Essay Abstract

Dialectica: Mathematica and Physica, Truth and Justice, Trick and Life. Mathematica as the Constructive Metaphysica and Ontology. Mathematica as the constructive existential method. Сonsciousness and Mathematica: Dialectica of "eidos" and "logos". Mathematica is the Total Dialectica. The basic maternal Structure - "La Structure mère". Mathematica and Physica: loss of existential certainty. Is effectiveness of Mathematica "unreasonable"? The ontological structure of space. Axiomatization of the ontological basis of knowledge: one axiom, one principle and one mathematical object. The main ideas and concepts of the ontological construction/ "Point with a vector germ" and "heavenly triangle". "Ordo geometricus" and "Ordo onto-topological". Architecture of the onto-topological basis of knowledge: general framework structure, carcass and foundation. The absolute space and the absolute field. The absolute (natural) system of coordinates of Universum. Eidos of "idea of ideas", the symbol and the "formula of Justice".

Author Bio

Engineer (MPEI), economist (Russian Foreign Trade Academy), independent researcher since 1989: ontology, philosophy of physics and mathematics, philosophy of Сonsciousness, member of XX World Congress of Philosophy (Boston, 1998), I-IV Russian Philosophical Congress (1997-2005), The First Conference "Philosophy of Physics: actual problems", The Third Russian Conference "Philosophy of Mathematics: actual problems" (MSU, 2013). My daughter Victoria supported me at creation of my essay. We are convinced that Philosophy - the most rigorous and joyous Science.

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EpiLog-I:Truth & Justice

On the Pacific Ocean shore two friends were sitting. One of them was Physicist, and other was Mathematician.

What is the truth? - Physicist asked

Justice, - Mathematician answered.

Then draw it, - Physicist asked. Mathematician, drew absolutely symmetric geometrical symbol without tearing off his hand from sand.

How did you come to it? - Physicist asked.

Mathematician smiled and, tool the guitar and started to sing the old kind song of bards of the 60th years of last century:

"I know, everything will be developed by Dialectica..."

Physicist placed his hand on his friend's shoulder and picks up the song, and the run wave washed away drawing to the Ocean ... 竊' Dubito竊' Ergo 竊' Cogito竊'

It is by a mathematical point only that we are wise,

as the sailor or the fugitive slave keeps the polestar in his eye;

but that is sufficient guidance for all our life.

We may not arrive at our port within a calculable period,

but we would preserve the true course.

Henry David Thoreau

Dear Mr. Rogozhin,

Thank you for the enjoyable essay and nice journey through the history and evolution of math, physics and metaphysics from ancient times to our days.To some extent, I share the view about constructive metaphysics: "We must replace the obscure metaphysics by metaphysics the application of which takes place in natural sciences, and first of all, in geometry and in different areas of mathematics."

In my view, math and physics are not entirely each other's mirror and not necessarily each physical phenomenon can fit into math and vice versa, they only can intersect in our world to certain extent and sometimes just roughly and sometimes not even in slightest manner.聽聽But whenever they get right fitting, then it is a beauty of our world.聽聽Why math fits physics sometimes? I believe, it is because we get a "quantity" and a quantity means measurements, whenever we don't get a quantity we searching for simply we make interpretations instead to fill that gap or discontinuity.聽聽

Warm regards

Koorosh

    Dear Koorosh,

    Thank you for your kind and insightful commentary. Yes, I agree with you. I would add that the solution to the problem of the ontological justification of Mathematics (and, consequently, Physics) will give a push to promote heuristic Mathematics aside "quality quantity" all-powerful expansion of the kingdom of the all-powerful "Queen" and the faithful "Servant".

    Good luck in the Сontest,

    Kind regards,

    Vladimir

    Dear Joe,

    Thank you for your insightful and interesting commentary. I agree that the two key concept to find an answer to the questions of the Contest - "reality" and "structure". The task of the Contest - the search for new fundamental ideas. I offered my version of primordial structure - the "maternal (generating) structure" for all levels of the Universum, which can be one of the candidates as a unified ontological basis of fundamental knowledge. Mathematics and Physics will not be able to make a new dialectical breakthrough without wide philosophical synthesis. In fundamental Physics is necessary to introduce an ontological standard justification along with the empirical standard. I'll see certainly your ideas and "structure" in the near future.

