis.
Then, even better, there are doubling spaces and doubling measures,
and halving spaces and halving measures, and pi-ratio spaces,
that make accounts of equi-decomposability, that _since the
time of Zeno_, that not only the usual account of the ant's march
and iterative halves their sum equaling one the geometric series,
the bee's flights that are actually _double_, _and_, there already
exist in many derivations in physics these "spurious" factors,
that _really_ have an explanation.
So, for many matters of convergence, then emergence, and the
many counter-examples of convergence according to the law of
small numbers as "the" law of large numbers, instead has that
_infinity_ is _real_ and _necessary_ for _continuity_.
And what you have there "grounding in a truth value" that you
make your mind, is known since antiquity to be _ungrounded_
itself, and instead of making a first-class science of it,
as conscientious scientists may, you, sir, are an idiot.
Can't have finite without infinite. Otherwise you got few,
that people the usual third word for numbers in primitive
societies "one, two, a few, ..., too many to count".
There are my hundeds hours low-key lectures in my video channel,
suitable for inobtrusive background noise of the mathematically
(and physically) enriching variety.
Read some Ernst Cassirer and get back to yourself.
On 5/21/2026 11:03 PM, Ross Finlayson wrote:
On 05/21/2026 08:34 PM, olcott wrote:
On 5/21/2026 7:45 PM, Ross Finlayson wrote:
On 05/21/2026 11:14 AM, dart200 wrote:
On 5/21/26 9:54 AM, Ross Finlayson wrote:
On 05/21/2026 06:02 AM, olcott wrote:
On 5/18/2026 11:44 AM, Ross Finlayson wrote:
On 05/18/2026 09:03 AM, olcott wrote:
On 5/18/2026 10:14 AM, Ross Finlayson wrote:
On 05/17/2026 08:48 PM, Chris M. Thomasson wrote:How can a man as smart as you get this so incorrectly?
On 5/17/2026 8:46 PM, Chris M. Thomasson wrote:
On 5/17/2026 5:24 PM, Ross Finlayson wrote:
On 05/17/2026 05:10 PM, Ross Finlayson wrote:
On 05/17/2026 02:46 PM, Chris M. Thomasson wrote: >>>>>>>>>>>>>>> On 5/17/2026 2:21 PM, phoenix wrote:
Chris M. Thomasson wrote:
On 5/16/2026 2:30 PM, phoenix wrote:
Chris M. Thomasson wrote:
Or maybe a different tarot, "the star" because you have >>>>>>>>>>>>>>>>>> such aI find that 'except' paired with 'yet' covers every >>>>>>>>>>>>>>>>>>>> instance of
Yet that yet that yet that yet that yet that it is so: >>>>>>>>>>>>>>>>>>>>> that that that that that it is so.
'but.' If you can find an exception to this, please >>>>>>>>>>>>>>>>>>>> show
me.
fascination with me?
I think you are a sock puppet for olcott.
I know you think that, but I don't see any motivation on my >>>>>>>>>>>>>>>> part to
disabuse you of the notion. Why not play into it and >>>>>>>>>>>>>>>> further
befuddle
you? If it were the case that I were not olcott, that is. >>>>>>>>>>>>>>>>
Ask your self what his halting decider would say... Look in >>>>>>>>>>>>>>> the
mirror?
One of the problems of environments of the unmoderated and >>>>>>>>>>>>>> pseudonymous
sort is that there are all kinds of trolls. There are plain >>>>>>>>>>>>>> rage- bait
and flamer trolls, looky-loos and non-sequitur types, then, >>>>>>>>>>>>>> also
all
sorts of anti-trolls, and these and those.
Then, for example, for something like "it's a free country", >>>>>>>>>>>>>> then
when I see stuff like either
"smell the new normal, you're living in a dictatorship", >>>>>>>>>>>>>> or,
"suffer the children, so your social media and phone get >>>>>>>>>>>>>> hacked",
then either way the idea of being aware ("woke" wasn't a word >>>>>>>>>>>>>> and I'd imagine it would be "awoke" or "woken", or, "woke" >>>>>>>>>>>>>> will
do),
and caring (although, you know, not _too_ caring), that >>>>>>>>>>>>>> trolls
and repeti-bots on "social" media are anti-social. >>>>>>>>>>>>>>
So, it's fair that people get wary of trolls, and, begin to >>>>>>>>>>>>>> suspect
trolls in the likely places, and learn to make a
troll-filter,
and basically a skeptical if not cynical outlook on the world >>>>>>>>>>>>>> today,
that there are trolls and trolls, and sometimes it's >>>>>>>>>>>>>> easiest to
ignore them away.
Then, there are cranks, ....
The crank is one of the easiest sorts of identities to mimic, >>>>>>>>>>>>>> give it a howler fallacy it won't let go and the plain >>>>>>>>>>>>>> obstinance
combined with the stubbornness along with the sort of plain >>>>>>>>>>>>>> unwarranted persistence, then it's not always easy to tell >>>>>>>>>>>>>> the
difference between cranks and trolls, though often it is, >>>>>>>>>>>>>> and between persons and bots, though often it is.
'Murica.
Then, about the thread, the idea is that it's great if these >>>>>>>>>>>>>> long-running mostly-empty tit-for-tat nonsense threads get >>>>>>>>>>>>>> hijacked by passers-by then into discussions about the issues >>>>>>>>>>>>>> at hand, like about the many, many things to do with the >>>>>>>>>>>>>> "mathematics" of continuity and infinity, since, despite >>>>>>>>>>>>>> the idea of some retro-finitists that their world is a >>>>>>>>>>>>>> dot, and not even like AP a giant plutonium atom, there's >>>>>>>>>>>>>> much to be done to bring real infinite and continuity into >>>>>>>>>>>>>> mathematics, then for physics and so on.
So, new blood (or fresh meat) writing on the thread so >>>>>>>>>>>>>> it's not just an echo-chamber of trolls and anti-trolls >>>>>>>>>>>>>> which is one big troll, is not necessarily a bad thing. >>>>>>>>>>>>>>
I enjoy CMT's usual spontaneous cheerful enthusiasm, >>>>>>>>>>>>> though as a perceived bot itself when it once-a-year >>>>>>>>>>>>> cites its prompter, then though the affected anxiety >>>>>>>>>>>>> pronation reminds me of too many lessons learned like >>>>>>>>>>>>> not to smell fear or flinch or beg or impose or presume >>>>>>>>>>>>> or assume or judge or telepathically scan or lurk or >>>>>>>>>>>>> menace or make gossip or berate or scoff.
Fwiw, check out these funny halt deciders... They only halt >>>>>>>>>>>> when
all
possible paths are hit. If you think about its kind of akin to >>>>>>>>>>>> olcotts
DD. i simply hijack its result. Here is a version that uses >>>>>>>>>>>> random
numbers for the fuzzer:
In applesoft basic for fun. ;^D
You can run these here:
https://www.calormen.com/jsbasic/
_____________________________
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
1010 PRINT "FIN... All paths hit."
1020 PRINT "NON_HALT P0 = "; P0
1030 PRINT "HALT P1 = "; P1
_____________________________
Here is one that requires input from a user:
_____________________________
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 INPUT "Shall DD halt or not? " ; A$
110 REM 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
^^^^^^^^^^^^
_____________________________
God damn it forgot to add in line 1000 onward! Shit happens: >>>>>>>>>>>
1000
1010 PRINT "FIN... All paths hit."
1020 PRINT "NON_HALT P0 = "; P0
1030 PRINT "HALT P1 = "; P1
Corrected user input one:
_______________
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 INPUT "Shall DD halt or not? " ; A$
110 REM 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
1010 PRINT "FIN... All paths hit."
1020 PRINT "NON_HALT P0 = "; P0
1030 PRINT "HALT P1 = "; P1
_______________
Sorry about that shit!
It only halts when all paths have been hit.
About cranks then, there's something about a crank I admire, >>>>>>>>>>>>> not so much the being wrong part yet the dream, having the >>>>>>>>>>>>> dreams, I'm all for people having the dream when it's not >>>>>>>>>>>>> frustrating or threatening other people's dreams.
So, as I usually enough put it, "retro-finitist crankety >>>>>>>>>>>>> trolls can step off and get bent".
I'm not a fan of any "new" normal, we already have plain >>>>>>>>>>>>> old "normal normal".
Hm.
There are at least three accounts of programs whether they halt. >>>>>>>>>>
A) almost-all programs halt
B) almost-all programs don't halt
C) half of programs halt
The number of programs that halt is between 0 and 100%
excluding the endpoints.
https://arxiv.org/abs/math/0611740
"The Halting Probability Omega: Irreducible Complexity in Pure >>>>>>>> Mathematics", G. Chaitin
"Gödel himself did not think that his theorem showed that
mathematics
has limitations. In several essays he made it clear that he
believed
that mathematicians could eventually settle any significant
question by
using their mathematical intuition, their ability to directly
perceive
the Platonic world of mathematical ideas, and by inventing or
discovering new concepts and new axioms, new principles.
Furthermore, I share Enriques’s faith in intuition. I think that >>>>>>>> excessive formalism and abstraction is killing mathematics. In my >>>>>>>> opinion math papers shouldn’t attempt to replace all words by >>>>>>>> formulas,
instead they should be like literary essays, they should attempt to >>>>>>>> explain and convince.
Extending Dag Prawitz's Theory of Grounds while remaining
directly within the realm of proof theoretic Semantics then
G simply becomes ungrounded in PA and grounded in meta-math.
It has taken PTS quite a few decades, all the way up to 2012
to catch up with what Wittgenstein said decades earlier:
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's
system' means: the opposite has been proved in Russell's
system. https://www.liarparadox.org/Wittgenstein.pdf
So let me tell you the story of metamathematics, of how
mathematicians
have tried to use mathematical methods to study the power and the >>>>>>>> limitations of math itself. It’s a fairly dramatic story; in a >>>>>>>> previous
era it might have been the subject of epic poems, of Iliads and >>>>>>>> Odysseys
of verse. I’ll start with David Hilbert."
"In my opinion this is a fundamental step forward in the
philosophy of
mathematics because it makes incompleteness seem much more
concrete and
much more natural. It’s almost a problem in physics, it’s about a >>>>>>>> machine, you just ask whether or not it’s going to eventually >>>>>>>> stop, and
it turns out there’s no way, no general way, to answer that
question.
Let me emphasize that if a program does halt, we can eventually >>>>>>>> discover
that. The problem, an extremely deep one, is to show that a program >>>>>>>> will
never halt if this is in fact so. One can settle many special
cases,
even an infinity of them, but no finite set of axioms can enable >>>>>>>> you to
settle all possible cases."
