I want to call people's attention to a YouTube video "Time in physics and intuitionistic mathematics", which is a lecture by Nicolas Gisin, who has a very good reputation in the field of quantum physics.

https://youtu.be/3qKXRTUUd7E

Here's a quote from his lecture that appears in large letters in one of his slides:

"The mathematical language we use when speaking physics has a huge influence on the worldview that physics presents to us"

In this lecture, he presents an argument that intuitionistic mathematics is the right mathematical foundation for quantum mechanics, and that classical mathematics has actually held back progess in the field.

Ok, I realize that people in this newsgroup have little interest in intuitionistic mathematics, and even less interest in physics. So let me just repeat a point I've been making forever and ever: Someday, classical (Cantorian) mathematics will be seen as a wrong turn in the development of the foundations of mathematics.

David Petry wrote:
>
>
> I want to call people's attention to a YouTube video "Time in physics and intuitionistic mathematics", which is a lecture by Nicolas Gisin, who has a very good reputation in the field of quantum physics.
>
> https://youtu.be/3qKXRTUUd7E
>
> Here's a quote from his lecture that appears in large letters in one of his slides:
>
> "The mathematical language we use when speaking physics has a huge influence on the worldview that physics presents to us"
>
> In this lecture, he presents an argument that intuitionistic mathematics is the right mathematical foundation for quantum mechanics, and that classical mathematics has actually held back progess in the field.
>
> Ok, I realize that people in this newsgroup have little interest in intuitionistic mathematics, and even less interest in physics.

Quite the opposite. But you, David, has shown *no* interest at all to
intuitionistic mathematics when actual work from this field was pointed
out to you. Clearly, repeatedly and explicitely.

> So let me just repeat a point I've been making forever and ever: Someday, classical (Cantorian) mathematics will be seen as a wrong turn in the development of the foundations of mathematics.

If you knew only a little about intuitionistic logic you would know that
your claim is absurd.

Why did you turn the back on maths when you were a student instead
of studying intuitionist logic and maths? I know the answer.

classical ≠ Cantorian

In classical set theory free use is made of the logical
principle known as the Law of Excluded Middle (LEM):
for any proposition p, either p holds or its negation ~p holds.
As we see below, there are a number of intriguing mathematical
possibilities which are rendered inconsistent with classical set
theory solely as a result of the presence of LEM. This suggests
the idea of dropping LEM in set- theoretical arguments, or, more
precisely, basing set theory on intuitionistic logic. Accordingly,
let us define Intuitionistic Set Theory (IST) to be any of the
usual axiomatic set theories (e.g. Zermelo-Fraenkel set theory ZF)
based on intuitionistic – rather than classical - logic.
https://publish.uwo.ca/~jbell/INTBOOK(Repaired).pdf

Now you got an intuitionistic Cantorian paradise.

In particular:

Perhaps Cantor’s most celebrated theorem is the uncountability
of the set R of real numbers. Cantor first published a proof of
this theorem in 1874, but much better known is his second proof,
published in 1890, in which he introduces his famous method of
“diagonalization”. In essence, Cantor’s argument establishes that
the set of all maps is uncountable in the above sense. For given
a map g: the map f: defined by
(*) f(n) = g(n)(n) + 1
clearly cannot belong to range(g), so that g cannot be surjective.
This argument does not use LEM, and is in fact perfectly
valid within IST.

Python schrieb am Donnerstag, 12. August 2021 um 17:17:02 UTC+2:
> David Petry wrote:
> >
> >
> > I want to call people's attention to a YouTube video "Time in physics and intuitionistic mathematics", which is a lecture by Nicolas Gisin, who has a very good reputation in the field of quantum physics.
> >
> > https://youtu.be/3qKXRTUUd7E
> >
> > Here's a quote from his lecture that appears in large letters in one of his slides:
> >
> > "The mathematical language we use when speaking physics has a huge influence on the worldview that physics presents to us"
> >
> > In this lecture, he presents an argument that intuitionistic mathematics is the right mathematical foundation for quantum mechanics, and that classical mathematics has actually held back progess in the field.
> >
> > Ok, I realize that people in this newsgroup have little interest in intuitionistic mathematics, and even less interest in physics.
> Quite the opposite. But you, David, has shown *no* interest at all to
> intuitionistic mathematics when actual work from this field was pointed
> out to you. Clearly, repeatedly and explicitely.
> > So let me just repeat a point I've been making forever and ever: Someday, classical (Cantorian) mathematics will be seen as a wrong turn in the development of the foundations of mathematics.
> If you knew only a little about intuitionistic logic you would know that
> your claim is absurd.
>
> Why did you turn the back on maths when you were a student instead
> of studying intuitionist logic and maths? I know the answer.

That Cantor’s most celebrated theorem goes trough in
IST might have to do that intuitionistic logic has still reduction
ad absurdum, so this is valid in intuitionistic logic:

G, A |- ff
-----------------
G |- ~A

Is there a computer proof of Bells claim?

