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
Yet that yet that yet that yet that yet that it is so: >>>>>>>>>>>>>> that that that that that it is so.
instance of
'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 05/18/2026 09:44 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.
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.
"But, but, but,
my "language oracle"
didn't tell me that
"oracle numbers" are "real numbers"
and that "P(Halts)" is alike P(Rational)".
Yet, ..., _yet_: doesn't it?
"Marcia, Marcia, Marcia, ...."
On 05/18/2026 09:51 AM, Ross Finlayson wrote:
On 05/18/2026 09:44 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.
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.
"But, but, but,
my "language oracle"
didn't tell me that
"oracle numbers" are "real numbers"
and that "P(Halts)" is alike P(Rational)".
Yet, ..., _yet_: doesn't it?
"Marcia, Marcia, Marcia, ...."
Eve Plumb's famous rendition of "Marcia Marcia Marcia"
was considered in her exasperation one of the greatest
or most memorable moments from "Brady Bunch", which was
a prime-time and later syndicated television show,
among other lines like "Mom always said don't play
ball in the house" and "Pork chops: and apple sauce".
(That and that "freaky tiki" bit, ....)
So, it's one of the great mysteries of syndicated television,
about Mrs. Brady, the lovely lady, and three very lovely girls,
besides whether Florence Henderson had a glass eye,
is that they're always referred to as "the Brady's", yet,
presuming that Mike Brady adopted the Brady girls and they
took his name: _who is the father on Marcia Brady's
birth certificate_? And, is it even one person?
It's similarly for the Brady boys: "Mom always said,
don't play ball in the house", _who is this person_.
"Enquiring minds want to know", was the tagline of
what was a super-market tabloid in the '80's considered
to be the worst of yellow and trash journalism at the
time, vis-a-vis, "Weekly World News".
No, infinity disagrees that "infinity does not count at all".
Look to "fallacies of induction" or "fallacies of empiricism".
Then, look into these paradoxes.
induction
quantification
identity
infinity
continuity
Now resolve them.
Not ignore them: resolve them.
There's nothing necessarily wrong with ordinary, proper (non-logical) theories, they're just not both consistent and complete if they claim
to talk about models of (all of the) integers.
Thusly a consistent and complete theory of integers is extra-ordinary.
Then, induction the inference doesn't suffice, there's instead for
accounts of deductive inference to make analytical bridges, since
otherwise there's just counter-induction.
Anyways, "Science", then for actual theory there's theatheory with
an account after axiomless natural deduction
and making for Principle
of Inverse instead of Non-Contradiction,
and Thorough Reason besides
merely Sufficient Reason, so, Aristotle won't be made a fool, because
he has both prior and posterior analytics, and most accounts are as
of half-Aristotleans.
It's sort of like about Aquinas, Scotus, and Occam, Aquinas read one
book of Aristotle and says one thing, Occam read another book of
Aristotle and says another, Scotus read both books and points out
that infinity is "in".
Dependence on induction and empiricism is a usual failing,
it's not just retro-finitist crankety trolls,
indeed the usual idea of the dialectic is for the dialectic
in complementary duals, not merely competing claims.
Then, "dialectic" is confiscated from Marxists and "totalism" from
fascists, those words for judgments in reason are taken away from
the "neo-Stoics" who aren't Stoics and "neo-Hegelians" who aren't
Hegelians and "neo-Platonists" who aren't Platonists, all of whom
can be simply put down as not conscientious or _thorough_,
so that material-implication is kicked to the curb (or left to
its devices in its little box), making claims as they would for
the authority of the Platonists and Hegelians, according to reason.
Then, "Science" here has a very principled account that involves
an _ethics_ of its interpretation to be conscientious, that most
sorts empirical and inductive reasoners _fail_ because the very
point is that first principles and final cause of "Science" _are_
Science, not the stipulations/assumptions.
On 5/22/2026 10:06 AM, Ross Finlayson wrote:
No, infinity disagrees that "infinity does not count at all".
Look to "fallacies of induction" or "fallacies of empiricism".
Then, look into these paradoxes.
induction
quantification
identity
infinity
continuity
Now resolve them.
Not ignore them: resolve them.
You did a very excellent job of showing the great depth
of your understanding.
They cannot be resolved. It is logically impossible for
humans to acquire knowledge that is 100% perfectly
logically certainly correct. Humans can, however derive
a verbal model of the world that is a best model of
the world within the best measures that humans have.
Humans acquire knowledge of the world fundamentally
through the problem of induction.
On 5/22/2026 10:06 AM, Ross Finlayson wrote:
No, infinity disagrees that "infinity does not count at all".
Look to "fallacies of induction" or "fallacies of empiricism".
Then, look into these paradoxes.
induction
quantification
identity
infinity
continuity
Now resolve them.
Not ignore them: resolve them.
You did a very excellent job of showing the great depth
of your understanding.
They cannot be resolved. It is logically impossible for
humans to acquire knowledge that is 100% perfectly
logically certainly correct. Humans can, however derive
a verbal model of the world that is a best model of
the world within the best measures that humans have.
Humans acquire knowledge of the world fundamentally
through the problem of induction.
When we hypothesize the this best model of the world
exists as a finite list of "atomic facts" of general
knowledge, this is where my system begins. All of the
stuff that you list above then becomes implementation
details. With such a list then every element of
general knowledge that can be expressed in language
can be derived by semantic entailment specified
syntactically.
Two elements of this general knowledge that can be
so derived are that:
(1) Trump exactly copied Hitler in his "big lie"
about election fraud.
(2) Severe climate change is caused by humans and
will eventually have very drastic consequences if
not sufficiently mitigated.
There's nothing necessarily wrong with ordinary, proper (non-logical)
theories, they're just not both consistent and complete if they claim
to talk about models of (all of the) integers.
Unless and until you toss out model theory itself as an incoherent
basis. You are going to have to actually learn much more about
proof theoretic semantics before you can possibly understand this.
On the basis of the quality of this reply from you I now know
that you can easily acquire this much deeper understanding.
Thusly a consistent and complete theory of integers is extra-ordinary.
Then, induction the inference doesn't suffice, there's instead for
accounts of deductive inference to make analytical bridges, since
otherwise there's just counter-induction.
The simple essence of my slight extension to proof theoretic semantics
is that what cannot be proven in PA is ungrounded in PA thus excluded
from PA. PTS itself never examines truth relative to a formal system
and from what I can see never extends beyond propositional logic. For
me to really understand this I will need to totally understand Natural Deduction and possibly Sequent calculus.
Anyways, "Science", then for actual theory there's theatheory with
an account after axiomless natural deduction
My own system requires a finite list of "atomic facts" specified within simple type theory and at least Rudolf Carnap Meaning Postulates or
its equivalents such as the CycL language of the Cyc project.
and making for Principle
of Inverse instead of Non-Contradiction,
I see no relationship between the two.
Principle of Inverse (Mathematics & Logic)
Examples: Subtraction is the inverse of addition;
division is the inverse of multiplication; the cube
root is the inverse of cubing a number.
Non-Contradiction is treated differently, Instead of the
principle of explosion (POE) a Contradiction merely proves
that the expression is false. I never could understand how
the POE is not merely a psychotic break from reality.
and Thorough Reason besides
merely Sufficient Reason, so, Aristotle won't be made a fool, because
he has both prior and posterior analytics, and most accounts are as
of half-Aristotleans.
I have accounted for both sides.
It's sort of like about Aquinas, Scotus, and Occam, Aquinas read one
book of Aristotle and says one thing, Occam read another book of
Aristotle and says another, Scotus read both books and points out
that infinity is "in".
Dependence on induction and empiricism is a usual failing,
Cannot possibly be overcome so we work with what we have and
do the best that we possibly can within this.
it's not just retro-finitist crankety trolls,
indeed the usual idea of the dialectic is for the dialectic
in complementary duals, not merely competing claims.
Then, "dialectic" is confiscated from Marxists and "totalism" from
fascists, those words for judgments in reason are taken away from
the "neo-Stoics" who aren't Stoics and "neo-Hegelians" who aren't
Hegelians and "neo-Platonists" who aren't Platonists, all of whom
can be simply put down as not conscientious or _thorough_,
so that material-implication is kicked to the curb (or left to
its devices in its little box), making claims as they would for
the authority of the Platonists and Hegelians, according to reason.
The ultimate basis of the system that I propose is logical
necessity. When this cannot possibly be achieved then we
maximize reasonable plausibility within the total evidence
available at the them. This last aspect is where conspiracy
theorists fail most direly. They maintain theories on the
basis of insufficient evidence and/or sufficient counter-evidence.
Then, "Science" here has a very principled account that involves
an _ethics_ of its interpretation to be conscientious, that most
sorts empirical and inductive reasoners _fail_ because the very
point is that first principles and final cause of "Science" _are_
Science, not the stipulations/assumptions.
All of science depends on this https://plato.stanford.edu/entries/induction-problem/
Yet science seems to have consistently proven to be
very reliable.
On 05/22/2026 10:01 AM, olcott wrote:
On 5/22/2026 10:06 AM, Ross Finlayson wrote:
No, infinity disagrees that "infinity does not count at all".
Look to "fallacies of induction" or "fallacies of empiricism".
Then, look into these paradoxes.
induction
quantification
identity
infinity
continuity
Now resolve them.
Not ignore them: resolve them.
You did a very excellent job of showing the great depth
of your understanding.
They cannot be resolved. It is logically impossible for
humans to acquire knowledge that is 100% perfectly
logically certainly correct. Humans can, however derive
a verbal model of the world that is a best model of
the world within the best measures that humans have.
Humans acquire knowledge of the world fundamentally
through the problem of induction.
When we hypothesize the this best model of the world
exists as a finite list of "atomic facts" of general
knowledge, this is where my system begins. All of the
stuff that you list above then becomes implementation
details. With such a list then every element of
general knowledge that can be expressed in language
can be derived by semantic entailment specified
syntactically.
Two elements of this general knowledge that can be
so derived are that:
(1) Trump exactly copied Hitler in his "big lie"
about election fraud.
(2) Severe climate change is caused by humans and
will eventually have very drastic consequences if
not sufficiently mitigated.
There's nothing necessarily wrong with ordinary, proper (non-logical)
theories, they're just not both consistent and complete if they claim
to talk about models of (all of the) integers.
Unless and until you toss out model theory itself as an incoherent
basis. You are going to have to actually learn much more about
proof theoretic semantics before you can possibly understand this.
On the basis of the quality of this reply from you I now know
that you can easily acquire this much deeper understanding.