Hm, " ... no finite set of axioms ...", ..., how about "no axioms". >>>>>>>>
"The real numbers are the simplest thing in the world
geometrically,
they are just points on a line. But arithmetically, as individuals, >>>>>>>> real
numbers are actually rather unreal. Turing’s 1936 uncomputable >>>>>>>> real is
just the tip of the iceberg, the problem is a lot more serious than >>>>>>>> that."
Here the iota-values are points _in_ a line, field-reals _on_ a >>>>>>>> line,
and signal-reals _about_ and _around_ a line.
So, Chaitin doesn't even have three models of continuous domains, >>>>>>>> or "repleteness", of concepts like Lebnitz' principle of perfection >>>>>>>> and Hilbert's postulate of continuity.
Mathematics really _does_ define continuity:
and there are at least three models of continuous domains.
So, say you want to sample a real number from [0,1] the interval >>>>>>>> at uniform random, and all you have is a fair coin that
gives samples from {0, 1} the set.
So, you start flipping coins and marking the result to make
a sequence of 0's and 1's. Each coin toss _refines_ the
sample.
Yet, each coin toss also _begins_ a new sample. So, to sample
one real number, the super-task results sampling infinitely-many >>>>>>>> real numbers.
So, the probability of the first sample being a rational value >>>>>>>> is, according to the law of large numbers the law of small numbers, >>>>>>>> small, and arbitrarily and infinitesimally small. In theories
that are Pythagorean it's almost-all rationals, while in theories >>>>>>>> that are Cantorian it's almost-all transcendentals.
Yet, if a sample arrives at a rational, the repeating character >>>>>>>> of rationals means that thusly the _one_ sample of a rational
number is automatically _infinitely-many_ samples of rational
numbers.
So, it makes sense to consider that the probability of sampling >>>>>>>> a rational number from [0,1] is about 0.5.
This isn't Pythagorean by itself, and isn't Cantorian by itself. >>>>>>>> It's them together according to accounts of paradox-free reason, >>>>>>>> not "non-classical logics where we ignore contradiction",
which is _hypocrisy_ and furthermore _fallacious_,
since "infinity" and "continuity" are "absolute" and "replete". >>>>>>>>
"Let’s start with Borel’s know-it-all number, but now let’s use >>>>>>>> the Nth
binary digit to tell us whether or not the Nth computer program >>>>>>>> ever
halts. So now Borel’s number is an oracle for the halting problem. >>>>>>>> For
example, there is a bit which tells us whether or not the Riemann >>>>>>>> hypothesis is true, for that is equivalent to the statement that a >>>>>>>> program that systematically searches for zeros of the zeta function >>>>>>>> that
are in the wrong place, never halts.
It turns out that this number, which I’ll call Turing’s number even
though it does not occur in Turing’s paper, is wasting bits, it is >>>>>>>> actually highly redundant. We don’t really need N bits to answer N >>>>>>>> cases
of the halting problem, a much smaller number of bits will do. Why? >>>>>>>>
Well, consider some large number N of cases of the halting problem, >>>>>>>> some
large number N of individual programs for which we want to know >>>>>>>> whether
or not each one halts. Is this really N bits of mathematical
information? No, the answers are not independent, they are highly >>>>>>>> correlated. How? Well, in order to answer N cases of the halting >>>>>>>> problem, we don’t really need to know each individual answer; it >>>>>>>> suffices to know how many of these N programs will eventually halt. >>>>>>>> Once
we know this number, which is only about log_2 N
bits of information, we can run the N programs in parallel until >>>>>>>> exactly
this number of them halt, and then we know that none of the
remaining
programs will ever halt. And log_2 N is much, much less than N for >>>>>>>> all
sufficiently large N. In other words, Turing’s number isn’t the >>>>>>>> best
possible oracle for the halting problem. It is highly redundant, it >>>>>>>> uses
far too many bits.
Using essentially this idea, we can get the best possible oracle >>>>>>>> number
for the halting problem; that is the halting probability Ω, which >>>>>>>> has no
redundancy, none at all.
So, now that there's readily equipped a notion of uniform sampling >>>>>>>> that results "oracle numbers", always _infinitely-many_ just to get >>>>>>>> one,
then Chaitin's quote is equipped some context that makes
quite a fresh reading.
This goes for all y'all.
Actually, thousands of years before Russell or Tarski claimed that >>>>>> "truth is whatever I, Lord Russell or Tsar Tarski, say that agrees >>>>>> with myself", the notion that mathematical truth is _discovered_ not >>>>>> _invented_ was "the truth", then that structural realism and realist >>>>>> structuralism make for an account with both an idealistic and an
analytical tradition, keeping science for itself as a strengthened >>>>>> analytical position and the idealistic getting equipped with mental >>>>>> senses of the faculties of reason about logic and mathematics (and >>>>>> infinity and continuity) so that Kant is satisfied that "1 + 1 = 2". >>>>>>
Then, Wittgenstein is just a cad, and while it's respected
his right to say "I, wild Wittgenstein, say that you can't say
that you say anything at all", it's ignored as saying jack squat.
Natural reasoners can simply arrive at grounds for reason after
axiomless natural deduction making for logic, geometry, number
theory,
with infinity and continuity, and so on. Then formalisms follow as >>>>>> after perspectival accounts of restriction-of-comprehension given a >>>>>> thorough account of expansion-of-comprehension.
Plato could be proud.
hey ross what group are you commenting from?
I usually read sci.math and sci.logic, and sometimes
comp.ai.philosophy,
not so much comp.theory, though,
here there's a general idea that "Zeno machines"
are a model of computation vis-a-vis usual accounts
after Turing machines or Frege's concept-script or
MiX or stack machines or Harvard/vonNeumann or
finite-state-machines the automata.
For decades and since I formalized a few key aspects
of models of continuous domains, nobody tells me I'm
wrong anymore since I'm not wrong, or rather,
the mathematics isn't wrong.
Arriving at that though involves of a bit of a
thorough account of theory for reason, which
here is a paleo-classical post-modern account.
Anyways "olcott" is just the latest spam troll
in a sense - then that it doesn't much matter
whether it was standard accounts or non-standard accounts
or plain retro-finitist crankety troll accounts,
I can offer a sound criticism to any.
Infinity does not actually count at all for the
crucial things of the world such as the survival
of the species and the health of the planet.
On the other hand my inter-linked finite semantic
tautologies (or something like them) are required
for dividing truth from dangerous lies.
You seem to be coming off as a mere pseudo-intellectual
in that you judge people instead of the soundness of
their ideas.
If nothing grounds an expression of language in a
truth value then (well duh) it remains ungrounded
in a truth value.
Infinity disagrees.
Infinity disagrees that an expression of language
not grounded in a truth value is not grounded in a truth value?
Does infinity disagree that black cats are black?
tautology, in logic, a statement so framed that it
cannot be denied without inconsistency. https://www.britannica.com/topic/tautology
All black cats are black.
If nothing grounds an expression of language in a
truth value then (well duh) it remains ungrounded
in a truth value.
There are results due infinitary reasoning simply not available
to finitary reasoning. The Dirac delta function, if you've
ever heard of that, of course is ubiquitous in physics, signal
theory, differential analysis, Fourier-style analysis, and so
on, and its width is _infinitesimal_ and its height is _infinite_
and it's integrable and has area _one_.
Similarly, the perfect results of the calculus are not so
for _any_ _finite_ difference, only "in the limit" and
for the _infinitesimal_ _differential_, simply not being
so for any _finite_ difference.
There are results, furthermore, in the analysis that simply
_belie_, make false, not only any non-infinite limit, also
any _finite_ initial approximation, that even approximations
fail, not merely having a "nominally non-zero error",
actually that there error bound is the same as the approximation,
with regards to numerical methods and other usual accounts of
finite-element analysis.
Then, even better, there are doubling spaces and doubling measures,
and halving spaces and halving measures, and pi-ratio spaces,
that make accounts of equi-decomposability, that _since the
time of Zeno_, that not only the usual account of the ant's march
and iterative halves their sum equaling one the geometric series,
the bee's flights that are actually _double_, _and_, there already
exist in many derivations in physics these "spurious" factors,
that _really_ have an explanation.
So, for many matters of convergence, then emergence, and the
many counter-examples of convergence according to the law of
small numbers as "the" law of large numbers, instead has that
_infinity_ is _real_ and _necessary_ for _continuity_.
And what you have there "grounding in a truth value" that you
make your mind, is known since antiquity to be _ungrounded_
itself, and instead of making a first-class science of it,
as conscientious scientists may, you, sir, are an idiot.
Can't have finite without infinite. Otherwise you got few,
that people the usual third word for numbers in primitive
societies "one, two, a few, ..., too many to count".
There are my hundeds hours low-key lectures in my video channel,
suitable for inobtrusive background noise of the mathematically
(and physically) enriching variety.
Read some Ernst Cassirer and get back to yourself.
On 5/21/26 5:45 PM, Ross Finlayson wrote:
On 05/21/2026 11:14 AM, dart200 wrote:
On 5/21/26 9:54 AM, Ross Finlayson wrote:
On 05/21/2026 06:02 AM, olcott wrote:
On 5/18/2026 11:44 AM, Ross Finlayson wrote:
On 05/18/2026 09:03 AM, olcott wrote:
On 5/18/2026 10:14 AM, Ross Finlayson wrote:
On 05/17/2026 08:48 PM, Chris M. Thomasson wrote:How can a man as smart as you get this so incorrectly?
On 5/17/2026 8:46 PM, Chris M. Thomasson wrote:
On 5/17/2026 5:24 PM, Ross Finlayson wrote:
On 05/17/2026 05:10 PM, Ross Finlayson wrote:
On 05/17/2026 02:46 PM, Chris M. Thomasson wrote:
On 5/17/2026 2:21 PM, phoenix wrote:
Chris M. Thomasson wrote:
On 5/16/2026 2:30 PM, phoenix wrote:
Chris M. Thomasson wrote:
Or maybe a different tarot, "the star" because you have >>>>>>>>>>>>>>>> such aI find that 'except' paired with 'yet' covers every >>>>>>>>>>>>>>>>>> instance of
Yet that yet that yet that yet that yet that it is so: >>>>>>>>>>>>>>>>>>> that that that that that it is so.
'but.' If you can find an exception to this, please show >>>>>>>>>>>>>>>>>> me.
fascination with me?
I think you are a sock puppet for olcott.
I know you think that, but I don't see any motivation on my >>>>>>>>>>>>>> part to
disabuse you of the notion. Why not play into it and further >>>>>>>>>>>>>> befuddle
you? If it were the case that I were not olcott, that is. >>>>>>>>>>>>>>
Ask your self what his halting decider would say... Look in >>>>>>>>>>>>> the
mirror?
One of the problems of environments of the unmoderated and >>>>>>>>>>>> pseudonymous
sort is that there are all kinds of trolls. There are plain >>>>>>>>>>>> rage- bait
and flamer trolls, looky-loos and non-sequitur types, then, >>>>>>>>>>>> also
all
sorts of anti-trolls, and these and those.