Mostowski Collapse schrieb am Donnerstag, 12. August 2021 um 18:10:34 UTC+2:
> classical ≠ Cantorian
>
> In classical set theory free use is made of the logical
> principle known as the Law of Excluded Middle (LEM):
> for any proposition p, either p holds or its negation ~p holds.
> As we see below, there are a number of intriguing mathematical
> possibilities which are rendered inconsistent with classical set
> theory solely as a result of the presence of LEM. This suggests
> the idea of dropping LEM in set- theoretical arguments, or, more
> precisely, basing set theory on intuitionistic logic. Accordingly,
> let us define Intuitionistic Set Theory (IST) to be any of the
> usual axiomatic set theories (e.g. Zermelo-Fraenkel set theory ZF)
> based on intuitionistic – rather than classical - logic.
> https://publish.uwo.ca/~jbell/INTBOOK(Repaired).pdf
>
> Now you got an intuitionistic Cantorian paradise.
>
> In particular:
>
> Perhaps Cantor’s most celebrated theorem is the uncountability
> of the set R of real numbers. Cantor first published a proof of
> this theorem in 1874, but much better known is his second proof,
> published in 1890, in which he introduces his famous method of
> “diagonalization”. In essence, Cantor’s argument establishes that
> the set of all maps is uncountable in the above sense. For given
> a map g: the map f: defined by
> (*) f(n) = g(n)(n) + 1
> clearly cannot belong to range(g), so that g cannot be surjective.
> This argument does not use LEM, and is in fact perfectly
> valid within IST.
> Python schrieb am Donnerstag, 12. August 2021 um 17:17:02 UTC+2:
> > David Petry wrote:
> > >
> > >
> > > I want to call people's attention to a YouTube video "Time in physics and intuitionistic mathematics", which is a lecture by Nicolas Gisin, who has a very good reputation in the field of quantum physics.
> > >
> > > https://youtu.be/3qKXRTUUd7E
> > >
> > > Here's a quote from his lecture that appears in large letters in one of his slides:
> > >
> > > "The mathematical language we use when speaking physics has a huge influence on the worldview that physics presents to us"
> > >
> > > In this lecture, he presents an argument that intuitionistic mathematics is the right mathematical foundation for quantum mechanics, and that classical mathematics has actually held back progess in the field.
> > >
> > > Ok, I realize that people in this newsgroup have little interest in intuitionistic mathematics, and even less interest in physics.
> > Quite the opposite. But you, David, has shown *no* interest at all to
> > intuitionistic mathematics when actual work from this field was pointed
> > out to you. Clearly, repeatedly and explicitely.
> > > So let me just repeat a point I've been making forever and ever: Someday, classical (Cantorian) mathematics will be seen as a wrong turn in the development of the foundations of mathematics.
> > If you knew only a little about intuitionistic logic you would know that
> > your claim is absurd.
> >
> > Why did you turn the back on maths when you were a student instead
> > of studying intuitionist logic and maths? I know the answer.

On 8/12/2021 9:19 AM, David Petry wrote:
>
>
> I want to call people's attention to a YouTube video "Time in physics and intuitionistic mathematics", which is a lecture by Nicolas Gisin, who has a very good reputation in the field of quantum physics.
>
> https://youtu.be/3qKXRTUUd7E
>
> Here's a quote from his lecture that appears in large letters in one of his slides:
>
> "The mathematical language we use when speaking physics has a huge influence on the worldview that physics presents to us"
>
> In this lecture, he presents an argument that intuitionistic mathematics is the right mathematical foundation for quantum mechanics, and that classical mathematics has actually held back progess in the field.

Intuitionistic mathematics for QM, sure,
you are dense. (insert UA rant here)

>
> Ok, I realize that people in this newsgroup have little interest in intuitionistic mathematics, and even less interest in physics. So let me just repeat a point I've been making forever and ever: Someday, classical (Cantorian) mathematics will be seen as a wrong turn in the development of the foundations of mathematics.

QM thinks you retard.

Go ahead with your Creative Cantorian Chanting in yer Closet.

I always use Set Theory on QM. - David Petry

On 8/12/2021 11:10 AM, Mostowski Collapse wrote:
> classical ≠ Cantorian
>
> In classical set theory free use is made of the logical
> principle known as the Law of Excluded Middle (LEM):
> for any proposition p, either p holds or its negation ~p holds.
> As we see below, there are a number of intriguing mathematical
> possibilities which are rendered inconsistent with classical set
> theory solely as a result of the presence of LEM. This suggests
> the idea of dropping LEM in set- theoretical arguments, or, more
> precisely, basing set theory on intuitionistic logic. Accordingly,
> let us define Intuitionistic Set Theory (IST) to be any of the
> usual axiomatic set theories (e.g. Zermelo-Fraenkel set theory ZF)
> based on intuitionistic – rather than classical - logic.
> https://publish.uwo.ca/~jbell/INTBOOK(Repaired).pdf
>
> Now you got an intuitionistic Cantorian paradise.
>
> In particular:
>
> Perhaps Cantor’s most celebrated theorem is the uncountability
> of the set R of real numbers. Cantor first published a proof of
> this theorem in 1874, but much better known is his second proof,
> published in 1890, in which he introduces his famous method of
> “diagonalization”. In essence, Cantor’s argument establishes that
> the set of all maps is uncountable in the above sense. For given
> a map g: the map f: defined by
> (*) f(n) = g(n)(n) + 1
> clearly cannot belong to range(g), so that g cannot be surjective.
> This argument does not use LEM, and is in fact perfectly
> valid within IST.
>
> Python schrieb am Donnerstag, 12. August 2021 um 17:17:02 UTC+2:
>> David Petry wrote:
>>>
>>>
>>> I want to call people's attention to a YouTube video "Time in physics and intuitionistic mathematics", which is a lecture by Nicolas Gisin, who has a very good reputation in the field of quantum physics.
>>>
>>> https://youtu.be/3qKXRTUUd7E
>>>
>>> Here's a quote from his lecture that appears in large letters in one of his slides:
>>>
>>> "The mathematical language we use when speaking physics has a huge influence on the worldview that physics presents to us"
>>>
>>> In this lecture, he presents an argument that intuitionistic mathematics is the right mathematical foundation for quantum mechanics, and that classical mathematics has actually held back progess in the field.
>>>
>>> Ok, I realize that people in this newsgroup have little interest in intuitionistic mathematics, and even less interest in physics.
>> Quite the opposite. But you, David, has shown *no* interest at all to
>> intuitionistic mathematics when actual work from this field was pointed
>> out to you. Clearly, repeatedly and explicitely.
>>> So let me just repeat a point I've been making forever and ever: Someday, classical (Cantorian) mathematics will be seen as a wrong turn in the development of the foundations of mathematics.
>> If you knew only a little about intuitionistic logic you would know that
>> your claim is absurd.
>>
>> Why did you turn the back on maths when you were a student instead
>> of studying intuitionist logic and maths? I know the answer.

