Thursday, August 11, 2011

The Contributions of Marxian Dialectics to Modern, "Mathematico-Science"

Dear Readers,

First off -- when considering whether or not [Marxian] dialectics has, as yet, made major contributions to modern science -- it is crucial to distinguish dialectics consciously applied from dialectics unconsciously present in the content/structure of scientific work.

Dialectical content-structuring can certainly be detected, by a conscious dialectician, in the content-structure of Newton's <<Philosophia Naturalis Principia Mathematica>> ["Mathematical Principles of Natural Philosophy"], though it is unlikely, to my mind, that Newton consciously employed any version of Platonian proto-Systematic Dialectics in the composition of his magnum opus, viz. --

thesis + contra-thesis + uni-thesis    (----)   


abstract, "celestial" motion-theory + more concrete, "terrestrial" motion theory  

+ The System of the World.

Likewise, dialectical content-structuring can be readily discerned in the content-organization of Maxwell's Treatise on Electricity and Magnetism, synthesizing the theretofore disparately-categorized phenomena of electricity and magnetism into a unitary theory of "electro-magnetism" as universal "field", viz. --



thesis + contra-thesis + uni-thesis    (----)    electricity + magnetism + electro-magnetism.

Maxwell's dynamical electro-magnetic field theory was, in turn, a crucial foundation and inspiration for Einstein's work -- not just for Einstein's Special Theory of Relativity, which abstracts from acceleration, but for his General Theory of Relativity, which is a Universal Field Theory of Gravity and of equivalent acceleration, and for his work toward a Unitary Field Theory of the total Cosmos, encompassing and unifying/synthesizing the phenomena of electromagnetism and gravity, and, today, seeking to encompass also the [nuclear] "strong" and "weak" "forces", "dark matter", and the "dark energy", or the "dark force", of the recently-discovered self-acceleration of the self-expansion of universal space-time, viz., for the actual history of Einstein's work-foci, rather than for his system of presentation of his results, viz. --

 thesis + contra-thesis + uni-thesis    (----)    Special Relativity + General Relativity + Unitary Field Theory.


In Maxwell's case, the dialectical content-structure may have been at least partially a conscious application of a version of "Systematic Dialectics".

Maxwell was a follower of two philosophers who represented a partial overcoming of the Kantian radical dualism of the knowledge-intelligible versus of the "thing-in-itself" -- namely, William Hamilton [the logician; not William Rowan Hamilton, the mathematician and scientist], and William Whewell -- although Maxwell was not, to my knowledge, a direct follower of the "full", but, in part, specious overcoming of that radical dualism via Hegel's version of idealism.



For diagrammatic as well as textual renditions of the "dialecticity", or "dialecticality", in all three of these cases, see --


http://www.dialectics.org/dialectics/Applications.html

http://www.dialectics.org/dialectics/Applications_files/F.E.D.,%20Dialectical%20Pictography,%20I.,%20Systematic%20Dialectics,%20Parts%20I-IX,%2018MAY2008_OCR.pdf


-- slides 42-44 for Newton's work; slides 48-52 for Maxwell's work, and --


http://www.dialectics.org/dialectics/Applications_files/F.E.D.,Dialectical%20Pictography,Part%20III.,Meta-Systematic%20Dialectics,05MAR2008_OCR.pdf


-- slides 18 & 19 for Einstein's work.



With regard to the unquestionably conscious application of specifically Marxian, "psycho-historical materialist dialectics", to the advancement of science, we have the example of the works of Marx, and, to a lesser extent, that of the works of Engels, as the primary examples.

In particular, the most fully-worked out conscious application of Marxian dialectics to a capitalist-ideology-adulterated science is that of Marx's immanent critique of bourgeois political economy, in the four volumes of Capital, and, especially, in volume one, the productions-process of capitals -- the only one of the four that Marx himself actually completed for publication.

These works of Marx and Engels, particularly the latter, represent, IMHO, and epochal breakthrough and watershed in the history of human science, "human-social" and "natural" alike, albeit with emphasis on "human-social science".

The positive fruition of Marx's dialectical, immanent critique of capitalist economics, as a theory of the global dynamics -- and of the self-revolutionary "meta-dynamics" -- of the capitalist system still towers above the increasingly ideology-vitiated productions of capitalist economics to this very day, over 150 years since the inception of that Marxian critique.

Unfortunately, Marx's followers have not, for the most part, systematically continued, and advanced, Marx's programme.

Remember, Marx's programme for the, in part, Systematic-Dialectical exposition of his critique of the political economy of the capitals-system, alone, encompassed six planned [massive] treatises --

1. Capital

2. Landed Property

3. Wage-Labor

4. The [National] State

5. Inter-National Commerce

6. The World Market [as a Whole] and Crises


Marx lived to publish only the first "fourth" of the first treatise of these six -- <<Buch>> I: the productions-process of capitals.

