On 2/10/2026 4:17 PM, Ross Finlayson wrote:
On 02/10/2026 06:05 AM, Maciej Wo+|niak wrote:
On 2/10/2026 2:30 PM, Ross Finlayson wrote:
On 02/10/2026 03:44 AM, Maciej Wo+|niak wrote:
On 2/10/2026 10:54 AM, Ross Finlayson wrote:
On 02/10/2026 01:17 AM, Maciej Wo+|niak wrote:
On 2/10/2026 9:27 AM, Ross Finlayson wrote:
On 02/10/2026 12:21 AM, Maciej Wo+|niak wrote:
On 2/10/2026 8:35 AM, Ross Finlayson wrote:
On 02/04/2026 07:55 AM, Python wrote:
Le 04/02/2026 |a 16:48, Maciej Wo+|niak a |-crit :
On 2/4/2026 3:19 PM, Thomas 'PointedEars' Lahn wrote: >>>>>>>>>>>>> Thomas 'PointedEars' Lahn wrote:
One must distinguish between a function that is _identically_ >>>>>>>>>>>>>> zero,Actually, one has to be even more careful with one's wording. >>>>>>>>>>>>>
i.e.
whose value is zero _everywhere_, and a function whose >>>>>>>>>>>>>> value is
zero
_for a
finite number of arguments in its domain_.
> The derivative of the former function *is* actually zero >>>>>>>>>>>>>> because
it is a
special case of a constant function, but the derivative of >>>>>>>>>>>>>> the
latter
function is not necessarily zero.
As we can see from periodic functions like the sine function, >>>>>>>>>>>>> it is
even
possible that a function is zero for a countably infinite >>>>>>>>>>>>> number of
arguments (e.g. all integer multiples of -C) but still not all >>>>>>>>>>>>> arguments.
And one can even think of a pathological case: The Dirichlet >>>>>>>>>>>>> function
1_raU(x) = {1 if x ree raU;
0 if x ree raU
is zero for *uncountably* infinitely many arguments in its >>>>>>>>>>>>> domain
because
they are real numbers but not rational numbers, and
non-zero for
*countably*
infinitely made arguments in its domain because they are >>>>>>>>>>>>> rational
numbers
(the latter are members of a countably infinite set, as Cantor >>>>>>>>>>>>> proved).
Thomas, poor trash, Pythagoreas has proven
that for any right triangle a^2+b^2 =c^2.
Than a hundred of others provided a hundred
of independent proofs for the same.
Did it prevent idiots like yourself
from denying that?
Do you think Cantor's theorems are more
proven?
It is, to say the least, somewhat surreal to have a
discussion on
the
fondations of mathematics and the status of mathematical truth, >>>>>>>>>>> theorems, etc. involving Maciej Wozniak.
The ontological status of mathematical truth involves
the teleological status of mathematical truth as is
a usual conversation of Derrida on Husserl "proto-geometry". >>>>>>>>>
But this pseudophilosophical mumble is no
answer to the question whether Cantor's
theorems are proven somehow better than
Pythagorean.
Well that's simple, they're both what they are,
then the issue must be underneath them both, that
they have made what results mostly a usual ignorance
about the law of large numbers being the law of small numbers. >>>>>>>>
Somebody like Hilbert with a "postulate of continuity"
after somebody like Leibnitz with a "postulate of perfection"
or otherwise making lines from points or points from lines,
harken to Xenocrates and Democritus, or about that Aristotle
has at least two models of continua.
Integer Continuum <- Duns Scotus, Spinoza
Line-Reals <- Xenocrates, Hilbert
Field-Reals <- Archimedes, Weierstrass
Signal-Reals <- Shannon/Nyquist
Long-Line Continuum <- duBois-Reymond
But this pseudophilosophical mumble (well,
I can delete pseudo, but I can't delete mumble)
is no answer to the question whether Cantor's
theorems are proven somehow better than
Pythagorean.
The answer is they're not,
Right. That leads to the next one.
Why for a relativistic idiot Cantor's
(and any other except Euclidean set)
theorems are (proven so undeniable)
and Pythagorean theorem (and any other
from Euclidean set) is (proven
but counterexampled).
Where does the difference come from?
Not from the proofs, we already agreed
(?) that. Would it be possible that
mathematical proofs are really just
some smokescreen for pure faith?
Not necessarily, since proofs are believable.
Well, proofs of Pythagorean theorem HAVE
BEEN believable - for 2000 years - until
some idiots asserted they're really not and
waved their arms. How does it correspond to
"neo-Platonism", Epicurean sense-relations,
occamism and nominalism?
The "riddle of induction" is that since the time
of Aristotle, with both prior and posterior analytics,
since Philo and Plotinus the "neo-Platonists",
a simple inductive half-account grounded in the
Epicurean sense-relations simply makes for
Occamism the nominalism a bare skein of truth,
since its greater account demands experience of reason.
Then, that it's "truth" involved is a matter of
the voluntary, has that it's a tragedy that since
the humility demands letting it be optional,
that the vainglorious twist it.
Or, you know, it varies.
The "strong mathematical platonism", though,
and the "strong logicist positivism", together,
may make for better than a "weak logicist positivism".
Make for better, you say? Any proof
of that? What does "better" mean,
anyway?
Anyway, when the culture recognizes a string
of letters as good for itself it's getting
the stamp "true" to be repeated. When the
culture recognizes a string of letters as
not good for itself it's getting the stamp
"false"to be blocked. That's basically it.
Mistakes happen.
Now if you read something like the "T-theory,
A-theory, theatheory" thread, after that
"The fundamental joke of logic" bit,
where I made all the AI reasoners of the
day fall in line and agree to converge,
these might answer your questions.
Then, here, about "Galaxies don't fly apart
because their entire frame is rotating",
where I begin to describe why Dark Matter
is really Luminous Matter that's been
misunderstood, and about continuum mechanics
and all, then at least there's a Mathematical
Foundations that's strong.
And it's stronger than Euclidean theory
- because....