Phycists and mathematicians both calculate in time.

On Thursday, August 12, 2021 at 9:10:34 AM UTC-7, Mostowski Collapse wrote:
> classical ≠ Cantorian
>
> In classical set theory free use is made of the logical
> principle known as the Law of Excluded Middle (LEM):
> for any proposition p, either p holds or its negation ~p holds.
> As we see below, there are a number of intriguing mathematical
> possibilities which are rendered inconsistent with classical set
> theory solely as a result of the presence of LEM. This suggests
> the idea of dropping LEM in set- theoretical arguments, or, more
> precisely, basing set theory on intuitionistic logic. Accordingly,
> let us define Intuitionistic Set Theory (IST) to be any of the
> usual axiomatic set theories (e.g. Zermelo-Fraenkel set theory ZF)
> based on intuitionistic – rather than classical - logic.
> https://publish.uwo.ca/~jbell/INTBOOK(Repaired).pdf
>
> Now you got an intuitionistic Cantorian paradise.
>
> In particular:
>
> Perhaps Cantor’s most celebrated theorem is the uncountability
> of the set R of real numbers. Cantor first published a proof of
> this theorem in 1874, but much better known is his second proof,
> published in 1890, in which he introduces his famous method of
> “diagonalization”. In essence, Cantor’s argument establishes that
> the set of all maps is uncountable in the above sense. For given
> a map g: the map f: defined by
> (*) f(n) = g(n)(n) + 1
> clearly cannot belong to range(g), so that g cannot be surjective.
> This argument does not use LEM, and is in fact perfectly
> valid within IST.
> Python schrieb am Donnerstag, 12. August 2021 um 17:17:02 UTC+2:
> > David Petry wrote:
> > >
> > >
> > > I want to call people's attention to a YouTube video "Time in physics and intuitionistic mathematics", which is a lecture by Nicolas Gisin, who has a very good reputation in the field of quantum physics.
> > >
> > > https://youtu.be/3qKXRTUUd7E
> > >
> > > Here's a quote from his lecture that appears in large letters in one of his slides:
> > >
> > > "The mathematical language we use when speaking physics has a huge influence on the worldview that physics presents to us"
> > >
> > > In this lecture, he presents an argument that intuitionistic mathematics is the right mathematical foundation for quantum mechanics, and that classical mathematics has actually held back progess in the field.
> > >
> > > Ok, I realize that people in this newsgroup have little interest in intuitionistic mathematics, and even less interest in physics.
> > Quite the opposite. But you, David, has shown *no* interest at all to
> > intuitionistic mathematics when actual work from this field was pointed
> > out to you. Clearly, repeatedly and explicitely.
> > > So let me just repeat a point I've been making forever and ever: Someday, classical (Cantorian) mathematics will be seen as a wrong turn in the development of the foundations of mathematics.
> > If you knew only a little about intuitionistic logic you would know that
> > your claim is absurd.
> >
> > Why did you turn the back on maths when you were a student instead
> > of studying intuitionist logic and maths? I know the answer.

Intuitionism seems comes from the Brouwerian,
as from the time it's held up as exemplar, though really
it's just a free sense of deductive inference.

Constructivism is usual and the rule,
for conscientious formalists.

The tertium non datur aka LEM aka PEM,
the law or principle of excluded middle,
isn't so much for writing out contradictions
in the intuitionist as not writing them out
in the constructive, which requires objects
with what properties after quantifier disambiguation,
explains why there is a middle.

The "para-consistent" here is the goal in after
the dialetheic, or in terms an "infra-consistency".

Physics need mathematics of infinity because
it's a continuum mechanics, for example at
"the edge of chaos, or the quasi-invariant after measure"
it's as simple as that 1/n goes to zero but n/n goes to one,
what is intuitive about the middle here constructively either way.

Ultrafilters, infinitesimals, grossone, a Cantor space
with half sequences half-1's/half-0's, time is a quantity
is quite most concisely modeled by line-drawing.

Keep in mind a difference "spaces in words" and "spaces in numbers".

Time follows a course-of-passage through values in [0,1].