Thusly a consistent and complete theory of integers is extra-ordinary.
Then, induction the inference doesn't suffice, there's instead for
accounts of deductive inference to make analytical bridges, since
otherwise there's just counter-induction.
The simple essence of my slight extension to proof theoretic semantics
is that what cannot be proven in PA is ungrounded in PA thus excluded
from PA. PTS itself never examines truth relative to a formal system
and from what I can see never extends beyond propositional logic. For
me to really understand this I will need to totally understand Natural
Deduction and possibly Sequent calculus.
Anyways, "Science", then for actual theory there's theatheory with
an account after axiomless natural deduction
My own system requires a finite list of "atomic facts" specified within
simple type theory and at least Rudolf Carnap Meaning Postulates or
its equivalents such as the CycL language of the Cyc project.
and making for Principle
of Inverse instead of Non-Contradiction,
I see no relationship between the two.
Principle of Inverse (Mathematics & Logic)
Examples: Subtraction is the inverse of addition;
division is the inverse of multiplication; the cube
root is the inverse of cubing a number.
Non-Contradiction is treated differently, Instead of the
principle of explosion (POE) a Contradiction merely proves
that the expression is false. I never could understand how
the POE is not merely a psychotic break from reality.
and Thorough Reason besides
merely Sufficient Reason, so, Aristotle won't be made a fool, because
he has both prior and posterior analytics, and most accounts are as
of half-Aristotleans.
I have accounted for both sides.
It's sort of like about Aquinas, Scotus, and Occam, Aquinas read one
book of Aristotle and says one thing, Occam read another book of
Aristotle and says another, Scotus read both books and points out
that infinity is "in".
Dependence on induction and empiricism is a usual failing,
Cannot possibly be overcome so we work with what we have and
do the best that we possibly can within this.
it's not just retro-finitist crankety trolls,
indeed the usual idea of the dialectic is for the dialectic
in complementary duals, not merely competing claims.
Then, "dialectic" is confiscated from Marxists and "totalism" from
fascists, those words for judgments in reason are taken away from
the "neo-Stoics" who aren't Stoics and "neo-Hegelians" who aren't
Hegelians and "neo-Platonists" who aren't Platonists, all of whom
can be simply put down as not conscientious or _thorough_,
so that material-implication is kicked to the curb (or left to
its devices in its little box), making claims as they would for
the authority of the Platonists and Hegelians, according to reason.
The ultimate basis of the system that I propose is logical
necessity. When this cannot possibly be achieved then we
maximize reasonable plausibility within the total evidence
available at the them. This last aspect is where conspiracy
theorists fail most direly. They maintain theories on the
basis of insufficient evidence and/or sufficient counter-evidence.
Then, "Science" here has a very principled account that involves
an _ethics_ of its interpretation to be conscientious, that most
sorts empirical and inductive reasoners _fail_ because the very
point is that first principles and final cause of "Science" _are_
Science, not the stipulations/assumptions.
All of science depends on this
https://plato.stanford.edu/entries/induction-problem/
Yet science seems to have consistently proven to be
very reliable.
"Science" does not say what's "true", only between two given
theories, whether one of them is "falsified".
This is that "Science" has three aspects:
observable: meaning accessible to the senses (or instruments for operationalists/instrumentalists)
repeatable: meaning that experiments can be given the same energy
and configuration of experiment and result the same
falsifiable: meaning that configurations and energies of experiment
enumerate cases where the theory does/doesn't hold with regards to others
"Science" thusly is never the "best" theory,
only "less worse",
and never is "confirmed",
only not rejected, and, much like
"Statistics", even exactly the same, never "predicts" anything,
only increases the confidence that other theories are rejected.
"Theory" then is a broader account, about theories of science,
theories of reason, and theories of mathematical objects, among
theories about theory ("meta-theory").
"Reason" then is a particular account, about what's true and
what's not un-true, and then "Mathematics" is, according to
the idealistic tradition where there's a real and true truth,
or strong mathematical platonism, the discovery of structural
relations that describe geometrical measures of quantities,
about the quantified vis-a-vis the qualified.
Then, "Inverse" is an account of expansion-of-comprehension,
making for diversity and variety among complementary duals
and contiguous neighbors, in spaces of things (like geometry's,
grammar's, etc.) and the "Thorough" doesn't only claim to have
read Aristotle's reasoning, yet always does all the time.
Three-legged dog: is an account here that your fact-book
rules-engine is simpy not both of complete and consistent,
and, is not an account of a modal temporal relevance logic.
Infinity: is in.
On 5/22/2026 8:30 PM, Ross Finlayson wrote:
On 05/22/2026 10:01 AM, olcott wrote:
On 5/22/2026 10:06 AM, Ross Finlayson wrote:
No, infinity disagrees that "infinity does not count at all".
Look to "fallacies of induction" or "fallacies of empiricism".
Then, look into these paradoxes.
induction
quantification
identity
infinity
continuity
Now resolve them.
Not ignore them: resolve them.
You did a very excellent job of showing the great depth
of your understanding.
They cannot be resolved. It is logically impossible for
humans to acquire knowledge that is 100% perfectly
logically certainly correct. Humans can, however derive
a verbal model of the world that is a best model of
the world within the best measures that humans have.
Humans acquire knowledge of the world fundamentally
through the problem of induction.
When we hypothesize the this best model of the world
exists as a finite list of "atomic facts" of general
knowledge, this is where my system begins. All of the
stuff that you list above then becomes implementation
details. With such a list then every element of
general knowledge that can be expressed in language
can be derived by semantic entailment specified
syntactically.
Two elements of this general knowledge that can be
so derived are that:
(1) Trump exactly copied Hitler in his "big lie"
about election fraud.
(2) Severe climate change is caused by humans and
will eventually have very drastic consequences if
not sufficiently mitigated.
There's nothing necessarily wrong with ordinary, proper (non-logical)
theories, they're just not both consistent and complete if they claim
to talk about models of (all of the) integers.
Unless and until you toss out model theory itself as an incoherent
basis. You are going to have to actually learn much more about
proof theoretic semantics before you can possibly understand this.
On the basis of the quality of this reply from you I now know
that you can easily acquire this much deeper understanding.
Thusly a consistent and complete theory of integers is extra-ordinary. >>>> Then, induction the inference doesn't suffice, there's instead for
accounts of deductive inference to make analytical bridges, since
otherwise there's just counter-induction.
The simple essence of my slight extension to proof theoretic semantics
is that what cannot be proven in PA is ungrounded in PA thus excluded
from PA. PTS itself never examines truth relative to a formal system
and from what I can see never extends beyond propositional logic. For
me to really understand this I will need to totally understand Natural
Deduction and possibly Sequent calculus.
Anyways, "Science", then for actual theory there's theatheory with
an account after axiomless natural deduction
My own system requires a finite list of "atomic facts" specified within
simple type theory and at least Rudolf Carnap Meaning Postulates or
its equivalents such as the CycL language of the Cyc project.
and making for Principle
of Inverse instead of Non-Contradiction,
I see no relationship between the two.
Principle of Inverse (Mathematics & Logic)
Examples: Subtraction is the inverse of addition;
division is the inverse of multiplication; the cube
root is the inverse of cubing a number.
Non-Contradiction is treated differently, Instead of the
principle of explosion (POE) a Contradiction merely proves
that the expression is false. I never could understand how
the POE is not merely a psychotic break from reality.
and Thorough Reason besides
merely Sufficient Reason, so, Aristotle won't be made a fool, because
he has both prior and posterior analytics, and most accounts are as
of half-Aristotleans.
I have accounted for both sides.
It's sort of like about Aquinas, Scotus, and Occam, Aquinas read one
book of Aristotle and says one thing, Occam read another book of
Aristotle and says another, Scotus read both books and points out
that infinity is "in".
Dependence on induction and empiricism is a usual failing,
Cannot possibly be overcome so we work with what we have and
do the best that we possibly can within this.
it's not just retro-finitist crankety trolls,
indeed the usual idea of the dialectic is for the dialectic
in complementary duals, not merely competing claims.
Then, "dialectic" is confiscated from Marxists and "totalism" from
fascists, those words for judgments in reason are taken away from
the "neo-Stoics" who aren't Stoics and "neo-Hegelians" who aren't
Hegelians and "neo-Platonists" who aren't Platonists, all of whom
can be simply put down as not conscientious or _thorough_,
so that material-implication is kicked to the curb (or left to
its devices in its little box), making claims as they would for
the authority of the Platonists and Hegelians, according to reason.
The ultimate basis of the system that I propose is logical
necessity. When this cannot possibly be achieved then we
maximize reasonable plausibility within the total evidence
available at the them. This last aspect is where conspiracy
theorists fail most direly. They maintain theories on the
basis of insufficient evidence and/or sufficient counter-evidence.
Then, "Science" here has a very principled account that involves
an _ethics_ of its interpretation to be conscientious, that most
sorts empirical and inductive reasoners _fail_ because the very
point is that first principles and final cause of "Science" _are_
Science, not the stipulations/assumptions.
All of science depends on this
https://plato.stanford.edu/entries/induction-problem/
Yet science seems to have consistently proven to be
very reliable.
"Science" does not say what's "true", only between two given
theories, whether one of them is "falsified".
So water does not freeze at 32F at standard pressure?
This is that "Science" has three aspects:
observable: meaning accessible to the senses (or instruments for
operationalists/instrumentalists)
repeatable: meaning that experiments can be given the same energy
and configuration of experiment and result the same
falsifiable: meaning that configurations and energies of experiment
enumerate cases where the theory does/doesn't hold with regards to others
"Science" thusly is never the "best" theory,
Best compared to infallibility? No.
Best available to humans? Yes.
only "less worse",
and never is "confirmed",
So there is no such thing as replicated experiments?
only not rejected, and, much like
"Statistics", even exactly the same, never "predicts" anything,
only increases the confidence that other theories are rejected.
"Theory" then is a broader account, about theories of science,
theories of reason, and theories of mathematical objects, among
theories about theory ("meta-theory").
"Reason" then is a particular account, about what's true and
what's not un-true, and then "Mathematics" is, according to
the idealistic tradition where there's a real and true truth,
or strong mathematical platonism, the discovery of structural
relations that describe geometrical measures of quantities,
about the quantified vis-a-vis the qualified.
Then, "Inverse" is an account of expansion-of-comprehension,
making for diversity and variety among complementary duals
and contiguous neighbors, in spaces of things (like geometry's,
grammar's, etc.) and the "Thorough" doesn't only claim to have
read Aristotle's reasoning, yet always does all the time.