On 02/10/2026 07:29 AM, Maciej Wo+|niak wrote:
On 2/10/2026 4:17 PM, Ross Finlayson wrote:
On 02/10/2026 06:05 AM, Maciej Wo+|niak wrote:
On 2/10/2026 2:30 PM, Ross Finlayson wrote:
On 02/10/2026 03:44 AM, Maciej Wo+|niak wrote:
On 2/10/2026 10:54 AM, Ross Finlayson wrote:
On 02/10/2026 01:17 AM, Maciej Wo+|niak wrote:
On 2/10/2026 9:27 AM, Ross Finlayson wrote:
On 02/10/2026 12:21 AM, Maciej Wo+|niak wrote:
On 2/10/2026 8:35 AM, Ross Finlayson wrote:
On 02/04/2026 07:55 AM, Python wrote:
Le 04/02/2026 |a 16:48, Maciej Wo+|niak a |-crit :
On 2/4/2026 3:19 PM, Thomas 'PointedEars' Lahn wrote: >>>>>>>>>>>>>> Thomas 'PointedEars' Lahn wrote:
One must distinguish between a function that is >>>>>>>>>>>>>>> _identically_Actually, one has to be even more careful with one's wording. >>>>>>>>>>>>>>
zero,
i.e.
whose value is zero _everywhere_, and a function whose >>>>>>>>>>>>>>> value is
zero
_for a
finite number of arguments in its domain_.
-a > The derivative of the former function *is* actually zero >>>>>>>>>>>>>>> because
it is a
special case of a constant function, but the derivative of >>>>>>>>>>>>>>> the
latter
function is not necessarily zero.
As we can see from periodic functions like the sine function, >>>>>>>>>>>>>> it is
even
possible that a function is zero for a countably infinite >>>>>>>>>>>>>> number of
arguments (e.g. all integer multiples of -C) but still not all >>>>>>>>>>>>>> arguments.
And one can even think of a pathological case: The Dirichlet >>>>>>>>>>>>>> function
-a-a 1_raU(x) = {1 if x ree raU;
-a-a-a-a-a-a-a-a-a-a-a-a 0 if x ree raU
is zero for *uncountably* infinitely many arguments in its >>>>>>>>>>>>>> domain
because
they are real numbers but not rational numbers, and >>>>>>>>>>>>>> non-zero for
*countably*
infinitely made arguments in its domain because they are >>>>>>>>>>>>>> rational
numbers
(the latter are members of a countably infinite set, as >>>>>>>>>>>>>> Cantor
proved).
Thomas, poor trash, Pythagoreas has proven
that for any right triangle a^2+b^2 =c^2.
Than a hundred of others provided-a a hundred
of independent proofs for the same.
Did it prevent-a idiots like yourself
from denying-a that?
Do you think Cantor's theorems are more
proven?
It is, to say the least, somewhat surreal to have a
discussion on
the
fondations of mathematics and the status of mathematical truth, >>>>>>>>>>>> theorems, etc. involving Maciej Wozniak.
The ontological status of mathematical truth involves
the teleological status of mathematical truth as is
a usual conversation of Derrida on Husserl "proto-geometry". >>>>>>>>>>
But this pseudophilosophical mumble is no
answer to the question whether Cantor's
theorems are proven somehow better than
Pythagorean.
Well that's simple, they're both what they are,
then the issue must be underneath them both, that
they have made what results mostly a usual ignorance
about the law of large numbers being the law of small numbers. >>>>>>>>>
Somebody like Hilbert with a "postulate of continuity"
after somebody like Leibnitz with a "postulate of perfection" >>>>>>>>> or otherwise making lines from points or points from lines,
harken to Xenocrates and Democritus, or about that Aristotle >>>>>>>>> has at least two models of continua.
Integer Continuum <- Duns Scotus, Spinoza
Line-Reals <- Xenocrates, Hilbert
Field-Reals <- Archimedes, Weierstrass
Signal-Reals <- Shannon/Nyquist
Long-Line Continuum <- duBois-Reymond
But this pseudophilosophical mumble (well,
I can delete pseudo, but I can't delete mumble)
is no answer to the question whether Cantor's
theorems are proven somehow better than
Pythagorean.
The answer is they're not,
Right. That leads to the next one.
Why for a relativistic idiot Cantor's
(and any other except Euclidean set)
theorems are (proven so undeniable)
and Pythagorean theorem (and any other
from Euclidean set) is (proven
but counterexampled).
Where does the-a difference come from?
Not from the proofs, we already agreed
(?) that. Would it be possible that
mathematical proofs are really just
some smokescreen for pure faith?
Not necessarily, since proofs are believable.
Well, proofs of Pythagorean theorem HAVE
BEEN believable - for 2000 years - until
some idiots asserted they're really not and
waved-a their arms. How-a does it correspond to
"neo-Platonism", Epicurean sense-relations,
occamism and nominalism?
The "riddle of induction" is that since the time
of Aristotle, with both prior and posterior analytics,
since Philo and Plotinus the "neo-Platonists",
a simple inductive half-account grounded in the
Epicurean sense-relations simply makes for
Occamism the nominalism a bare skein of truth,
since its greater account demands experience of reason.
Then, that it's "truth" involved is a matter of
the voluntary, has that it's a tragedy that since
the humility demands letting it be optional,
that the vainglorious twist it.
Or, you know, it varies.
The "strong mathematical platonism", though,
and the "strong logicist positivism", together,
may make for better than a "weak logicist positivism".
Make for better, you say? Any proof
of that? What does "better" mean,
anyway?
Anyway, when the culture recognizes a string
of letters as good for itself it's getting
the stamp "true" to be repeated. When the
culture recognizes a string of letters-a as
not good for itself it's getting the stamp
"false"to be blocked. That's basically it.
Mistakes happen.
Now if you read something like the "T-theory,
A-theory, theatheory" thread, after that
"The fundamental joke of logic" bit,
where I made all the AI reasoners of the
day fall in line and agree to converge,
these might answer your questions.
Then, here, about "Galaxies don't fly apart
because their entire frame is rotating",
where I begin to describe why Dark Matter
is really Luminous Matter that's been
misunderstood, and about continuum mechanics
and all, then at least there's a Mathematical
Foundations that's strong.
