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Clarifying my position on intuitionsim
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David Petry
Aug 12, 2021, 2:46:43 PM8/12/21
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In a different thread, I wrote:
>> I realize that people in this newsgroup have little interest in intuitionistic mathematics, and even less interest in physics.
Jeanj Pierre Messager (aka Python) responded:
> 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.
I want to clairify my position on intuitionism. I find intuitionism to be cringeworthy. Nevertheless, I sometimes encourage people to think about it. Let me explain why.
Here's the idea that I have been promoting. The idea of falsifiability, which the scientists use to distinguish science from pseudoscience, can be formalized and integrated into mathematics at the foundational level. It could be used to distinguish mathematics from pseudo-mathematics.
Adding falsifiability to mathematical reasoning would not in any way impair the mathematics that is relevant to science and technology. In fact, it would strengthen such mathematics. And if it's not added to mathematics, then mathematics will remain deficient as a language for science.
So, as I see, the intuitionists (e.g. Brouwer) could easily have thought of this idea in the early 1930's when Popper introduced the idea of falsifiability. It could have completely cleared up the debate between the formalists (Cantorians) and the intuitionists.
Had someone introduced this idea into mathematics, then based on my understanding of the motivations of the intuitionists, they would have responded with, "this idea does show that we got some things wrong, but also it shows that we have been headed in the right direction." In contrast, the Cantorians would have been forced to admit that they were headed in the wrong direction.
I also like to point out that a set theory based on Gauss' understanding of infinity would be compatible with falsifiability: in mathematics, infinity is nothing more than a figure of speech that mathematics find to be very useful when reasoning about limits (that's a paraphrase of Gauss).
So, I find it plausible that if I could get people to understand why some researchers in the fields of physics and artificial intelligence find intuitionism to be the right kind of mathematics for their field, then they would be on the path to understanding why I promote falsifiability in mathematics.
Anyways, Jean Pierre Messager seems to be clueless about what I am promoting, and I have no idea how to break through his misunderstandings. He has never made any intelligent contributions to the discussions I start.
>> I realize that people in this newsgroup have little interest in intuitionistic mathematics, and even less interest in physics.
Jeanj Pierre Messager (aka Python) responded:
> 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.
I want to clairify my position on intuitionism. I find intuitionism to be cringeworthy. Nevertheless, I sometimes encourage people to think about it. Let me explain why.
Here's the idea that I have been promoting. The idea of falsifiability, which the scientists use to distinguish science from pseudoscience, can be formalized and integrated into mathematics at the foundational level. It could be used to distinguish mathematics from pseudo-mathematics.
Adding falsifiability to mathematical reasoning would not in any way impair the mathematics that is relevant to science and technology. In fact, it would strengthen such mathematics. And if it's not added to mathematics, then mathematics will remain deficient as a language for science.
So, as I see, the intuitionists (e.g. Brouwer) could easily have thought of this idea in the early 1930's when Popper introduced the idea of falsifiability. It could have completely cleared up the debate between the formalists (Cantorians) and the intuitionists.
Had someone introduced this idea into mathematics, then based on my understanding of the motivations of the intuitionists, they would have responded with, "this idea does show that we got some things wrong, but also it shows that we have been headed in the right direction." In contrast, the Cantorians would have been forced to admit that they were headed in the wrong direction.
I also like to point out that a set theory based on Gauss' understanding of infinity would be compatible with falsifiability: in mathematics, infinity is nothing more than a figure of speech that mathematics find to be very useful when reasoning about limits (that's a paraphrase of Gauss).
So, I find it plausible that if I could get people to understand why some researchers in the fields of physics and artificial intelligence find intuitionism to be the right kind of mathematics for their field, then they would be on the path to understanding why I promote falsifiability in mathematics.
Anyways, Jean Pierre Messager seems to be clueless about what I am promoting, and I have no idea how to break through his misunderstandings. He has never made any intelligent contributions to the discussions I start.
FredJeffries
Aug 12, 2021, 3:21:12 PM8/12/21
to
On Thursday, August 12, 2021 at 11:46:43 AM UTC-7, david...@gmail.com wrote:
> Here's the idea that I have been promoting. The idea of falsifiability, which the scientists use to distinguish science from pseudoscience, can be formalized and integrated into mathematics at the foundational level.
Then do it.
> Here's the idea that I have been promoting. The idea of falsifiability, which the scientists use to distinguish science from pseudoscience, can be formalized and integrated into mathematics at the foundational level.
Sergio
Aug 12, 2021, 4:08:00 PM8/12/21
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cringeworthy institutionalism ?
pseudoscience of falsifiability ?
infinity is a figure of speech ?
your intelligence is artificial ?
you are clueless about what you are promoting ?
FredJeffries
Aug 12, 2021, 4:54:29 PM8/12/21
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On Thursday, August 12, 2021 at 11:46:43 AM UTC-7, david...@gmail.com wrote:
Python
Aug 12, 2021, 7:21:47 PM8/12/21
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you are spouting out in a context that you do not understand.