Three-legged dog: is an account here that your fact-book
rules-engine is simpy not both of complete and consistent,
and, is not an account of a modal temporal relevance logic.
Infinity: is in.
Infinity has nothing to do with key truths the human survival
depends on such as this one.
https://www.researchgate.net/publication/336568434_Severe_anthropogenic_climate_change_proven_entirely_with_verifiable_facts
All the time that humans play the entertainment game
of finding any excuse to disagree with me the liars
hired by the fossil fuel companies kill the planet
a little more.
A system such as mine does unequivocally compute the
truth about climate change and that Trump did exactly
copy Hitler in his lies about election fraud.
On 05/23/2026 07:01 AM, olcott wrote:
On 5/22/2026 8:30 PM, Ross Finlayson wrote:
On 05/22/2026 10:01 AM, olcott wrote:
On 5/22/2026 10:06 AM, Ross Finlayson wrote:
No, infinity disagrees that "infinity does not count at all".
Look to "fallacies of induction" or "fallacies of empiricism".
Then, look into these paradoxes.
induction
quantification
identity
infinity
continuity
Now resolve them.
Not ignore them: resolve them.
You did a very excellent job of showing the great depth
of your understanding.
They cannot be resolved. It is logically impossible for
humans to acquire knowledge that is 100% perfectly
logically certainly correct. Humans can, however derive
a verbal model of the world that is a best model of
the world within the best measures that humans have.
Humans acquire knowledge of the world fundamentally
through the problem of induction.
When we hypothesize the this best model of the world
exists as a finite list of "atomic facts" of general
knowledge, this is where my system begins. All of the
stuff that you list above then becomes implementation
details. With such a list then every element of
general knowledge that can be expressed in language
can be derived by semantic entailment specified
syntactically.
Two elements of this general knowledge that can be
so derived are that:
(1) Trump exactly copied Hitler in his "big lie"
about election fraud.
(2) Severe climate change is caused by humans and
will eventually have very drastic consequences if
not sufficiently mitigated.
There's nothing necessarily wrong with ordinary, proper (non-logical) >>>>> theories, they're just not both consistent and complete if they claim >>>>> to talk about models of (all of the) integers.
Unless and until you toss out model theory itself as an incoherent
basis. You are going to have to actually learn much more about
proof theoretic semantics before you can possibly understand this.
On the basis of the quality of this reply from you I now know
that you can easily acquire this much deeper understanding.
Thusly a consistent and complete theory of integers is extra-ordinary. >>>>> Then, induction the inference doesn't suffice, there's instead for
accounts of deductive inference to make analytical bridges, since
otherwise there's just counter-induction.
The simple essence of my slight extension to proof theoretic semantics >>>> is that what cannot be proven in PA is ungrounded in PA thus excluded
from PA. PTS itself never examines truth relative to a formal system
and from what I can see never extends beyond propositional logic. For
me to really understand this I will need to totally understand Natural >>>> Deduction and possibly Sequent calculus.
Anyways, "Science", then for actual theory there's theatheory with
an account after axiomless natural deduction
My own system requires a finite list of "atomic facts" specified within >>>> simple type theory and at least Rudolf Carnap Meaning Postulates or
its equivalents such as the CycL language of the Cyc project.
and making for Principle
of Inverse instead of Non-Contradiction,
I see no relationship between the two.
Principle of Inverse (Mathematics & Logic)
Examples: Subtraction is the inverse of addition;
division is the inverse of multiplication; the cube
root is the inverse of cubing a number.
Non-Contradiction is treated differently, Instead of the
principle of explosion (POE) a Contradiction merely proves
that the expression is false. I never could understand how
the POE is not merely a psychotic break from reality.
and Thorough Reason besides
merely Sufficient Reason, so, Aristotle won't be made a fool, because >>>>> he has both prior and posterior analytics, and most accounts are as
of half-Aristotleans.
I have accounted for both sides.
It's sort of like about Aquinas, Scotus, and Occam, Aquinas read one >>>>> book of Aristotle and says one thing, Occam read another book of
Aristotle and says another, Scotus read both books and points out
that infinity is "in".
Dependence on induction and empiricism is a usual failing,
Cannot possibly be overcome so we work with what we have and
do the best that we possibly can within this.
it's not just retro-finitist crankety trolls,
indeed the usual idea of the dialectic is for the dialectic
in complementary duals, not merely competing claims.
Then, "dialectic" is confiscated from Marxists and "totalism" from
fascists, those words for judgments in reason are taken away from
the "neo-Stoics" who aren't Stoics and "neo-Hegelians" who aren't
Hegelians and "neo-Platonists" who aren't Platonists, all of whom
can be simply put down as not conscientious or _thorough_,
so that material-implication is kicked to the curb (or left to
its devices in its little box), making claims as they would for
the authority of the Platonists and Hegelians, according to reason.
The ultimate basis of the system that I propose is logical
necessity. When this cannot possibly be achieved then we
maximize reasonable plausibility within the total evidence
available at the them. This last aspect is where conspiracy
theorists fail most direly. They maintain theories on the
basis of insufficient evidence and/or sufficient counter-evidence.
Then, "Science" here has a very principled account that involves
an _ethics_ of its interpretation to be conscientious, that most
sorts empirical and inductive reasoners _fail_ because the very
point is that first principles and final cause of "Science" _are_
Science, not the stipulations/assumptions.
All of science depends on this
https://plato.stanford.edu/entries/induction-problem/
Yet science seems to have consistently proven to be
very reliable.
"Science" does not say what's "true", only between two given
theories, whether one of them is "falsified".
So water does not freeze at 32F at standard pressure?
This is that "Science" has three aspects:
observable: meaning accessible to the senses (or instruments for
operationalists/instrumentalists)
repeatable: meaning that experiments can be given the same energy
and configuration of experiment and result the same
falsifiable: meaning that configurations and energies of experiment
enumerate cases where the theory does/doesn't hold with regards to
others
"Science" thusly is never the "best" theory,
Best compared to infallibility? No.
Best available to humans? Yes.
only "less worse",
and never is "confirmed",
So there is no such thing as replicated experiments?
only not rejected, and, much like
"Statistics", even exactly the same, never "predicts" anything,
only increases the confidence that other theories are rejected.
"Theory" then is a broader account, about theories of science,
theories of reason, and theories of mathematical objects, among
theories about theory ("meta-theory").
"Reason" then is a particular account, about what's true and
what's not un-true, and then "Mathematics" is, according to
the idealistic tradition where there's a real and true truth,
or strong mathematical platonism, the discovery of structural
relations that describe geometrical measures of quantities,
about the quantified vis-a-vis the qualified.
Then, "Inverse" is an account of expansion-of-comprehension,
making for diversity and variety among complementary duals
and contiguous neighbors, in spaces of things (like geometry's,
grammar's, etc.) and the "Thorough" doesn't only claim to have
read Aristotle's reasoning, yet always does all the time.
Three-legged dog: is an account here that your fact-book
rules-engine is simpy not both of complete and consistent,
and, is not an account of a modal temporal relevance logic.
Infinity: is in.
Infinity has nothing to do with key truths the human survival
depends on such as this one.
https://www.researchgate.net/
publication/336568434_Severe_anthropogenic_climate_change_proven_entirely_with_verifiable_facts
All the time that humans play the entertainment game
of finding any excuse to disagree with me the liars
hired by the fossil fuel companies kill the planet
a little more.
A system such as mine does unequivocally compute the
truth about climate change and that Trump did exactly
copy Hitler in his lies about election fraud.
Nope, anybody's ordinary theories can do that.
That seems to have combined a number of different fallacies there.
Infinity, and continuity, are key and central concepts in
mathematics, the objects of which, the universe of objects
and the domain of discourse about them the mathematical
objects the mathematical universe, in their infinite
_completions_, about
geometry and number theory and
arithmetic and analysis and algebra for
arithmetizations and geometrizations and algebraizations
with function-theory and topology as usually least-well-defined
and the operator calculi about these, "mathematics",
has that there the merely-finite just won't do.
Similarly, for physics, the partial-differential and usual
accounts of approximations and truncations are merely-partial,
and while good, say, to the first-order for the expansions
or second-order for the quadratic, also are nominally not-good
beyond the limits of the guarantees of their bounds, these
sorts ordinary theories.
So, there are _guarantees_, mathematical, that usual sorts
ordinary theories of the merely-finite or merely-partial
don't have a full account of the objects of the theory.
"Why do they hire weathermen?" "To make economists look good."
(Since they are often wrong, pointing out somebody more wrong.) Blame-shifting is fallacious and not a valid response to criticism,
such attempts at justification or setting things aright aren't
of a "better", only a "less worse". Science overall though is
overall "less worse", and, given accounts of symmetrical information
about perfect and imperfect information, is _fair_ meaning
egalitarian and non-biased. (As a joke it goes both ways.)
Repeatability is a _requirement_ of science, not a result.
That practically it's an expectation and an estimate, in
the statistical sense, is not a guarantee. Usually loose
language about science & statistics points to obvious
failings of the comprehension of the meaning of the terms,
and immediately paints "non-scientists" and "non-statisticians",
as alike dogmatic followers of empiricist schemes of induction,
some of which are doomed to fail.
Paradoxes are none.
An account of dual-monism then the dialectic is since
Heraclitus and Parmenides, these the earlier Greeks,
for something like Barnes' copy of the fragments,
these influences in thought for the academy, as
they're also according to the pre-historic influences
and the traditions these sums-of-influences, then
something like McKeon's Aristotle and Proclus' Euclid
help advise that Reason is a Verb. Also a Noun, ....
A post-modern sort of account since Derrida has that
first there's Husserl and both of them agree that
_geometry_ (standing in for mathematics) is still
somehow _true_, then a greater post-modernist's, and,
postmodernists', account of disfiguration the differance
after de-construction, is a structural realists' for
whom proof-theory is always equi-interpretable as a model-theory,
and a universal model-theory with a model of the universe,
for realists and structuralists, a model of the universe.
There simply aren't universes in accounts of ordinary
theories, only extra-ordinary theories.
Paradoxes are none.
So, is there a real true theory of truth? That's the idea.
In fact, it's such a great idea that I don't even have to
have it for it to always be the idea.
And, science will
never know the difference. So, the great account as after
the analytical tradition gets equipped with the great account
as after the idealistic tradition, since neither can really
do without the other, in an overall sort of _Thorough_ account,
for conscientious logicians and mathematicians and scientists
and physicists the reasoners.