But he referred regularly to the elaborations, outside of the scope of the Capital treatise, but belonging natively to one of the planned later treatises, throughout the books of the Capital treatise.

Many of the mis-apprehensions of Marxian theory that have compromised the praxis of the "Marxian" movement owe, at least in part, to the under-representation, within the Capital treatise, of themes proper to the later planned, and partially-drafted, treatises.

A key to all of these mis-apprehensions is the mis-apprehension of their most central and unifying technology: the Marxian dialectic.


Moreover, Marx's announced plan for the totality of his programme goes far beyond his dialectical, immanent critique of the capitalist ideological-science of political economy, encompassing the dialectical, immanent critique of the capitalist, ahistorical abstract-reductionist / atomistic ideological-sciences as a totality: ideology-infested sciences that Marx criticized as such, episodically but not yet systematically, throughout his extant works:

"According to a plan that Marx had developed in 1844, political economy was the first of the topics to be investigated, and critical treatment of that theme was to be followed by the "critique of law, morality, politics, etc." The project was to be wound up with a "special work" that would demonstrate the unity of the whole, and show the relations between the various parts and finally end with "a critique of the speculative [e.g., ahistorical/abstract, & subject/object-inverted -- M.D.] manner in which these subjects have been dealt with up to now."

In other words, Marx had, at an early date envisaged the critique of political economy as being but one brochure among several, all designed as prolegomena to a fundamental work whose thematic construction was to be the systematic critique of bourgeois social institutions and ideologies.
"

[Maximilien Rubel, Rubel on Marx: Five Essays, ed. & tr. by Joseph O'Malley and Keith Algozin, Cambridge U. Press (NY: 1981), p. 190. emphasis added by M. D.].


Apart from, but crucially enabling, the necessary work of organizational preparation for the revolutionary overthrow of the capital/wage-labor/sold-labor[-power] = alienated-labor[-power] "social relation of production" as predominant relation of social reproduction, by alienated-labor-thereby-dis-alienating-itself, is the theory-work of the critique of the totality of the capitalist ideology / ideological-science --  of both of its conscious and unconscious ideological content -- that otherwise imprisons the minds of all social individuals within the capitals-system.

This was Marx's programme for [Marxian] theory, precisely.

Unfortunately, most "Marxists" have not continued Marx's programme.

There have been a few glimmers of this continuation -- some consciously Marxian, some not -- among which I would include Engels's works, after Marx's death, E. V. Ilyenkov's Dialectical Logic: Essays in its History and Theory, key works by Oparin and Vernadsky, V. F. Turchin's The Phenomenon of Science, Joachim Israel's The Language of Dialectics and the Dialectics of Language, David Bohm's Wholeness and the Implicate Order [especially], and [the Hegelian] Errol Harris's Formal, Transcendental, and Dialectical Thinking: Logic and Reality, for example, to name a few.

But the comprehensive continuation of Marx's theoretical work -- of his dialectical, immanent critique of capitalist ideological science in its totality -- has not yet been fully resumed.

Hence, my interest in F.E.D.

They have, in my opinion, "cracked the code" on the core technology of Marxian, dialectical-immanent critique, and truly-scientific critique, of all ideology: i.e., on the Marxian dialectic itself.

In all of my life-long search, it is only in their work that I have found what I was looking for: a fundamental analysis of the entire, ancient-and-modern, occidental-and-oriental history of dialectics, allowing the extraction of the very core of all dialectic -- its <<genos>> -- from out of all of its manifold, and mutually-qualitatively-different, apparently disparate historical <<species>>, as codified, in its most simple/abstract form, in the axioms of F.E.D.'s NQ "First Dialectical Arithmetic", given here --

http://www.dialectics.org/dialectics/Correspondence_files/Letter17-06JUN2009.pdf



It is F.E.D.'s extraction of that core of dialectic -- of the universal, concrete <<aufheben>> operation/process of "self-meta-<<monad>>-ization", "self-meta-unit-ization", or of "self-meta-holon-ization" -- that provides the key to their "cracking the code" of The Dialectic of Nature in its totality, so that they are thereby enabled to express this <<Kosmos>> totality-dialectic -- to categorially summarize the Historical Dialectic of Natural History to-date, for taxonomy level 1 -- in the compact form of their "Theory of Everything" Dialectical Equation, per which the universal "common ancestor" ontological category, for the "meta-genealogy" of all cosmological ontology since, is that of the "pre-nuclear particles" [e.g., the quarks], which can be rendered as --


1>-|-<tau = <1n>^(2^tau)


-- [given typological limitations herein], for epochs tau = 0 through tau = 8, and so that they are thereby also enabled to predict a next emergence of a taxonomy level 1 new ontology -- a new kind of being -- generated categorially by this equation as its "meristem" ontological category for epoch tau = 9, as well as to express the countless other "dialectical meta-models" for the sub-totalities of that maximal totality of Nature/Universe as a whole, which constitute the contents of their Encyclopedia Dialectica.