Then, for example, for something like "it's a free country", >>>>>>>>>>>> then
when I see stuff like either
"smell the new normal, you're living in a dictatorship", >>>>>>>>>>>> or,
"suffer the children, so your social media and phone get >>>>>>>>>>>> hacked",
then either way the idea of being aware ("woke" wasn't a word >>>>>>>>>>>> and I'd imagine it would be "awoke" or "woken", or, "woke" will >>>>>>>>>>>> do),
and caring (although, you know, not _too_ caring), that trolls >>>>>>>>>>>> and repeti-bots on "social" media are anti-social.
So, it's fair that people get wary of trolls, and, begin to >>>>>>>>>>>> suspect
trolls in the likely places, and learn to make a troll-filter, >>>>>>>>>>>> and basically a skeptical if not cynical outlook on the world >>>>>>>>>>>> today,
that there are trolls and trolls, and sometimes it's easiest to >>>>>>>>>>>> ignore them away.
Then, there are cranks, ....
The crank is one of the easiest sorts of identities to mimic, >>>>>>>>>>>> give it a howler fallacy it won't let go and the plain >>>>>>>>>>>> obstinance
combined with the stubbornness along with the sort of plain >>>>>>>>>>>> unwarranted persistence, then it's not always easy to tell the >>>>>>>>>>>> difference between cranks and trolls, though often it is, >>>>>>>>>>>> and between persons and bots, though often it is.
'Murica.
Then, about the thread, the idea is that it's great if these >>>>>>>>>>>> long-running mostly-empty tit-for-tat nonsense threads get >>>>>>>>>>>> hijacked by passers-by then into discussions about the issues >>>>>>>>>>>> at hand, like about the many, many things to do with the >>>>>>>>>>>> "mathematics" of continuity and infinity, since, despite >>>>>>>>>>>> the idea of some retro-finitists that their world is a >>>>>>>>>>>> dot, and not even like AP a giant plutonium atom, there's >>>>>>>>>>>> much to be done to bring real infinite and continuity into >>>>>>>>>>>> mathematics, then for physics and so on.
So, new blood (or fresh meat) writing on the thread so >>>>>>>>>>>> it's not just an echo-chamber of trolls and anti-trolls >>>>>>>>>>>> which is one big troll, is not necessarily a bad thing. >>>>>>>>>>>>
I enjoy CMT's usual spontaneous cheerful enthusiasm,
though as a perceived bot itself when it once-a-year
cites its prompter, then though the affected anxiety
pronation reminds me of too many lessons learned like
not to smell fear or flinch or beg or impose or presume
or assume or judge or telepathically scan or lurk or
menace or make gossip or berate or scoff.
Fwiw, check out these funny halt deciders... They only halt when >>>>>>>>>> all
possible paths are hit. If you think about its kind of akin to >>>>>>>>>> olcotts
DD. i simply hijack its result. Here is a version that uses >>>>>>>>>> random
numbers for the fuzzer:
In applesoft basic for fun. ;^D
You can run these here:
https://www.calormen.com/jsbasic/
_____________________________
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
1010 PRINT "FIN... All paths hit."
1020 PRINT "NON_HALT P0 = "; P0
1030 PRINT "HALT P1 = "; P1
_____________________________
Here is one that requires input from a user:
_____________________________
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 INPUT "Shall DD halt or not? " ; A$
110 REM 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
^^^^^^^^^^^^
_____________________________
God damn it forgot to add in line 1000 onward! Shit happens: >>>>>>>>>
1000
1010 PRINT "FIN... All paths hit."
1020 PRINT "NON_HALT P0 = "; P0
1030 PRINT "HALT P1 = "; P1
Corrected user input one:
_______________
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 INPUT "Shall DD halt or not? " ; A$
110 REM 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
1010 PRINT "FIN... All paths hit."
1020 PRINT "NON_HALT P0 = "; P0
1030 PRINT "HALT P1 = "; P1
_______________
Sorry about that shit!
It only halts when all paths have been hit.
About cranks then, there's something about a crank I admire, >>>>>>>>>>> not so much the being wrong part yet the dream, having the >>>>>>>>>>> dreams, I'm all for people having the dream when it's not >>>>>>>>>>> frustrating or threatening other people's dreams.
So, as I usually enough put it, "retro-finitist crankety >>>>>>>>>>> trolls can step off and get bent".
I'm not a fan of any "new" normal, we already have plain >>>>>>>>>>> old "normal normal".
Hm.
There are at least three accounts of programs whether they halt. >>>>>>>>
A) almost-all programs halt
B) almost-all programs don't halt
C) half of programs halt
The number of programs that halt is between 0 and 100%
excluding the endpoints.
https://arxiv.org/abs/math/0611740
"The Halting Probability Omega: Irreducible Complexity in Pure
Mathematics", G. Chaitin
"Gödel himself did not think that his theorem showed that mathematics >>>>>> has limitations. In several essays he made it clear that he believed >>>>>> that mathematicians could eventually settle any significant
question by
using their mathematical intuition, their ability to directly
perceive
the Platonic world of mathematical ideas, and by inventing or
discovering new concepts and new axioms, new principles.
Furthermore, I share Enriques’s faith in intuition. I think that >>>>>> excessive formalism and abstraction is killing mathematics. In my
opinion math papers shouldn’t attempt to replace all words by
formulas,
instead they should be like literary essays, they should attempt to >>>>>> explain and convince.
Extending Dag Prawitz's Theory of Grounds while remaining
directly within the realm of proof theoretic Semantics then
G simply becomes ungrounded in PA and grounded in meta-math.
It has taken PTS quite a few decades, all the way up to 2012
to catch up with what Wittgenstein said decades earlier:
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's
system' means: the opposite has been proved in Russell's
system. https://www.liarparadox.org/Wittgenstein.pdf
So let me tell you the story of metamathematics, of how
mathematicians
have tried to use mathematical methods to study the power and the
limitations of math itself. It’s a fairly dramatic story; in a
previous
era it might have been the subject of epic poems, of Iliads and
Odysseys
of verse. I’ll start with David Hilbert."
"In my opinion this is a fundamental step forward in the
philosophy of
mathematics because it makes incompleteness seem much more
concrete and
much more natural. It’s almost a problem in physics, it’s about a >>>>>> machine, you just ask whether or not it’s going to eventually
stop, and
it turns out there’s no way, no general way, to answer that question. >>>>>> Let me emphasize that if a program does halt, we can eventually
discover
that. The problem, an extremely deep one, is to show that a program >>>>>> will
never halt if this is in fact so. One can settle many special cases, >>>>>> even an infinity of them, but no finite set of axioms can enable
you to
settle all possible cases."
Hm, " ... no finite set of axioms ...", ..., how about "no axioms". >>>>>>
"The real numbers are the simplest thing in the world geometrically, >>>>>> they are just points on a line. But arithmetically, as individuals, >>>>>> real
numbers are actually rather unreal. Turing’s 1936 uncomputable
real is
just the tip of the iceberg, the problem is a lot more serious than >>>>>> that."
Here the iota-values are points _in_ a line, field-reals _on_ a line, >>>>>> and signal-reals _about_ and _around_ a line.
So, Chaitin doesn't even have three models of continuous domains,
or "repleteness", of concepts like Lebnitz' principle of perfection >>>>>> and Hilbert's postulate of continuity.
Mathematics really _does_ define continuity:
and there are at least three models of continuous domains.
So, say you want to sample a real number from [0,1] the interval
at uniform random, and all you have is a fair coin that
gives samples from {0, 1} the set.
So, you start flipping coins and marking the result to make
a sequence of 0's and 1's. Each coin toss _refines_ the
sample.
Yet, each coin toss also _begins_ a new sample. So, to sample
one real number, the super-task results sampling infinitely-many
real numbers.
So, the probability of the first sample being a rational value
is, according to the law of large numbers the law of small numbers, >>>>>> small, and arbitrarily and infinitesimally small. In theories
that are Pythagorean it's almost-all rationals, while in theories
that are Cantorian it's almost-all transcendentals.
Yet, if a sample arrives at a rational, the repeating character
of rationals means that thusly the _one_ sample of a rational
number is automatically _infinitely-many_ samples of rational
numbers.
So, it makes sense to consider that the probability of sampling
a rational number from [0,1] is about 0.5.
This isn't Pythagorean by itself, and isn't Cantorian by itself.
It's them together according to accounts of paradox-free reason,
not "non-classical logics where we ignore contradiction",
which is _hypocrisy_ and furthermore _fallacious_,
since "infinity" and "continuity" are "absolute" and "replete".
"Let’s start with Borel’s know-it-all number, but now let’s use >>>>>> the Nth
binary digit to tell us whether or not the Nth computer program ever >>>>>> halts. So now Borel’s number is an oracle for the halting problem. >>>>>> For
example, there is a bit which tells us whether or not the Riemann
hypothesis is true, for that is equivalent to the statement that a >>>>>> program that systematically searches for zeros of the zeta function >>>>>> that
are in the wrong place, never halts.
It turns out that this number, which I’ll call Turing’s number even >>>>>> though it does not occur in Turing’s paper, is wasting bits, it is >>>>>> actually highly redundant. We don’t really need N bits to answer N >>>>>> cases
of the halting problem, a much smaller number of bits will do. Why? >>>>>>
Well, consider some large number N of cases of the halting problem, >>>>>> some
large number N of individual programs for which we want to know
whether
or not each one halts. Is this really N bits of mathematical
information? No, the answers are not independent, they are highly
correlated. How? Well, in order to answer N cases of the halting
problem, we don’t really need to know each individual answer; it >>>>>> suffices to know how many of these N programs will eventually halt. >>>>>> Once
we know this number, which is only about log_2 N
bits of information, we can run the N programs in parallel until
exactly
this number of them halt, and then we know that none of the remaining >>>>>> programs will ever halt. And log_2 N is much, much less than N for >>>>>> all
sufficiently large N. In other words, Turing’s number isn’t the best >>>>>> possible oracle for the halting problem. It is highly redundant, it >>>>>> uses
far too many bits.
Using essentially this idea, we can get the best possible oracle
number
for the halting problem; that is the halting probability Ω, which >>>>>> has no
redundancy, none at all.
So, now that there's readily equipped a notion of uniform sampling >>>>>> that results "oracle numbers", always _infinitely-many_ just to get >>>>>> one,
then Chaitin's quote is equipped some context that makes
quite a fresh reading.
This goes for all y'all.