"What time is it?"
^- statements automatically have infinitely-deep implicit quoting,
along with infinitely-deep implicit quantifiers on the terms, which
are implicitly both constants and variables, all one term
So, reasoning about universes is all in one Universe,
for accounts like Duns Scotus and univocity, while that expansion-of-comprehension makes diversity & variety then
that restriction-of-comprehension is justly perspectival
and first-class perspectival, not just blindered, dumbed,
and following along.
Then of course independence of thought basically defines individuals,
with regards to matters of consciousness and will of feeling and
thinking beings, and the universe of conjecture can entertain any
number of theories, while yet there is one at all. Or, "yet-like".
If you look at something like my essays/posts on the "Infinity" thread
since at least a couple decades ago, there's a great long quotation
there to the thousands and thousands of pages, which, according to
a scheme of compression that de-duplicates repetition, makes for so
that the more times you have to say something, the less it seems right.
People like software engineers in information theory get entirely
irritated when anybody says something twice. So, I always try to
bring something novel to little essays like these, here that
I've said most all these things before. (And yet-now they're always.)
Nope, anybody's ordinary theories can do that.
That seems to have combined a number of different fallacies there.
Infinity, and continuity, are key and central concepts in
mathematics, the objects of which, the universe of objects
and the domain of discourse about them the mathematical
objects the mathematical universe, in their infinite
_completions_, about
geometry and number theory and
arithmetic and analysis and algebra for
arithmetizations and geometrizations and algebraizations
with function-theory and topology as usually least-well-defined
and the operator calculi about these, "mathematics",
has that there the merely-finite just won't do.
On 5/23/2026 10:46 AM, Ross Finlayson wrote:
On 05/23/2026 07:01 AM, olcott wrote:
On 5/22/2026 8:30 PM, Ross Finlayson wrote:
On 05/22/2026 10:01 AM, olcott wrote:
On 5/22/2026 10:06 AM, Ross Finlayson wrote:
No, infinity disagrees that "infinity does not count at all".
Look to "fallacies of induction" or "fallacies of empiricism".
Then, look into these paradoxes.
induction
quantification
identity
infinity
continuity
Now resolve them.
Not ignore them: resolve them.
You did a very excellent job of showing the great depth
of your understanding.
They cannot be resolved. It is logically impossible for
humans to acquire knowledge that is 100% perfectly
logically certainly correct. Humans can, however derive
a verbal model of the world that is a best model of
the world within the best measures that humans have.
Humans acquire knowledge of the world fundamentally
through the problem of induction.
When we hypothesize the this best model of the world
exists as a finite list of "atomic facts" of general
knowledge, this is where my system begins. All of the
stuff that you list above then becomes implementation
details. With such a list then every element of
general knowledge that can be expressed in language
can be derived by semantic entailment specified
syntactically.
Two elements of this general knowledge that can be
so derived are that:
(1) Trump exactly copied Hitler in his "big lie"
about election fraud.
(2) Severe climate change is caused by humans and
will eventually have very drastic consequences if
not sufficiently mitigated.
There's nothing necessarily wrong with ordinary, proper (non-logical) >>>>>> theories, they're just not both consistent and complete if they claim >>>>>> to talk about models of (all of the) integers.
Unless and until you toss out model theory itself as an incoherent
basis. You are going to have to actually learn much more about
proof theoretic semantics before you can possibly understand this.
On the basis of the quality of this reply from you I now know
that you can easily acquire this much deeper understanding.
Thusly a consistent and complete theory of integers is
extra-ordinary.
Then, induction the inference doesn't suffice, there's instead for >>>>>> accounts of deductive inference to make analytical bridges, since
otherwise there's just counter-induction.
The simple essence of my slight extension to proof theoretic semantics >>>>> is that what cannot be proven in PA is ungrounded in PA thus excluded >>>>> from PA. PTS itself never examines truth relative to a formal system >>>>> and from what I can see never extends beyond propositional logic. For >>>>> me to really understand this I will need to totally understand Natural >>>>> Deduction and possibly Sequent calculus.
Anyways, "Science", then for actual theory there's theatheory with >>>>>> an account after axiomless natural deduction
My own system requires a finite list of "atomic facts" specified
within
simple type theory and at least Rudolf Carnap Meaning Postulates or
its equivalents such as the CycL language of the Cyc project.
and making for Principle
of Inverse instead of Non-Contradiction,
I see no relationship between the two.
Principle of Inverse (Mathematics & Logic)
Examples: Subtraction is the inverse of addition;
division is the inverse of multiplication; the cube
root is the inverse of cubing a number.
Non-Contradiction is treated differently, Instead of the
principle of explosion (POE) a Contradiction merely proves
that the expression is false. I never could understand how
the POE is not merely a psychotic break from reality.
and Thorough Reason besides
merely Sufficient Reason, so, Aristotle won't be made a fool, because >>>>>> he has both prior and posterior analytics, and most accounts are as >>>>>> of half-Aristotleans.
I have accounted for both sides.
It's sort of like about Aquinas, Scotus, and Occam, Aquinas read one >>>>>> book of Aristotle and says one thing, Occam read another book of
Aristotle and says another, Scotus read both books and points out
that infinity is "in".
Dependence on induction and empiricism is a usual failing,
Cannot possibly be overcome so we work with what we have and
do the best that we possibly can within this.
it's not just retro-finitist crankety trolls,
indeed the usual idea of the dialectic is for the dialectic
in complementary duals, not merely competing claims.
Then, "dialectic" is confiscated from Marxists and "totalism" from >>>>>> fascists, those words for judgments in reason are taken away from
the "neo-Stoics" who aren't Stoics and "neo-Hegelians" who aren't
Hegelians and "neo-Platonists" who aren't Platonists, all of whom
can be simply put down as not conscientious or _thorough_,
so that material-implication is kicked to the curb (or left to
its devices in its little box), making claims as they would for
the authority of the Platonists and Hegelians, according to reason. >>>>>>
The ultimate basis of the system that I propose is logical
necessity. When this cannot possibly be achieved then we
maximize reasonable plausibility within the total evidence
available at the them. This last aspect is where conspiracy
theorists fail most direly. They maintain theories on the
basis of insufficient evidence and/or sufficient counter-evidence.
Then, "Science" here has a very principled account that involves
an _ethics_ of its interpretation to be conscientious, that most
sorts empirical and inductive reasoners _fail_ because the very
point is that first principles and final cause of "Science" _are_
Science, not the stipulations/assumptions.
All of science depends on this
https://plato.stanford.edu/entries/induction-problem/
Yet science seems to have consistently proven to be
very reliable.
"Science" does not say what's "true", only between two given
theories, whether one of them is "falsified".
So water does not freeze at 32F at standard pressure?
This is that "Science" has three aspects:
observable: meaning accessible to the senses (or instruments for
operationalists/instrumentalists)
repeatable: meaning that experiments can be given the same energy
and configuration of experiment and result the same
falsifiable: meaning that configurations and energies of experiment
enumerate cases where the theory does/doesn't hold with regards to
others
"Science" thusly is never the "best" theory,
Best compared to infallibility? No.
Best available to humans? Yes.
only "less worse",
and never is "confirmed",
So there is no such thing as replicated experiments?
only not rejected, and, much like
"Statistics", even exactly the same, never "predicts" anything,
only increases the confidence that other theories are rejected.
"Theory" then is a broader account, about theories of science,
theories of reason, and theories of mathematical objects, among
theories about theory ("meta-theory").
"Reason" then is a particular account, about what's true and
what's not un-true, and then "Mathematics" is, according to
the idealistic tradition where there's a real and true truth,
or strong mathematical platonism, the discovery of structural
relations that describe geometrical measures of quantities,
about the quantified vis-a-vis the qualified.
Then, "Inverse" is an account of expansion-of-comprehension,
making for diversity and variety among complementary duals
and contiguous neighbors, in spaces of things (like geometry's,
grammar's, etc.) and the "Thorough" doesn't only claim to have
read Aristotle's reasoning, yet always does all the time.
Three-legged dog: is an account here that your fact-book
rules-engine is simpy not both of complete and consistent,
and, is not an account of a modal temporal relevance logic.
Infinity: is in.
Infinity has nothing to do with key truths the human survival
depends on such as this one.
https://www.researchgate.net/
publication/336568434_Severe_anthropogenic_climate_change_proven_entirely_with_verifiable_facts
All the time that humans play the entertainment game
of finding any excuse to disagree with me the liars
hired by the fossil fuel companies kill the planet
a little more.
A system such as mine does unequivocally compute the
truth about climate change and that Trump did exactly
copy Hitler in his lies about election fraud.
Nope, anybody's ordinary theories can do that.
Show me the underlying structural details of how this
is actually computed as I have done in my new signature
line. Ordinary theories don't have a slight clue of how
to mathematically formalize natural language they simply
guess that this is impossible not even being away of all
of the work by Richard Montague, Rudolf Carnap and
that Cyc project.
That seems to have combined a number of different fallacies there.
Infinity, and continuity, are key and central concepts in
mathematics, the objects of which, the universe of objects
and the domain of discourse about them the mathematical
objects the mathematical universe, in their infinite
_completions_, about
The have almost nothing to do with the finite body of
general knowledge about most everything.
geometry and number theory and
arithmetic and analysis and algebra for
arithmetizations and geometrizations and algebraizations
with function-theory and topology as usually least-well-defined
and the operator calculi about these, "mathematics",
has that there the merely-finite just won't do.
Within math and science that depends on this math infinity
is usually very important. Within the structure of the body
of general knowledge about most everything else we only need
a the subset of discrete math not involving infinity.
Similarly, for physics, the partial-differential and usual
accounts of approximations and truncations are merely-partial,
and while good, say, to the first-order for the expansions
or second-order for the quadratic, also are nominally not-good
beyond the limits of the guarantees of their bounds, these
sorts ordinary theories.
So, there are _guarantees_, mathematical, that usual sorts
ordinary theories of the merely-finite or merely-partial
don't have a full account of the objects of the theory.
"Why do they hire weathermen?" "To make economists look good."
(Since they are often wrong, pointing out somebody more wrong.)
Blame-shifting is fallacious and not a valid response to criticism,
such attempts at justification or setting things aright aren't
of a "better", only a "less worse". Science overall though is
overall "less worse", and, given accounts of symmetrical information
about perfect and imperfect information, is _fair_ meaning
egalitarian and non-biased. (As a joke it goes both ways.)
Repeatability is a _requirement_ of science, not a result.
