Bernado's Mathematical Universe

[SanteriSatama]

Have you tried Neven Knezevic's take on an ontological mathematics? His arguments are well formulated but also long winded (which might be necessary for this kind of mapping).

https://www.goodreads.com/book/show/521 ... domorphism

This is his first attempt, although i know he is working on a more independent model since he fell out with the authors of some of his sources

Thanks, but "united in unit-point entities outside of space and time" is not my cup of tea, point-reductionism is the plage of Cantor's joke and formalism.

[Squidgers]

Have you tried Neven Knezevic's take on an ontological mathematics? His arguments are well formulated but also long winded (which might be necessary for this kind of mapping).

https://www.goodreads.com/book/show/521 ... domorphism

This is his first attempt, although i know he is working on a more independent model since he fell out with the authors of some of his sources

Thanks, but "united in unit-point entities outside of space and time" is not my cup of tea, point-reductionism is the plage of Cantor's joke and formalism.

It's a type of mathematical idealism, not a formalist aproach. There are some decent arguments against formalism in there, and he deals with the Münchausen trilemma. But obviously, you do you

[Soul_of_Shu]

Have you tried Neven Knezevic's take on an ontological mathematics? His arguments are well formulated but also long winded (which might be necessary for this kind of mapping).

https://www.goodreads.com/book/show/521 ... domorphism

This is his first attempt, although i know he is working on a more independent model since he fell out with the authors of some of his sources

Re: eidomorphism, is this the meaning of the term 'eido' being used in the compound word?

Eido or Oida is knowledge by perception/awareness, when the knower and the knowledge become one

[Squidgers]

Have you tried Neven Knezevic's take on an ontological mathematics? His arguments are well formulated but also long winded (which might be necessary for this kind of mapping).

https://www.goodreads.com/book/show/521 ... domorphism

This is his first attempt, although i know he is working on a more independent model since he fell out with the authors of some of his sources

Re: eidomorphism, is this the meaning of the term 'eido' be used in the compound word?

Eido or Oida is knowledge by perception/awareness, when the knower and the knowledge become one

From the book:

"This spirit is the basis of the theory of eidomorphism, or, the notion that with every experience there is accompanied a fundamental mathematical form—a form which serves as the carrier for all information in the universe. Thus, this theory is a double aspect theory: one which says that instead of there being two distinct substances to answer the question of why there is mind in the universe, we give two distinct attributes to one substance, and this substance is mathematical substance alone.

Implicit in this mathematical substance, or form, is experiential content or representation (eidolon, eido- for idea or representation; morphe for form), hence the name, eidomorphism, or ideas coupled to form. Hence, eidomorphism, or form and representation in a single existent object."

[Squidgers]

Without getting too sidetracked, the task i am proposing here is to determine the way we can interface any analytic idealism with present physics, with mathematical foundations, and with cosmology.

Why is this necessary?

My suggestion is that the very attempt would alter and refine the map, as well as bring in more rigour and possibilities for a true Theory of Everything (not just quantum gravity but also the interaction problem, the mind-body problem and the hard problem of consciousness)

[SanteriSatama]

It's a type of mathematical idealism, not a formalist aproach. There are some decent arguments agaijst formalism in there, and he deals with Münchausen trilemma. But obviously, you do you

Obviously I have not read the book, only the short abstract. Based on that it looks like extending point-reductionism of formalism to idealism, which IMO is a very bad idea. I have plenty of respect towards Alain Badiou, for explicating set theoretical ontology in philosophically lucid way that exposes it to foundational critique and project of constructing alternative and better ontology based on process philosophical intuitionism with point-free approach, which can be generally characterized as Whitehead's paradigm.

In that sense, Badiou self-constructs himself and set-theoretical ontology as Worthy Enemy, while his deep critique of math based social alienation and oppression offers the motivation, and his process philosophical truth theory and notion of 'Event' provide possibility of liberation and evolution of mathematical onto-dia-logos.

Badious self-identifies as (dialectical) materialist, but his version of mathematical Platonism cannot be considered as anything but idealism.