Actually, thousands of years before Russell or Tarski claimed that
"truth is whatever I, Lord Russell or Tsar Tarski, say that agrees
with myself", the notion that mathematical truth is _discovered_ not
_invented_ was "the truth", then that structural realism and realist
structuralism make for an account with both an idealistic and an
analytical tradition, keeping science for itself as a strengthened
analytical position and the idealistic getting equipped with mental
senses of the faculties of reason about logic and mathematics (and
infinity and continuity) so that Kant is satisfied that "1 + 1 = 2".
Then, Wittgenstein is just a cad, and while it's respected
his right to say "I, wild Wittgenstein, say that you can't say
that you say anything at all", it's ignored as saying jack squat.
Natural reasoners can simply arrive at grounds for reason after
axiomless natural deduction making for logic, geometry, number theory, >>>> with infinity and continuity, and so on. Then formalisms follow as
after perspectival accounts of restriction-of-comprehension given a
thorough account of expansion-of-comprehension.
Plato could be proud.
hey ross what group are you commenting from?
I usually read sci.math and sci.logic, and sometimes comp.ai.philosophy,
ah ok i'll copy sci.logic on some threads in the future
not so much comp.theory, though,
here there's a general idea that "Zeno machines"
are a model of computation vis-a-vis usual accounts
after Turing machines or Frege's concept-script or
MiX or stack machines or Harvard/vonNeumann or
finite-state-machines the automata.
For decades and since I formalized a few key aspects
of models of continuous domains, nobody tells me I'm
wrong anymore since I'm not wrong, or rather,
the mathematics isn't wrong.
Arriving at that though involves of a bit of a
thorough account of theory for reason, which
here is a paleo-classical post-modern account.
Anyways "olcott" is just the latest spam troll
he has been posting about roughly the same stuff for decades now. i
never got any useful interaction with him in the 9 months i've been
posting on usenet tho, unfortunately
others have been useful for sure, in entirely antagonistic manners tho...
i thirst for meaningful cooperation lol
in a sense - then that it doesn't much matter
whether it was standard accounts or non-standard accounts
or plain retro-finitist crankety troll accounts,
I can offer a sound criticism to any.
i could use a sound criticism on this draft i've written:
https://www.academia.edu/143540657/re_turings_diagonals_how_to_decide_on_the_sequence_of_computable_numbers
definitely not perfect, and i have fleshed out the ideas a lot in
various post since then ... but the core logic from that paper that
motivates me hasn't changed
On 05/21/2026 10:18 PM, dart200 wrote:
On 5/21/26 5:45 PM, Ross Finlayson wrote:
On 05/21/2026 11:14 AM, dart200 wrote:
On 5/21/26 9:54 AM, Ross Finlayson wrote:
On 05/21/2026 06:02 AM, olcott wrote:
On 5/18/2026 11:44 AM, Ross Finlayson wrote:
On 05/18/2026 09:03 AM, olcott wrote:
On 5/18/2026 10:14 AM, Ross Finlayson wrote:
On 05/17/2026 08:48 PM, Chris M. Thomasson wrote:How can a man as smart as you get this so incorrectly?
On 5/17/2026 8:46 PM, Chris M. Thomasson wrote:
On 5/17/2026 5:24 PM, Ross Finlayson wrote:
On 05/17/2026 05:10 PM, Ross Finlayson wrote:
On 05/17/2026 02:46 PM, Chris M. Thomasson wrote:
On 5/17/2026 2:21 PM, phoenix wrote:
Chris M. Thomasson wrote:
On 5/16/2026 2:30 PM, phoenix wrote:
Chris M. Thomasson wrote:
Or maybe a different tarot, "the star" because you have >>>>>>>>>>>>>>>>> such aI find that 'except' paired with 'yet' covers every >>>>>>>>>>>>>>>>>>> instance of
Yet that yet that yet that yet that yet that it is so: >>>>>>>>>>>>>>>>>>>> that that that that that it is so.
'but.' If you can find an exception to this, please show >>>>>>>>>>>>>>>>>>> me.
fascination with me?
I think you are a sock puppet for olcott.
I know you think that, but I don't see any motivation on my >>>>>>>>>>>>>>> part to
disabuse you of the notion. Why not play into it and further >>>>>>>>>>>>>>> befuddle
you? If it were the case that I were not olcott, that is. >>>>>>>>>>>>>>>
Ask your self what his halting decider would say... Look in >>>>>>>>>>>>>> the
mirror?
One of the problems of environments of the unmoderated and >>>>>>>>>>>>> pseudonymous
sort is that there are all kinds of trolls. There are plain >>>>>>>>>>>>> rage- bait
and flamer trolls, looky-loos and non-sequitur types, then, >>>>>>>>>>>>> also
all
sorts of anti-trolls, and these and those.
Then, for example, for something like "it's a free country", >>>>>>>>>>>>> then
when I see stuff like either
"smell the new normal, you're living in a dictatorship", >>>>>>>>>>>>> or,
"suffer the children, so your social media and phone get >>>>>>>>>>>>> hacked",
then either way the idea of being aware ("woke" wasn't a word >>>>>>>>>>>>> and I'd imagine it would be "awoke" or "woken", or, "woke" >>>>>>>>>>>>> will
do),
and caring (although, you know, not _too_ caring), that trolls >>>>>>>>>>>>> and repeti-bots on "social" media are anti-social.
So, it's fair that people get wary of trolls, and, begin to >>>>>>>>>>>>> suspect
trolls in the likely places, and learn to make a troll-filter, >>>>>>>>>>>>> and basically a skeptical if not cynical outlook on the world >>>>>>>>>>>>> today,
that there are trolls and trolls, and sometimes it's >>>>>>>>>>>>> easiest to
ignore them away.
Then, there are cranks, ....
The crank is one of the easiest sorts of identities to mimic, >>>>>>>>>>>>> give it a howler fallacy it won't let go and the plain >>>>>>>>>>>>> obstinance
combined with the stubbornness along with the sort of plain >>>>>>>>>>>>> unwarranted persistence, then it's not always easy to tell the >>>>>>>>>>>>> difference between cranks and trolls, though often it is, >>>>>>>>>>>>> and between persons and bots, though often it is.
'Murica.
Then, about the thread, the idea is that it's great if these >>>>>>>>>>>>> long-running mostly-empty tit-for-tat nonsense threads get >>>>>>>>>>>>> hijacked by passers-by then into discussions about the issues >>>>>>>>>>>>> at hand, like about the many, many things to do with the >>>>>>>>>>>>> "mathematics" of continuity and infinity, since, despite >>>>>>>>>>>>> the idea of some retro-finitists that their world is a >>>>>>>>>>>>> dot, and not even like AP a giant plutonium atom, there's >>>>>>>>>>>>> much to be done to bring real infinite and continuity into >>>>>>>>>>>>> mathematics, then for physics and so on.
So, new blood (or fresh meat) writing on the thread so >>>>>>>>>>>>> it's not just an echo-chamber of trolls and anti-trolls >>>>>>>>>>>>> which is one big troll, is not necessarily a bad thing. >>>>>>>>>>>>>
I enjoy CMT's usual spontaneous cheerful enthusiasm,
though as a perceived bot itself when it once-a-year
cites its prompter, then though the affected anxiety
pronation reminds me of too many lessons learned like
not to smell fear or flinch or beg or impose or presume >>>>>>>>>>>> or assume or judge or telepathically scan or lurk or
menace or make gossip or berate or scoff.
Fwiw, check out these funny halt deciders... They only halt when >>>>>>>>>>> all
possible paths are hit. If you think about its kind of akin to >>>>>>>>>>> olcotts
DD. i simply hijack its result. Here is a version that uses >>>>>>>>>>> random
numbers for the fuzzer:
In applesoft basic for fun. ;^D
You can run these here:
https://www.calormen.com/jsbasic/
_____________________________
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
1010 PRINT "FIN... All paths hit."
1020 PRINT "NON_HALT P0 = "; P0
1030 PRINT "HALT P1 = "; P1
_____________________________
Here is one that requires input from a user:
_____________________________
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 INPUT "Shall DD halt or not? " ; A$
110 REM 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
^^^^^^^^^^^^
_____________________________
God damn it forgot to add in line 1000 onward! Shit happens: >>>>>>>>>>
1000
1010 PRINT "FIN... All paths hit."
1020 PRINT "NON_HALT P0 = "; P0
1030 PRINT "HALT P1 = "; P1
Corrected user input one:
_______________
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 INPUT "Shall DD halt or not? " ; A$
110 REM 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
1010 PRINT "FIN... All paths hit."
1020 PRINT "NON_HALT P0 = "; P0
1030 PRINT "HALT P1 = "; P1
_______________
Sorry about that shit!
It only halts when all paths have been hit.
About cranks then, there's something about a crank I admire, >>>>>>>>>>>> not so much the being wrong part yet the dream, having the >>>>>>>>>>>> dreams, I'm all for people having the dream when it's not >>>>>>>>>>>> frustrating or threatening other people's dreams.
So, as I usually enough put it, "retro-finitist crankety >>>>>>>>>>>> trolls can step off and get bent".
I'm not a fan of any "new" normal, we already have plain >>>>>>>>>>>> old "normal normal".
Hm.
There are at least three accounts of programs whether they halt. >>>>>>>>>
A) almost-all programs halt
B) almost-all programs don't halt
C) half of programs halt
The number of programs that halt is between 0 and 100%
excluding the endpoints.
https://arxiv.org/abs/math/0611740
"The Halting Probability Omega: Irreducible Complexity in Pure
Mathematics", G. Chaitin
"Gödel himself did not think that his theorem showed that
mathematics
has limitations. In several essays he made it clear that he believed >>>>>>> that mathematicians could eventually settle any significant
question by
using their mathematical intuition, their ability to directly
perceive
the Platonic world of mathematical ideas, and by inventing or
discovering new concepts and new axioms, new principles.
Furthermore, I share Enriques’s faith in intuition. I think that >>>>>>> excessive formalism and abstraction is killing mathematics. In my >>>>>>> opinion math papers shouldn’t attempt to replace all words by
formulas,
instead they should be like literary essays, they should attempt to >>>>>>> explain and convince.
Extending Dag Prawitz's Theory of Grounds while remaining
directly within the realm of proof theoretic Semantics then
G simply becomes ungrounded in PA and grounded in meta-math.
It has taken PTS quite a few decades, all the way up to 2012
to catch up with what Wittgenstein said decades earlier:
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's
system' means: the opposite has been proved in Russell's
system. https://www.liarparadox.org/Wittgenstein.pdf
So let me tell you the story of metamathematics, of how
mathematicians
have tried to use mathematical methods to study the power and the >>>>>>> limitations of math itself. It’s a fairly dramatic story; in a >>>>>>> previous
era it might have been the subject of epic poems, of Iliads and
Odysseys
of verse. I’ll start with David Hilbert."
"In my opinion this is a fundamental step forward in the
philosophy of
mathematics because it makes incompleteness seem much more
concrete and
much more natural. It’s almost a problem in physics, it’s about a >>>>>>> machine, you just ask whether or not it’s going to eventually
stop, and
it turns out there’s no way, no general way, to answer that
question.