The above "dialectical equation", using the new F.E.D. "mathematics of dialectics", describes the totality of cosmological "Natural History", including the history of human Nature, as a self-continuing, "self-iterated" <<aufheben>> process.

This continuing <<aufheben>> process, in actuality, and as modeled by F.E.D., both generates / irrupts each next, new, emergent "natural-historically-specific"<<aufheben>> operator/operation, and also, in due course, applies that <<aufheben>> operator/operation to itself, to generate the next "self-revolution in Nature", and so on . . ..

The German and Hegelian term <<aufheben>>, recall, refers to a non-propositional, non-formal-logical operation of dialectical, determinate [not "abstract"] self-negation of systems, by which the ontological content of a system simultaneously (1) elevates itself [e.g., to higher "meta-fractal" scale], (2) transforms itself [quanto-]qualitatively, "negating", or changing, one or more of its former key "determinations", i.e., of its past key qualities or "predicates", and also (3) conserves itself in terms of the core of its past reality.

For example, if a denotes the ontological category / activity / operator / operation of "atoms", and if m denotes the ontological category / operation of "molecules", then we have, using the F.E.D. dialectical algebra --

self-<<aufheben>> of a = a of a = a x a = a + m

-- wherein a is "conserved" in both the first / left-more term of the right-hand-side product/result above, and also in its second / right-more term, and also "elevated" and "determinately negated" in that right-more term, because molecules contain atoms, and also because molecules represent a "self-elevation" -- to a higher [meta-]fractal scale of the self-organization-via-aperiodic-self-dis-organization / self-revolution of the content of the cosmos -- than do atoms, and also because molecules emerge new qualities / predicates of behavior / action / process in the universe, that were unprecedented prior to the emergence / revolutionary-irruption of molecules.


In short, each molecule is an <<aufheben>> "meta-atom", because each molecule is [typically] made up out of a [usually] heterogeneous multiplicity of atoms:


"meta-unit-ization" of atoms = molecules as meta-units relative to atoms as mere units; the irruption of a new kind of <<arithmos>> of units, one of molecules;

"meta-<<monad>>-ization" of atoms = molecules as meta-<<monads>> relative to atoms as mere <<monads>>; the irruption of a new kind of <<arithmos>> of <<monads>>, one of molecules;

"meta-holon-ization" of atoms = molecules as meta-holons relative to atoms as mere holons; the irruption of a new kind of <<arithmos>> of holons, one of molecules;

"meta-acton-ization" of atoms = molecules as meta-actons relative to atoms as mere actons; the irruption of a new kind of <<arithmos>> of actons, one of molecules;



For more on these F.E.D. "dialectical meta-models", see --

http://www.dialectics.org/dialectics/Primer.html

http://www.dialectics.org/dialectics/Primer_files/4_F.E.D.%20Intro.%20Letter,%20Supplement%20B-1,%20v.2_OCR.pdf

-- especially pages B-4 through B-38.



Regards,

Miguel





 
F.E.D. definitions for some of the special terms applied in the narrative above --


<<arithmos>>
http://www.point-of-departure.org/Point-Of-Departure/ClarificationsArchive/Arithmos/Arithmos.htm

[self-]<<aufheben>>
http://www.point-of-departure.org/Point-Of-Departure/ClarificationsArchive/Aufheben/Aufheben.htm

dialectical, immanent critique
http://point-of-departure.org/Point-Of-Departure/ClarificationsArchive/ImmanentCritique/ImmanentCritique.htm
A Dialectical Theory of Everything, module # 11

immanent
http://point-of-departure.org/Point-Of-Departure/ClarificationsArchive/Immanent/Immanent.htm
A Dialectical Theory of Everything, module # 11

<<monad>>
http://www.point-of-departure.org/Point-Of-Departure/ClarificationsArchive/Monad/Monad.htm

ontological category
http://www.point-of-departure.org/Point-Of-Departure/ClarificationsArchive/Onto/Onto.htm

self-meta-holon-ization
self-meta-<<monad>>-ization
self-meta-unit-ization
http://www.point-of-departure.org/Point-Of-Departure/ClarificationsArchive/Meta/Meta.htm
http://www.point-of-departure.org/Point-Of-Departure/ClarificationsArchive/MetaMonadization/MetaMonadization.htm

systematic dialectics
http://point-of-departure.org/Point-Of-Departure/ClarificationsArchive/SystematicDialectics/SystematicDialectics.htm
http://www.dialectics.org/dialectics/Applications.html
http://www.dialectics.org/dialectics/Applications_files/F.E.D.,%20Dialectical%20Pictography,%20I.,%20Systematic%20Dialectics,%20Parts%20I-IX,%2018MAY2008_OCR.pdf

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