That practically it's an expectation and an estimate, in
the statistical sense, is not a guarantee. Usually loose
language about science & statistics points to obvious
failings of the comprehension of the meaning of the terms,
and immediately paints "non-scientists" and "non-statisticians",
as alike dogmatic followers of empiricist schemes of induction,
some of which are doomed to fail.
Paradoxes are none.
An account of dual-monism then the dialectic is since
Heraclitus and Parmenides, these the earlier Greeks,
for something like Barnes' copy of the fragments,
these influences in thought for the academy, as
they're also according to the pre-historic influences
and the traditions these sums-of-influences, then
something like McKeon's Aristotle and Proclus' Euclid
help advise that Reason is a Verb. Also a Noun, ....
A post-modern sort of account since Derrida has that
first there's Husserl and both of them agree that
_geometry_ (standing in for mathematics) is still
somehow _true_, then a greater post-modernist's, and,
postmodernists', account of disfiguration the differance
after de-construction, is a structural realists' for
whom proof-theory is always equi-interpretable as a model-theory,
and a universal model-theory with a model of the universe,
for realists and structuralists, a model of the universe.
There simply aren't universes in accounts of ordinary
theories, only extra-ordinary theories.
Paradoxes are none.
So, is there a real true theory of truth? That's the idea.
In fact, it's such a great idea that I don't even have to
have it for it to always be the idea.
Yes. Most fundamentally "Truth that can be expressed in language"
(excluding things such as the actual smell of strawberries)
is different kinds of semantic relations (expressed syntactically)
between finite strings.
"water freezes at 32 degrees Fahrenheit at standard pressure"
Вода замерзает при 32 градусах по Фаренгейту при стандартном давлении
在標準氣壓下，水在華氏32度結冰
If Google translate is accurate the above "atomic fact"
stipulates that same semantic meaning across encoding systems.
And, science will
never know the difference. So, the great account as after
the analytical tradition gets equipped with the great account
as after the idealistic tradition, since neither can really
do without the other, in an overall sort of _Thorough_ account,
for conscientious logicians and mathematicians and scientists
and physicists the reasoners.
"What time is it?"
^- statements automatically have infinitely-deep implicit quoting,
along with infinitely-deep implicit quantifiers on the terms, which
are implicitly both constants and variables, all one term
So, reasoning about universes is all in one Universe,
for accounts like Duns Scotus and univocity, while that
expansion-of-comprehension makes diversity & variety then
that restriction-of-comprehension is justly perspectival
and first-class perspectival, not just blindered, dumbed,
and following along.
Then of course independence of thought basically defines individuals,
with regards to matters of consciousness and will of feeling and
thinking beings, and the universe of conjecture can entertain any
number of theories, while yet there is one at all. Or, "yet-like".
If you look at something like my essays/posts on the "Infinity" thread
since at least a couple decades ago, there's a great long quotation
there to the thousands and thousands of pages, which, according to
a scheme of compression that de-duplicates repetition, makes for so
that the more times you have to say something, the less it seems right.
People like software engineers in information theory get entirely
irritated when anybody says something twice. So, I always try to
bring something novel to little essays like these, here that
I've said most all these things before. (And yet-now they're always.)
On 05/23/2026 09:27 AM, olcott wrote:
On 5/23/2026 10:46 AM, Ross Finlayson wrote:
On 05/23/2026 07:01 AM, olcott wrote:
On 5/22/2026 8:30 PM, Ross Finlayson wrote:
On 05/22/2026 10:01 AM, olcott wrote:
On 5/22/2026 10:06 AM, Ross Finlayson wrote:
No, infinity disagrees that "infinity does not count at all".
Look to "fallacies of induction" or "fallacies of empiricism".
Then, look into these paradoxes.
induction
quantification
identity
infinity
continuity
Now resolve them.
Not ignore them: resolve them.
You did a very excellent job of showing the great depth
of your understanding.
They cannot be resolved. It is logically impossible for
humans to acquire knowledge that is 100% perfectly
logically certainly correct. Humans can, however derive
a verbal model of the world that is a best model of
the world within the best measures that humans have.
Humans acquire knowledge of the world fundamentally
through the problem of induction.
When we hypothesize the this best model of the world
exists as a finite list of "atomic facts" of general
knowledge, this is where my system begins. All of the
stuff that you list above then becomes implementation
details. With such a list then every element of
general knowledge that can be expressed in language
can be derived by semantic entailment specified
syntactically.
Two elements of this general knowledge that can be
so derived are that:
(1) Trump exactly copied Hitler in his "big lie"
about election fraud.
(2) Severe climate change is caused by humans and
will eventually have very drastic consequences if
not sufficiently mitigated.
There's nothing necessarily wrong with ordinary, proper
(non-logical)
theories, they're just not both consistent and complete if they
claim
to talk about models of (all of the) integers.
Unless and until you toss out model theory itself as an incoherent >>>>>> basis. You are going to have to actually learn much more about
proof theoretic semantics before you can possibly understand this. >>>>>> On the basis of the quality of this reply from you I now know
that you can easily acquire this much deeper understanding.
Thusly a consistent and complete theory of integers is
extra-ordinary.
Then, induction the inference doesn't suffice, there's instead for >>>>>>> accounts of deductive inference to make analytical bridges, since >>>>>>> otherwise there's just counter-induction.
The simple essence of my slight extension to proof theoretic
semantics
is that what cannot be proven in PA is ungrounded in PA thus excluded >>>>>> from PA. PTS itself never examines truth relative to a formal system >>>>>> and from what I can see never extends beyond propositional logic. For >>>>>> me to really understand this I will need to totally understand
Natural
Deduction and possibly Sequent calculus.
Anyways, "Science", then for actual theory there's theatheory with >>>>>>> an account after axiomless natural deduction
My own system requires a finite list of "atomic facts" specified
within
simple type theory and at least Rudolf Carnap Meaning Postulates or >>>>>> its equivalents such as the CycL language of the Cyc project.
and making for Principle
of Inverse instead of Non-Contradiction,
I see no relationship between the two.
Principle of Inverse (Mathematics & Logic)
Examples: Subtraction is the inverse of addition;
division is the inverse of multiplication; the cube
root is the inverse of cubing a number.
Non-Contradiction is treated differently, Instead of the
principle of explosion (POE) a Contradiction merely proves
that the expression is false. I never could understand how
the POE is not merely a psychotic break from reality.
and Thorough Reason besides
merely Sufficient Reason, so, Aristotle won't be made a fool,
because
he has both prior and posterior analytics, and most accounts are as >>>>>>> of half-Aristotleans.
I have accounted for both sides.
It's sort of like about Aquinas, Scotus, and Occam, Aquinas read one >>>>>>> book of Aristotle and says one thing, Occam read another book of >>>>>>> Aristotle and says another, Scotus read both books and points out >>>>>>> that infinity is "in".
Dependence on induction and empiricism is a usual failing,
Cannot possibly be overcome so we work with what we have and
do the best that we possibly can within this.
it's not just retro-finitist crankety trolls,
indeed the usual idea of the dialectic is for the dialectic
in complementary duals, not merely competing claims.
Then, "dialectic" is confiscated from Marxists and "totalism" from >>>>>>> fascists, those words for judgments in reason are taken away from >>>>>>> the "neo-Stoics" who aren't Stoics and "neo-Hegelians" who aren't >>>>>>> Hegelians and "neo-Platonists" who aren't Platonists, all of whom >>>>>>> can be simply put down as not conscientious or _thorough_,
so that material-implication is kicked to the curb (or left to
its devices in its little box), making claims as they would for
the authority of the Platonists and Hegelians, according to reason. >>>>>>>
The ultimate basis of the system that I propose is logical
necessity. When this cannot possibly be achieved then we
maximize reasonable plausibility within the total evidence
available at the them. This last aspect is where conspiracy
theorists fail most direly. They maintain theories on the
basis of insufficient evidence and/or sufficient counter-evidence. >>>>>>
Then, "Science" here has a very principled account that involves >>>>>>> an _ethics_ of its interpretation to be conscientious, that most >>>>>>> sorts empirical and inductive reasoners _fail_ because the very
point is that first principles and final cause of "Science" _are_ >>>>>>> Science, not the stipulations/assumptions.
All of science depends on this
https://plato.stanford.edu/entries/induction-problem/
Yet science seems to have consistently proven to be
very reliable.
"Science" does not say what's "true", only between two given
theories, whether one of them is "falsified".
So water does not freeze at 32F at standard pressure?
This is that "Science" has three aspects:
observable: meaning accessible to the senses (or instruments for
operationalists/instrumentalists)
repeatable: meaning that experiments can be given the same energy
and configuration of experiment and result the same
falsifiable: meaning that configurations and energies of experiment
enumerate cases where the theory does/doesn't hold with regards to
others
"Science" thusly is never the "best" theory,
Best compared to infallibility? No.
Best available to humans? Yes.
only "less worse",
and never is "confirmed",
So there is no such thing as replicated experiments?
only not rejected, and, much like
"Statistics", even exactly the same, never "predicts" anything,
only increases the confidence that other theories are rejected.
"Theory" then is a broader account, about theories of science,
theories of reason, and theories of mathematical objects, among
theories about theory ("meta-theory").
"Reason" then is a particular account, about what's true and
what's not un-true, and then "Mathematics" is, according to
the idealistic tradition where there's a real and true truth,
or strong mathematical platonism, the discovery of structural
relations that describe geometrical measures of quantities,
about the quantified vis-a-vis the qualified.
Then, "Inverse" is an account of expansion-of-comprehension,
making for diversity and variety among complementary duals
and contiguous neighbors, in spaces of things (like geometry's,
grammar's, etc.) and the "Thorough" doesn't only claim to have
read Aristotle's reasoning, yet always does all the time.
Three-legged dog: is an account here that your fact-book
rules-engine is simpy not both of complete and consistent,
and, is not an account of a modal temporal relevance logic.
Infinity: is in.
Infinity has nothing to do with key truths the human survival
depends on such as this one.
https://www.researchgate.net/
publication/336568434_Severe_anthropogenic_climate_change_proven_entirely_with_verifiable_facts
All the time that humans play the entertainment game
of finding any excuse to disagree with me the liars
hired by the fossil fuel companies kill the planet
a little more.
A system such as mine does unequivocally compute the
truth about climate change and that Trump did exactly
copy Hitler in his lies about election fraud.
Nope, anybody's ordinary theories can do that.