Let me emphasize that if a program does halt, we can eventually
discover
that. The problem, an extremely deep one, is to show that a program >>>>>>> will
never halt if this is in fact so. One can settle many special cases, >>>>>>> even an infinity of them, but no finite set of axioms can enable >>>>>>> you to
settle all possible cases."
Hm, " ... no finite set of axioms ...", ..., how about "no axioms". >>>>>>>
"The real numbers are the simplest thing in the world geometrically, >>>>>>> they are just points on a line. But arithmetically, as individuals, >>>>>>> real
numbers are actually rather unreal. Turing’s 1936 uncomputable >>>>>>> real is
just the tip of the iceberg, the problem is a lot more serious than >>>>>>> that."
Here the iota-values are points _in_ a line, field-reals _on_ a >>>>>>> line,
and signal-reals _about_ and _around_ a line.
So, Chaitin doesn't even have three models of continuous domains, >>>>>>> or "repleteness", of concepts like Lebnitz' principle of perfection >>>>>>> and Hilbert's postulate of continuity.
Mathematics really _does_ define continuity:
and there are at least three models of continuous domains.
So, say you want to sample a real number from [0,1] the interval >>>>>>> at uniform random, and all you have is a fair coin that
gives samples from {0, 1} the set.
So, you start flipping coins and marking the result to make
a sequence of 0's and 1's. Each coin toss _refines_ the
sample.
Yet, each coin toss also _begins_ a new sample. So, to sample
one real number, the super-task results sampling infinitely-many >>>>>>> real numbers.
So, the probability of the first sample being a rational value
is, according to the law of large numbers the law of small numbers, >>>>>>> small, and arbitrarily and infinitesimally small. In theories
that are Pythagorean it's almost-all rationals, while in theories >>>>>>> that are Cantorian it's almost-all transcendentals.
Yet, if a sample arrives at a rational, the repeating character
of rationals means that thusly the _one_ sample of a rational
number is automatically _infinitely-many_ samples of rational
numbers.
So, it makes sense to consider that the probability of sampling
a rational number from [0,1] is about 0.5.
This isn't Pythagorean by itself, and isn't Cantorian by itself. >>>>>>> It's them together according to accounts of paradox-free reason, >>>>>>> not "non-classical logics where we ignore contradiction",
which is _hypocrisy_ and furthermore _fallacious_,
since "infinity" and "continuity" are "absolute" and "replete".
"Let’s start with Borel’s know-it-all number, but now let’s use >>>>>>> the Nth
binary digit to tell us whether or not the Nth computer program ever >>>>>>> halts. So now Borel’s number is an oracle for the halting problem. >>>>>>> For
example, there is a bit which tells us whether or not the Riemann >>>>>>> hypothesis is true, for that is equivalent to the statement that a >>>>>>> program that systematically searches for zeros of the zeta function >>>>>>> that
are in the wrong place, never halts.
It turns out that this number, which I’ll call Turing’s number even >>>>>>> though it does not occur in Turing’s paper, is wasting bits, it is >>>>>>> actually highly redundant. We don’t really need N bits to answer N >>>>>>> cases
of the halting problem, a much smaller number of bits will do. Why? >>>>>>>
Well, consider some large number N of cases of the halting problem, >>>>>>> some
large number N of individual programs for which we want to know
whether
or not each one halts. Is this really N bits of mathematical
information? No, the answers are not independent, they are highly >>>>>>> correlated. How? Well, in order to answer N cases of the halting >>>>>>> problem, we don’t really need to know each individual answer; it >>>>>>> suffices to know how many of these N programs will eventually halt. >>>>>>> Once
we know this number, which is only about log_2 N
bits of information, we can run the N programs in parallel until >>>>>>> exactly
this number of them halt, and then we know that none of the
remaining
programs will ever halt. And log_2 N is much, much less than N for >>>>>>> all
sufficiently large N. In other words, Turing’s number isn’t the best
possible oracle for the halting problem. It is highly redundant, it >>>>>>> uses
far too many bits.
Using essentially this idea, we can get the best possible oracle >>>>>>> number
for the halting problem; that is the halting probability Ω, which >>>>>>> has no
redundancy, none at all.
So, now that there's readily equipped a notion of uniform sampling >>>>>>> that results "oracle numbers", always _infinitely-many_ just to get >>>>>>> one,
then Chaitin's quote is equipped some context that makes
quite a fresh reading.
This goes for all y'all.
Actually, thousands of years before Russell or Tarski claimed that
"truth is whatever I, Lord Russell or Tsar Tarski, say that agrees
with myself", the notion that mathematical truth is _discovered_ not >>>>> _invented_ was "the truth", then that structural realism and realist >>>>> structuralism make for an account with both an idealistic and an
analytical tradition, keeping science for itself as a strengthened
analytical position and the idealistic getting equipped with mental
senses of the faculties of reason about logic and mathematics (and
infinity and continuity) so that Kant is satisfied that "1 + 1 = 2". >>>>>
Then, Wittgenstein is just a cad, and while it's respected
his right to say "I, wild Wittgenstein, say that you can't say
that you say anything at all", it's ignored as saying jack squat.
Natural reasoners can simply arrive at grounds for reason after
axiomless natural deduction making for logic, geometry, number theory, >>>>> with infinity and continuity, and so on. Then formalisms follow as
after perspectival accounts of restriction-of-comprehension given a
thorough account of expansion-of-comprehension.
Plato could be proud.
hey ross what group are you commenting from?
I usually read sci.math and sci.logic, and sometimes comp.ai.philosophy,
ah ok i'll copy sci.logic on some threads in the future
not so much comp.theory, though,
here there's a general idea that "Zeno machines"
are a model of computation vis-a-vis usual accounts
after Turing machines or Frege's concept-script or
MiX or stack machines or Harvard/vonNeumann or
finite-state-machines the automata.
For decades and since I formalized a few key aspects
of models of continuous domains, nobody tells me I'm
wrong anymore since I'm not wrong, or rather,
the mathematics isn't wrong.
Arriving at that though involves of a bit of a
thorough account of theory for reason, which
here is a paleo-classical post-modern account.
Anyways "olcott" is just the latest spam troll
he has been posting about roughly the same stuff for decades now. i
never got any useful interaction with him in the 9 months i've been
posting on usenet tho, unfortunately
others have been useful for sure, in entirely antagonistic manners tho...
i thirst for meaningful cooperation lol
in a sense - then that it doesn't much matter
whether it was standard accounts or non-standard accounts
or plain retro-finitist crankety troll accounts,
I can offer a sound criticism to any.
i could use a sound criticism on this draft i've written:
https://www.academia.edu/143540657/
re_turings_diagonals_how_to_decide_on_the_sequence_of_computable_numbers
definitely not perfect, and i have fleshed out the ideas a lot in
various post since then ... but the core logic from that paper that
motivates me hasn't changed
https://plato.stanford.edu/archives/fall2012/entries/induction-problem/
It seems you'd want to read about Goedel's account first of arithmetic completeness, which would be much like Frege's, then about the incompleteness, which basically establishes that ordinary theory
is incomplete, then for Mirimanoff, that there's to be the:
"extra-ordinary".
So, here are three paradoxes to resolve:
Russell's: set contains itself
Cantor's: universe contains itself
Burali-Forti: infinity contains itself
Mirimanoff points out "yeah, they do".
Here then it's that "analytical bridges" or "ponts" make for
what are the _super-classical results_, like for Zeno's continuity,
to begin, then as with regards to nature, that continuity in nature
makes for at least three different models of integers: fragments,
extensions, and only the standard as a "middle-of-nowhere".
So, inductive inference is also "invincible ignorance".
There are other wider, fuller accounts of inference.
On 5/22/26 8:17 AM, Ross Finlayson wrote:
On 05/21/2026 10:18 PM, dart200 wrote:
On 5/21/26 5:45 PM, Ross Finlayson wrote:
On 05/21/2026 11:14 AM, dart200 wrote:
On 5/21/26 9:54 AM, Ross Finlayson wrote:
On 05/21/2026 06:02 AM, olcott wrote:
On 5/18/2026 11:44 AM, Ross Finlayson wrote:
On 05/18/2026 09:03 AM, olcott wrote:
On 5/18/2026 10:14 AM, Ross Finlayson wrote:
On 05/17/2026 08:48 PM, Chris M. Thomasson wrote:How can a man as smart as you get this so incorrectly?
On 5/17/2026 8:46 PM, Chris M. Thomasson wrote:
On 5/17/2026 5:24 PM, Ross Finlayson wrote:
On 05/17/2026 05:10 PM, Ross Finlayson wrote:
On 05/17/2026 02:46 PM, Chris M. Thomasson wrote: >>>>>>>>>>>>>>> On 5/17/2026 2:21 PM, phoenix wrote:
Chris M. Thomasson wrote:
On 5/16/2026 2:30 PM, phoenix wrote:
Chris M. Thomasson wrote:
Or maybe a different tarot, "the star" because you have >>>>>>>>>>>>>>>>>> such aI find that 'except' paired with 'yet' covers every >>>>>>>>>>>>>>>>>>>> instance of
Yet that yet that yet that yet that yet that it is so: >>>>>>>>>>>>>>>>>>>>> that that that that that it is so.
'but.' If you can find an exception to this, please >>>>>>>>>>>>>>>>>>>> show
me.
fascination with me?
I think you are a sock puppet for olcott.
I know you think that, but I don't see any motivation on my >>>>>>>>>>>>>>>> part to
disabuse you of the notion. Why not play into it and >>>>>>>>>>>>>>>> further
befuddle
you? If it were the case that I were not olcott, that is. >>>>>>>>>>>>>>>>
Ask your self what his halting decider would say... Look in >>>>>>>>>>>>>>> the
mirror?
One of the problems of environments of the unmoderated and >>>>>>>>>>>>>> pseudonymous
sort is that there are all kinds of trolls. There are plain >>>>>>>>>>>>>> rage- bait
and flamer trolls, looky-loos and non-sequitur types, then, >>>>>>>>>>>>>> also
all
sorts of anti-trolls, and these and those.
Then, for example, for something like "it's a free country", >>>>>>>>>>>>>> then
when I see stuff like either
"smell the new normal, you're living in a dictatorship", >>>>>>>>>>>>>> or,
"suffer the children, so your social media and phone get >>>>>>>>>>>>>> hacked",
then either way the idea of being aware ("woke" wasn't a word >>>>>>>>>>>>>> and I'd imagine it would be "awoke" or "woken", or, "woke" >>>>>>>>>>>>>> will
do),
and caring (although, you know, not _too_ caring), that >>>>>>>>>>>>>> trolls
and repeti-bots on "social" media are anti-social. >>>>>>>>>>>>>>
So, it's fair that people get wary of trolls, and, begin to >>>>>>>>>>>>>> suspect
trolls in the likely places, and learn to make a
troll-filter,
and basically a skeptical if not cynical outlook on the world >>>>>>>>>>>>>> today,
that there are trolls and trolls, and sometimes it's >>>>>>>>>>>>>> easiest to
ignore them away.