    Kind regards,

    Vladimir

    Dear Vladimir ! In my impression, the soul of matter is a re-search question of deep mysticism,e.g. are stones sleeping energy, do they have a memory? This is actually the theology of maths and spiritual physics; the triangular geo-metric form represents possibly the basic grammar of universal law, i.e. the creative logos of the eternal upper force or the ontological physics of meta-maths.Congratulations, your essay explores new knowledge territory for modern methodical science; I am sure, we can learn a lot from ancient spiritual wisdom, for example, Kabbalistic, Gnostic and Sufi approaches, in this respect. It is this modern fusion of scientific knowledge and classical wisdom that is really needed in our turbulent times. Best wishes, cordially: stephen

      Dear Stephen,

      Many thanks for your kind and insightful comments. Yes, today requires the most profound synthesis of the entire system knowledge, including the Tradition. Only in this way we can reach a common basis "fundamental knowledge". Today, knowledge has no ontological foundation. In my concept of "ontological (structural, space) memory" is what creates all. It permeates Universum both vertically and horizontally. Ontological memory "holds", retains and develops the Universum. Memory - the motor, engine of evolution. Information, time, consciousness - a polyvalent phenomena of ontological (structural) memory. Physics should include the category of "memory" in the scientific picture of the world.

      Kind regards,

      Vladimir

      Dear Vladimir! YOU HAVE HIT THE NAIL: modern knowledge has no ontological foundation. I am grateful to fqxi, it provides us with Options for a new dialogue.New ontoligical foundations have to be worked out; it is a great pleasure to communicating with you this great challenge of humanity.Should you visit Munich, let me known in advance. Cordially: stephen

        Dear Stephen,

        Thank you very much for your kind words, understanding and invitation! Yes, you're absolutely right: Contests FQXi is Perfect meeting place for new fundamental ideas, a place for a large polylogue.

        Indeed, prompt Henry David Thoreau:"It is by a mathematical point only that we are wise, ..." gives access to metaphysics, ontology and physics of "point", on unified base of knowledge - the basic maternal structure ("La Structure mère"). Obviously, the "Life in the Woods" makes it possible not only to see the harmony of the Nature, but also the way and the "starting point". ..."but we would preserve the true course. "

        Good luck in the Contest!

        Kind regards,

        Vladimir

        Dear Vladimir,

        I believe I understood your earlier essay on consciousness, but I am somewhat lost on your current essay. You cover much historical development, and my lack of awareness of certain players may account for this.

        You speak of "eidos" as "idea of idea" and state as the basic problem "to find one single structure", the source of "unreasonable effectiveness of mathematics".

        My essay begins with a brief overview of my Automatic Theory of Physics which is an attempt to develop "A Theory of theories", based on logical structure (NOT and AND) as physically real and as sufficient basis for counters, counting, and arithmetic-logic of natural numbers, from whence, per Kronecker, all else mathematical follows. The differences or 'distance' between measurements can be used to extract 'features' and this leads (through entropy) to a 'best feature vector' as the prototypical Hilbert space vector. Conservation over eigenvalues leads to eigenvalue equations, and this vector is perhaps the single structure best characterizing the math map of the world. I imagine that this maps, in some way, into your ontological vector, but I'm not sure in what way.

        Most of my essay is focused on Bell's confusion between two of the eigenvalue equations, and the erroneous conclusion he draws from a mathematically correct analysis of a physically incorrect (oversimplified) assumption.

        I invite you to read my essay and comment, and hope that you find some significant connection between our essays.

        My best regards,

        Edwin Eugene Klingman

          Dear Edwin,

          Thank you for your insightful and interesting commentary. Modern fundamental science is experiencing the most profound in the history of its development, "the crisis of understanding", "crisis of interpretation and representation" - onto-gnoseo-axiological crisis. To understand meaning "seize the structure" ( G.Gutner "Ontology of mathematical discourse").

          Overcoming the "crisis of understanding" - the construction of primordial structure of the Universum as a result of a comprehensive synthesis of all knowledge accumulated by mankind. On the basis of ontological design, I build a model (eidos = image) such as the primordial structure of the Universum, "the idea of all ideasﾂｻ (idea of ideas) or Absolute generating structure - "La Structure mﾃｨre" - the basis of fundamental knowledge: framework (limit), carcass and foundation of knowledge. It represents the ontological structure of the first-process of the Universum, as the triunity of absolute states of matter (absolute rest & absolute movement & absolute becoming), the time before "the beginning of times" ("sub specie aeternitatis"). When designing I proceed from the principle of identity of being and thinking (Parmenides 竊' Hegel).

          Mathematics and Physics must hold today the most profound revision of the philosophical grounds. I am seeking today with interest your essay.

          Kind regards,

          Vladimir

          Your insightful work grabs some more mirror to regard the philosophical breakthrough.

          Great job, indeed!

          Respectfully,

          Miss. Sujatha Jagannathan

            Dear Miss. Sujatha Jagannathan,

            Many thanks for your kind and insightful commentary. Today, more than ever, are relevant philosophical covenants of A. Einstein and J. Wheeler:

            "In our time, physicists have to deal with philosophical problems to a much greater extent than it had to do physicists previous generations. To it physicists are compelled by difficulties of their own science."