On Thursday, August 12, 2021 at 11:58:51 AM UTC-7, Ross A. Finlayson wrote:
> On Thursday, August 12, 2021 at 9:10:34 AM UTC-7, Mostowski Collapse wrote:
> > classical ≠ Cantorian
> >
> > In classical set theory free use is made of the logical
> > principle known as the Law of Excluded Middle (LEM):
> > for any proposition p, either p holds or its negation ~p holds.
> > As we see below, there are a number of intriguing mathematical
> > possibilities which are rendered inconsistent with classical set
> > theory solely as a result of the presence of LEM. This suggests
> > the idea of dropping LEM in set- theoretical arguments, or, more
> > precisely, basing set theory on intuitionistic logic. Accordingly,
> > let us define Intuitionistic Set Theory (IST) to be any of the
> > usual axiomatic set theories (e.g. Zermelo-Fraenkel set theory ZF)
> > based on intuitionistic – rather than classical - logic.
> > https://publish.uwo.ca/~jbell/INTBOOK(Repaired).pdf
> >
> > Now you got an intuitionistic Cantorian paradise.
> >
> > In particular:
> >
> > Perhaps Cantor’s most celebrated theorem is the uncountability
> > of the set R of real numbers. Cantor first published a proof of
> > this theorem in 1874, but much better known is his second proof,
> > published in 1890, in which he introduces his famous method of
> > “diagonalization”. In essence, Cantor’s argument establishes that
> > the set of all maps is uncountable in the above sense. For given
> > a map g: the map f: defined by
> > (*) f(n) = g(n)(n) + 1
> > clearly cannot belong to range(g), so that g cannot be surjective.
> > This argument does not use LEM, and is in fact perfectly
> > valid within IST.
> > Python schrieb am Donnerstag, 12. August 2021 um 17:17:02 UTC+2:
> > > David Petry wrote:
> > > >
> > > >
> > > > I want to call people's attention to a YouTube video "Time in physics and intuitionistic mathematics", which is a lecture by Nicolas Gisin, who has a very good reputation in the field of quantum physics.
> > > >
> > > > https://youtu.be/3qKXRTUUd7E
> > > >
> > > > Here's a quote from his lecture that appears in large letters in one of his slides:
> > > >
> > > > "The mathematical language we use when speaking physics has a huge influence on the worldview that physics presents to us"
> > > >
> > > > In this lecture, he presents an argument that intuitionistic mathematics is the right mathematical foundation for quantum mechanics, and that classical mathematics has actually held back progess in the field.
> > > >
> > > > Ok, I realize that people in this newsgroup have little interest in intuitionistic mathematics, and even less interest in physics.
> > > Quite the opposite. But you, David, has shown *no* interest at all to
> > > intuitionistic mathematics when actual work from this field was pointed
> > > out to you. Clearly, repeatedly and explicitely.
> > > > So let me just repeat a point I've been making forever and ever: Someday, classical (Cantorian) mathematics will be seen as a wrong turn in the development of the foundations of mathematics.
> > > If you knew only a little about intuitionistic logic you would know that
> > > your claim is absurd.
> > >
> > > Why did you turn the back on maths when you were a student instead
> > > of studying intuitionist logic and maths? I know the answer.
> Intuitionism seems comes from the Brouwerian,
> as from the time it's held up as exemplar, though really
> it's just a free sense of deductive inference.
>
> Constructivism is usual and the rule,
> for conscientious formalists.
>
> The tertium non datur aka LEM aka PEM,
> the law or principle of excluded middle,
> isn't so much for writing out contradictions
> in the intuitionist as not writing them out
> in the constructive, which requires objects
> with what properties after quantifier disambiguation,
> explains why there is a middle.
>
> The "para-consistent" here is the goal in after
> the dialetheic, or in terms an "infra-consistency".
>
> Physics need mathematics of infinity because
> it's a continuum mechanics, for example at
> "the edge of chaos, or the quasi-invariant after measure"
> it's as simple as that 1/n goes to zero but n/n goes to one,
> what is intuitive about the middle here constructively either way.
>
> Ultrafilters, infinitesimals, grossone, a Cantor space
> with half sequences half-1's/half-0's, time is a quantity
> is quite most concisely modeled by line-drawing.
>
> Keep in mind a difference "spaces in words" and "spaces in numbers".
>
> Time follows a course-of-passage through values in [0,1].

People have their fake version of intuition...

