Here's the argument I have been making over the years:

1) The important purpose of mathematics is to provide a conceptual framework for reasoning about the real world. IOW, mathematics is the language of science.

2) We should apply Occam's razor when building a foundation for mathematics: we should minimize the number of assumptions we make, or as Einstein reportedly put it, everything (e.g. the foundations of mathematics) should be as simple as possible, but no simpler.

3) Every abstract principle that is essential for reasoning about the real world (i.e. essential to science) should be formalized and integrated into the foundations of mathematics. Mathematicians should accept it as their moral responsibility to produce something that is beneficial to society.

4) Over the last century or so, there have been several advances in our understanding of scientific reasoning for which there have not been any corresponding advances in mathematical reasoning, and this is something that needs to be corrected.

5) The advances in scientific reasoning that I mention most often include reasoning under uncertainty and falsifiability, though there are others. These can and should be formalized and integrated into mathematics at the foundational level.

6)The reason that mathematicians reject the ideas that I put forth is because if they accepted them, they would be forced to admit that Cantor's set theory is not essential for scientific reasoning, and does not belong in mathematics. Cantor's set theory cannot be included in a consistent way with the modern advances in scientific reasoning that I suggest should be accepted as part of mathematical reasoning.

7) Since there are many outspoken mathematicians who label anyone who suggests that Cantor's set theory doesn't belong in mathematics as a stupid, delusional crank (or worse), and the mathematics community as a whole does nothing to reign in these outspoken mathematicians, the (pure) mathematics community as a whole should be seen as fraudulent.

David Petry <davidlpetry@gmail.com> wrote:

> Here's the argument I have been making over the years:

> 1) The important purpose of mathematics is to provide a conceptual
> framework for reasoning about the real world. IOW, mathematics is the
> language of science.

_An_ important purpose, but not the primary one.

> 2) We should apply Occam's razor when building a foundation for
> mathematics: we should minimize the number of assumptions we make, or
> as Einstein reportedly put it, everything (e.g. the foundations of
> mathematics) should be as simple as possible, but no simpler.

This is currently done. The foundations of maths are currently based on
set theory, which only contains a small number of axioms.

> 3) Every abstract principle that is essential for reasoning about the
> real world (i.e. essential to science) should be formalized and
> integrated into the foundations of mathematics. Mathematicians should
> accept it as their moral responsibility to produce something that is
> beneficial to society.

Why should they, any more than any other academics, or indeed anybody
else at all?

> 4) Over the last century or so, there have been several advances in our
> understanding of scientific reasoning for which there have not been any
> corresponding advances in mathematical reasoning, and this is something
> that needs to be corrected.

There have been great advances in mathematics.

> 5) The advances in scientific reasoning that I mention most often
> include reasoning under uncertainty and falsifiability, though there
> are others. These can and should be formalized and integrated into
> mathematics at the foundational level.

Absolutely not. Mathematics operates under different rules from science.
Falsifiability doesn't apply to maths.

> 6)The reason that mathematicians reject the ideas that I put forth is
> because if they accepted them, they would be forced to admit that
> Cantor's set theory is not essential for scientific reasoning, .....

Why get so personal? Set theory is currently essential for the
foundations of mathematics, and as such, is needed by science. If you
disagree, perhaps you should consider the question "what is a number?".

> .... and does not belong in mathematics.

On what, then, are the foundation of mathematics to be based? If you
want that to be something other than set theory, you must research and
develop some alternative.

> Cantor's set theory cannot be included in a consistent way with the
> modern advances in scientific reasoning that I suggest should be
> accepted as part of mathematical reasoning.

> 7) Since there are many outspoken mathematicians who label anyone who
> suggests that Cantor's set theory doesn't belong in mathematics as a
> stupid, delusional crank (or worse), ....

They're probably right, though none that I've known would express
themselves in such a manner. Can you give an example of such an
"outspoken mathematician"? I suspect they are few in number, if indeed
they exist at all.

Such an attitude would be much milder, if these critics of set theory
(why does it always have to be personalised as _Cantor_'s set theory?)
proposed something else to put in its place.

> .... and the mathematics community as a whole does nothing to reign in
> these outspoken mathematicians, the (pure) mathematics community as a
> whole should be seen as fraudulent.

Your tone of expression has now descended into crankery.

--
Alan Mackenzie (Nuremberg, Germany).

On 4/13/2022 2:36 PM, David Petry wrote:
>
> Here's the argument I have been making over the years:
>
> 1) The important purpose of mathematics is to provide a conceptual framework for reasoning about the real world. IOW, mathematics is the language of science.
>
> 2) We should apply Occam's razor when building a foundation for mathematics: we should minimize the number of assumptions we make, or as Einstein reportedly put it, everything (e.g. the foundations of mathematics) should be as simple as possible, but no simpler.

that depends on the accuracy required, over the dimentions included. Simple models are less accurate. Many problems do not have accurate solutions
either, so your #2 applies to the simpler problems.

>
> 3) Every abstract principle that is essential for reasoning about the real world (i.e. essential to science) should be formalized and integrated into the foundations of mathematics.

Why put abstract foundations into math ?

> Mathematicians should accept it as their moral responsibility to produce something that is beneficial to society.

A feel good thing, not a requirement.

>
> 4) Over the last century or so, there have been several advances in our understanding of scientific reasoning for which there have not been any corresponding advances in mathematical reasoning, and this is something that needs to be corrected.

can you be specific? or are you making stuff up again ?

>
> 5) The advances in scientific reasoning that I mention most often include reasoning under uncertainty and falsifiability, though there are others. These can and should be formalized and integrated into mathematics at the foundational level.

can you be more specific ? What areas of Math are you talking about ?

>
> 6)The reason that mathematicians reject the ideas that I put forth is because if they accepted them, they would be forced to admit that Cantor's set theory

Wrong. Cantor and his sets have nothing to do with it, you are not specific, your at 200,000 foot level.

> is not essential for scientific reasoning, and does not belong in mathematics. Cantor's set theory cannot be included in a consistent way with the modern advances in scientific reasoning that I suggest should be accepted as part of mathematical reasoning.

Not true at all.

>
> 7) Since there are many outspoken mathematicians who label anyone who suggests that Cantor's set theory doesn't belong in mathematics as a stupid, delusional crank (or worse),

you mean WM.

> and the mathematics community as a whole does nothing to reign in these outspoken mathematicians, the (pure) mathematics community as a whole should be seen as fraudulent.

sergio wrote:

> that depends on the accuracy required, over the dimentions included.
> Simple models are less accurate. Many problems do not have accurate
> solutions either, so your #2 applies to the simpler problems.

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