And it's stronger than Euclidean theory
- because....
Axiomless natural geometry: may arrive after
inference itself after axiomless natural deduction
On 2/10/2026 4:56 PM, Ross Finlayson wrote:
On 02/10/2026 07:29 AM, Maciej Wo+|niak wrote:
On 2/10/2026 4:17 PM, Ross Finlayson wrote:
On 02/10/2026 06:05 AM, Maciej Wo+|niak wrote:
On 2/10/2026 2:30 PM, Ross Finlayson wrote:
On 02/10/2026 03:44 AM, Maciej Wo+|niak wrote:
On 2/10/2026 10:54 AM, Ross Finlayson wrote:
On 02/10/2026 01:17 AM, Maciej Wo+|niak wrote:
On 2/10/2026 9:27 AM, Ross Finlayson wrote:
On 02/10/2026 12:21 AM, Maciej Wo+|niak wrote:
On 2/10/2026 8:35 AM, Ross Finlayson wrote:
On 02/04/2026 07:55 AM, Python wrote:
Le 04/02/2026 |a 16:48, Maciej Wo+|niak a |-crit :
On 2/4/2026 3:19 PM, Thomas 'PointedEars' Lahn wrote: >>>>>>>>>>>>>>> Thomas 'PointedEars' Lahn wrote:
One must distinguish between a function that is >>>>>>>>>>>>>>>> _identically_Actually, one has to be even more careful with one's >>>>>>>>>>>>>>> wording.
zero,
i.e.
whose value is zero _everywhere_, and a function whose >>>>>>>>>>>>>>>> value is
zero
_for a
finite number of arguments in its domain_.
> The derivative of the former function *is* actually >>>>>>>>>>>>>>>> zero
because
it is a
special case of a constant function, but the derivative of >>>>>>>>>>>>>>>> the
latter
function is not necessarily zero.
As we can see from periodic functions like the sine >>>>>>>>>>>>>>> function,
it is
even
possible that a function is zero for a countably infinite >>>>>>>>>>>>>>> number of
arguments (e.g. all integer multiples of -C) but still not >>>>>>>>>>>>>>> all
arguments.
And one can even think of a pathological case: The Dirichlet >>>>>>>>>>>>>>> function
1_raU(x) = {1 if x ree raU;
0 if x ree raU
is zero for *uncountably* infinitely many arguments in its >>>>>>>>>>>>>>> domain
because
they are real numbers but not rational numbers, and >>>>>>>>>>>>>>> non-zero for
*countably*
infinitely made arguments in its domain because they are >>>>>>>>>>>>>>> rational
numbers
(the latter are members of a countably infinite set, as >>>>>>>>>>>>>>> Cantor
proved).
Thomas, poor trash, Pythagoreas has proven
that for any right triangle a^2+b^2 =c^2.
Than a hundred of others provided a hundred
of independent proofs for the same.
Did it prevent idiots like yourself
from denying that?
Do you think Cantor's theorems are more
proven?
It is, to say the least, somewhat surreal to have a
discussion on
the
fondations of mathematics and the status of mathematical >>>>>>>>>>>>> truth,
theorems, etc. involving Maciej Wozniak.
The ontological status of mathematical truth involves
the teleological status of mathematical truth as is
a usual conversation of Derrida on Husserl "proto-geometry". >>>>>>>>>>>
But this pseudophilosophical mumble is no
answer to the question whether Cantor's
theorems are proven somehow better than
Pythagorean.
Well that's simple, they're both what they are,
then the issue must be underneath them both, that
they have made what results mostly a usual ignorance
about the law of large numbers being the law of small numbers. >>>>>>>>>>
Somebody like Hilbert with a "postulate of continuity"
after somebody like Leibnitz with a "postulate of perfection" >>>>>>>>>> or otherwise making lines from points or points from lines, >>>>>>>>>> harken to Xenocrates and Democritus, or about that Aristotle >>>>>>>>>> has at least two models of continua.
Integer Continuum <- Duns Scotus, Spinoza
Line-Reals <- Xenocrates, Hilbert
Field-Reals <- Archimedes, Weierstrass
Signal-Reals <- Shannon/Nyquist
Long-Line Continuum <- duBois-Reymond
But this pseudophilosophical mumble (well,
I can delete pseudo, but I can't delete mumble)
is no answer to the question whether Cantor's
theorems are proven somehow better than
Pythagorean.
The answer is they're not,
Right. That leads to the next one.
Why for a relativistic idiot Cantor's
(and any other except Euclidean set)
theorems are (proven so undeniable)
and Pythagorean theorem (and any other
from Euclidean set) is (proven
but counterexampled).
Where does the difference come from?
Not from the proofs, we already agreed
(?) that. Would it be possible that
mathematical proofs are really just
some smokescreen for pure faith?
Not necessarily, since proofs are believable.
Well, proofs of Pythagorean theorem HAVE
BEEN believable - for 2000 years - until
some idiots asserted they're really not and
waved their arms. How does it correspond to
"neo-Platonism", Epicurean sense-relations,
occamism and nominalism?
The "riddle of induction" is that since the time
of Aristotle, with both prior and posterior analytics,
since Philo and Plotinus the "neo-Platonists",
a simple inductive half-account grounded in the
Epicurean sense-relations simply makes for
Occamism the nominalism a bare skein of truth,
since its greater account demands experience of reason.
Then, that it's "truth" involved is a matter of
the voluntary, has that it's a tragedy that since
the humility demands letting it be optional,
that the vainglorious twist it.
Or, you know, it varies.
The "strong mathematical platonism", though,
and the "strong logicist positivism", together,
may make for better than a "weak logicist positivism".
Make for better, you say? Any proof
of that? What does "better" mean,
anyway?
Anyway, when the culture recognizes a string
of letters as good for itself it's getting
the stamp "true" to be repeated. When the
culture recognizes a string of letters as
not good for itself it's getting the stamp
"false"to be blocked. That's basically it.
Mistakes happen.
Now if you read something like the "T-theory,
A-theory, theatheory" thread, after that
"The fundamental joke of logic" bit,
where I made all the AI reasoners of the
day fall in line and agree to converge,
these might answer your questions.
