Elucidating the Place of Dialectic in Marx’s Thought According to Marx
[Some key passages from Marx’s writings, plus from those of Hegel and Engels, about dialectics, or exemplifying their application thereof, with commentary]

  0.    Self-Production

  1.    Self-Negation

  2.    Constant Change

  3.    Laws of Change[-in-General]

  4.    Change of Laws

  5.    The Whole-Parts Relation

  6.    Internality

Conceptual Unification of the Material Gathered Together in Part I

  0.    Section Introduction

  1.    Whole and Parts

  2.    The “World Market” [The Global Human Social Reproduction Process within the Epoch of the Capital-Relation] as Human Social Totality

  3.    The Reflexivity Paradigm of Dialectics

  4.    Dialectical Contradiction as Existential/Ontological Self-Contradiction

  5.    Dialectics = The Dynamics of Autopoiesis

  6.    ‘Self-Reflexion’ and Self-Negation

  7.    Heraclitean versus Cumulative Continuity

  8.    Definition of the Symbol ‘#’ for the Calculus of Dialectics

  9.    The Helical Course of Development as a Model of “Negation of Negation”

10.    The “State-Space” Concept and Dialectics

11.    The “Dialectic of Nature” Controversy:  ‘Proto-Subjectivity’ and ‘Pre-Dialectic’

12.    What is “Mathematics”?

Marx’s Contribution to Breaking Through the Impasse of Modern ‘Mathematico-Science’

  1.    The Mathematics of Whole and Parts:  The “Many-Body Problem”

  2.    The Nonlinearity Barrier

  3.    The Phenomenology of Nonlinearity:  Nonlinearity and ‘Organity’

[Synergy]

         a.    Non-Linearity and Non-Equilibrium
         b.    Non-Linearity as “Reflexiveness”
         c.    Non-Linearity and Logical Paradox
         d.    Reflexivity and the Problem of “Self-Forces” in Physics
         e.    The Algebraic and Geometric Phenomenology of Non-Linearity
         f.     Hyperalgebra

  4.    The ‘Operatorial’ Concept of Generalized Multiplication

[Aside:  Why Mathematics is “Greek” to So Many of Us]

  5.    ‘The Method of Flexions’

  6.    The Necessity of "Higher Operations" to Equational Solvability

  7.    The Historical Phenomenology of ‘Unsolvability’

  8.    Generalized Numbers as ‘Forces’ in Generalized-Numbers-Space

  9.    Nonlinear Numbers?

10.    Toward A Mathematics of ‘Quanto-QUALITATIVE’ CHANGE
        a.    The Biology Barrier
        b.    A Specimen of Nonlinear Arithmetic
        c.    Conjecture Concerning the ‘Fundamental Theorem of Nonlinear Algebra’

11.    TOWARD SOLUTION:  Some Possible Approaches
        a.    ‘Linguification’
        b.    ‘Logification’
        c.    ‘Reverse Analysis’
        d.    Arithmeticization

12.    ‘Idea-Dynamics’:  Boole’s “Laws of Thought” – A Newtonian Mechanics of the Human Mind, and Beyond
        a.    The Fundamental Law of Formalism
        b.    The Ideography of Simple Reproduction
        c.    The Simple Reproduction of Ideas and the Idea of Simple Reproduction
        d.    The 'Chemistry of Ideas'

  1.    Introduction to ‘The Process Algebra’
        a.    ‘Ideogrammar’ –  The ‘Chemistry of Numbers'; The 'Stoichiometry of Operations’
        b.    ‘Ideogrammar’ – The Symbolical ‘Leverage Principle’
        c.    The Process-Geometry:  Process as Operation and as Movement
              i.     State-Space Choreography
              ii.    Hypernumber State-Spaces

  2.    Dialectical Models

  3.    Existential Self-Contradiction – The Dialectical Self-Propulsion of State-Motion
        a.    An Innovation in the Ideography of Dialectical Negation
        b.    The Fundamental Equation [“Law”] of Self-Activity

  4.    Temporal Acceleration

  5.    The Ideography of Creative Processes

  6.    Power-Orbits & Limit-Cycles:  Hypernumber-Valued Dynamical Reflexive Functions as Closed-Form Solutions to Nonlinear Differential Equations?

  7.    Logical Paradoxes as “Self-Oscillators” in ‘Truth-[State-]Space’?

  8.    Asymptotically-Periodic Limit-Cycle Attractors and Non-Cyclical, Aperiodic Dynamics

  9.    Anisotropic, Inhomogeneous Hypernumber Spaces:  Multi-Qualitative Analytical Geometries

10.    The Meaning of Number-Space Anisotropy:  ‘Quanto-Qualitative Metrics’

11.    CONCLUSION:  Dialectical Process Algebra – The Musean Hypernumbers as an Engelsian Taxonomy for a Dialectical General Systems Theory?
        a.    A Logic of Verbs
        b.    The Unity of the State-Vector — Dynamical ”Laws” as Patterns of Co-Variation among the State-Variables
        c.    The “Grain”, “Gist”, or “Flow” of a Space
        d.    The “Function” of “Ordinary Numbers”
        e.    Hypernumbers and the End of Pre-History
        f.     Closing:  Opening Again

A.    Notes on Dialectics and the History of Nonlinear Dynamical Systems Theory

B.    Notes on the Qualitative Content of Arithmetic

C.    Cumulative Dynamics vs. "State Determinism" — The Dynamics of «Aufheben» Accumulative Processes

Part I:    Exegesis:

0.    Self-Production

The three quotes to follow all exemplify the concept of "self-development" or 'self-production'.  They are drawn from the most fundamental texts of three periods of Marx's work — namely, the early period [Economic-Philosophic Manuscripts], the middle period [The Grundrisse], and the late period [Capital]. They thus demonstrate the consistency with which Marx employed this concept as a basic concept, as well as instantiating a different nuance of this concept in each case.