            "Philosophy is too important to be left to the philosophers."

            There is no doubt that the picture of the world of physicists and mathematicians should be the same rich senses of life as a picture of the world lyricists.

            I'll read your essay in the near future.

            Kind regards,

            Vladimir Rogozhin

            Dear Vladimir,

            From our previous communications about consciousness I know that there is much overlap in our understanding. For this reason I feel that I agree with your second paragraph above despite that our terminology tends to differ. I tried to look at the paper you link to on 'Ontology of Mathematical Discourse' but it is one of my many failings that I do not read Russian.

            Finally, we agree about math and physics and the need for profound revision of the philosophical grounds. That has been my focus on Bell, and it extends beyond Bell.

            Best regards,

            Edwin Eugene Klingman

            5 days later

            Vladimir

            Your essay is a view of the historical development of math and physics. It shows some evolution to the current practice. It also shows several changes of definition of words. Each new set of definitions resulted in advancement of understanding. What is the next set of definitions that may help human advancement? Where do we need new definitions?

              Dear John,

              Thank you very much for your comment and the good question. G.Gutner in "The Ontology of mathematical discourse" made a good conclusion: "to understand - then grab the structure." In the last section of essay "Eidos of" Idea of Ideas ", the Symbol and" Formula of Justice ", I introduced a new model onto-topological basis of fundamental knowledge - Absolute generating structure as the framework, carcass and foundation of knowledge, first of all mathematics and physics. The core of the new model of the Universum - concept of ontological (structural, cosmic) memory as the measure, "qualitative quantity" of absolute states of matter. Other new concepts: 1) the vector of absolute states of matter; 2) the triune (absolute) space 9 measurements; 3) the absolute coordinate system as a geometric reprezentant of triunity of absolute states of matter: absolute rest & absolute motion & absolute becoming (triune absolute field); 4) the triune (absolute) space-matter-time 12 measurements (9 spatial measurements 3 "temporary").

              Kind regards,

              Vladimir

              I once had a course in History of Philosophy in which I learned about and learned to love Plato's Forms. But I agree that philosophy now has to be brought up to date and its concepts somewhat revised to be more applicable (and I like that statement by Wheeler that `Philosophy is too important to be left to the philosophers.'). Regarding your question on Lifeworld (Lebenswelt), I agree provided that our knowledge and experience is more constrained by our knowledge of science (effectively from the so-called `scientific method'). Language is hard, and we often talk past each other because of lack of careful definition (e.g., ``reality.''). The problem with physics is that Nature is the owner of the definitions, and we keep revising ours in an attempt to match as we learn more. It would be wonderful if we all had a deep appreciation of Nature, but most of us are limited by our core biology, history, training and culture--and that often dominates over rationality. You mentioned that the origins of the words mathematics and physics derive from primitive views of the order, generating structure and harmony of the Cosmos (and it would be nice to keep that perspective). I like your terms ``loss of existential certainty'' and ``crisis of interpretation'' which certainly applies now to the quantum world. And I liked the comment that `modern knowledge has no ontological foundation.' Many people are working on trying to fix that. We wish ourselves luck.

                Dear David,

                Thank you for your comment and deep detailed answer to my questions on your forum. Given the title of your essay I have emphasized the idea of "celestial triangle" of Plato as a measure of any sensible thing, as well as the very notion of "measures" by Plato. Physics and mathematics have to make new turn to the foundations of knowledge to set the ontological basis - framework, carcass and foundation of knowledge. There must work together "ratio", "emotio", "intuitio" to overcome the "crisis of representation and interpretation". In fundamental physics is necessary to introduce an ontological standard of justification (substantiation) addition to the empirical standard. All the ancient Greek concepts require a deeper understanding, especially the concept of "quantum" and its ontological status.

                Kind regards,

                Vladimir

                Dear Edwin,

                Yes, the problem of philosophical (ontological) foundations of Mathematics and Physics is today the main problem. I would use here a second concept - "ontological basification": the establishment of a framework, carcass and foundation of knowledge. The main idea in the "Ontology of mathematical Discourse": "Event setting structure means understanding".

                Contemporary "crisis of understanding"(K.Kopeykin "Souls" of atoms and "atoms" of soul: Wolfgang Ernst Pauli, Carl Gustav Jung and "three great problems of physics") in fundamental science requires a new conceptual revolution, the result of which - a model of the Universum as a whole. Quantum theory and relativity theory - the parametric theory without ontological justification (basification). Let work everyone in the sphere as Ptolemaeus's theory worked.

                Kind regards,

                Vladimir