Then, here, about "Galaxies don't fly apart
because their entire frame is rotating",
where I begin to describe why Dark Matter
is really Luminous Matter that's been
misunderstood, and about continuum mechanics
and all, then at least there's a Mathematical
Foundations that's strong.
And it's stronger than Euclidean theory
- because....
Axiomless natural geometry: may arrive after
inference itself after axiomless natural deduction
And jedi knights may wave their lightsabers.
The truth is, however, an evolutionary
[thus - random, but not quite] fluctuation
of our culture, and so is logic.
On 02/10/2026 08:10 AM, Maciej Wo+|niak wrote:
On 2/10/2026 4:56 PM, Ross Finlayson wrote:
On 02/10/2026 07:29 AM, Maciej Wo+|niak wrote:
On 2/10/2026 4:17 PM, Ross Finlayson wrote:
On 02/10/2026 06:05 AM, Maciej Wo+|niak wrote:
On 2/10/2026 2:30 PM, Ross Finlayson wrote:
On 02/10/2026 03:44 AM, Maciej Wo+|niak wrote:
On 2/10/2026 10:54 AM, Ross Finlayson wrote:
On 02/10/2026 01:17 AM, Maciej Wo+|niak wrote:
On 2/10/2026 9:27 AM, Ross Finlayson wrote:
On 02/10/2026 12:21 AM, Maciej Wo+|niak wrote:
On 2/10/2026 8:35 AM, Ross Finlayson wrote:
On 02/04/2026 07:55 AM, Python wrote:
Le 04/02/2026 |a 16:48, Maciej Wo+|niak a |-crit : >>>>>>>>>>>>>>> On 2/4/2026 3:19 PM, Thomas 'PointedEars' Lahn wrote: >>>>>>>>>>>>>>>> Thomas 'PointedEars' Lahn wrote:
One must distinguish between a function that is >>>>>>>>>>>>>>>>> _identically_Actually, one has to be even more careful with one's >>>>>>>>>>>>>>>> wording.
zero,
i.e.
whose value is zero _everywhere_, and a function whose >>>>>>>>>>>>>>>>> value is
zero
_for a
finite number of arguments in its domain_.
-a > The derivative of the former function *is* actually >>>>>>>>>>>>>>>>> zero
because
it is a
special case of a constant function, but the derivative of >>>>>>>>>>>>>>>>> the
latter
function is not necessarily zero.
As we can see from periodic functions like the sine >>>>>>>>>>>>>>>> function,
it is
even
possible that a function is zero for a countably infinite >>>>>>>>>>>>>>>> number of
arguments (e.g. all integer multiples of -C) but still not >>>>>>>>>>>>>>>> all
arguments.
And one can even think of a pathological case: The >>>>>>>>>>>>>>>> Dirichlet
function
-a-a 1_raU(x) = {1 if x ree raU;
-a-a-a-a-a-a-a-a-a-a-a-a 0 if x ree raU
is zero for *uncountably* infinitely many arguments in its >>>>>>>>>>>>>>>> domain
because
they are real numbers but not rational numbers, and >>>>>>>>>>>>>>>> non-zero for
*countably*
infinitely made arguments in its domain because they are >>>>>>>>>>>>>>>> rational
numbers
(the latter are members of a countably infinite set, as >>>>>>>>>>>>>>>> Cantor
proved).
Thomas, poor trash, Pythagoreas has proven
that for any right triangle a^2+b^2 =c^2.
Than a hundred of others provided-a a hundred
of independent proofs for the same.
Did it prevent-a idiots like yourself
from denying-a that?
Do you think Cantor's theorems are more
proven?
It is, to say the least, somewhat surreal to have a >>>>>>>>>>>>>> discussion on
the
fondations of mathematics and the status of mathematical >>>>>>>>>>>>>> truth,
theorems, etc. involving Maciej Wozniak.
The ontological status of mathematical truth involves >>>>>>>>>>>>> the teleological status of mathematical truth as is
a usual conversation of Derrida on Husserl "proto-geometry". >>>>>>>>>>>>
But this pseudophilosophical mumble is no
answer to the question whether Cantor's
theorems are proven somehow better than
Pythagorean.
Well that's simple, they're both what they are,
then the issue must be underneath them both, that
they have made what results mostly a usual ignorance
about the law of large numbers being the law of small numbers. >>>>>>>>>>>
Somebody like Hilbert with a "postulate of continuity"
after somebody like Leibnitz with a "postulate of perfection" >>>>>>>>>>> or otherwise making lines from points or points from lines, >>>>>>>>>>> harken to Xenocrates and Democritus, or about that Aristotle >>>>>>>>>>> has at least two models of continua.
Integer Continuum <- Duns Scotus, Spinoza
Line-Reals <- Xenocrates, Hilbert
Field-Reals <- Archimedes, Weierstrass
Signal-Reals <- Shannon/Nyquist
Long-Line Continuum <- duBois-Reymond
But this pseudophilosophical mumble (well,
I can delete pseudo, but I can't delete mumble)
is no answer to the question whether Cantor's
theorems are proven somehow better than
Pythagorean.
The answer is they're not,
Right. That leads to the next one.
Why for a relativistic idiot Cantor's
(and any other except Euclidean set)
theorems are (proven so undeniable)
and Pythagorean theorem (and any other
from Euclidean set) is (proven
but counterexampled).
Where does the-a difference come from?
Not from the proofs, we already agreed
(?) that. Would it be possible that
mathematical proofs are really just
some smokescreen for pure faith?
Not necessarily, since proofs are believable.
Well, proofs of Pythagorean theorem HAVE
BEEN believable - for 2000 years - until
some idiots asserted they're really not and
waved-a their arms. How-a does it correspond to
"neo-Platonism", Epicurean sense-relations,
occamism and nominalism?
The "riddle of induction" is that since the time
of Aristotle, with both prior and posterior analytics,
since Philo and Plotinus the "neo-Platonists",
a simple inductive half-account grounded in the
Epicurean sense-relations simply makes for
Occamism the nominalism a bare skein of truth,
since its greater account demands experience of reason.