The concept of "self-development" is often not even mentioned in discussions of the Marxian dialectic.  But in Part II we will propose this as the resolving concept for dialectics, the key to the unity of all of its moments — contradiction, negation of negation, etc. — and, via that unity, as the key to solving the central difficulties which the critics of dialectics have identified.

In the Economic-Philosophic Manuscripts [hereafter referenced as "EPM"], Marx closely connects the concept of the '''self-creation of humanity''' with the legacy he has taken over from Hegel:

"The outstanding achievement of Hegel's Phanomenologie and its final outcome, the dialectic of negativity as the moving and generating principle is ... first that Hegel conceives the self-creation of man as a process ... that he thus grasps the essence of labour and comprehends objective man ... as the outcome of man's own labour." [c1-2] [emphasis added].

This same conception reoccurs, in terms somewhat more concrete, in the section of The Grundrisse devoted to pre-capitalist social evolution («Formen Die Der Kapitalistischen Produktion Vorhergehen»):

"The act of reproduction itself changes not only the objective conditions — e.g., transforming village into town, the wilderness into agricultural clearings, etc., — but the producers change with it, by the emergence of new qualities, by transforming and developing themselves in production, forming new powers and new conceptions, new modes of intercourse, new needs, and new speech." [c1-3] [emphasis added].

In Capital, this notion forms the core of no less fundamental a definition than that of human labor itself:

"Labour is, in the first place, a process in which both man and nature participate ... he opposes himself to nature as one of her own  forces, setting in motion arms and legs, head and hands, the natural forces of his body, in order appropriate nature's productions in a form adapted to his own wants. By thus acting on the external world and changing it, he at the same time changes his own nature.  He develops his slumbering powers... " [c1-4] [emphasis added ].

This last passage beautifully embodies a dialectical overcoming of one of the most debilitating radical dualisms afflicting contemporary thought:  "humanity versus nature"; «Geistes» versus «Natur».  In this passage, humanity is recognized as a natural force, an outgrowth of nature, however unique and special.  Any opposition between humanity and the rest of nature is an internal opposition of nature, inside nature as a whole, since nature includes humanity; any such opposition is thus an inherent, immanent, self-opposition of nature. Human social development ["history"] is grasped as part of the self-activity of nature. Through human activity and industry, nature acts upon itself, works itself up. Not just humanity, but Nature also "produces". This opens upon a perspective for which humanity's 'self-production' in interaction with itself and with the rest of nature is the latest episode in the "self-development" of nature as a whole, itself. This passage thus already intimates the solution to the controversy surrounding the dialectic of nature proposed herein at the end of Part II.

Recall too that, in the "Theses on Feuerbach", Marx resolves the paradox of social change and revolution ["the educators must be educated", Thesis III] in terms of the concept of "self-change": 

"The materialistic doctrine concerning the change of circumstances and education forgets that circumstances are changed by men and that the educator must himself be educated. Hence this doctrine must divide society into two parts — one of which towers above [as in Robert Owen, Engels added]. The coincidence of the change of circumstances and of human activity or self-change can be comprehended and rationally understood only as revolutionary practice." [c1-5] Lloyd D. Easton, Kurt H. Guddat; Writings of the Young Marx on Philosophy and Society; Doubleday Anchor (NY:  1967); page 401. [emphasis added ].

1.    Self-Negation

The paradox of social change involves also the fact that "human nature" deploys itself historically — given what the historical "retroscope" of contemporary scientific tools can reveal to us — in a series of distinct social formations which differ from one another qualitatively; which disagree, in terms of their characteristic world-views, about the most fundamental issues; which display different social ontologies — albeit, cumulatively so — in terms of the subjectively and objectively existing categories of social relations of production, and which are separated temporally by human-social "catastrophes" — by periods of 'social singularity'; of mutation, collapse, or transition, quite sudden relative to what had gone on before, whose phenomena are abnormal with respect both to the periods they succeeded, and to the periods they preceded and led into.

Despite these manifest human-social-evolutionary '''singularities''', Marx definitely finds in this pattern a progressive continuum — one connected to the growth of the productive forces — but also a continuum which, apparently paradoxically at first sight, contains discontinuities; which is punctuated by revolutions and social explosions.   So distinct are the "human natures", the cultural qualities and social phenomena, internal to each of these successive social formations, that it almost appears that distinct human species with distinct human natures inhabit each one. The 'self-production' of a single — human — species propagates itself in a series of apparently incommensurable waves which rise and then fall; which build up, only to dissolve again, into an undertow which is also drawing together the succeeding wave.

This consideration of the demise of social formations brings us to a second key Marxian concept, one which contrasts sharply with, and which is in fact the exact contrary of, the one treated up to now:  The concept of "self-destruction" or 'self-negation'.  We say 'self-negation'  because Marx definitely regards these serial instances of societal demise as primarily self-caused; these social formations as bearing within themselves '''the seeds of their own destruction'''.  This concept, too, is a prominent theme in Marx's writings, as the following selections recall.  In an 1842 letter to Arnold Ruge, Marx asserts that:

" ... The main thing is to fight against the constitutional monarchy, as a hybrid creature, full of internal contradictions and bound to be self-destroying." [c1-6] [emphasis added].