Intuitionistic logic makes a LOT of sense (especially in computing
assisting software or software proving tools).
You, David, are a BIG failure. Intuitionistic logic (you never even dare
to consider) is not.
You are just ranting because you failed in math when younger. We do not
care. Fuck off.
Python
Aug 12, 2021, 7:23:51 PM8/12/21
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zelos...@gmail.com
Aug 13, 2021, 1:05:38 AM8/13/21
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>Here's the idea that I have been promoting. The idea of falsifiability, which the scientists use to distinguish science from pseudoscience, can be formalized and integrated into mathematics at the foundational level. It could be used to distinguish mathematics from pseudo-mathematics.
How are you gonna do that when mathematics do not deal with reality?
>Adding falsifiability to mathematical reasoning would not in any way impair the mathematics that is relevant to science and technology. In fact, it would strengthen such mathematics. And if it's not added to mathematics, then mathematics will remain deficient as a language for science.
Ross A. Finlayson
Aug 13, 2021, 2:13:49 AM8/13/21
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For most of history mathematics was way ahead of physics....
Having a theory that is a science can still be a mathematical science.
Science makes for a natural theory, for what there's mathematical physics.
I.e., a mathematics can be simply seen as a science, or a part of any science.
zelos...@gmail.com
Aug 13, 2021, 6:48:19 AM8/13/21
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>Mathematics owes physics actually.
Nope
>For most of history mathematics was way ahead of physics....
Thanks to being dettatched.
>Having a theory that is a science can still be a mathematical science.
Mathematics do not deal with the scientific method, they use the axiomatic method.
>I.e., a mathematics can be simply seen as a science, or a part of any science.
How are you gonna do this when you cannot present the physical thing of "three"? Not 3 of something, not the symbol 3, not anything but the threeness itself.
Nope
>For most of history mathematics was way ahead of physics....
>Having a theory that is a science can still be a mathematical science.
>I.e., a mathematics can be simply seen as a science, or a part of any science.
Ross A. Finlayson
Aug 13, 2021, 4:51:43 PM8/13/21
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For some this is after axiomatics that the objects do have platonic reality,
or, that they don't.
Then, furthermore, some strong platonists, have the objects exist
even if "we" didn't exist to "axiomatize" them, that only purely formal
axioms that result in logical structure are "true axioms".
Then, some realists, are "not platonists", while, some are, "strong platonists",
that with respect to the operationalists, the "quantities are always in units"
with respect to "numbers: dimensionless quantities".
Examples of physics needing mathematics include the N-body problem,
wave equation, ..., functional freedom, parastatistics, .... I.e. that
mathematics owes physics strong enough mathematics for quite a
variety of concerns what must make for the derivations as in the applied.
(Physics writ large is already using an often very regular and usual stack
of derivations and mathematics, eg defined under formula.)
I totally agree that the threeness, of, of a quantity or a count or a number
or "anything in the equivalence class that the count of which is three",
is just that numbers are simply enough classes under values.
That that's a giant class while instead something like von Neumann ordinals
make for a model that also "an ordinal assignment" for a count, for that
"things with counts are in a cardinal, the equivalence class of sets with those",
sets, makes for that threeness is as direct as things with the number and
things with the count.
I.e., that threeness relates to fourness, counting separately each,
is as a larger space than even a cardinal, that Peano's counting is
about as drawn down as it can be while for example something like
the "Principia Mathematica to arrive at 1+1 = 2" has that the implicit
space exists for all the non-logical theories one model of numbers.
This is for that mathematics is a _part_ of (any) science, as is for pure
logic and then that numbers strongly platonically exist, that overall,
the theory, i.e. some ideal unified theory, is a science.
Surely I'll agree "there's a theory where it's immaterial whether I'm
a strong platonist or platonist where in terms of mostly reason or
even the empirical, apples are to apples and apples are to oranges,
that validity of arithmetic is so falsifiable is that invalidities of arithmetic
are falsifiable".
Here of course "falsifiable" means independent under concerns not "contradictable".
I.e., not necessarily contradictable where it's not false.
Formalism's key strengths include axiomatics and thusly the fundamental.
Fundamentalist formalism these days has ZF set theory the most explored
milieu for the descriptive, what resultingly most formalisms trace formalization.
Of course domains like real analysis or for example topology are as much
"independent in the descriptive", what that largely set theory and then for
type-theories-and-category-theories-sons-of-set-theory, if a strong platonist
is conscientious to bring that on down from utter fundamentalism,
that from pure logic in mathematics is usually numbers (or form, structure).
That the mathematical models for mathematical physics have a
physical interpretation (or the intended intepretation), is for that
there's the fundamental success of mathematics in physics for its
validities, that modeling the total or universal in mathematical objects,
needs mathematics of those kinds of infinities for physics.
Where for example real analysis with the differential for
the integral calculus for the applied is ubiquitous...,
in infinite limits.
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