Then, that it's "truth" involved is a matter of
the voluntary, has that it's a tragedy that since
the humility demands letting it be optional,
that the vainglorious twist it.
Or, you know, it varies.
The "strong mathematical platonism", though,
and the "strong logicist positivism", together,
may make for better than a "weak logicist positivism".
Make for better, you say? Any proof
of that? What does "better" mean,
anyway?
Anyway, when the culture recognizes a string
of letters as good for itself it's getting
the stamp "true" to be repeated. When the
culture recognizes a string of letters-a as
not good for itself it's getting the stamp
"false"to be blocked. That's basically it.
Mistakes happen.
Now if you read something like the "T-theory,
A-theory, theatheory" thread, after that
"The fundamental joke of logic" bit,
where I made all the AI reasoners of the
day fall in line and agree to converge,
these might answer your questions.
Then, here, about "Galaxies don't fly apart
because their entire frame is rotating",
where I begin to describe why Dark Matter
is really Luminous Matter that's been
misunderstood, and about continuum mechanics
and all, then at least there's a Mathematical
Foundations that's strong.
And it's stronger than Euclidean theory
- because....
Axiomless natural geometry: may arrive after
inference itself after axiomless natural deduction
And jedi knights may wave their lightsabers.
The truth is, however, an evolutionary
[thus - random, but not quite] fluctuation
of our culture, and so is logic.
It's Euclidean, ....
It's a "strong super-euclidean geometry".
Don't worry, you can't break it with logic.
On 2/10/2026 5:15 PM, Ross Finlayson wrote:
On 02/10/2026 08:10 AM, Maciej Wo+|niak wrote:
On 2/10/2026 4:56 PM, Ross Finlayson wrote:
On 02/10/2026 07:29 AM, Maciej Wo+|niak wrote:
On 2/10/2026 4:17 PM, Ross Finlayson wrote:
On 02/10/2026 06:05 AM, Maciej Wo+|niak wrote:
On 2/10/2026 2:30 PM, Ross Finlayson wrote:
On 02/10/2026 03:44 AM, Maciej Wo+|niak wrote:
On 2/10/2026 10:54 AM, Ross Finlayson wrote:
On 02/10/2026 01:17 AM, Maciej Wo+|niak wrote:
On 2/10/2026 9:27 AM, Ross Finlayson wrote:
On 02/10/2026 12:21 AM, Maciej Wo+|niak wrote:
On 2/10/2026 8:35 AM, Ross Finlayson wrote:
On 02/04/2026 07:55 AM, Python wrote:
Le 04/02/2026 |a 16:48, Maciej Wo+|niak a |-crit : >>>>>>>>>>>>>>>> On 2/4/2026 3:19 PM, Thomas 'PointedEars' Lahn wrote: >>>>>>>>>>>>>>>>> Thomas 'PointedEars' Lahn wrote:
One must distinguish between a function that is >>>>>>>>>>>>>>>>>> _identically_Actually, one has to be even more careful with one's >>>>>>>>>>>>>>>>> wording.
zero,
i.e.
whose value is zero _everywhere_, and a function whose >>>>>>>>>>>>>>>>>> value is
zero
_for a
finite number of arguments in its domain_. >>>>>>>>>>>>>>>>>> > The derivative of the former function *is* actually >>>>>>>>>>>>>>>>>> zero
because
it is a
special case of a constant function, but the >>>>>>>>>>>>>>>>>> derivative of
the
latter
function is not necessarily zero.
As we can see from periodic functions like the sine >>>>>>>>>>>>>>>>> function,
it is
even
possible that a function is zero for a countably infinite >>>>>>>>>>>>>>>>> number of
arguments (e.g. all integer multiples of -C) but still not >>>>>>>>>>>>>>>>> all
arguments.
And one can even think of a pathological case: The >>>>>>>>>>>>>>>>> Dirichlet
function
1_raU(x) = {1 if x ree raU;
0 if x ree raU
is zero for *uncountably* infinitely many arguments in its >>>>>>>>>>>>>>>>> domain
because
they are real numbers but not rational numbers, and >>>>>>>>>>>>>>>>> non-zero for
*countably*
infinitely made arguments in its domain because they are >>>>>>>>>>>>>>>>> rational
numbers
(the latter are members of a countably infinite set, as >>>>>>>>>>>>>>>>> Cantor
proved).
Thomas, poor trash, Pythagoreas has proven
that for any right triangle a^2+b^2 =c^2.
Than a hundred of others provided a hundred
of independent proofs for the same.
Did it prevent idiots like yourself
from denying that?
Do you think Cantor's theorems are more
proven?
It is, to say the least, somewhat surreal to have a >>>>>>>>>>>>>>> discussion on
the
fondations of mathematics and the status of mathematical >>>>>>>>>>>>>>> truth,
theorems, etc. involving Maciej Wozniak.
The ontological status of mathematical truth involves >>>>>>>>>>>>>> the teleological status of mathematical truth as is >>>>>>>>>>>>>> a usual conversation of Derrida on Husserl "proto-geometry". >>>>>>>>>>>>>
But this pseudophilosophical mumble is no
answer to the question whether Cantor's
theorems are proven somehow better than
Pythagorean.
Well that's simple, they're both what they are,
then the issue must be underneath them both, that
they have made what results mostly a usual ignorance
about the law of large numbers being the law of small numbers. >>>>>>>>>>>>
Somebody like Hilbert with a "postulate of continuity" >>>>>>>>>>>> after somebody like Leibnitz with a "postulate of perfection" >>>>>>>>>>>> or otherwise making lines from points or points from lines, >>>>>>>>>>>> harken to Xenocrates and Democritus, or about that Aristotle >>>>>>>>>>>> has at least two models of continua.
Integer Continuum <- Duns Scotus, Spinoza
Line-Reals <- Xenocrates, Hilbert
Field-Reals <- Archimedes, Weierstrass
Signal-Reals <- Shannon/Nyquist
Long-Line Continuum <- duBois-Reymond
But this pseudophilosophical mumble (well,
I can delete pseudo, but I can't delete mumble)
is no answer to the question whether Cantor's
theorems are proven somehow better than
Pythagorean.