Show me the underlying structural details of how this
is actually computed as I have done in my new signature
line. Ordinary theories don't have a slight clue of how
to mathematically formalize natural language they simply
guess that this is impossible not even being away of all
of the work by Richard Montague, Rudolf Carnap and
that Cyc project.
That seems to have combined a number of different fallacies there.
Infinity, and continuity, are key and central concepts in
mathematics, the objects of which, the universe of objects
and the domain of discourse about them the mathematical
objects the mathematical universe, in their infinite
_completions_, about
The have almost nothing to do with the finite body of
general knowledge about most everything.
geometry and number theory and
arithmetic and analysis and algebra for
arithmetizations and geometrizations and algebraizations
with function-theory and topology as usually least-well-defined
and the operator calculi about these, "mathematics",
has that there the merely-finite just won't do.
Within math and science that depends on this math infinity
is usually very important. Within the structure of the body
of general knowledge about most everything else we only need
a the subset of discrete math not involving infinity.
Similarly, for physics, the partial-differential and usual
accounts of approximations and truncations are merely-partial,
and while good, say, to the first-order for the expansions
or second-order for the quadratic, also are nominally not-good
beyond the limits of the guarantees of their bounds, these
sorts ordinary theories.
So, there are _guarantees_, mathematical, that usual sorts
ordinary theories of the merely-finite or merely-partial
don't have a full account of the objects of the theory.
"Why do they hire weathermen?" "To make economists look good."
(Since they are often wrong, pointing out somebody more wrong.)
Blame-shifting is fallacious and not a valid response to criticism,
such attempts at justification or setting things aright aren't
of a "better", only a "less worse". Science overall though is
overall "less worse", and, given accounts of symmetrical information
about perfect and imperfect information, is _fair_ meaning
egalitarian and non-biased. (As a joke it goes both ways.)
Repeatability is a _requirement_ of science, not a result.
That practically it's an expectation and an estimate, in
the statistical sense, is not a guarantee. Usually loose
language about science & statistics points to obvious
failings of the comprehension of the meaning of the terms,
and immediately paints "non-scientists" and "non-statisticians",
as alike dogmatic followers of empiricist schemes of induction,
some of which are doomed to fail.
Paradoxes are none.
An account of dual-monism then the dialectic is since
Heraclitus and Parmenides, these the earlier Greeks,
for something like Barnes' copy of the fragments,
these influences in thought for the academy, as
they're also according to the pre-historic influences
and the traditions these sums-of-influences, then
something like McKeon's Aristotle and Proclus' Euclid
help advise that Reason is a Verb. Also a Noun, ....
A post-modern sort of account since Derrida has that
first there's Husserl and both of them agree that
_geometry_ (standing in for mathematics) is still
somehow _true_, then a greater post-modernist's, and,
postmodernists', account of disfiguration the differance
after de-construction, is a structural realists' for
whom proof-theory is always equi-interpretable as a model-theory,
and a universal model-theory with a model of the universe,
for realists and structuralists, a model of the universe.
There simply aren't universes in accounts of ordinary
theories, only extra-ordinary theories.
Paradoxes are none.
So, is there a real true theory of truth? That's the idea.
In fact, it's such a great idea that I don't even have to
have it for it to always be the idea.
Yes. Most fundamentally "Truth that can be expressed in language"
(excluding things such as the actual smell of strawberries)
is different kinds of semantic relations (expressed syntactically)
between finite strings.
"water freezes at 32 degrees Fahrenheit at standard pressure"
Вода замерзает при 32 градусах по Фаренгейту при стандартном давлении
在標準氣壓下，水在華氏32度結冰
If Google translate is accurate the above "atomic fact"
stipulates that same semantic meaning across encoding systems.
And, science will
never know the difference. So, the great account as after
the analytical tradition gets equipped with the great account
as after the idealistic tradition, since neither can really
do without the other, in an overall sort of _Thorough_ account,
for conscientious logicians and mathematicians and scientists
and physicists the reasoners.
"What time is it?"
^- statements automatically have infinitely-deep implicit quoting,
along with infinitely-deep implicit quantifiers on the terms, which
are implicitly both constants and variables, all one term
So, reasoning about universes is all in one Universe,
for accounts like Duns Scotus and univocity, while that
expansion-of-comprehension makes diversity & variety then
that restriction-of-comprehension is justly perspectival
and first-class perspectival, not just blindered, dumbed,
and following along.
Then of course independence of thought basically defines individuals,
with regards to matters of consciousness and will of feeling and
thinking beings, and the universe of conjecture can entertain any
number of theories, while yet there is one at all. Or, "yet-like".
If you look at something like my essays/posts on the "Infinity" thread
since at least a couple decades ago, there's a great long quotation
there to the thousands and thousands of pages, which, according to
a scheme of compression that de-duplicates repetition, makes for so
that the more times you have to say something, the less it seems right.
People like software engineers in information theory get entirely
irritated when anybody says something twice. So, I always try to
bring something novel to little essays like these, here that
I've said most all these things before. (And yet-now they're always.)
Montague's considered a hypocritical flake with quasi-modal baggage,
there's something like Herbrand semantics for that,
then Carnap is considered a genial convener and not saying much.
Vienna school y u no Berlin school or Frankfurt school?
We're full Hegelians and full Aristotleans here,
not "pseudo" nor "neo" partial half-accounts.
On 05/23/2026 12:50 PM, Ross Finlayson wrote:
On 05/23/2026 09:27 AM, olcott wrote:
On 5/23/2026 10:46 AM, Ross Finlayson wrote:
On 05/23/2026 07:01 AM, olcott wrote:
On 5/22/2026 8:30 PM, Ross Finlayson wrote:
On 05/22/2026 10:01 AM, olcott wrote:
On 5/22/2026 10:06 AM, Ross Finlayson wrote:
No, infinity disagrees that "infinity does not count at all".
Look to "fallacies of induction" or "fallacies of empiricism". >>>>>>>>
Then, look into these paradoxes.
induction
quantification
identity
infinity
continuity
Now resolve them.
Not ignore them: resolve them.
You did a very excellent job of showing the great depth
of your understanding.
They cannot be resolved. It is logically impossible for
humans to acquire knowledge that is 100% perfectly
logically certainly correct. Humans can, however derive
a verbal model of the world that is a best model of
the world within the best measures that humans have.
Humans acquire knowledge of the world fundamentally
through the problem of induction.
When we hypothesize the this best model of the world
exists as a finite list of "atomic facts" of general
knowledge, this is where my system begins. All of the
stuff that you list above then becomes implementation
details. With such a list then every element of
general knowledge that can be expressed in language
can be derived by semantic entailment specified
syntactically.
Two elements of this general knowledge that can be
so derived are that:
(1) Trump exactly copied Hitler in his "big lie"
about election fraud.
(2) Severe climate change is caused by humans and
will eventually have very drastic consequences if
not sufficiently mitigated.
There's nothing necessarily wrong with ordinary, proper
(non-logical)
theories, they're just not both consistent and complete if they >>>>>>>> claim
to talk about models of (all of the) integers.
Unless and until you toss out model theory itself as an incoherent >>>>>>> basis. You are going to have to actually learn much more about
proof theoretic semantics before you can possibly understand this. >>>>>>> On the basis of the quality of this reply from you I now know
that you can easily acquire this much deeper understanding.
Thusly a consistent and complete theory of integers is
extra-ordinary.
Then, induction the inference doesn't suffice, there's instead for >>>>>>>> accounts of deductive inference to make analytical bridges, since >>>>>>>> otherwise there's just counter-induction.
The simple essence of my slight extension to proof theoretic
semantics
is that what cannot be proven in PA is ungrounded in PA thus
excluded
from PA. PTS itself never examines truth relative to a formal system >>>>>>> and from what I can see never extends beyond propositional logic. >>>>>>> For
me to really understand this I will need to totally understand
Natural
Deduction and possibly Sequent calculus.
Anyways, "Science", then for actual theory there's theatheory with >>>>>>>> an account after axiomless natural deduction
My own system requires a finite list of "atomic facts" specified >>>>>>> within
simple type theory and at least Rudolf Carnap Meaning Postulates or >>>>>>> its equivalents such as the CycL language of the Cyc project.
and making for Principle
of Inverse instead of Non-Contradiction,
I see no relationship between the two.
Principle of Inverse (Mathematics & Logic)
Examples: Subtraction is the inverse of addition;
division is the inverse of multiplication; the cube
root is the inverse of cubing a number.
Non-Contradiction is treated differently, Instead of the
principle of explosion (POE) a Contradiction merely proves
that the expression is false. I never could understand how
the POE is not merely a psychotic break from reality.
and Thorough Reason besides
merely Sufficient Reason, so, Aristotle won't be made a fool,
because
he has both prior and posterior analytics, and most accounts are as >>>>>>>> of half-Aristotleans.
I have accounted for both sides.
It's sort of like about Aquinas, Scotus, and Occam, Aquinas read >>>>>>>> one
book of Aristotle and says one thing, Occam read another book of >>>>>>>> Aristotle and says another, Scotus read both books and points out >>>>>>>> that infinity is "in".
Dependence on induction and empiricism is a usual failing,
Cannot possibly be overcome so we work with what we have and
do the best that we possibly can within this.
it's not just retro-finitist crankety trolls,
indeed the usual idea of the dialectic is for the dialectic
in complementary duals, not merely competing claims.
Then, "dialectic" is confiscated from Marxists and "totalism" from >>>>>>>> fascists, those words for judgments in reason are taken away from >>>>>>>> the "neo-Stoics" who aren't Stoics and "neo-Hegelians" who aren't >>>>>>>> Hegelians and "neo-Platonists" who aren't Platonists, all of whom >>>>>>>> can be simply put down as not conscientious or _thorough_,
so that material-implication is kicked to the curb (or left to >>>>>>>> its devices in its little box), making claims as they would for >>>>>>>> the authority of the Platonists and Hegelians, according to reason. >>>>>>>>
The ultimate basis of the system that I propose is logical
necessity. When this cannot possibly be achieved then we
maximize reasonable plausibility within the total evidence
available at the them. This last aspect is where conspiracy
theorists fail most direly. They maintain theories on the
basis of insufficient evidence and/or sufficient counter-evidence. >>>>>>>
Then, "Science" here has a very principled account that involves >>>>>>>> an _ethics_ of its interpretation to be conscientious, that most >>>>>>>> sorts empirical and inductive reasoners _fail_ because the very >>>>>>>> point is that first principles and final cause of "Science" _are_ >>>>>>>> Science, not the stipulations/assumptions.