On Thursday, August 12, 2021 at 12:05:31 PM UTC-7, mitchr...@gmail.com wrote:
> On Thursday, August 12, 2021 at 11:58:51 AM UTC-7, Ross A. Finlayson wrote:
> > On Thursday, August 12, 2021 at 9:10:34 AM UTC-7, Mostowski Collapse wrote:
> > > classical ≠ Cantorian
> > >
> > > In classical set theory free use is made of the logical
> > > principle known as the Law of Excluded Middle (LEM):
> > > for any proposition p, either p holds or its negation ~p holds.
> > > As we see below, there are a number of intriguing mathematical
> > > possibilities which are rendered inconsistent with classical set
> > > theory solely as a result of the presence of LEM. This suggests
> > > the idea of dropping LEM in set- theoretical arguments, or, more
> > > precisely, basing set theory on intuitionistic logic. Accordingly,
> > > let us define Intuitionistic Set Theory (IST) to be any of the
> > > usual axiomatic set theories (e.g. Zermelo-Fraenkel set theory ZF)
> > > based on intuitionistic – rather than classical - logic.
> > > https://publish.uwo.ca/~jbell/INTBOOK(Repaired).pdf
> > >
> > > Now you got an intuitionistic Cantorian paradise.
> > >
> > > In particular:
> > >
> > > Perhaps Cantor’s most celebrated theorem is the uncountability
> > > of the set R of real numbers. Cantor first published a proof of
> > > this theorem in 1874, but much better known is his second proof,
> > > published in 1890, in which he introduces his famous method of
> > > “diagonalization”. In essence, Cantor’s argument establishes that
> > > the set of all maps is uncountable in the above sense. For given
> > > a map g: the map f: defined by
> > > (*) f(n) = g(n)(n) + 1
> > > clearly cannot belong to range(g), so that g cannot be surjective.
> > > This argument does not use LEM, and is in fact perfectly
> > > valid within IST.
> > > Python schrieb am Donnerstag, 12. August 2021 um 17:17:02 UTC+2:
> > > > David Petry wrote:
> > > > >
> > > > >
> > > > > I want to call people's attention to a YouTube video "Time in physics and intuitionistic mathematics", which is a lecture by Nicolas Gisin, who has a very good reputation in the field of quantum physics.
> > > > >
> > > > > https://youtu.be/3qKXRTUUd7E
> > > > >
> > > > > Here's a quote from his lecture that appears in large letters in one of his slides:
> > > > >
> > > > > "The mathematical language we use when speaking physics has a huge influence on the worldview that physics presents to us"
> > > > >
> > > > > In this lecture, he presents an argument that intuitionistic mathematics is the right mathematical foundation for quantum mechanics, and that classical mathematics has actually held back progess in the field.
> > > > >
> > > > > Ok, I realize that people in this newsgroup have little interest in intuitionistic mathematics, and even less interest in physics.
> > > > Quite the opposite. But you, David, has shown *no* interest at all to
> > > > intuitionistic mathematics when actual work from this field was pointed
> > > > out to you. Clearly, repeatedly and explicitely.
> > > > > So let me just repeat a point I've been making forever and ever: Someday, classical (Cantorian) mathematics will be seen as a wrong turn in the development of the foundations of mathematics.
> > > > If you knew only a little about intuitionistic logic you would know that
> > > > your claim is absurd.
> > > >
> > > > Why did you turn the back on maths when you were a student instead
> > > > of studying intuitionist logic and maths? I know the answer.
> > Intuitionism seems comes from the Brouwerian,
> > as from the time it's held up as exemplar, though really
> > it's just a free sense of deductive inference.
> >
> > Constructivism is usual and the rule,
> > for conscientious formalists.
> >
> > The tertium non datur aka LEM aka PEM,
> > the law or principle of excluded middle,
> > isn't so much for writing out contradictions
> > in the intuitionist as not writing them out
> > in the constructive, which requires objects
> > with what properties after quantifier disambiguation,
> > explains why there is a middle.
> >
> > The "para-consistent" here is the goal in after
> > the dialetheic, or in terms an "infra-consistency".
> >
> > Physics need mathematics of infinity because
> > it's a continuum mechanics, for example at
> > "the edge of chaos, or the quasi-invariant after measure"
> > it's as simple as that 1/n goes to zero but n/n goes to one,
> > what is intuitive about the middle here constructively either way.
> >
> > Ultrafilters, infinitesimals, grossone, a Cantor space
> > with half sequences half-1's/half-0's, time is a quantity
> > is quite most concisely modeled by line-drawing.
> >
> > Keep in mind a difference "spaces in words" and "spaces in numbers".
> >
> > Time follows a course-of-passage through values in [0,1].
> People have their fake version of intuition...

Right or Wrong: right or wrong.

On Thursday, August 12, 2021 at 12:23:52 PM UTC-7, Ross A. Finlayson wrote:
> On Thursday, August 12, 2021 at 12:05:31 PM UTC-7, mitchr...@gmail.com wrote:
> > On Thursday, August 12, 2021 at 11:58:51 AM UTC-7, Ross A. Finlayson wrote:
> > > On Thursday, August 12, 2021 at 9:10:34 AM UTC-7, Mostowski Collapse wrote:
> > > > classical ≠ Cantorian
> > > >
> > > > In classical set theory free use is made of the logical
> > > > principle known as the Law of Excluded Middle (LEM):
> > > > for any proposition p, either p holds or its negation ~p holds.
> > > > As we see below, there are a number of intriguing mathematical
> > > > possibilities which are rendered inconsistent with classical set
> > > > theory solely as a result of the presence of LEM. This suggests
> > > > the idea of dropping LEM in set- theoretical arguments, or, more
> > > > precisely, basing set theory on intuitionistic logic. Accordingly,
> > > > let us define Intuitionistic Set Theory (IST) to be any of the
> > > > usual axiomatic set theories (e.g. Zermelo-Fraenkel set theory ZF)
> > > > based on intuitionistic – rather than classical - logic.
> > > > https://publish.uwo.ca/~jbell/INTBOOK(Repaired).pdf
> > > >
> > > > Now you got an intuitionistic Cantorian paradise.
> > > >
> > > > In particular:
> > > >
> > > > Perhaps Cantor’s most celebrated theorem is the uncountability
> > > > of the set R of real numbers. Cantor first published a proof of
> > > > this theorem in 1874, but much better known is his second proof,
> > > > published in 1890, in which he introduces his famous method of
> > > > “diagonalization”. In essence, Cantor’s argument establishes that
> > > > the set of all maps is uncountable in the above sense. For given
> > > > a map g: the map f: defined by
> > > > (*) f(n) = g(n)(n) + 1
> > > > clearly cannot belong to range(g), so that g cannot be surjective.
> > > > This argument does not use LEM, and is in fact perfectly
> > > > valid within IST.
> > > > Python schrieb am Donnerstag, 12. August 2021 um 17:17:02 UTC+2:
> > > > > David Petry wrote:
> > > > > >
> > > > > >
> > > > > > I want to call people's attention to a YouTube video "Time in physics and intuitionistic mathematics", which is a lecture by Nicolas Gisin, who has a very good reputation in the field of quantum physics.
> > > > > >
> > > > > > https://youtu.be/3qKXRTUUd7E
> > > > > >
> > > > > > Here's a quote from his lecture that appears in large letters in one of his slides:
> > > > > >
> > > > > > "The mathematical language we use when speaking physics has a huge influence on the worldview that physics presents to us"
> > > > > >
> > > > > > In this lecture, he presents an argument that intuitionistic mathematics is the right mathematical foundation for quantum mechanics, and that classical mathematics has actually held back progess in the field.
> > > > > >
> > > > > > Ok, I realize that people in this newsgroup have little interest in intuitionistic mathematics, and even less interest in physics.
> > > > > Quite the opposite. But you, David, has shown *no* interest at all to
> > > > > intuitionistic mathematics when actual work from this field was pointed
> > > > > out to you. Clearly, repeatedly and explicitely.
> > > > > > So let me just repeat a point I've been making forever and ever: Someday, classical (Cantorian) mathematics will be seen as a wrong turn in the development of the foundations of mathematics.
> > > > > If you knew only a little about intuitionistic logic you would know that
> > > > > your claim is absurd.
> > > > >
> > > > > Why did you turn the back on maths when you were a student instead
> > > > > of studying intuitionist logic and maths? I know the answer.
> > > Intuitionism seems comes from the Brouwerian,
> > > as from the time it's held up as exemplar, though really
> > > it's just a free sense of deductive inference.
> > >
> > > Constructivism is usual and the rule,
> > > for conscientious formalists.
> > >
> > > The tertium non datur aka LEM aka PEM,
> > > the law or principle of excluded middle,
> > > isn't so much for writing out contradictions
> > > in the intuitionist as not writing them out
> > > in the constructive, which requires objects
> > > with what properties after quantifier disambiguation,
> > > explains why there is a middle.
> > >
> > > The "para-consistent" here is the goal in after
> > > the dialetheic, or in terms an "infra-consistency".
> > >
> > > Physics need mathematics of infinity because
> > > it's a continuum mechanics, for example at
> > > "the edge of chaos, or the quasi-invariant after measure"
> > > it's as simple as that 1/n goes to zero but n/n goes to one,
> > > what is intuitive about the middle here constructively either way.
> > >
> > > Ultrafilters, infinitesimals, grossone, a Cantor space
> > > with half sequences half-1's/half-0's, time is a quantity
> > > is quite most concisely modeled by line-drawing.
> > >
> > > Keep in mind a difference "spaces in words" and "spaces in numbers".
> > >
> > > Time follows a course-of-passage through values in [0,1].
> > People have their fake version of intuition...