Intuitionism is ontologically and fundementally an empirical approach to philosophy of mathematics. So, we start from accepting Zeno's empirical proof by contradiction as empirically valid and true refutation of point reductionism, and that intuitively empirical continuum/continua are not reducible to discrete quantification. Euclid provides intuitively coherent definition of point (definitions 1 and 3): Point has no part, point is end of a line and in that sense a part of a line. Hence, point has no independent substantial existence, but is mereologically intuitied and defined in relation to line and plane and affine parallelism.

On the other hand, if we start from the set theoretical and physicalist point-reductionism, where everly line segment consists of infinity of points, we can't draw a line, as drawing a line from point to point would take infinite time. Hence in ontology of point reductionsim we would lose also Platonic Solids, which were the teleology of Euclids constructive proof strategy. Ethically and aesthetically I like Platonic Solids, and would like to have them around and be able to draw and build e.g. Geodesic Domes.

Of course Euclid is not the final word, e.g. his definition "line has no width" is counter-intuitive and unnecessary, and we can let go of that. But if and when the choise is between Euclid and Platonic solids etc. continuous geometry vs. point-reductionism of Hilbert and Cantor, I choose Zeno, Euclid, Nagarjuna, Bergson, Wittgenstein and Whitehead any day. So I don't think it's just "me", IMHO I'm in a rather good company.

[SanteriSatama]

Have you tried Neven Knezevic's take on an ontological mathematics? His arguments are well formulated but also long winded (which might be necessary for this kind of mapping).

https://www.goodreads.com/book/show/521 ... domorphism

This is his first attempt, although i know he is working on a more independent model since he fell out with the authors of some of his sources

Re: eidomorphism, is this the meaning of the term 'eido' be used in the compound word?

Eido or Oida is knowledge by perception/awareness, when the knower and the knowledge become one

Those are part of the concept family (cf. Lating video) which refer to visual sense, whether looking with the double slit experiment above the nose and beneath the brow, or with minds eye.

[SanteriSatama]

Implicit in this mathematical substance, or form, is experiential content or representation (eidolon, eido- for idea or representation; morphe for form), hence the name, eidomorphism, or ideas coupled to form. Hence, eidomorphism, or form and representation in a single existent object."

Mathematics is a general study of relations, not of substance. There is no such thing as "mathematical substance".

I'll try to show you how to see a point in intuitively coherent and relational way. Imagine that you are a flatlander living on flat plane, traveling along a straight line. While traveling, you start erasing the line as you go, the after a duration stop and look back. Behold, a point! at end of a straight line, when looking from an end of straight line over a gap in the straight line.

If the plane is curved instead of flat, you don't see a point, you see a line. If there are other lines on the flat plane, they will need to be parallel and not meet in horizon, or else you see a line instead of point.

If you can find some other way to really see a point instead of line, that would be very interesting, so far this is the only way to see a point that I'm aware of. And the ability to see a point this way is relational and depends at least from the notions of line, straight, plane, flat and parallel.

On the other hand, the axiomatic postulation of 'point' as a "single existent object" of ontology of point-reductionism leads to the counter-empirical and counter-intuitive absurdity that Zeno pointed out.

[Squidgers]

Implicit in this mathematical substance, or form, is experiential content or representation (eidolon, eido- for idea or representation; morphe for form), hence the name, eidomorphism, or ideas coupled to form. Hence, eidomorphism, or form and representation in a single existent object."

Mathematics is a general study of relations, not of substance. There is no such thing as "mathematical substance".

If someone is making a model where they are defining mathematics in a particular way, it doesn't make much sense to interpret their findings or arguments from your own definition of mathematics.

I don't think he is defining a point in the same way that you are either as he calls them dimentionless flowing points. There are mathematical definitions and proofs in the book.

"Every flowing point moves according to the Euler formula, and since there are as many flowing points as there are complex numbers, it follows that every monad is akin to a container of infinitely many concentric circles of flowing points.

This is also evidenced a posteriori when we go backwards to ultimate reality from empirical data. For instance, the Navier-Stokes equations, the relativistic and classical Doppler effects, Fourier analysis solutions to the heat equation, wave equations in classical and quantum mechanics, and much more all go on to show that waves are ubiquitous in nature.