This passage is important in suggesting a connection between the concept of 'self-negation' and that of "internal contradiction" or "self-contradiction". In The Grundrisse, we find Marx declaring with regard to capitalist society in particular, that "the present conditions of production can be seen as self-terminating, and thus at the same time as establishing historical presuppositions for a new kind of society." [c1-7]  And, at the climax of Capital (volume I), we find him writing:  "... capitalist production begets, with the inexorability of a law of nature, its own negation." [c1-8] [emphasis added].

2.    Constant Change

How can we resolve these two antithetical concepts, one of 'self-construction' or '''self-production''', the other of '''self-destruction''' or 'self-negation', into a single, unified, and coherent notion of the Marxian dialectic as a whole? The obvious first approximation to an answer is to posit them as mutually successive, that is as moments alternating in time, one characterizing a formation during its "rise" or "ascendant phase", the other during its 'descendant phase', "decadent phase", or "fall".  The following passage, concerning the rise and fall of the "primitive communistic" formations of human social evolution, summarizes just such a notion:

"In the last instance the community and the property resting upon it can be reduced to a specific stage in the development of the forces of production of the labouring subjects — to which correspond specific relations of these subjects with each other and with nature.  Up to a certain point, reproduction, Thereafter, it turns into dissolution."  [c1-9] [emphasis added].

So far, however, we have no indication as to why "[self-]reproduction" turns into "[self-]dissolution"; as to the causation of this turning point. Why does "continuous" 'self-construction' "suddenly" pass "dis-continuously" into 'self-destruction' at/after a certain point?  Does the system in question abruptly alter its basic behavior at that point? Or does the mere continuation and repetition of the same activity somehow build-up to a break[down]? The following quotation, drawn from the same exposition as is the previous one, gives a clue toward Marx's answer:

"The object of all these communities is preservation, i.e., the production of the individuals which constitute them as proprietors, i.e., in the same objective mode of existence, which also forms the relationship of the members to each other, and therefore forms the community itself.  But this reproduction is at the same time necessarily new production and the destruction of the old form." [c1-10] [emphasis added].

This notion implicit in the above, of the impossibility of perfect repetition, or "simple reproduction", is closely related to another major theme of the Marxian dialectic.  That latter theme holds that the world is characterized by a fundamental unity of opposites, the unity of "constancy" and "change".  Incessant [but lawful] motion, or "constant change" is inherent in material existence, which is thus not a static state of "being", but an activity:  existence is activity; existence is not a "thing", but a process, a process of existence; "existence" is made of processes.  This "Heraclitean" [c1-11] moment of dialectic is expressed by Marx in the preface to Capital (volume I), as follows:  "... the present society is no solid crystal, but an organism capable of change, and is constantly changing." [c1-12] Engels goes so far as to conceive matter as inseparable from motion. [c1-13]  He asserts that motion is "the form of existence of matter" [c1-14], and quotes with approval a passage from Hegel which states:  "... just as there is no motion without matter, so there is no matter without motion." [c1-15]  Engels makes the "indestructibility of motion" a basic premise of his dialectics. [c1-16]  By "motion", he understands "not merely crude mechanical motion, mere change of place" [c1-17], but change-in-general.  "Motion" is "heat and light, electric and magnetic stress, chemical combination and dissociation, life, and finally, consciousness." [c1-18]  Throughout his writings, Marx too refers to every sort of process — not merely mechanical, spatial motions — by the term "movement".

3.    Laws of Change[-in-General]

So far, we have cited "self-development", 'self-negation', and the 'constancy of change', or 'Heraclitean-ness', as qualities belonging to reality per Marx's dialectics.  Seeking the unity of these qualities, we can certainly attempt to find it in the "different forms of motion" paradigm suggested by the above. Of course, Engels has done just that, defining dialectics as "the science of the most general laws of all motion." [c1-19]

The concept of "laws" of motion brings out the "constancy" side of that "conjunction of contraries" named by the phrase, constant change.  Per this account, change never ceases, but it never ceases to be lawful either, and the ultimate dialectical laws of change are the "constants" within this "constant change".

Within this unceasing variation, they are the IN-variants, describing what, amidst all the change, does not change.

If Marx's major work is an exposition of "the dialectic of capital", then his own characterization of the goal of that work indicates his own embrace of a "laws of motion" definition of dialectic:

"...it is the ultimate aim of this work, to lay bare the economic law of motion of modern society." [c1-20] [emphasis added ].

But this "laws of change" definition of dialectic immediately raises new problems. What distinguishes dialectical laws of motion from, e.g., Newton's "laws of motion", i.e., from mechanics, traditionally accounted the opposite and adversary of dialectics?  Engels posits three basic "laws of motion" as constituting dialectic — quantitative-into-qualitative change, interpenetration of opposites, and negation of negation. Wherein resides the unity of these three "species", that justifies their grouping under the single, "genus", heading of "dialectic"? In Dialectics of Nature, Engels declines to deal with this question:

"we are not concerned here with writing a handbook of dialectics...hence, we cannot go into the inner interconnection of these laws with one another." [c1-21] [emphasis added ].

Nor has Marx explicitly addressed this problem in any of his writings known to this writer. Finally, we will shortly take up a central aspect of dialectic in Marx, the relation of whole and part, which at first sight seems to have nothing to do with either "motion" or "laws of motion". Does this theme too — this theme of the whole-parts relation — belong under the "laws of change" rubric from a deeper vantage-point?

Putting these objections aside for the moment, however, let us look at the patterns of change which characterize the dialectical movement according to Marx's writings.  Only after this material has been placed before us can we effectively take up the resolution of these objections in Part II.