The answer is they're not,
Right. That leads to the next one.
Why for a relativistic idiot Cantor's
(and any other except Euclidean set)
theorems are (proven so undeniable)
and Pythagorean theorem (and any other
from Euclidean set) is (proven
but counterexampled).
Where does the difference come from?
Not from the proofs, we already agreed
(?) that. Would it be possible that
mathematical proofs are really just
some smokescreen for pure faith?
Not necessarily, since proofs are believable.
Well, proofs of Pythagorean theorem HAVE
BEEN believable - for 2000 years - until
some idiots asserted they're really not and
waved their arms. How does it correspond to
"neo-Platonism", Epicurean sense-relations,
occamism and nominalism?
The "riddle of induction" is that since the time
of Aristotle, with both prior and posterior analytics,
since Philo and Plotinus the "neo-Platonists",
a simple inductive half-account grounded in the
Epicurean sense-relations simply makes for
Occamism the nominalism a bare skein of truth,
since its greater account demands experience of reason.
Then, that it's "truth" involved is a matter of
the voluntary, has that it's a tragedy that since
the humility demands letting it be optional,
that the vainglorious twist it.
Or, you know, it varies.
The "strong mathematical platonism", though,
and the "strong logicist positivism", together,
may make for better than a "weak logicist positivism".
Make for better, you say? Any proof
of that? What does "better" mean,
anyway?
Anyway, when the culture recognizes a string
of letters as good for itself it's getting
the stamp "true" to be repeated. When the
culture recognizes a string of letters as
not good for itself it's getting the stamp
"false"to be blocked. That's basically it.
Mistakes happen.
Now if you read something like the "T-theory,
A-theory, theatheory" thread, after that
"The fundamental joke of logic" bit,
where I made all the AI reasoners of the
day fall in line and agree to converge,
these might answer your questions.
Then, here, about "Galaxies don't fly apart
because their entire frame is rotating",
where I begin to describe why Dark Matter
is really Luminous Matter that's been
misunderstood, and about continuum mechanics
and all, then at least there's a Mathematical
Foundations that's strong.
And it's stronger than Euclidean theory
- because....
Axiomless natural geometry: may arrive after
inference itself after axiomless natural deduction
And jedi knights may wave their lightsabers.
The truth is, however, an evolutionary
[thus - random, but not quite] fluctuation
of our culture, and so is logic.
It's Euclidean, ....
It's a "strong super-euclidean geometry".
Doesn't matter.
Don't worry, you can't break it with logic.
Logic is greatly overestimated, it never
worked against faith. And anyway, breaking
with it anything it can break would be as
wise as it is in the case of muscles.
On 02/10/2026 08:31 AM, Maciej Wo+|niak wrote:
On 2/10/2026 5:15 PM, Ross Finlayson wrote:
On 02/10/2026 08:10 AM, Maciej Wo+|niak wrote:
On 2/10/2026 4:56 PM, Ross Finlayson wrote:
On 02/10/2026 07:29 AM, Maciej Wo+|niak wrote:
On 2/10/2026 4:17 PM, Ross Finlayson wrote:
On 02/10/2026 06:05 AM, Maciej Wo+|niak wrote:
On 2/10/2026 2:30 PM, Ross Finlayson wrote:
On 02/10/2026 03:44 AM, Maciej Wo+|niak wrote:
On 2/10/2026 10:54 AM, Ross Finlayson wrote:
On 02/10/2026 01:17 AM, Maciej Wo+|niak wrote:
On 2/10/2026 9:27 AM, Ross Finlayson wrote:
On 02/10/2026 12:21 AM, Maciej Wo+|niak wrote:
On 2/10/2026 8:35 AM, Ross Finlayson wrote:
On 02/04/2026 07:55 AM, Python wrote:
Le 04/02/2026 |a 16:48, Maciej Wo+|niak a |-crit : >>>>>>>>>>>>>>>>> On 2/4/2026 3:19 PM, Thomas 'PointedEars' Lahn wrote: >>>>>>>>>>>>>>>>>> Thomas 'PointedEars' Lahn wrote:
One must distinguish between a function that is >>>>>>>>>>>>>>>>>>> _identically_Actually, one has to be even more careful with one's >>>>>>>>>>>>>>>>>> wording.
zero,
i.e.
whose value is zero _everywhere_, and a function whose >>>>>>>>>>>>>>>>>>> value is
zero
_for a
finite number of arguments in its domain_. >>>>>>>>>>>>>>>>>>> > The derivative of the former function *is* actually >>>>>>>>>>>>>>>>>>> zero
because
it is a
special case of a constant function, but the >>>>>>>>>>>>>>>>>>> derivative of
the
latter
function is not necessarily zero.
As we can see from periodic functions like the sine >>>>>>>>>>>>>>>>>> function,
it is
even
possible that a function is zero for a countably infinite >>>>>>>>>>>>>>>>>> number of
arguments (e.g. all integer multiples of -C) but still not >>>>>>>>>>>>>>>>>> all
arguments.
And one can even think of a pathological case: The >>>>>>>>>>>>>>>>>> Dirichlet
function
1_raU(x) = {1 if x ree raU;
0 if x ree raU
is zero for *uncountably* infinitely many arguments in >>>>>>>>>>>>>>>>>> its
domain
because
they are real numbers but not rational numbers, and >>>>>>>>>>>>>>>>>> non-zero for
*countably*
infinitely made arguments in its domain because they are >>>>>>>>>>>>>>>>>> rational
numbers
(the latter are members of a countably infinite set, as >>>>>>>>>>>>>>>>>> Cantor
proved).
Thomas, poor trash, Pythagoreas has proven
that for any right triangle a^2+b^2 =c^2.
Than a hundred of others provided a hundred >>>>>>>>>>>>>>>>> of independent proofs for the same.
Did it prevent idiots like yourself
from denying that?
Do you think Cantor's theorems are more
proven?
It is, to say the least, somewhat surreal to have a >>>>>>>>>>>>>>>> discussion on
the
fondations of mathematics and the status of mathematical >>>>>>>>>>>>>>>> truth,
theorems, etc. involving Maciej Wozniak.