If scientists and mathematicians are calculating they will
have to calculate forever and that does not end.
Calculating to infinity has never belonged...
Science will never go completely accurate.

Mitchell Raemsch

On Thursday, August 12, 2021 at 12:36:23 PM UTC-7, mitchr...@gmail.com wrote:
> On Thursday, August 12, 2021 at 12:23:52 PM UTC-7, Ross A. Finlayson wrote:
> > On Thursday, August 12, 2021 at 12:05:31 PM UTC-7, mitchr...@gmail.com wrote:
> > > On Thursday, August 12, 2021 at 11:58:51 AM UTC-7, Ross A. Finlayson wrote:
> > > > On Thursday, August 12, 2021 at 9:10:34 AM UTC-7, Mostowski Collapse wrote:
> > > > > classical ≠ Cantorian
> > > > >
> > > > > In classical set theory free use is made of the logical
> > > > > principle known as the Law of Excluded Middle (LEM):
> > > > > for any proposition p, either p holds or its negation ~p holds.
> > > > > As we see below, there are a number of intriguing mathematical
> > > > > possibilities which are rendered inconsistent with classical set
> > > > > theory solely as a result of the presence of LEM. This suggests
> > > > > the idea of dropping LEM in set- theoretical arguments, or, more
> > > > > precisely, basing set theory on intuitionistic logic. Accordingly,
> > > > > let us define Intuitionistic Set Theory (IST) to be any of the
> > > > > usual axiomatic set theories (e.g. Zermelo-Fraenkel set theory ZF)
> > > > > based on intuitionistic – rather than classical - logic.
> > > > > https://publish.uwo.ca/~jbell/INTBOOK(Repaired).pdf
> > > > >
> > > > > Now you got an intuitionistic Cantorian paradise.
> > > > >
> > > > > In particular:
> > > > >
> > > > > Perhaps Cantor’s most celebrated theorem is the uncountability
> > > > > of the set R of real numbers. Cantor first published a proof of
> > > > > this theorem in 1874, but much better known is his second proof,
> > > > > published in 1890, in which he introduces his famous method of
> > > > > “diagonalization”. In essence, Cantor’s argument establishes that
> > > > > the set of all maps is uncountable in the above sense. For given
> > > > > a map g: the map f: defined by
> > > > > (*) f(n) = g(n)(n) + 1
> > > > > clearly cannot belong to range(g), so that g cannot be surjective..
> > > > > This argument does not use LEM, and is in fact perfectly
> > > > > valid within IST.
> > > > > Python schrieb am Donnerstag, 12. August 2021 um 17:17:02 UTC+2:
> > > > > > David Petry wrote:
> > > > > > >
> > > > > > >
> > > > > > > I want to call people's attention to a YouTube video "Time in physics and intuitionistic mathematics", which is a lecture by Nicolas Gisin, who has a very good reputation in the field of quantum physics.
> > > > > > >
> > > > > > > https://youtu.be/3qKXRTUUd7E
> > > > > > >
> > > > > > > Here's a quote from his lecture that appears in large letters in one of his slides:
> > > > > > >
> > > > > > > "The mathematical language we use when speaking physics has a huge influence on the worldview that physics presents to us"
> > > > > > >
> > > > > > > In this lecture, he presents an argument that intuitionistic mathematics is the right mathematical foundation for quantum mechanics, and that classical mathematics has actually held back progess in the field.
> > > > > > >
> > > > > > > Ok, I realize that people in this newsgroup have little interest in intuitionistic mathematics, and even less interest in physics.
> > > > > > Quite the opposite. But you, David, has shown *no* interest at all to
> > > > > > intuitionistic mathematics when actual work from this field was pointed
> > > > > > out to you. Clearly, repeatedly and explicitely.
> > > > > > > So let me just repeat a point I've been making forever and ever: Someday, classical (Cantorian) mathematics will be seen as a wrong turn in the development of the foundations of mathematics.
> > > > > > If you knew only a little about intuitionistic logic you would know that
> > > > > > your claim is absurd.
> > > > > >
> > > > > > Why did you turn the back on maths when you were a student instead
> > > > > > of studying intuitionist logic and maths? I know the answer.
> > > > Intuitionism seems comes from the Brouwerian,
> > > > as from the time it's held up as exemplar, though really
> > > > it's just a free sense of deductive inference.
> > > >
> > > > Constructivism is usual and the rule,
> > > > for conscientious formalists.
> > > >
> > > > The tertium non datur aka LEM aka PEM,
> > > > the law or principle of excluded middle,
> > > > isn't so much for writing out contradictions
> > > > in the intuitionist as not writing them out
> > > > in the constructive, which requires objects
> > > > with what properties after quantifier disambiguation,
> > > > explains why there is a middle.
> > > >
> > > > The "para-consistent" here is the goal in after
> > > > the dialetheic, or in terms an "infra-consistency".
> > > >
> > > > Physics need mathematics of infinity because
> > > > it's a continuum mechanics, for example at
> > > > "the edge of chaos, or the quasi-invariant after measure"
> > > > it's as simple as that 1/n goes to zero but n/n goes to one,
> > > > what is intuitive about the middle here constructively either way.
> > > >
> > > > Ultrafilters, infinitesimals, grossone, a Cantor space
> > > > with half sequences half-1's/half-0's, time is a quantity
> > > > is quite most concisely modeled by line-drawing.
> > > >
> > > > Keep in mind a difference "spaces in words" and "spaces in numbers"..
> > > >
> > > > Time follows a course-of-passage through values in [0,1].
> > > People have their fake version of intuition...
> If scientists and mathematicians are calculating they will
> have to calculate forever and that does not end.
> Calculating to infinity has never belonged...
> Science will never go completely accurate.
>
> Mitchell Raemsch