All of science depends on this
https://plato.stanford.edu/entries/induction-problem/
Yet science seems to have consistently proven to be
very reliable.
"Science" does not say what's "true", only between two given
theories, whether one of them is "falsified".
So water does not freeze at 32F at standard pressure?
This is that "Science" has three aspects:
observable: meaning accessible to the senses (or instruments for
operationalists/instrumentalists)
repeatable: meaning that experiments can be given the same energy
and configuration of experiment and result the same
falsifiable: meaning that configurations and energies of experiment >>>>>> enumerate cases where the theory does/doesn't hold with regards to >>>>>> others
"Science" thusly is never the "best" theory,
Best compared to infallibility? No.
Best available to humans? Yes.
only "less worse",
and never is "confirmed",
So there is no such thing as replicated experiments?
only not rejected, and, much like
"Statistics", even exactly the same, never "predicts" anything,
only increases the confidence that other theories are rejected.
"Theory" then is a broader account, about theories of science,
theories of reason, and theories of mathematical objects, among
theories about theory ("meta-theory").
"Reason" then is a particular account, about what's true and
what's not un-true, and then "Mathematics" is, according to
the idealistic tradition where there's a real and true truth,
or strong mathematical platonism, the discovery of structural
relations that describe geometrical measures of quantities,
about the quantified vis-a-vis the qualified.
Then, "Inverse" is an account of expansion-of-comprehension,
making for diversity and variety among complementary duals
and contiguous neighbors, in spaces of things (like geometry's,
grammar's, etc.) and the "Thorough" doesn't only claim to have
read Aristotle's reasoning, yet always does all the time.
Three-legged dog: is an account here that your fact-book
rules-engine is simpy not both of complete and consistent,
and, is not an account of a modal temporal relevance logic.
Infinity: is in.
Infinity has nothing to do with key truths the human survival
depends on such as this one.
https://www.researchgate.net/
publication/336568434_Severe_anthropogenic_climate_change_proven_entirely_with_verifiable_facts
All the time that humans play the entertainment game
of finding any excuse to disagree with me the liars
hired by the fossil fuel companies kill the planet
a little more.
A system such as mine does unequivocally compute the
truth about climate change and that Trump did exactly
copy Hitler in his lies about election fraud.
Nope, anybody's ordinary theories can do that.
Show me the underlying structural details of how this
is actually computed as I have done in my new signature
line. Ordinary theories don't have a slight clue of how
to mathematically formalize natural language they simply
guess that this is impossible not even being away of all
of the work by Richard Montague, Rudolf Carnap and
that Cyc project.
That seems to have combined a number of different fallacies there.
Infinity, and continuity, are key and central concepts in
mathematics, the objects of which, the universe of objects
and the domain of discourse about them the mathematical
objects the mathematical universe, in their infinite
_completions_, about
The have almost nothing to do with the finite body of
general knowledge about most everything.
geometry and number theory and
arithmetic and analysis and algebra for
arithmetizations and geometrizations and algebraizations
with function-theory and topology as usually least-well-defined
and the operator calculi about these, "mathematics",
has that there the merely-finite just won't do.
Within math and science that depends on this math infinity
is usually very important. Within the structure of the body
of general knowledge about most everything else we only need
a the subset of discrete math not involving infinity.
Similarly, for physics, the partial-differential and usual
accounts of approximations and truncations are merely-partial,
and while good, say, to the first-order for the expansions
or second-order for the quadratic, also are nominally not-good
beyond the limits of the guarantees of their bounds, these
sorts ordinary theories.
So, there are _guarantees_, mathematical, that usual sorts
ordinary theories of the merely-finite or merely-partial
don't have a full account of the objects of the theory.
"Why do they hire weathermen?" "To make economists look good."
(Since they are often wrong, pointing out somebody more wrong.)
Blame-shifting is fallacious and not a valid response to criticism,
such attempts at justification or setting things aright aren't
of a "better", only a "less worse". Science overall though is
overall "less worse", and, given accounts of symmetrical information
about perfect and imperfect information, is _fair_ meaning
egalitarian and non-biased. (As a joke it goes both ways.)
Repeatability is a _requirement_ of science, not a result.
That practically it's an expectation and an estimate, in
the statistical sense, is not a guarantee. Usually loose
language about science & statistics points to obvious
failings of the comprehension of the meaning of the terms,
and immediately paints "non-scientists" and "non-statisticians",
as alike dogmatic followers of empiricist schemes of induction,
some of which are doomed to fail.
Paradoxes are none.
An account of dual-monism then the dialectic is since
Heraclitus and Parmenides, these the earlier Greeks,
for something like Barnes' copy of the fragments,
these influences in thought for the academy, as
they're also according to the pre-historic influences
and the traditions these sums-of-influences, then
something like McKeon's Aristotle and Proclus' Euclid
help advise that Reason is a Verb. Also a Noun, ....
A post-modern sort of account since Derrida has that
first there's Husserl and both of them agree that
_geometry_ (standing in for mathematics) is still
somehow _true_, then a greater post-modernist's, and,
postmodernists', account of disfiguration the differance
after de-construction, is a structural realists' for
whom proof-theory is always equi-interpretable as a model-theory,
and a universal model-theory with a model of the universe,
for realists and structuralists, a model of the universe.
There simply aren't universes in accounts of ordinary
theories, only extra-ordinary theories.
Paradoxes are none.
So, is there a real true theory of truth? That's the idea.
In fact, it's such a great idea that I don't even have to
have it for it to always be the idea.
Yes. Most fundamentally "Truth that can be expressed in language"
(excluding things such as the actual smell of strawberries)
is different kinds of semantic relations (expressed syntactically)
between finite strings.
"water freezes at 32 degrees Fahrenheit at standard pressure"
Вода замерзает при 32 градусах по Фаренгейту при стандартном давлении
在標準氣壓下，水在華氏32度結冰
If Google translate is accurate the above "atomic fact"
stipulates that same semantic meaning across encoding systems.
And, science will
never know the difference. So, the great account as after
the analytical tradition gets equipped with the great account
as after the idealistic tradition, since neither can really
do without the other, in an overall sort of _Thorough_ account,
for conscientious logicians and mathematicians and scientists
and physicists the reasoners.
"What time is it?"
^- statements automatically have infinitely-deep implicit quoting,
along with infinitely-deep implicit quantifiers on the terms, which
are implicitly both constants and variables, all one term
So, reasoning about universes is all in one Universe,
for accounts like Duns Scotus and univocity, while that
expansion-of-comprehension makes diversity & variety then
that restriction-of-comprehension is justly perspectival
and first-class perspectival, not just blindered, dumbed,
and following along.
Then of course independence of thought basically defines individuals,
with regards to matters of consciousness and will of feeling and
thinking beings, and the universe of conjecture can entertain any
number of theories, while yet there is one at all. Or, "yet-like".
If you look at something like my essays/posts on the "Infinity" thread >>>> since at least a couple decades ago, there's a great long quotation
there to the thousands and thousands of pages, which, according to
a scheme of compression that de-duplicates repetition, makes for so
that the more times you have to say something, the less it seems right. >>>>
People like software engineers in information theory get entirely
irritated when anybody says something twice. So, I always try to
bring something novel to little essays like these, here that
I've said most all these things before. (And yet-now they're always.)
Montague's considered a hypocritical flake with quasi-modal baggage,
there's something like Herbrand semantics for that,
then Carnap is considered a genial convener and not saying much.
Vienna school y u no Berlin school or Frankfurt school?
We're full Hegelians and full Aristotleans here,
not "pseudo" nor "neo" partial half-accounts.
Otherwise those "circles" there are mostly "nazis versus commies"
with no not common ground, and people who steal accounts of reason
for rhetoric.
The 20'th century isn't absent or bereft accounts of the idealistic
tradition its usual role in counterpart and complement to the analytical tradition, for examples like Collingwood, W.H.F. Barnes,
Huntington, McKeon with his "Aristotle" (still in print and in a
thirtieth or more printing), A.C. Ewing being a great example, A.C.
Grayling, and Gadamer for example with "amicus Plato", Sartre in a
variety of senses, Husserl the transcendental, Lyotard in a sense,
technical sorts with the technical philosophy and its grounds for
reason, then for example I'm mostly 21'st century.
Accounts like Frege or Peirce give most of what formal abstract methods
would ever need, after De Morgan, for ordinary theories, those are 19'th century, though. Then an account is to be made for where
the fundamental "relation" is "relation".
https://en.wikipedia.org/wiki/Relation_(philosophy)#History
On 05/23/2026 09:27 AM, olcott wrote:
On 5/23/2026 10:46 AM, Ross Finlayson wrote:
On 05/23/2026 07:01 AM, olcott wrote:
On 5/22/2026 8:30 PM, Ross Finlayson wrote:
On 05/22/2026 10:01 AM, olcott wrote:
On 5/22/2026 10:06 AM, Ross Finlayson wrote:
No, infinity disagrees that "infinity does not count at all".
Look to "fallacies of induction" or "fallacies of empiricism".
Then, look into these paradoxes.
induction
quantification
identity
infinity
continuity
Now resolve them.
Not ignore them: resolve them.
You did a very excellent job of showing the great depth
of your understanding.
They cannot be resolved. It is logically impossible for
humans to acquire knowledge that is 100% perfectly
logically certainly correct. Humans can, however derive
a verbal model of the world that is a best model of
the world within the best measures that humans have.
Humans acquire knowledge of the world fundamentally
through the problem of induction.
When we hypothesize the this best model of the world
exists as a finite list of "atomic facts" of general
knowledge, this is where my system begins. All of the
stuff that you list above then becomes implementation
details. With such a list then every element of
general knowledge that can be expressed in language
can be derived by semantic entailment specified
syntactically.
Two elements of this general knowledge that can be
so derived are that:
(1) Trump exactly copied Hitler in his "big lie"
about election fraud.
(2) Severe climate change is caused by humans and
will eventually have very drastic consequences if
not sufficiently mitigated.
There's nothing necessarily wrong with ordinary, proper (non-
logical)
theories, they're just not both consistent and complete if they >>>>>>> claim
to talk about models of (all of the) integers.
Unless and until you toss out model theory itself as an incoherent >>>>>> basis. You are going to have to actually learn much more about
proof theoretic semantics before you can possibly understand this. >>>>>> On the basis of the quality of this reply from you I now know
that you can easily acquire this much deeper understanding.
Thusly a consistent and complete theory of integers is
extra-ordinary.
Then, induction the inference doesn't suffice, there's instead for >>>>>>> accounts of deductive inference to make analytical bridges, since >>>>>>> otherwise there's just counter-induction.