Further, everywhere we look empirically, we also find instances of the Euler formula. This formula turns up in every field of physics and mathematics, and its applications and uses are seemingly inexhaustible. It is no surprise, given empirical considerations, that the Euler formula would be at the very root of the natural order."

[Squidgers]

It's a type of mathematical idealism, not a formalist aproach. There are some decent arguments agaijst formalism in there, and he deals with Münchausen trilemma. But obviously, you do you

Obviously I have not read the book, only the short abstract. Based on that it looks like extending point-reductionism of formalism to idealism, which IMO is a very bad idea. I have plenty of respect towards Alain Badiou, for explicating set theoretical ontology in philosophically lucid way that exposes it to foundational critique and project of constructing alternative and better ontology based on process philosophical intuitionism with point-free approach, which can be generally characterized as Whitehead's paradigm.

In that sense, Badiou self-constructs himself and set-theoretical ontology as Worthy Enemy, while his deep critique of math based social alienation and oppression offers the motivation, and his process philosophical truth theory and notion of 'Event' provide possibility of liberation and evolution of mathematical onto-dia-logos.

Badious self-identifies as (dialectical) materialist, but his version of mathematical Platonism cannot be considered as anything but idealism.

Intuitionism is ontologically and fundementally an empirical approach to philosophy of mathematics. So, we start from accepting Zeno's empirical proof by contradiction as empirically valid and true refutation of point reductionism, and that intuitively empirical continuum/continua are not reducible to discrete quantification. Euclid provides intuitively coherent definition of point (definitions 1 and 3): Point has no part, point is end of a line and in that sense a part of a line. Hence, point has no independent substantial existence, but is mereologically intuitied and defined in relation to line and plane and affine parallelism.

On the other hand, if we start from the set theoretical and physicalist point-reductionism, where everly line segment consists of infinity of points, we can't draw a line, as drawing a line from point to point would take infinite time. Hence in ontology of point reductionsim we would lose also Platonic Solids, which were the teleology of Euclids constructive proof strategy. Ethically and aesthetically I like Platonic Solids, and would like to have them around and be able to draw and build e.g. Geodesic Domes.

Of course Euclid is not the final word, e.g. his definition "line has no width" is counter-intuitive and unnecessary, and we can let go of that. But if and when the choise is between Euclid and Platonic solids etc. continuous geometry vs. point-reductionism of Hilbert and Cantor, I choose Zeno, Euclid, Nagarjuna, Bergson, Wittgenstein and Whitehead any day. So I don't think it's just "me", IMHO I'm in a rather good company.

I don't think you are accurate with your assumptions about this book at all. He makes some of the same criticisms as you are.

But here is a section of what he has to say on intuitionalism and category theory:

"Intuitionism is the position in the philosophy of mathematics which states that mathematics is a product of the mental activity of humans, constructed from exact propositions whose validity is no more than the intersubjective agreement which we can attain by guiding our own reasoning according to these shared mental constructs. Though the weight of the arguments directed against formalism also count against intuitionism and category theory, there are some distinct issues concerning intuitionism that need to be addressed. For the sake of brevity, we will restrict the critique of intuitionism to a few short paragraphs given that the bulk of the arguments against formalism also count for intuitionism.

The arch-intuitionist L.E.J. Brouwer believed that we had an inherent faculty for exact propositions, namely that our minds work according to some well-defined structure. Brouwer’s own philosophical preferences were a variation of Kant’s, with the same unexplained faculties propelling us to unjustified conclusions. The fundamental problem of Brouwer’s claim is that, like Kant’s synthetic a priori, there is no reason why we should have a faculty which gives us exact thinking, and the origin of such a faculty cannot be explained in and of itself without resorting to pure subjectivism.

Intuitionism also has the same problem that idealism faces, namely that the structure of the universe remains unexplained if we are just forming conclusions based upon subjective propositions that our minds can inherently produce. Further, as shown by Robert S. Tragesser in Husserl and Realism in Logic and Mathematics, mathematics is not merely about interpreted objects and rules of use.

The very fact that we can independently reach the same conclusions using identical reasoning and without doing so according to mere preference only goes to show that we are dealing with something that already meets conditions for objectivity. In addition to this, the ontological considerations we have given for mathematics only serves to strengthen the case against intuitionism and category theory."