Still, the Computer Algebra System can operate formulaically,
before farming to the fields the abacus.

The whole point is get formulas for example the forms for
real analysis what work out _perfectly_, according to a theory
of infinite limits, besides noting that numerical methods and
means of approximation though exhausting have error terms.

Usual linear formulas are totally accurate.
Whether they're exhaustible in or under inputs is or isn't so....

Fundamentally there's a unified organization.

torsdag 12 augusti 2021 kl. 16:19:10 UTC+2 skrev david...@gmail.com:
> I want to call people's attention to a YouTube video "Time in physics and intuitionistic mathematics", which is a lecture by Nicolas Gisin, who has a very good reputation in the field of quantum physics.
>
> https://youtu.be/3qKXRTUUd7E
>
> Here's a quote from his lecture that appears in large letters in one of his slides:
>
> "The mathematical language we use when speaking physics has a huge influence on the worldview that physics presents to us"
>
> In this lecture, he presents an argument that intuitionistic mathematics is the right mathematical foundation for quantum mechanics, and that classical mathematics has actually held back progess in the field.
>
> Ok, I realize that people in this newsgroup have little interest in intuitionistic mathematics, and even less interest in physics. So let me just repeat a point I've been making forever and ever: Someday, classical (Cantorian) mathematics will be seen as a wrong turn in the development of the foundations of mathematics.

It won't be seen as that unless you can show an inherent contradiction that cannot be avoided with it.

Good luck with this!

On Sunday, August 15, 2021 at 10:14:20 PM UTC-7, zelos...@gmail.com wrote:
> torsdag 12 augusti 2021 kl. 16:19:10 UTC+2 skrev david...@gmail.com:

>> Someday, classical (Cantorian) mathematics will be seen as a wrong turn in the development of the foundations of mathematics.

> It won't be seen as that unless you can show an inherent contradiction that cannot be avoided with it.
> Good luck with this!

How many times have you said I'm "retarded"? I don't count these things, but it's been a few times. Let me, just this once, return the compliment.

You are really really really retarded, Zelos.

There are other reasons mathematicians could have for choosing a different foundation for mathematics. Mathematicians could say, "let's remember what the purpose of mathematics is. Let's remember why society pays our salaries. It's because we produce something of value for society. To the extent that mathematics is of value to society, it's because the mathematics we produce serves as a conceptual framework for reasoning about the real world. But as more and more physicists and computer scientists are forced to switch to other foundations (e.g. intuitionism), we must think about the question of whether we made the right choice in following Cantor down his rabbit hole of different sizes of infinite sets. Did we make the right choice?"

>How many times have you said I'm "retarded"?

Not enough.

>You are really really really retarded, Zelos.

Feel free to say so, but I demonstrably know mathematics way better than you :)

>There are other reasons mathematicians could have for choosing a different foundation for mathematics.

There are, we mathematicians have discussed it many times but ZFC was chosen because it is elegant and powerful.