Then, there are cranks, ....
The crank is one of the easiest sorts of identities to mimic, >>>>>>>>>>>>>> give it a howler fallacy it won't let go and the plain >>>>>>>>>>>>>> obstinance
combined with the stubbornness along with the sort of plain >>>>>>>>>>>>>> unwarranted persistence, then it's not always easy to tell >>>>>>>>>>>>>> the
difference between cranks and trolls, though often it is, >>>>>>>>>>>>>> and between persons and bots, though often it is.
'Murica.
Then, about the thread, the idea is that it's great if these >>>>>>>>>>>>>> long-running mostly-empty tit-for-tat nonsense threads get >>>>>>>>>>>>>> hijacked by passers-by then into discussions about the issues >>>>>>>>>>>>>> at hand, like about the many, many things to do with the >>>>>>>>>>>>>> "mathematics" of continuity and infinity, since, despite >>>>>>>>>>>>>> the idea of some retro-finitists that their world is a >>>>>>>>>>>>>> dot, and not even like AP a giant plutonium atom, there's >>>>>>>>>>>>>> much to be done to bring real infinite and continuity into >>>>>>>>>>>>>> mathematics, then for physics and so on.
So, new blood (or fresh meat) writing on the thread so >>>>>>>>>>>>>> it's not just an echo-chamber of trolls and anti-trolls >>>>>>>>>>>>>> which is one big troll, is not necessarily a bad thing. >>>>>>>>>>>>>>
I enjoy CMT's usual spontaneous cheerful enthusiasm, >>>>>>>>>>>>> though as a perceived bot itself when it once-a-year >>>>>>>>>>>>> cites its prompter, then though the affected anxiety >>>>>>>>>>>>> pronation reminds me of too many lessons learned like >>>>>>>>>>>>> not to smell fear or flinch or beg or impose or presume >>>>>>>>>>>>> or assume or judge or telepathically scan or lurk or >>>>>>>>>>>>> menace or make gossip or berate or scoff.
Fwiw, check out these funny halt deciders... They only halt >>>>>>>>>>>> when
all
possible paths are hit. If you think about its kind of akin to >>>>>>>>>>>> olcotts
DD. i simply hijack its result. Here is a version that uses >>>>>>>>>>>> random
numbers for the fuzzer:
In applesoft basic for fun. ;^D
You can run these here:
https://www.calormen.com/jsbasic/
_____________________________
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
1010 PRINT "FIN... All paths hit."
1020 PRINT "NON_HALT P0 = "; P0
1030 PRINT "HALT P1 = "; P1
_____________________________
Here is one that requires input from a user:
_____________________________
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 INPUT "Shall DD halt or not? " ; A$
110 REM 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
^^^^^^^^^^^^
_____________________________
God damn it forgot to add in line 1000 onward! Shit happens: >>>>>>>>>>>
1000
1010 PRINT "FIN... All paths hit."
1020 PRINT "NON_HALT P0 = "; P0
1030 PRINT "HALT P1 = "; P1
Corrected user input one:
_______________
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 INPUT "Shall DD halt or not? " ; A$
110 REM 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
1010 PRINT "FIN... All paths hit."
1020 PRINT "NON_HALT P0 = "; P0
1030 PRINT "HALT P1 = "; P1
_______________
Sorry about that shit!
It only halts when all paths have been hit.
About cranks then, there's something about a crank I admire, >>>>>>>>>>>>> not so much the being wrong part yet the dream, having the >>>>>>>>>>>>> dreams, I'm all for people having the dream when it's not >>>>>>>>>>>>> frustrating or threatening other people's dreams.
So, as I usually enough put it, "retro-finitist crankety >>>>>>>>>>>>> trolls can step off and get bent".
I'm not a fan of any "new" normal, we already have plain >>>>>>>>>>>>> old "normal normal".
Hm.
There are at least three accounts of programs whether they halt. >>>>>>>>>>
A) almost-all programs halt
B) almost-all programs don't halt
C) half of programs halt
The number of programs that halt is between 0 and 100%
excluding the endpoints.
https://arxiv.org/abs/math/0611740
"The Halting Probability Omega: Irreducible Complexity in Pure >>>>>>>> Mathematics", G. Chaitin
"Gödel himself did not think that his theorem showed that
mathematics
has limitations. In several essays he made it clear that he
believed
that mathematicians could eventually settle any significant
question by
using their mathematical intuition, their ability to directly
perceive
the Platonic world of mathematical ideas, and by inventing or
discovering new concepts and new axioms, new principles.
Furthermore, I share Enriques’s faith in intuition. I think that >>>>>>>> excessive formalism and abstraction is killing mathematics. In my >>>>>>>> opinion math papers shouldn’t attempt to replace all words by >>>>>>>> formulas,
instead they should be like literary essays, they should attempt to >>>>>>>> explain and convince.
Extending Dag Prawitz's Theory of Grounds while remaining
directly within the realm of proof theoretic Semantics then
G simply becomes ungrounded in PA and grounded in meta-math.
It has taken PTS quite a few decades, all the way up to 2012
to catch up with what Wittgenstein said decades earlier:
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's
system' means: the opposite has been proved in Russell's
system. https://www.liarparadox.org/Wittgenstein.pdf
So let me tell you the story of metamathematics, of how
mathematicians
have tried to use mathematical methods to study the power and the >>>>>>>> limitations of math itself. It’s a fairly dramatic story; in a >>>>>>>> previous
era it might have been the subject of epic poems, of Iliads and >>>>>>>> Odysseys
of verse. I’ll start with David Hilbert."
"In my opinion this is a fundamental step forward in the
philosophy of
mathematics because it makes incompleteness seem much more
concrete and
much more natural. It’s almost a problem in physics, it’s about a >>>>>>>> machine, you just ask whether or not it’s going to eventually >>>>>>>> stop, and
it turns out there’s no way, no general way, to answer that
question.
Let me emphasize that if a program does halt, we can eventually >>>>>>>> discover
that. The problem, an extremely deep one, is to show that a program >>>>>>>> will
never halt if this is in fact so. One can settle many special
cases,
even an infinity of them, but no finite set of axioms can enable >>>>>>>> you to
settle all possible cases."
Hm, " ... no finite set of axioms ...", ..., how about "no axioms". >>>>>>>>
"The real numbers are the simplest thing in the world
geometrically,
they are just points on a line. But arithmetically, as individuals, >>>>>>>> real
numbers are actually rather unreal. Turing’s 1936 uncomputable >>>>>>>> real is
just the tip of the iceberg, the problem is a lot more serious than >>>>>>>> that."
Here the iota-values are points _in_ a line, field-reals _on_ a >>>>>>>> line,
and signal-reals _about_ and _around_ a line.
So, Chaitin doesn't even have three models of continuous domains, >>>>>>>> or "repleteness", of concepts like Lebnitz' principle of perfection >>>>>>>> and Hilbert's postulate of continuity.
Mathematics really _does_ define continuity:
and there are at least three models of continuous domains.
So, say you want to sample a real number from [0,1] the interval >>>>>>>> at uniform random, and all you have is a fair coin that
gives samples from {0, 1} the set.
So, you start flipping coins and marking the result to make
a sequence of 0's and 1's. Each coin toss _refines_ the
sample.
Yet, each coin toss also _begins_ a new sample. So, to sample
one real number, the super-task results sampling infinitely-many >>>>>>>> real numbers.
So, the probability of the first sample being a rational value >>>>>>>> is, according to the law of large numbers the law of small numbers, >>>>>>>> small, and arbitrarily and infinitesimally small. In theories
that are Pythagorean it's almost-all rationals, while in theories >>>>>>>> that are Cantorian it's almost-all transcendentals.
Yet, if a sample arrives at a rational, the repeating character >>>>>>>> of rationals means that thusly the _one_ sample of a rational
number is automatically _infinitely-many_ samples of rational
numbers.
So, it makes sense to consider that the probability of sampling >>>>>>>> a rational number from [0,1] is about 0.5.
This isn't Pythagorean by itself, and isn't Cantorian by itself. >>>>>>>> It's them together according to accounts of paradox-free reason, >>>>>>>> not "non-classical logics where we ignore contradiction",
which is _hypocrisy_ and furthermore _fallacious_,
since "infinity" and "continuity" are "absolute" and "replete". >>>>>>>>
"Let’s start with Borel’s know-it-all number, but now let’s use >>>>>>>> the Nth
binary digit to tell us whether or not the Nth computer program >>>>>>>> ever
halts. So now Borel’s number is an oracle for the halting problem. >>>>>>>> For
example, there is a bit which tells us whether or not the Riemann >>>>>>>> hypothesis is true, for that is equivalent to the statement that a >>>>>>>> program that systematically searches for zeros of the zeta function >>>>>>>> that
are in the wrong place, never halts.
It turns out that this number, which I’ll call Turing’s number even
though it does not occur in Turing’s paper, is wasting bits, it is >>>>>>>> actually highly redundant. We don’t really need N bits to answer N >>>>>>>> cases
of the halting problem, a much smaller number of bits will do. Why? >>>>>>>>
Well, consider some large number N of cases of the halting problem, >>>>>>>> some
large number N of individual programs for which we want to know >>>>>>>> whether
or not each one halts. Is this really N bits of mathematical
information? No, the answers are not independent, they are highly >>>>>>>> correlated. How? Well, in order to answer N cases of the halting >>>>>>>> problem, we don’t really need to know each individual answer; it >>>>>>>> suffices to know how many of these N programs will eventually halt. >>>>>>>> Once
we know this number, which is only about log_2 N
bits of information, we can run the N programs in parallel until >>>>>>>> exactly
this number of them halt, and then we know that none of the
remaining
programs will ever halt. And log_2 N is much, much less than N for >>>>>>>> all
sufficiently large N. In other words, Turing’s number isn’t the >>>>>>>> best
possible oracle for the halting problem. It is highly redundant, it >>>>>>>> uses
far too many bits.
Using essentially this idea, we can get the best possible oracle >>>>>>>> number
for the halting problem; that is the halting probability Ω, which >>>>>>>> has no
redundancy, none at all.
So, now that there's readily equipped a notion of uniform sampling >>>>>>>> that results "oracle numbers", always _infinitely-many_ just to get >>>>>>>> one,
then Chaitin's quote is equipped some context that makes
quite a fresh reading.
This goes for all y'all.