In Marx's accounts, the "motion of development" of systems typically exhibit a 'helical' pattern whereby the original and final conditions of a system exhibit a marked mutual resemblance not shared with the intervening stage(s) of that system's [re]evolution(s), though this similarity never reduces to identity:

"... So-called original accumulation means nothing but a series of historical processes, resulting in a decomposition of the original union existing between the labouring man and his means of labor ... the separation between the man of labour and the means of labor once established, such a state of things will reproduce itself upon a constantly increasing scale, until a new and fundamental revolution in the mode of production should again overturn it, and restore the original union in a new historical  form." [c1-22] [emphasis added].

Another feature of the dialectical process in Marx's account is "transformation into the opposite", the movement of a system into a determination directly opposed to that which had previously characterized it [e.g., including, as a case in point, the self-transformation of the "ascendant phase" of a system's self-development into the 'descendant phase' of that system's self-development, i.e., the self-transitioning from system self-[re-]production / 'self-construction' to 'system self-dissolution'].

Marx's description of the historical evolution of the '''law of value''' is a classical rendition of a prime instance of this movement of diachronic / 'successional' self-opposition:

"... In so far as each single transaction invariably conforms to the laws of the exchange of commodities, the capitalist buying labour-power, the laborer selling it, and we will assume at its real value ... it is evident that the laws of appropriation or of private property, laws that are based on the production and circulation of commodities, become by their own inner and inexorable dialectic changed into their very opposite. The exchange of equivalents, the original operation with which we started, has now become turned around in such a way that there is only an apparent exchange.  This is owing to the fact:  first, that the capital which is exchanged for labour-power is itself but a portion of the product of others' labour appropriated without equivalent; and secondly, that this capital must not only be replaced by its producer, but replaced together with an added surplus ... the capitalist again and again appropriates, without equivalent, a portion of the previously materialized labour of others, and exchanges it for a greater quantity of living labour. At first, the rights of property seemed to us to be based on a man's own labour ... now, however, property turns out to be the right, on the part of the capitalist, to appropriate the unpaid labour of others or its product, and to be the impossibility, on the part of the labourer, of appropriating his own product. The separation of property from labour has become the necessary consequence of a law that apparently originated in their identity. Therefore, however much the capitalist mode of appropriation may seem to fly in the face of the original laws of commodity production, it nevertheless arises, not from a violation but, on the contrary, from the application of these laws." [c1-23] [emphasis added].

Observe what is going on in this movement. With the evolution of the commodity exchange praxis — of the becoming-commodity of an ever-widening range of previously 'unmarketed' objects of use-value, to the point, finally, that labor-power, the human power to create objects of use-value, itself becomes an object of sale or alienation — the law of exchange-value itself is evolving. The content of this law undergoes a fundamental revolution.  This law thus embodies a 'self-contradictory self-consistency', leading to a 'self-consistent self-violation'.  The cumulative, iterated application of this law, in a way which is consistent with the law itself, eventually, gradually, contradicts it. The law's application eventually leads to the negation of its original content.  Negation or contradiction of this content is thus consistent with this content — is, in fact, the consequence of continued, repeated application of that content.  This movement is thus a form of 'self-negation'.  This movement can be described as [both temporal and 'content-al'] 'advance by/leading to self-opposition'.

4.    Change of Laws

The reversal of signification of the ''law of value'' in the transition to capitalist or wage-labor-based economy points up a crucial, novel aspect of "laws of motion" in Marx's conception:  ''laws'' change.  ''Laws'' even change themselves [i.e., by their own cumulative, iterated "application", as we saw above].  This change of ''laws'' has 'meta-laws', 'transinvariants', of its own.  But even change changes.  The existence of "laws of change" dialectically entails the existence of "change of laws".

Though Marx may not have held this view with respect to "abstract", pre-human-natural "laws" [in his famous letter to Kugelmann, he states:  "... No natural laws may be done away with" [c1-24], perhaps including the three ''laws'' of dialectics stated by Engels, Marx does hold it to be true for the ''laws'' which characterize ''historically-specific'' social formations.  The qualitative gaps between successive human social formations in their evolutionary sequence of emergence — primitive communism, 'chattelism', feudalism, capitalism, socialism, or "lower communism", and ''higher communism'' — are precisely gaps separating distinct socio-politico-economic "laws" of internal self-reproduction:

"Accumulation of capital is, therefore, increase of the proletariat ... this is a law of population peculiar to the capitalist mode of production; and in fact every special historic mode of production has its own special laws of population, historically valid within its limits alone.  An abstract law of population exists for plants and animals only, and only in so far as man has not interfered with them." [c1-25] [emphasis added].

"... The present "spontaneous action of the natural laws of capital and landed property" — can only be superseded by "the spontaneous action of the laws of the social economy of free and associated labour" by the long process of development of new conditions, as was the "spontaneous action of the economical laws of slavery" and the "spontaneous action of the economical laws of serfdom." [c1-26]

5.    The Whole-Parts Relation

As noted in other terms by Bertell Ollman, key statements by Marx seem to presuppose, for their intelligibility, a peculiar kind of "non-Euclidean geometry" in which a whole is "contained" within each of its parts, the parts being at the same time "inside" that whole in the ordinary sense. [c1-27] Such a conception is paradoxical in the context of prevailing notions of wholes as mere sums, externally aggregated, of the "parts" or "part-icle-s" which they contain.