The ontological status of mathematical truth involves >>>>>>>>>>>>>>> the teleological status of mathematical truth as is >>>>>>>>>>>>>>> a usual conversation of Derrida on Husserl "proto-geometry". >>>>>>>>>>>>>>
But this pseudophilosophical mumble is no
answer to the question whether Cantor's
theorems are proven somehow better than
Pythagorean.
Well that's simple, they're both what they are,
then the issue must be underneath them both, that
they have made what results mostly a usual ignorance >>>>>>>>>>>>> about the law of large numbers being the law of small numbers. >>>>>>>>>>>>>
Somebody like Hilbert with a "postulate of continuity" >>>>>>>>>>>>> after somebody like Leibnitz with a "postulate of perfection" >>>>>>>>>>>>> or otherwise making lines from points or points from lines, >>>>>>>>>>>>> harken to Xenocrates and Democritus, or about that Aristotle >>>>>>>>>>>>> has at least two models of continua.
Integer Continuum <- Duns Scotus, Spinoza
Line-Reals <- Xenocrates, Hilbert
Field-Reals <- Archimedes, Weierstrass
Signal-Reals <- Shannon/Nyquist
Long-Line Continuum <- duBois-Reymond
But this pseudophilosophical mumble (well,
I can delete pseudo, but I can't delete mumble)
is no answer to the question whether Cantor's
theorems are proven somehow better than
Pythagorean.
The answer is they're not,
Right. That leads to the next one.
Why for a relativistic idiot Cantor's
(and any other except Euclidean set)
theorems are (proven so undeniable)
and Pythagorean theorem (and any other
from Euclidean set) is (proven
but counterexampled).
Where does the difference come from?
Not from the proofs, we already agreed
(?) that. Would it be possible that
mathematical proofs are really just
some smokescreen for pure faith?
Not necessarily, since proofs are believable.
Well, proofs of Pythagorean theorem HAVE
BEEN believable - for 2000 years - until
some idiots asserted they're really not and
waved their arms. How does it correspond to
"neo-Platonism", Epicurean sense-relations,
occamism and nominalism?
The "riddle of induction" is that since the time
of Aristotle, with both prior and posterior analytics,
since Philo and Plotinus the "neo-Platonists",
a simple inductive half-account grounded in the
Epicurean sense-relations simply makes for
Occamism the nominalism a bare skein of truth,
since its greater account demands experience of reason.
Then, that it's "truth" involved is a matter of
the voluntary, has that it's a tragedy that since
the humility demands letting it be optional,
that the vainglorious twist it.
Or, you know, it varies.
The "strong mathematical platonism", though,
and the "strong logicist positivism", together,
may make for better than a "weak logicist positivism".
Make for better, you say? Any proof
of that? What does "better" mean,
anyway?
Anyway, when the culture recognizes a string
of letters as good for itself it's getting
the stamp "true" to be repeated. When the
culture recognizes a string of letters as
not good for itself it's getting the stamp
"false"to be blocked. That's basically it.
Mistakes happen.
Now if you read something like the "T-theory,
A-theory, theatheory" thread, after that
"The fundamental joke of logic" bit,
where I made all the AI reasoners of the
day fall in line and agree to converge,
these might answer your questions.
Then, here, about "Galaxies don't fly apart
because their entire frame is rotating",
where I begin to describe why Dark Matter
is really Luminous Matter that's been
misunderstood, and about continuum mechanics
and all, then at least there's a Mathematical
Foundations that's strong.
And it's stronger than Euclidean theory
- because....
Axiomless natural geometry: may arrive after
inference itself after axiomless natural deduction
And jedi knights may wave their lightsabers.
The truth is, however, an evolutionary
[thus - random, but not quite] fluctuation
of our culture, and so is logic.
It's Euclidean, ....
It's a "strong super-euclidean geometry".
Doesn't matter.
Don't worry, you can't break it with logic.
Logic is greatly overestimated, it never
worked against faith. And anyway, breaking
with it anything it can break would be as
wise as it is in the case of muscles.
It's not just a good idea, ....
On 02/10/2026 08:32 AM, Ross Finlayson wrote:
On 02/10/2026 08:31 AM, Maciej Wo+|niak wrote:
On 2/10/2026 5:15 PM, Ross Finlayson wrote:
On 02/10/2026 08:10 AM, Maciej Wo+|niak wrote:
On 2/10/2026 4:56 PM, Ross Finlayson wrote:
On 02/10/2026 07:29 AM, Maciej Wo+|niak wrote:
On 2/10/2026 4:17 PM, Ross Finlayson wrote:
On 02/10/2026 06:05 AM, Maciej Wo+|niak wrote:
On 2/10/2026 2:30 PM, Ross Finlayson wrote:
On 02/10/2026 03:44 AM, Maciej Wo+|niak wrote:
On 2/10/2026 10:54 AM, Ross Finlayson wrote:
On 02/10/2026 01:17 AM, Maciej Wo+|niak wrote:
On 2/10/2026 9:27 AM, Ross Finlayson wrote:
On 02/10/2026 12:21 AM, Maciej Wo+|niak wrote:
On 2/10/2026 8:35 AM, Ross Finlayson wrote:
On 02/04/2026 07:55 AM, Python wrote:
Le 04/02/2026 |a 16:48, Maciej Wo+|niak a |-crit : >>>>>>>>>>>>>>>>>> On 2/4/2026 3:19 PM, Thomas 'PointedEars' Lahn wrote: >>>>>>>>>>>>>>>>>>> Thomas 'PointedEars' Lahn wrote:
One must distinguish between a function that is >>>>>>>>>>>>>>>>>>>> _identically_Actually, one has to be even more careful with one's >>>>>>>>>>>>>>>>>>> wording.
zero,
i.e.
whose value is zero _everywhere_, and a function whose >>>>>>>>>>>>>>>>>>>> value is
zero
_for a
finite number of arguments in its domain_. >>>>>>>>>>>>>>>>>>>> > The derivative of the former function *is* actually >>>>>>>>>>>>>>>>>>>> zero
because
it is a
special case of a constant function, but the >>>>>>>>>>>>>>>>>>>> derivative of
the
latter
function is not necessarily zero.