Actually, thousands of years before Russell or Tarski claimed that >>>>>> "truth is whatever I, Lord Russell or Tsar Tarski, say that agrees >>>>>> with myself", the notion that mathematical truth is _discovered_ not >>>>>> _invented_ was "the truth", then that structural realism and realist >>>>>> structuralism make for an account with both an idealistic and an
analytical tradition, keeping science for itself as a strengthened >>>>>> analytical position and the idealistic getting equipped with mental >>>>>> senses of the faculties of reason about logic and mathematics (and >>>>>> infinity and continuity) so that Kant is satisfied that "1 + 1 = 2". >>>>>>
Then, Wittgenstein is just a cad, and while it's respected
his right to say "I, wild Wittgenstein, say that you can't say
that you say anything at all", it's ignored as saying jack squat.
Natural reasoners can simply arrive at grounds for reason after
axiomless natural deduction making for logic, geometry, number
theory,
with infinity and continuity, and so on. Then formalisms follow as >>>>>> after perspectival accounts of restriction-of-comprehension given a >>>>>> thorough account of expansion-of-comprehension.
Plato could be proud.
hey ross what group are you commenting from?
I usually read sci.math and sci.logic, and sometimes
comp.ai.philosophy,
ah ok i'll copy sci.logic on some threads in the future
not so much comp.theory, though,
here there's a general idea that "Zeno machines"
are a model of computation vis-a-vis usual accounts
after Turing machines or Frege's concept-script or
MiX or stack machines or Harvard/vonNeumann or
finite-state-machines the automata.
For decades and since I formalized a few key aspects
of models of continuous domains, nobody tells me I'm
wrong anymore since I'm not wrong, or rather,
the mathematics isn't wrong.
Arriving at that though involves of a bit of a
thorough account of theory for reason, which
here is a paleo-classical post-modern account.
Anyways "olcott" is just the latest spam troll
he has been posting about roughly the same stuff for decades now. i
never got any useful interaction with him in the 9 months i've been
posting on usenet tho, unfortunately
others have been useful for sure, in entirely antagonistic manners
tho...
i thirst for meaningful cooperation lol
in a sense - then that it doesn't much matter
whether it was standard accounts or non-standard accounts
or plain retro-finitist crankety troll accounts,
I can offer a sound criticism to any.
i could use a sound criticism on this draft i've written:
https://www.academia.edu/143540657/
re_turings_diagonals_how_to_decide_on_the_sequence_of_computable_numbers >>>
definitely not perfect, and i have fleshed out the ideas a lot in
various post since then ... but the core logic from that paper that
motivates me hasn't changed
https://plato.stanford.edu/archives/fall2012/entries/induction-problem/
It seems you'd want to read about Goedel's account first of arithmetic
completeness, which would be much like Frege's, then about the
incompleteness, which basically establishes that ordinary theory
is incomplete, then for Mirimanoff, that there's to be the:
"extra-ordinary".
So, here are three paradoxes to resolve:
Russell's: set contains itself
Cantor's: universe contains itself
Burali-Forti: infinity contains itself
Mirimanoff points out "yeah, they do".
Here then it's that "analytical bridges" or "ponts" make for
what are the _super-classical results_, like for Zeno's continuity,
to begin, then as with regards to nature, that continuity in nature
makes for at least three different models of integers: fragments,
extensions, and only the standard as a "middle-of-nowhere".
So, inductive inference is also "invincible ignorance".
There are other wider, fuller accounts of inference.
my dude, the site i host my draft on tracks reads, and for sure no one
had read it in a month
u can't give sound criticism if u don't even open the paper for a
read...
On 05/23/2026 12:28 PM, dart200 wrote:
On 5/22/26 8:17 AM, Ross Finlayson wrote:
On 05/21/2026 10:18 PM, dart200 wrote:
On 5/21/26 5:45 PM, Ross Finlayson wrote:
On 05/21/2026 11:14 AM, dart200 wrote:
On 5/21/26 9:54 AM, Ross Finlayson wrote:
On 05/21/2026 06:02 AM, olcott wrote:
On 5/18/2026 11:44 AM, Ross Finlayson wrote:
On 05/18/2026 09:03 AM, olcott wrote:
On 5/18/2026 10:14 AM, Ross Finlayson wrote:
On 05/17/2026 08:48 PM, Chris M. Thomasson wrote:How can a man as smart as you get this so incorrectly?
On 5/17/2026 8:46 PM, Chris M. Thomasson wrote:
On 5/17/2026 5:24 PM, Ross Finlayson wrote:
On 05/17/2026 05:10 PM, Ross Finlayson wrote:
On 05/17/2026 02:46 PM, Chris M. Thomasson wrote: >>>>>>>>>>>>>>>> On 5/17/2026 2:21 PM, phoenix wrote:
Chris M. Thomasson wrote:
On 5/16/2026 2:30 PM, phoenix wrote:
Chris M. Thomasson wrote:
Or maybe a different tarot, "the star" because you have >>>>>>>>>>>>>>>>>>> such aI find that 'except' paired with 'yet' covers every >>>>>>>>>>>>>>>>>>>>> instance of
Yet that yet that yet that yet that yet that it is >>>>>>>>>>>>>>>>>>>>>> so:
that that that that that it is so. >>>>>>>>>>>>>>>>>>>>>>
'but.' If you can find an exception to this, please >>>>>>>>>>>>>>>>>>>>> show
me.
fascination with me?
I think you are a sock puppet for olcott.
I know you think that, but I don't see any motivation >>>>>>>>>>>>>>>>> on my
part to
disabuse you of the notion. Why not play into it and >>>>>>>>>>>>>>>>> further
befuddle
you? If it were the case that I were not olcott, that is. >>>>>>>>>>>>>>>>>
Ask your self what his halting decider would say... Look in >>>>>>>>>>>>>>>> the
mirror?
One of the problems of environments of the unmoderated and >>>>>>>>>>>>>>> pseudonymous
sort is that there are all kinds of trolls. There are plain >>>>>>>>>>>>>>> rage- bait
and flamer trolls, looky-loos and non-sequitur types, then, >>>>>>>>>>>>>>> also
all
sorts of anti-trolls, and these and those.
Then, for example, for something like "it's a free country", >>>>>>>>>>>>>>> then
when I see stuff like either
"smell the new normal, you're living in a dictatorship", >>>>>>>>>>>>>>> or,
"suffer the children, so your social media and phone get >>>>>>>>>>>>>>> hacked",
then either way the idea of being aware ("woke" wasn't a >>>>>>>>>>>>>>> word
and I'd imagine it would be "awoke" or "woken", or, "woke" >>>>>>>>>>>>>>> will
do),
and caring (although, you know, not _too_ caring), that >>>>>>>>>>>>>>> trolls
and repeti-bots on "social" media are anti-social. >>>>>>>>>>>>>>>
So, it's fair that people get wary of trolls, and, begin to >>>>>>>>>>>>>>> suspect
trolls in the likely places, and learn to make a >>>>>>>>>>>>>>> troll-filter,
and basically a skeptical if not cynical outlook on the >>>>>>>>>>>>>>> world
today,
that there are trolls and trolls, and sometimes it's >>>>>>>>>>>>>>> easiest to
ignore them away.
Then, there are cranks, ....
The crank is one of the easiest sorts of identities to >>>>>>>>>>>>>>> mimic,
give it a howler fallacy it won't let go and the plain >>>>>>>>>>>>>>> obstinance
combined with the stubbornness along with the sort of plain >>>>>>>>>>>>>>> unwarranted persistence, then it's not always easy to tell >>>>>>>>>>>>>>> the
difference between cranks and trolls, though often it is, >>>>>>>>>>>>>>> and between persons and bots, though often it is. >>>>>>>>>>>>>>>
'Murica.
Then, about the thread, the idea is that it's great if these >>>>>>>>>>>>>>> long-running mostly-empty tit-for-tat nonsense threads get >>>>>>>>>>>>>>> hijacked by passers-by then into discussions about the >>>>>>>>>>>>>>> issues
at hand, like about the many, many things to do with the >>>>>>>>>>>>>>> "mathematics" of continuity and infinity, since, despite >>>>>>>>>>>>>>> the idea of some retro-finitists that their world is a >>>>>>>>>>>>>>> dot, and not even like AP a giant plutonium atom, there's >>>>>>>>>>>>>>> much to be done to bring real infinite and continuity into >>>>>>>>>>>>>>> mathematics, then for physics and so on.
So, new blood (or fresh meat) writing on the thread so >>>>>>>>>>>>>>> it's not just an echo-chamber of trolls and anti-trolls >>>>>>>>>>>>>>> which is one big troll, is not necessarily a bad thing. >>>>>>>>>>>>>>>
I enjoy CMT's usual spontaneous cheerful enthusiasm, >>>>>>>>>>>>>> though as a perceived bot itself when it once-a-year >>>>>>>>>>>>>> cites its prompter, then though the affected anxiety >>>>>>>>>>>>>> pronation reminds me of too many lessons learned like >>>>>>>>>>>>>> not to smell fear or flinch or beg or impose or presume >>>>>>>>>>>>>> or assume or judge or telepathically scan or lurk or >>>>>>>>>>>>>> menace or make gossip or berate or scoff.
Fwiw, check out these funny halt deciders... They only halt >>>>>>>>>>>>> when
all
possible paths are hit. If you think about its kind of akin to >>>>>>>>>>>>> olcotts
DD. i simply hijack its result. Here is a version that uses >>>>>>>>>>>>> random
numbers for the fuzzer:
In applesoft basic for fun. ;^D
You can run these here:
https://www.calormen.com/jsbasic/
_____________________________
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
1010 PRINT "FIN... All paths hit."
1020 PRINT "NON_HALT P0 = "; P0
1030 PRINT "HALT P1 = "; P1
_____________________________
Here is one that requires input from a user:
_____________________________
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 INPUT "Shall DD halt or not? " ; A$
110 REM 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
^^^^^^^^^^^^
_____________________________
God damn it forgot to add in line 1000 onward! Shit happens: >>>>>>>>>>>>
1000
1010 PRINT "FIN... All paths hit."
1020 PRINT "NON_HALT P0 = "; P0
1030 PRINT "HALT P1 = "; P1
Corrected user input one:
_______________
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 INPUT "Shall DD halt or not? " ; A$
110 REM 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
1010 PRINT "FIN... All paths hit."
1020 PRINT "NON_HALT P0 = "; P0
1030 PRINT "HALT P1 = "; P1
_______________
Sorry about that shit!
It only halts when all paths have been hit.
About cranks then, there's something about a crank I admire, >>>>>>>>>>>>>> not so much the being wrong part yet the dream, having the >>>>>>>>>>>>>> dreams, I'm all for people having the dream when it's not >>>>>>>>>>>>>> frustrating or threatening other people's dreams.
So, as I usually enough put it, "retro-finitist crankety >>>>>>>>>>>>>> trolls can step off and get bent".