In an early manuscript, titled by its editors "Free Human Production", Marx, analyzing the process of social production as an 'interproduction' of human individuals, describes how, in such association, the other person is a "mediator between you and the species ... a redintegration of your own nature and a necessary part of your self." [c1-28] [emphasis added]. Thus, here, each part "contains" the other parts involved in their mutual whole.  In the EPM, he writes:

"It is above all necessary to avoid postulating "society" once again as an abstraction confronting the individual. The individual is the social being ... though man is a unique individual — and it is just his particularity which makes him an individual, a really individual communal being — he is equally the whole, the ideal whole, the subjective existence of society as thought and experience.  He exists in reality as the representation and the real mind of social existence, and as the sum of human manifestations of life." [c1-29] [emphasis added]

The "paradox" stated above is profoundly related to the "paradox" of self-consciousness itself.  If we describe, metaphorically, the consciousness of a human being as a "picture" of the world as a whole, including all of its parts [however distorted, biased, or disproportionate], we may describe that world as made up, in part, of beings, moving around within it, which "house" pictures of itself as a whole, moreover, pictures which include pictures of themselves [including of their own internal pictures] as well as of other, similar bodies, with their internal[ized] pictures. In that case, our mental picture of the world pictures it as containing little biased replicas of itself moving about inside it. The whole "reflects into" each of its parts.

Marx's fascinating and masterful discussions of the relations of the money commodity and of the labor-power commodity to the whole manifold of commodities in the early sections of Capital (volume 1) and, earlier, of Zur Kritik (A Contribution to the Critique of Political Economy) likewise invoke this kind of whole-parts topology. As universal equivalent and as substance of values, the money-commodity is the inner content of all other commodities as exchange-value, is "inside" each. But it is also their whole, and "contains" them; contains the whole manifold of their interconnections, the network of mutual exchange-relations ["expanded relative form of value" and "general form of value"], which renders them commodities:

"The third and lastly-developed form expresses the values of the whole world of commodities in terms of a single commodity set apart for the purpose ... a commodity can acquire a general expression of its value only by all other commodities, simultaneously with it, expressing their values in the same equivalent ... it thus becomes evident that, since the existence of commodities as values is purely social, this social existence can be expressed by the totality of their social relations alone ... the general form of relative value, embracing the whole world of commodities, converts the single commodity that is excluded from the rest, and made to play the part of the equivalent ... into the universal equivalent." [c1-30] [emphasis added].

Likewise, all normal commodities "contain" [consume] human labor-power as their source.  This labor-power is the creator of each and of their totality, of the whole manifold of commodities [a1-1].  Yet, in capitalist society, labor-power appears as but another commodity alongside all of the rest. Labor-power, grasped reproductively, also "contains" the entire manifold of commodities. The human labor-power commodity is itself the product of the consumption or "internalization" of all [other] commodity-products by their human producers. The [re]production of labor-power of appropriate quality requires food, clothing, housing, utensils, educational materials, etc., etc., etc., and therefore the machinery, raw materials, and other goods necessary to produce these. Human labor-power is thus both the ultimate producer and the ultimate consumer of the world of commodities, itself included: both of all other commodities, and of itself.

Thus, by this analysis, human social labor power is also the ultimate [re]producer of itself and consumer of itself. It contains its own past 'self' as its own source.  It contains the whole manifold of commodities and is that whole in the sense of containing all of the parts.  It dwells within each part, each commodity, as that commodity's direct socially-necessary labor-time value. Yet it also occurs "on" [inside] that manifold as but one particular commodity among others.

This quality of 'inter-presupposition' or 'inter-containment' of parts characterizing "organic wholes", in Marx's view, is highlighted in a passage from The Grundrisse describing capitalist society as an example of a concrete and of an historical totality:

"In a well-developed bourgeois system, every economic relationship presupposes other relationships in the bourgeois economic form so that every fact is at the same time also a presupposition. This is what happens in every organic system. This same organic system as a totality has its presuppositions, and its development as a totality consists precisely in subsuming all the elements of society or in creating those organs that it still lacks. It becomes an historical totality. The development towards this totality is a moment of its process and development." [c1-31] [emphasis added].

6.    Internality

Dialectical contradiction is sometimes construed as connoting what would be better termed external conflict — the collisional clash of two separate and separable entities. The quote to follow demonstrates a different conception.  Moreover, this passage is no obscure aside, but the classical formulation by Marx and Engels in their earliest collaborative book, The Holy Family, of the contradiction and mutual opposition of proletariat and bourgeoisie, one which encompasses the entire dialectic of capitalist society in their view:

"Proletariat and wealth are opposites; as such they form a single whole. They are both creations of the world of private property. The question is exactly what place each occupies in the antithesis.  It is not sufficient to declare them two sides of a single whole. [a1-2] Private property as private property, as wealth, is compelled to maintain itself, and thereby its opposite, the proletariat, in existence. That is the positive side of the antithesis, self-satisfied private property. The proletariat, on the contrary, is compelled, as proletariat, to abolish itself and thereby its opposite, private property, which determines its existence, and which makes it proletariat. It is the negative side of the antithesis, its restlessness within its very self, dissolved and self-dissolving private property.