The simple essence of my slight extension to proof theoretic
semantics
is that what cannot be proven in PA is ungrounded in PA thus excluded >>>>>> from PA. PTS itself never examines truth relative to a formal system >>>>>> and from what I can see never extends beyond propositional logic. For >>>>>> me to really understand this I will need to totally understand
Natural
Deduction and possibly Sequent calculus.
Anyways, "Science", then for actual theory there's theatheory with >>>>>>> an account after axiomless natural deduction
My own system requires a finite list of "atomic facts" specified
within
simple type theory and at least Rudolf Carnap Meaning Postulates or >>>>>> its equivalents such as the CycL language of the Cyc project.
and making for Principle
of Inverse instead of Non-Contradiction,
I see no relationship between the two.
Principle of Inverse (Mathematics & Logic)
Examples: Subtraction is the inverse of addition;
division is the inverse of multiplication; the cube
root is the inverse of cubing a number.
Non-Contradiction is treated differently, Instead of the
principle of explosion (POE) a Contradiction merely proves
that the expression is false. I never could understand how
the POE is not merely a psychotic break from reality.
and Thorough Reason besides
merely Sufficient Reason, so, Aristotle won't be made a fool,
because
he has both prior and posterior analytics, and most accounts are as >>>>>>> of half-Aristotleans.
I have accounted for both sides.
It's sort of like about Aquinas, Scotus, and Occam, Aquinas read one >>>>>>> book of Aristotle and says one thing, Occam read another book of >>>>>>> Aristotle and says another, Scotus read both books and points out >>>>>>> that infinity is "in".
Dependence on induction and empiricism is a usual failing,
Cannot possibly be overcome so we work with what we have and
do the best that we possibly can within this.
it's not just retro-finitist crankety trolls,
indeed the usual idea of the dialectic is for the dialectic
in complementary duals, not merely competing claims.
Then, "dialectic" is confiscated from Marxists and "totalism" from >>>>>>> fascists, those words for judgments in reason are taken away from >>>>>>> the "neo-Stoics" who aren't Stoics and "neo-Hegelians" who aren't >>>>>>> Hegelians and "neo-Platonists" who aren't Platonists, all of whom >>>>>>> can be simply put down as not conscientious or _thorough_,
so that material-implication is kicked to the curb (or left to
its devices in its little box), making claims as they would for
the authority of the Platonists and Hegelians, according to reason. >>>>>>>
The ultimate basis of the system that I propose is logical
necessity. When this cannot possibly be achieved then we
maximize reasonable plausibility within the total evidence
available at the them. This last aspect is where conspiracy
theorists fail most direly. They maintain theories on the
basis of insufficient evidence and/or sufficient counter-evidence. >>>>>>
Then, "Science" here has a very principled account that involves >>>>>>> an _ethics_ of its interpretation to be conscientious, that most >>>>>>> sorts empirical and inductive reasoners _fail_ because the very
point is that first principles and final cause of "Science" _are_ >>>>>>> Science, not the stipulations/assumptions.
All of science depends on this
https://plato.stanford.edu/entries/induction-problem/
Yet science seems to have consistently proven to be
very reliable.
"Science" does not say what's "true", only between two given
theories, whether one of them is "falsified".
So water does not freeze at 32F at standard pressure?
This is that "Science" has three aspects:
observable: meaning accessible to the senses (or instruments for
operationalists/instrumentalists)
repeatable: meaning that experiments can be given the same energy
and configuration of experiment and result the same
falsifiable: meaning that configurations and energies of experiment
enumerate cases where the theory does/doesn't hold with regards to
others
"Science" thusly is never the "best" theory,
Best compared to infallibility? No.
Best available to humans? Yes.
only "less worse",
and never is "confirmed",
So there is no such thing as replicated experiments?
only not rejected, and, much like
"Statistics", even exactly the same, never "predicts" anything,
only increases the confidence that other theories are rejected.
"Theory" then is a broader account, about theories of science,
theories of reason, and theories of mathematical objects, among
theories about theory ("meta-theory").
"Reason" then is a particular account, about what's true and
what's not un-true, and then "Mathematics" is, according to
the idealistic tradition where there's a real and true truth,
or strong mathematical platonism, the discovery of structural
relations that describe geometrical measures of quantities,
about the quantified vis-a-vis the qualified.
Then, "Inverse" is an account of expansion-of-comprehension,
making for diversity and variety among complementary duals
and contiguous neighbors, in spaces of things (like geometry's,
grammar's, etc.) and the "Thorough" doesn't only claim to have
read Aristotle's reasoning, yet always does all the time.
Three-legged dog: is an account here that your fact-book
rules-engine is simpy not both of complete and consistent,
and, is not an account of a modal temporal relevance logic.
Infinity: is in.
Infinity has nothing to do with key truths the human survival
depends on such as this one.
https://www.researchgate.net/
publication/336568434_Severe_anthropogenic_climate_change_proven_entirely_with_verifiable_facts
All the time that humans play the entertainment game
of finding any excuse to disagree with me the liars
hired by the fossil fuel companies kill the planet
a little more.
A system such as mine does unequivocally compute the
truth about climate change and that Trump did exactly
copy Hitler in his lies about election fraud.
Nope, anybody's ordinary theories can do that.
Show me the underlying structural details of how this
is actually computed as I have done in my new signature
line. Ordinary theories don't have a slight clue of how
to mathematically formalize natural language they simply
guess that this is impossible not even being away of all
of the work by Richard Montague, Rudolf Carnap and
that Cyc project.
That seems to have combined a number of different fallacies there.
Infinity, and continuity, are key and central concepts in
mathematics, the objects of which, the universe of objects
and the domain of discourse about them the mathematical
objects the mathematical universe, in their infinite
_completions_, about
The have almost nothing to do with the finite body of
general knowledge about most everything.
geometry and number theory and
arithmetic and analysis and algebra for
arithmetizations and geometrizations and algebraizations
with function-theory and topology as usually least-well-defined
and the operator calculi about these, "mathematics",
has that there the merely-finite just won't do.
Within math and science that depends on this math infinity
is usually very important. Within the structure of the body
of general knowledge about most everything else we only need
a the subset of discrete math not involving infinity.
Similarly, for physics, the partial-differential and usual
accounts of approximations and truncations are merely-partial,
and while good, say, to the first-order for the expansions
or second-order for the quadratic, also are nominally not-good
beyond the limits of the guarantees of their bounds, these
sorts ordinary theories.
So, there are _guarantees_, mathematical, that usual sorts
ordinary theories of the merely-finite or merely-partial
don't have a full account of the objects of the theory.
"Why do they hire weathermen?" "To make economists look good."
(Since they are often wrong, pointing out somebody more wrong.)
Blame-shifting is fallacious and not a valid response to criticism,
such attempts at justification or setting things aright aren't
of a "better", only a "less worse". Science overall though is
overall "less worse", and, given accounts of symmetrical information
about perfect and imperfect information, is _fair_ meaning
egalitarian and non-biased. (As a joke it goes both ways.)
Repeatability is a _requirement_ of science, not a result.
That practically it's an expectation and an estimate, in
the statistical sense, is not a guarantee. Usually loose
language about science & statistics points to obvious
failings of the comprehension of the meaning of the terms,
and immediately paints "non-scientists" and "non-statisticians",
as alike dogmatic followers of empiricist schemes of induction,
some of which are doomed to fail.
Paradoxes are none.
An account of dual-monism then the dialectic is since
Heraclitus and Parmenides, these the earlier Greeks,
for something like Barnes' copy of the fragments,
these influences in thought for the academy, as
they're also according to the pre-historic influences
and the traditions these sums-of-influences, then
something like McKeon's Aristotle and Proclus' Euclid
help advise that Reason is a Verb. Also a Noun, ....
A post-modern sort of account since Derrida has that
first there's Husserl and both of them agree that
_geometry_ (standing in for mathematics) is still
somehow _true_, then a greater post-modernist's, and,
postmodernists', account of disfiguration the differance
after de-construction, is a structural realists' for
whom proof-theory is always equi-interpretable as a model-theory,
and a universal model-theory with a model of the universe,
for realists and structuralists, a model of the universe.
There simply aren't universes in accounts of ordinary
theories, only extra-ordinary theories.
Paradoxes are none.
So, is there a real true theory of truth? That's the idea.
In fact, it's such a great idea that I don't even have to
have it for it to always be the idea.
Yes. Most fundamentally "Truth that can be expressed in language"
(excluding things such as the actual smell of strawberries)
is different kinds of semantic relations (expressed syntactically)
between finite strings.
"water freezes at 32 degrees Fahrenheit at standard pressure"
Вода замерзает при 32 градусах по Фаренгейту при стандартном давлении
在標準氣壓下，水在華氏32度結冰
If Google translate is accurate the above "atomic fact"
stipulates that same semantic meaning across encoding systems.
And, science will
never know the difference. So, the great account as after
the analytical tradition gets equipped with the great account
as after the idealistic tradition, since neither can really
do without the other, in an overall sort of _Thorough_ account,
for conscientious logicians and mathematicians and scientists
and physicists the reasoners.
"What time is it?"
^- statements automatically have infinitely-deep implicit quoting,
along with infinitely-deep implicit quantifiers on the terms, which
are implicitly both constants and variables, all one term
So, reasoning about universes is all in one Universe,
for accounts like Duns Scotus and univocity, while that
expansion-of-comprehension makes diversity & variety then
that restriction-of-comprehension is justly perspectival
and first-class perspectival, not just blindered, dumbed,
and following along.
Then of course independence of thought basically defines individuals,
with regards to matters of consciousness and will of feeling and
thinking beings, and the universe of conjecture can entertain any
number of theories, while yet there is one at all. Or, "yet-like".
If you look at something like my essays/posts on the "Infinity" thread
since at least a couple decades ago, there's a great long quotation
there to the thousands and thousands of pages, which, according to
a scheme of compression that de-duplicates repetition, makes for so
that the more times you have to say something, the less it seems right.
People like software engineers in information theory get entirely
irritated when anybody says something twice. So, I always try to
bring something novel to little essays like these, here that
I've said most all these things before. (And yet-now they're always.)
Montague's considered a hypocritical flake with quasi-modal baggage,
there's something like Herbrand semantics for that,
then Carnap is considered a genial convener and not saying much.
Vienna school y u no Berlin school or Frankfurt school?
We're full Hegelians and full Aristotleans here,
not "pseudo" nor "neo" partial half-accounts.
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