I'm not a fan of any "new" normal, we already have plain >>>>>>>>>>>>>> old "normal normal".
Hm.
There are at least three accounts of programs whether they halt. >>>>>>>>>>>
A) almost-all programs halt
B) almost-all programs don't halt
C) half of programs halt
The number of programs that halt is between 0 and 100%
excluding the endpoints.
https://arxiv.org/abs/math/0611740
"The Halting Probability Omega: Irreducible Complexity in Pure >>>>>>>>> Mathematics", G. Chaitin
"Gödel himself did not think that his theorem showed that
mathematics
has limitations. In several essays he made it clear that he
believed
that mathematicians could eventually settle any significant
question by
using their mathematical intuition, their ability to directly >>>>>>>>> perceive
the Platonic world of mathematical ideas, and by inventing or >>>>>>>>> discovering new concepts and new axioms, new principles.
Furthermore, I share Enriques’s faith in intuition. I think that >>>>>>>>> excessive formalism and abstraction is killing mathematics. In my >>>>>>>>> opinion math papers shouldn’t attempt to replace all words by >>>>>>>>> formulas,
instead they should be like literary essays, they should
attempt to
explain and convince.
Extending Dag Prawitz's Theory of Grounds while remaining
directly within the realm of proof theoretic Semantics then
G simply becomes ungrounded in PA and grounded in meta-math.
It has taken PTS quite a few decades, all the way up to 2012
to catch up with what Wittgenstein said decades earlier:
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's
system' means: the opposite has been proved in Russell's
system. https://www.liarparadox.org/Wittgenstein.pdf
So let me tell you the story of metamathematics, of how
mathematicians
have tried to use mathematical methods to study the power and the >>>>>>>>> limitations of math itself. It’s a fairly dramatic story; in a >>>>>>>>> previous
era it might have been the subject of epic poems, of Iliads and >>>>>>>>> Odysseys
of verse. I’ll start with David Hilbert."
"In my opinion this is a fundamental step forward in the
philosophy of
mathematics because it makes incompleteness seem much more
concrete and
much more natural. It’s almost a problem in physics, it’s about a >>>>>>>>> machine, you just ask whether or not it’s going to eventually >>>>>>>>> stop, and
it turns out there’s no way, no general way, to answer that >>>>>>>>> question.
Let me emphasize that if a program does halt, we can eventually >>>>>>>>> discover
that. The problem, an extremely deep one, is to show that a >>>>>>>>> program
will
never halt if this is in fact so. One can settle many special >>>>>>>>> cases,
even an infinity of them, but no finite set of axioms can enable >>>>>>>>> you to
settle all possible cases."
Hm, " ... no finite set of axioms ...", ..., how about "no
axioms".
"The real numbers are the simplest thing in the world
geometrically,
they are just points on a line. But arithmetically, as
individuals,
real
numbers are actually rather unreal. Turing’s 1936 uncomputable >>>>>>>>> real is
just the tip of the iceberg, the problem is a lot more serious >>>>>>>>> than
that."
Here the iota-values are points _in_ a line, field-reals _on_ a >>>>>>>>> line,
and signal-reals _about_ and _around_ a line.
So, Chaitin doesn't even have three models of continuous domains, >>>>>>>>> or "repleteness", of concepts like Lebnitz' principle of
perfection
and Hilbert's postulate of continuity.
Mathematics really _does_ define continuity:
and there are at least three models of continuous domains.
So, say you want to sample a real number from [0,1] the interval >>>>>>>>> at uniform random, and all you have is a fair coin that
gives samples from {0, 1} the set.
So, you start flipping coins and marking the result to make
a sequence of 0's and 1's. Each coin toss _refines_ the
sample.
Yet, each coin toss also _begins_ a new sample. So, to sample >>>>>>>>> one real number, the super-task results sampling infinitely-many >>>>>>>>> real numbers.
So, the probability of the first sample being a rational value >>>>>>>>> is, according to the law of large numbers the law of small
numbers,
small, and arbitrarily and infinitesimally small. In theories >>>>>>>>> that are Pythagorean it's almost-all rationals, while in theories >>>>>>>>> that are Cantorian it's almost-all transcendentals.
Yet, if a sample arrives at a rational, the repeating character >>>>>>>>> of rationals means that thusly the _one_ sample of a rational >>>>>>>>> number is automatically _infinitely-many_ samples of rational >>>>>>>>> numbers.
So, it makes sense to consider that the probability of sampling >>>>>>>>> a rational number from [0,1] is about 0.5.
This isn't Pythagorean by itself, and isn't Cantorian by itself. >>>>>>>>> It's them together according to accounts of paradox-free reason, >>>>>>>>> not "non-classical logics where we ignore contradiction",
which is _hypocrisy_ and furthermore _fallacious_,
since "infinity" and "continuity" are "absolute" and "replete". >>>>>>>>>
"Let’s start with Borel’s know-it-all number, but now let’s use >>>>>>>>> the Nth
binary digit to tell us whether or not the Nth computer program >>>>>>>>> ever
halts. So now Borel’s number is an oracle for the halting problem. >>>>>>>>> For
example, there is a bit which tells us whether or not the Riemann >>>>>>>>> hypothesis is true, for that is equivalent to the statement that a >>>>>>>>> program that systematically searches for zeros of the zeta
function
that
are in the wrong place, never halts.
It turns out that this number, which I’ll call Turing’s number >>>>>>>>> even
though it does not occur in Turing’s paper, is wasting bits, it is >>>>>>>>> actually highly redundant. We don’t really need N bits to answer N >>>>>>>>> cases
of the halting problem, a much smaller number of bits will do. >>>>>>>>> Why?
Well, consider some large number N of cases of the halting
problem,
some
large number N of individual programs for which we want to know >>>>>>>>> whether
or not each one halts. Is this really N bits of mathematical >>>>>>>>> information? No, the answers are not independent, they are highly >>>>>>>>> correlated. How? Well, in order to answer N cases of the halting >>>>>>>>> problem, we don’t really need to know each individual answer; it >>>>>>>>> suffices to know how many of these N programs will eventually >>>>>>>>> halt.
Once
we know this number, which is only about log_2 N
bits of information, we can run the N programs in parallel until >>>>>>>>> exactly
this number of them halt, and then we know that none of the
remaining
programs will ever halt. And log_2 N is much, much less than N for >>>>>>>>> all
sufficiently large N. In other words, Turing’s number isn’t the >>>>>>>>> best
possible oracle for the halting problem. It is highly
redundant, it
uses
far too many bits.
Using essentially this idea, we can get the best possible oracle >>>>>>>>> number
for the halting problem; that is the halting probability Ω, which >>>>>>>>> has no
redundancy, none at all.
So, now that there's readily equipped a notion of uniform sampling >>>>>>>>> that results "oracle numbers", always _infinitely-many_ just to >>>>>>>>> get
one,
then Chaitin's quote is equipped some context that makes
quite a fresh reading.
This goes for all y'all.
Actually, thousands of years before Russell or Tarski claimed that >>>>>>> "truth is whatever I, Lord Russell or Tsar Tarski, say that agrees >>>>>>> with myself", the notion that mathematical truth is _discovered_ not >>>>>>> _invented_ was "the truth", then that structural realism and realist >>>>>>> structuralism make for an account with both an idealistic and an >>>>>>> analytical tradition, keeping science for itself as a strengthened >>>>>>> analytical position and the idealistic getting equipped with mental >>>>>>> senses of the faculties of reason about logic and mathematics (and >>>>>>> infinity and continuity) so that Kant is satisfied that "1 + 1 = 2". >>>>>>>
Then, Wittgenstein is just a cad, and while it's respected
his right to say "I, wild Wittgenstein, say that you can't say
that you say anything at all", it's ignored as saying jack squat. >>>>>>>
Natural reasoners can simply arrive at grounds for reason after
axiomless natural deduction making for logic, geometry, number
theory,
with infinity and continuity, and so on. Then formalisms follow as >>>>>>> after perspectival accounts of restriction-of-comprehension given a >>>>>>> thorough account of expansion-of-comprehension.
Plato could be proud.
hey ross what group are you commenting from?
I usually read sci.math and sci.logic, and sometimes
comp.ai.philosophy,
ah ok i'll copy sci.logic on some threads in the future
not so much comp.theory, though,
here there's a general idea that "Zeno machines"
are a model of computation vis-a-vis usual accounts
after Turing machines or Frege's concept-script or
MiX or stack machines or Harvard/vonNeumann or
finite-state-machines the automata.
For decades and since I formalized a few key aspects
of models of continuous domains, nobody tells me I'm
wrong anymore since I'm not wrong, or rather,
the mathematics isn't wrong.
Arriving at that though involves of a bit of a
thorough account of theory for reason, which
here is a paleo-classical post-modern account.
Anyways "olcott" is just the latest spam troll
he has been posting about roughly the same stuff for decades now. i
never got any useful interaction with him in the 9 months i've been
posting on usenet tho, unfortunately
others have been useful for sure, in entirely antagonistic manners
tho...
i thirst for meaningful cooperation lol
in a sense - then that it doesn't much matter
whether it was standard accounts or non-standard accounts
or plain retro-finitist crankety troll accounts,
I can offer a sound criticism to any.
i could use a sound criticism on this draft i've written:
https://www.academia.edu/143540657/
re_turings_diagonals_how_to_decide_on_the_sequence_of_computable_numbers >>>>
definitely not perfect, and i have fleshed out the ideas a lot in
various post since then ... but the core logic from that paper that
motivates me hasn't changed
https://plato.stanford.edu/archives/fall2012/entries/induction-problem/
It seems you'd want to read about Goedel's account first of arithmetic
completeness, which would be much like Frege's, then about the
incompleteness, which basically establishes that ordinary theory
is incomplete, then for Mirimanoff, that there's to be the:
"extra-ordinary".
So, here are three paradoxes to resolve:
Russell's: set contains itself
Cantor's: universe contains itself
Burali-Forti: infinity contains itself
Mirimanoff points out "yeah, they do".
Here then it's that "analytical bridges" or "ponts" make for
what are the _super-classical results_, like for Zeno's continuity,
to begin, then as with regards to nature, that continuity in nature
makes for at least three different models of integers: fragments,
extensions, and only the standard as a "middle-of-nowhere".
So, inductive inference is also "invincible ignorance".
There are other wider, fuller accounts of inference.
my dude, the site i host my draft on tracks reads, and for sure no one
had read it in a month
u can't give sound criticism if u don't even open the paper for a
read...
I've seen "hit counters" roll backward too many times to count,
and, working in "clicks and impressions" in reasonably large
information systems, am familiar with "drops and dupes".
That said then no, I didn't, the abstract sufficed for what I
figured to read from it.
You're welcome though to go off about what you see fit,
thanks for writing.
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