The propertied class and the class of the proletariat present the same human self-estrangement.  But the former class feels at ease and strengthened in this self-estrangement, it recognizes estrangement as its own power and has in it the semblance of a human existence.  The latter feels annihilated in estrangement; it sees in it its own powerlessness and the reality of an inhuman existence.... Within this antithesis the private property-owner is therefore the conservative side, the proletarian the destructive side.  From the former arises the action of preserving the antithesis, from the latter the action of annihilating it. Indeed private property drives itself in its economic movement towards its own dissolution, but only through a development which does not depend on it, of which it is unconscious, and which takes place against the will of private property  by the very nature of things, only inasmuch as it produces the proletariat as proletariat, poverty which is conscious of its spiritual and physical poverty, dehumanization which is conscious of its dehumanization, and therefore self-abolishing ... when the proletariat is victorious, it by no means becomes the absolute side of society, for it is victorious only by abolishing itself and its opposite.  Then the proletariat disappears as well as the opposite which determines it, private property." [c1-32] [emphasis added]

This passage makes clear the 'internality' of dialectical contradiction according to Marx. According to that conception of dialectical contradiction, the proletariat and the bourgeoisie, the wage-labor class and the capital class, are not two mutually-external, independently self-subsistent, distinct species which could exist separately, on their own, one without the other, and which come into conflict only due to an accidental, contingent, merely external proximity.  On the contrary, there is a single totality, capitalist society, which cleaves against itself [c1-33] into two opposing "halves", owing to its own inherent nature as a totality.  The antithesis of bourgeoisie and proletariat expresses the internal contradiction  or self-contradiction of capitalist society.

Bourgeoisie as such and proletariat as such could not exist apart. They are 'inter-constitutive' and 'inter-generative'.  They are not merely externally connected, but internally connected as well; connected in their being, their inner constitution. The two cannot be separated any more than the two poles of a bar magnet can be separated. Try to cut off one pole and you end up with two new bar magnets, each one with its own instances of each of the two original poles.

It is impossible to destroy only one "side" of this cleavage and leave the other side still standing, standing alone as its own whole. To destroy one is to destroy both — is to destroy their whole, the whole out of which each derives/emerges, and within which, alone, each can exist; from which each is inseparable. It is impossible to act destructively, 'negatively', upon just one side alone.  To act upon one side, is to act upon the whole, for that side does not exist as such apart from the whole. When one side is negated, the other side is also, simultaneously, automatically, in the same single act, negated as well: the social whole of which the two sides are but [mutually opposite] parts, is negated as a whole. According to Marx' and Engels' analysis, if the proletariat abolishes capitalist private property, capital, and with it, the capitalist class, then it abolishes itself as proletariat in the same act — capitalist society as a whole is negated, and a new quality of social whole is constituted, by such negation.  Negation applies to the totality, not to only some of its parts taken separately. [Note:  This amounts to a kind of "distributive law" of the dialectical negation operation, and of the integrity of dialectical totality:  the dialectical negation operation distributes to both "sides" of a dialectical whole/antithesis, and cannot be applied to one side alone, but only to the Whole constituted of the two 'internally-related' sides — the "negative side" and the "positive side":  

It is impossible to destroy only one "side" of this human societal self-cleavage and leave the other side still standing, standing alone as its own whole. To destroy one is to destroy both — is to destroy their whole, the whole out of which each derives/emerges, and within which, alone, each can exist; from which each is inseparable. It is impossible to act destructively, 'negatively', upon just one side alone.  To act upon one side, is to act upon the whole, for that side does not exist as such apart from the whole. When one side is negated, the other side is also, simultaneously, automatically, in the same single act, negated as well: the social whole of which the two sides are but [mutually opposite] parts, is negated as a whole. According to Marx' and Engels' analysis, if the proletariat abolishes capitalist private property, capital, and with it, the capitalist class, then it abolishes itself as proletariat in the same act — capitalist society as a whole is negated, and a new quality of social whole is constituted, by such negation.  Negation applies to the totality, not to only some of its parts taken separately. [Note:  This amounts to a kind of "distributive law" of the dialectical negation operation, and of the integrity of dialectical totality:  the dialectical negation operation, n, distributes to both "sides" of a dialectical whole/antithesis, and cannot be applied to one side alone, but only to the Whole, W, constituted of the two 'internally-related' sides — the "negative side", s_—, and the "positive side", s₊.

W = [ s_— s₊ ]    n W  = n ( s_— s₊ )  =  [ ( n s_—  ) ( n s₊ ) ]  =  s_—   [ s_— s₊ ]  =  [ ( s_— s_— )    ( s_— s₊ ) ]    [ s_— ( n s₊ ) ]    [ ( n s_— )  s₊ ]

Though opposites, the two "sides" of capitalist society share at least one quality in common — "estrangement", founded in the fundamental, continually-repeated act of the society of capital itself, which is the "alienation", or selling, of labor-power — the selling-away, or "alienation", of the power to create, of the substance of human creative power itself.  This is simply the historically specific, essential quality of the whole to which they both belong:  capital; 'capital-ist society'.  It is only their relation to this same essential quality that is different and in fact, opposed.

The unified meaning of the terms "dialectical contradiction", "mutual opposition", and "antithesis", as it emerges from this passage, is best clarified by the term "internal contradiction" or, better still, by the term "self-contradiction". [c1-34]  We say "self-contradiction" because the "inner cleavage against itself" of a totality arises immanently from its own nature, from its own essence. The cause of the inner division of the totality is the totality itself; this internal cleavage is a 'self-cleavage'. [c1-35] The prefix "self" thus here refers to the totality or whole and not to either of its internal, opposed sides taken separately.