>Mathematicians could say, "let's remember what the purpose of mathematics is.

They DID, mathematics is about arguing and constructing ABSTRACT LOGICAL IDEAS.

>It's because we produce something of value for society.

Which they HAVE done for the last 200 years!

>it's because the mathematics we produce serves as a conceptual framework for reasoning about the real world

That is YOUR STUPID idea what "value" means, but that is not the idea the REST of the world thinks!

Mathematics HAS produced VALUE for ALL this time exactly BECAUSE it is separate.

>But as more and more physicists and computer scientists are forced to switch to other foundations (e.g. intuitionism),

Strange how they CONSTANTLY come to us mathematicians ASKING for things we ALREADY HAVE. Strange isn't it?

>we must think about the question of whether we made the right choice in following Cantor down his rabbit hole of different sizes of infinite sets. Did we make the right choice?"

Given mathematics has produced things that has helped humanity for the last 2 centuries and is always AHEAD of the need of sciences, the answer is YES, they made the right choice!

You cannot say anything bad about it because mathematics has ALWAYS in these centuries been AHEAD of the needs of sciences and engineering, and it couldn't be with your idiocy, the fact it CAN be this means it is RIGHT and the fact yorus CANT is why it is WRONG.

You ARE retarded.

David Petry submitted this idea :
> On Sunday, August 15, 2021 at 10:14:20 PM UTC-7, zelos...@gmail.com wrote:
>> torsdag 12 augusti 2021 kl. 16:19:10 UTC+2 skrev david...@gmail.com:
>
>>> Someday, classical (Cantorian) mathematics will be seen as a wrong turn in
>>> the development of the foundations of mathematics.
>
>> It won't be seen as that unless you can show an inherent contradiction that
>> cannot be avoided with it.
>
>> Good luck with this!
>
>
> How many times have you said I'm "retarded"? I don't count these things,
> but it's been a few times. Let me, just this once, return the compliment.
>
> You are really really really retarded, Zelos.
>
> There are other reasons mathematicians could have for choosing a different
> foundation for mathematics. Mathematicians could say, "let's remember what
> the purpose of mathematics is. Let's remember why society pays our salaries.
> It's because we produce something of value for society. To the extent that
> mathematics is of value to society, it's because the mathematics we produce
> serves as a conceptual framework for reasoning about the real world. But as
> more and more physicists and computer scientists are forced to switch to
> other foundations (e.g. intuitionism), we must think about the question of
> whether we made the right choice in following Cantor down his rabbit hole of
> different sizes of infinite sets. Did we make the right choice?"

How, in your scenario, would FLT (filed under 'yeah, but so what') get
generalized by Euler (filed under 'yeah, but it is just a bauble, a
gewgaw, an ornament, a trinket, of no practical use - so what) and
eventually find its way into being a very important part of our ability
to do e-commerce and have secure communications?

IMO your scenario cripples the best feature that mathematics has to
offer - exploration in pure mathematics without any regard to physics.
Shackling it with falsifiability requirements is counterproductive.

On Thursday, August 12, 2021 at 10:19:10 AM UTC-4, david...@gmail.com wrote:
> I want to call people's attention to a YouTube video "Time in physics and intuitionistic mathematics", which is a lecture by Nicolas Gisin, who has a very good reputation in the field of quantum physics.
>
> https://youtu.be/3qKXRTUUd7E
>
> Here's a quote from his lecture that appears in large letters in one of his slides:
>
> "The mathematical language we use when speaking physics has a huge influence on the worldview that physics presents to us"
>
> In this lecture, he presents an argument that intuitionistic mathematics is the right mathematical foundation for quantum mechanics, and that classical mathematics has actually held back progess in the field.
>
> Ok, I realize that people in this newsgroup have little interest in intuitionistic mathematics, and even less interest in physics. So let me just repeat a point I've been making forever and ever: Someday, classical (Cantorian) mathematics will be seen as a wrong turn in the development of the foundations of mathematics.

I did not give this video my full attention, but around 5.5 minutes in he gets into an anthropic principal that nearly marks doom. Still I did listen on, but not so seriously. It does seem like a serious attempt. As entertainment and possibly to spark your own ideas and variations it is good material. Yet the idea that a math ought to include the human's ability to discuss it is to obnoxiously overlook the human condition just as one inserts it into their fundamental consideration. It is obvious that we are not fully evolved. Clearly our linguistic skills could stand a further variation in FOXP2. That this would explain the human struggle is far more believable. Imagine the first class to get the gene splice (FOXP10) develops a new thinking and attempts to explain it to your average joe and it goes nowhere. I know it sounds familiar and of course it exposes a lack of compiler integrity even as mathematicians grant themselves a free ticket to that sort of ability. https://www.jneurosci.org/content/37/27/6575/tab-figures-data

To insert such an egotistical stance into a physics or math theory is a matter of tainted love and as to who did the tainting, well clearly it was the insertion of the human condition into the theory. The usage of an observer sits nearby to this but is of a generic form. To confess the human condition is good yet to claim that physics hinges upon it cannot be so good. Nearly all of us, brought up in a Taliban camp, would be living their laws. This is the human condition. Brought up in China you'd be speaking Chinese, no? How many of us have recovered Newton's laws of gravitation from scratch? Galileo's inclined plane experiments? Right: I'd just be watching the ball and enjoying its ride.

So the tension of the human condition is quite different than the anthropocentric theories allow for. We are more like mice squeaking against an avalanche, but squeak we must. https://www.youtube.com/watch?v=FyR0CSDxjkY