As we can see from periodic functions like the sine >>>>>>>>>>>>>>>>>>> function,
it is
even
possible that a function is zero for a countably >>>>>>>>>>>>>>>>>>> infinite
number of
arguments (e.g. all integer multiples of -C) but still >>>>>>>>>>>>>>>>>>> not
all
arguments.
And one can even think of a pathological case: The >>>>>>>>>>>>>>>>>>> Dirichlet
function
1_raU(x) = {1 if x ree raU;
0 if x ree raU
is zero for *uncountably* infinitely many arguments in >>>>>>>>>>>>>>>>>>> its
domain
because
they are real numbers but not rational numbers, and >>>>>>>>>>>>>>>>>>> non-zero for
*countably*
infinitely made arguments in its domain because they are >>>>>>>>>>>>>>>>>>> rational
numbers
(the latter are members of a countably infinite set, as >>>>>>>>>>>>>>>>>>> Cantor
proved).
Thomas, poor trash, Pythagoreas has proven >>>>>>>>>>>>>>>>>> that for any right triangle a^2+b^2 =c^2.
Than a hundred of others provided a hundred >>>>>>>>>>>>>>>>>> of independent proofs for the same.
Did it prevent idiots like yourself
from denying that?
Do you think Cantor's theorems are more
proven?
It is, to say the least, somewhat surreal to have a >>>>>>>>>>>>>>>>> discussion on
the
fondations of mathematics and the status of mathematical >>>>>>>>>>>>>>>>> truth,
theorems, etc. involving Maciej Wozniak.
The ontological status of mathematical truth involves >>>>>>>>>>>>>>>> the teleological status of mathematical truth as is >>>>>>>>>>>>>>>> a usual conversation of Derrida on Husserl
"proto-geometry".
But this pseudophilosophical mumble is no
answer to the question whether Cantor's
theorems are proven somehow better than
Pythagorean.
Well that's simple, they're both what they are,
then the issue must be underneath them both, that
they have made what results mostly a usual ignorance >>>>>>>>>>>>>> about the law of large numbers being the law of small >>>>>>>>>>>>>> numbers.
Somebody like Hilbert with a "postulate of continuity" >>>>>>>>>>>>>> after somebody like Leibnitz with a "postulate of perfection" >>>>>>>>>>>>>> or otherwise making lines from points or points from lines, >>>>>>>>>>>>>> harken to Xenocrates and Democritus, or about that Aristotle >>>>>>>>>>>>>> has at least two models of continua.
Integer Continuum <- Duns Scotus, Spinoza
Line-Reals <- Xenocrates, Hilbert
Field-Reals <- Archimedes, Weierstrass
Signal-Reals <- Shannon/Nyquist
Long-Line Continuum <- duBois-Reymond
But this pseudophilosophical mumble (well,
I can delete pseudo, but I can't delete mumble)
is no answer to the question whether Cantor's
theorems are proven somehow better than
Pythagorean.
The answer is they're not,
Right. That leads to the next one.
Why for a relativistic idiot Cantor's
(and any other except Euclidean set)
theorems are (proven so undeniable)
and Pythagorean theorem (and any other
from Euclidean set) is (proven
but counterexampled).
Where does the difference come from?
Not from the proofs, we already agreed
(?) that. Would it be possible that
mathematical proofs are really just
some smokescreen for pure faith?
Not necessarily, since proofs are believable.
Well, proofs of Pythagorean theorem HAVE
BEEN believable - for 2000 years - until
some idiots asserted they're really not and
waved their arms. How does it correspond to
"neo-Platonism", Epicurean sense-relations,
occamism and nominalism?
The "riddle of induction" is that since the time
of Aristotle, with both prior and posterior analytics,
since Philo and Plotinus the "neo-Platonists",
a simple inductive half-account grounded in the
Epicurean sense-relations simply makes for
Occamism the nominalism a bare skein of truth,
since its greater account demands experience of reason.
Then, that it's "truth" involved is a matter of
the voluntary, has that it's a tragedy that since
the humility demands letting it be optional,
that the vainglorious twist it.
Or, you know, it varies.
The "strong mathematical platonism", though,
and the "strong logicist positivism", together,
may make for better than a "weak logicist positivism".
Make for better, you say? Any proof
of that? What does "better" mean,
anyway?
Anyway, when the culture recognizes a string
of letters as good for itself it's getting
the stamp "true" to be repeated. When the
culture recognizes a string of letters as
not good for itself it's getting the stamp
"false"to be blocked. That's basically it.
Mistakes happen.
Now if you read something like the "T-theory,
A-theory, theatheory" thread, after that
"The fundamental joke of logic" bit,
where I made all the AI reasoners of the
day fall in line and agree to converge,
these might answer your questions.
Then, here, about "Galaxies don't fly apart
because their entire frame is rotating",
where I begin to describe why Dark Matter
is really Luminous Matter that's been
misunderstood, and about continuum mechanics
and all, then at least there's a Mathematical
Foundations that's strong.
And it's stronger than Euclidean theory
- because....
Axiomless natural geometry: may arrive after
inference itself after axiomless natural deduction
And jedi knights may wave their lightsabers.
The truth is, however, an evolutionary
[thus - random, but not quite] fluctuation
of our culture, and so is logic.
It's Euclidean, ....
It's a "strong super-euclidean geometry".
Doesn't matter.
Don't worry, you can't break it with logic.
Logic is greatly overestimated, it never
worked against faith. And anyway, breaking
with it anything it can break would be as
wise as it is in the case of muscles.
It's not just a good idea, ....
See, pretty simple.
"Logos 2000: Foundations briefly"
https://www.youtube.com/watch?v=fjtXZ5mBVOc&list=PLb7rLSBiE7F795DGcwSvwHj-GEbdhPJNe&index=40
This video essay briefly outlines Mathematical Foundations
with regards to "infinity" and "continuity", modernly.
There are a number of comments elicited from
one of those "AI systems" these days.
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