An important feature of the passage above is the connection it suggests, explicitly in the final paragraph, between continually-present inherent, immanent, internal, or self-contradiction and [eventual/future] self-negation. This connection is amplified in another early statement by Marx, written a year earlier than the one quoted above. In it, the proletariat, from which the negating action transforming the capitalist totality must finally arise according to Marx's theory [if the self-dissolution of capitalism is to result in something higher, as opposed to "the mutual ruin of the contending classes" [c1-36]] is defined as the already existing negation of that capital/private property totality; the negation of that totality which co-exists with it within it and which that totality engenders, and net-expandedly reproduces over the entirety of its [ascendant phase] historical time, but which that totality thus also always already contains inside itself, from the very inception of its self-reproduction as such, as the present seed of its eventual, future, passing away:

"When the proletariat announces the dissolution of the existing social order, it only declares the secret of its own existence, for it is the effective dissolution of this order.  When the proletariat demands the negation of private property it only lays down as a principle for society what society has already made a principle for the proletariat, and what the latter already involuntarily embodies as the negative result of [capitalist] society." [c1-37] [emphasis added]

Thus we begin to see, in the passage above, some connection between the concept of dialectical contradiction, or self-contradiction, and that of "self-induced motion/change" or "system-induced motion/change of a system" [as system "self-negation"] in the generalized sense of the term "motion" introduced earlier.

This concludes the task of exegesis and preliminary commentary.  With the material now before us, we can proceed to resolving the problems it raises, and to synthesizing the moments of the dialectic, as represented in this section, into a unified conception — the task to which Part II  is devoted.

Part II - Synthesis:

0.    Section Introduction
            

In Part I we observed the written recordings of Marx using the dialectic in his work, the dialectical conceptual process [or logic] at work in his mind, as objectified in his published and unpublished [posthumously published, private] writings, plus a few instances of direct 'meta-commentary' on the dialectic itself, i.e., comments with the dialectic as their object [and "subject" in the sense of "topic", as opposed to in the sense of "agent"]. That process of data gathering and observation has bequeathed to us a number of problems. The material collected in the last section comprises a variety of themes whose unity, though felt perhaps, is far from obvious [explicit] and articulated in that source material. The task of this middle section is to bring this feeling of unity up into articulation, to comprehend the unity of the themes broached in Part I, which unity is the "Dialectic" according to Marx. This task bridges the way to the next section, Part III, which is charged with bringing that conception of the dialectic up to date, and with locating its significance and utility/necessity in the context of twentieth century knowledge; in the context of the development of human science [and ideology] since Marx's time.

1.    Whole and Parts

The first four (4) themes brought forth in the last section, namely, dialectic as (0) 'self-production', as (1) 'self-negation' [including as "self-change" and as ''self-development''], as (2) "constant change", and as (3) patterns [or "general laws"] of that constant change, already bear at least a semblance of unity, via the concept of "Motion-in-General".  The question we raised there with regard to this rubric for the unity of dialectic still remains to be resolved.  The theme which still seems to except itself, to elude that unification, is the 6th theme that we introduced there, that of dialectic as (5) the whole-parts relation, i.e., the totality/constituents-of-totality relation. Therefore, let us "take this tiger by the tail", and begin with the whole/parts relation and, with it, with the most recalcitrant of our unification-tasks.

One way to get at this unification problem is to contrast the Marxian conception of the whole-parts relation with those of other, anti- or un-dialectical, traditions.  The major opponent of the Marxian view of the whole-parts relation is that historical tendency which has been named "Mechanism", "Atomism", or "Reductionism". According to this view, fundamental reality resides in a collection of "fundamental particles" or [conceptual] "atoms" [not [necessarily] the "atoms" of chemistry] — "physical" or "logical" atoms — which compose, by mere aggregation, all other formations in the universe.  The key feature of these "particles" is their independence and irreducibility. They are supposedly "simple", without parts or internal features [without any 'internity'], and therefore incapable of further subdivision.  And, most important of all, they are supposed to be individually, or separately and 'mutually-independently', self-subsistent.

That is, they are supposedly capable of existing alone, in isolation from any other particle or formation of particles, and, furthermore, their aggregation with other particles does not in any way alter their intrinsic qualities; they retain the same, immutable qualities whether alone or in aggregation with others.  In an atomistic theory, all systems are merely collections, merely [physicalized-spatialized or physical-spatially localized] "sets" — sums of parts — collections of mutually alienated part-iculars, and reducible thereto, those part-iculars being nothing other than these invariant part-icles. Different combinations of these part-icles produce different observable qualities.  But the [pseudo-]"wholes", formed by these particles, supposedly present only the "summed" qualities of the particles; there is nothing "more" to the whole than is contained in its part-icle-s. That is, from the point of view of the dialectical tradition, aggregate formations thusly conceived would, if they could actually exist as such, not really be "organic" or "organismic" wholes at all, but mere, essentially structureless "heaps", "piles", or "jumbles". Or, any actual difference at all between such a "jumble" and a structured organization of a second, similar mass and composition of materials would be denied by such an atomist/reductionist.

At this juncture it is perhaps best to proceed by taking as our example of a "whole" that societally-maximal "whole of reference" involved explicitly in Marx' Critique of Political Economy as such — namely, the World Market [not yet the material totality of Nature; the Cosmos as a whole].  In what way does this "whole" embody the dialectical whole-parts relation à la Marx? — the non-Euclidean geometry of "whole inside each part"?  An atomistic analysis of the World Market might see it as a mere collection of basically "autarkic", self-sufficient, self-subsistent regions, or nations, which could very well get on as they are without one another; which could just as well be situated on different planets, isolated from one another, and still present the same cultural, etc. qualities/phenomenologies as they do in their present, actual, and intricate inter-association, including through their actual, past and present, continual material interchange, mediated through the Capital-relation-based World-Market as presently-ultimate human social relation of  [human-society-re-]production.

A dialectical analysis, however, would bring out the significance of the division of activities, of the specialization and organization of labor, growing up among these nations and regions as a result of their interchange of people, raw materials, goods, commodities, money, capital, etc. Consider the actual, present World-Market of our globe.  How long could Japan continue to exist, continue to be "Japan" as we know it today, if it were suddenly severed from the World Market — if the incessant flow of imports and exports were cut off, even for a few months?  Or, West Germany? The cases of the U.S., the U.S.S.R., and mainland China are the exceptions — very partial exceptions, and becoming less exceptional by the day — but are ''exceptions which prove the rule'', rooted, in part, all the way back in the continental configuration aspect of the "natural basis" of human society on planet Earth!  The vast territorial expanses and populations of these three geographical colossi were large enough to allow, for them, a certain degree of independence from the emerging World Market; a degree of autarkic development.  They became "large" enough in these two dimensions — population and territory [with the latter tending to correlate, also, with vastness in natural resources of all kinds], to be, to a limited degree, "World-Markets unto themselves". Their presence in the world geo-political "field" has contributed a major perturbation to the evolution of the World-Market system as the totality "Capital", according to the first-approximation layer of the "laws of human social evolution", as discovered mainly by Marx. Their presence is nonetheless lawful, at a deeper, more concrete, layer of approximation of those "laws". However, from the point of view of the first approximation, their emergence appears as a detour or distortion.  However, this "detour" has been — and had to be, if the first approximation "laws" are correct for their level of abstraction — a "transient" of the global system of evolving humanity. This transient is presently "damping out", as Eastern Europe, the USSR, and China, not to mention the U.S., discover, in their subsequent development, the necessity for increasing involvement in world trade and the World Market division of labor.  Therefore, the trajectory of the evolution of world production-relations and production-forces is recently coming increasingly, "asymptotically", to exemplify more closely the 'first-approximation' ' "law"-of-value lawful'  trajectory.

2.    The “World Market” [The Global Human Social Reproduction Process within the Epoch of the Capital-Relation] as Human Social Totality

Perhaps the single most important discovery of Marx — his ' "law" [dynamic] of human social evolution' — is rooted in this very realization of human society — of the capital-based World-Market in particular — as a dialectical whole, not an atomistic, pseudo-, whole. This "law" is that the growth of the human-productive force — of the "self-force" or actualized acceleratory capacity of human-societal self-reproduction, the societal self-reproductive power of human society, or human-societal self-[re-]productivity — is the fundamental "subversive" human social force which reshapes human "society" as a system of social relationships — of social relations of [human social self-re-]production; which propels the leap from one human social formation into a qualitatively different, higher one [higher in the sense of increased net human social negentropy and of increased spiritual/regenerative/remedial value] — not conscious social or political will alone — throughout the period of human pre-history [which, for Marx, ends with the end of Capitalism, and which "pre-historical times" are, thus, by that definition, very much still underway today!

This "law" or dynamic, that is, links the quality of human society — the overall flavor and character of the prevailing system of social relations and "culture" — with the quantity of human society, that is, with a measure of the magnitude of human society's self-reproductive force, whose first-level approximation is the quantity of the human social population itself, and whose successively more accurate approximations include the quantity of the adult, social-negentropically productive population, coupled with a measure of the total fund of the productive skills or creative powers developed in that population.

First of all — it must be reclarified — due especially to the impacts of the prolonged disinformation campaign of the 'Zeroist'/'Negativist' ideology — the plutocracy-sponsored ideology advocating  "Zero" [in truth, catastrophic, "Negative"] economic growth, and "Zero" [in truth, omni-genocidal, "Negative"] population growth — that a certain level of per capita social productivity, or of the society-productive forces, is necessary to sustain a human population beyond a certain quantity of human social individuals. So far, this assertion stays within the "quantity" side of Marx's "law". Tribal hunting, gathering, foraging, and scavenging — predation technology — cannot support anywhere near as high a level of human population as can Neolithic agriculture/domestication technology. Likewise, industrialized agriculture, and industrialized manufacturing in general — using mechanized and electronic/partially-automated collective tools — can support a much larger population than can Neolithic agriculture/plant-and-animal-societies-domestication.

Secondly, a definite range of the quantitative level of human population is necessary to each level of elaboration of the wealth of human culture. This has to do with the depth of texture of the division of labor, and the depth of cultivation and specialization of activity, one of whose limiting factors is the size of the 'inter-producing' and self-reproducing human population. You're not going to get great pianists, great orchestras, great symphonic works, from a Paleolithic tribe. You're not even going to get pianos! You'd be lucky to get even relatively developed stringed instruments. A Paleolithic tribe cannot afford, and cannot achieve, the depth of development of interacting creative capabilities, of interacting specializations, that such qualities of individual human development, such levels of cultural attainment, require.

One of the reasons is that there simply aren't enough people in such a tribe.  There are certain social "positions" which must be "manned" and/or "womanned" if the tribal society is to continue — is to be reproduced — for another day, for another month, for another year, or for another generation; certain "battle stations" in the tribe's struggle for existence that must be covered.  And there are only so many social individuals to go around.  Nor is the social surplus product of a Paleolithic tribe sufficient to support a deep elaboration of human faculties in a multitude of different directions. Human populations of successively larger size-ranges form a necessary pre-condition for progressively higher degrees of differentiation and elaboration of human powers and, therefore, of cultural richness, of social wealth.  Such population growth ranges or levels do not, in and of themselves alone, guarantee the potentially corresponding levels of such societal wealth, or richness of quality of life.  Such size ranges do not constitute sufficient conditions, but they do constitute pre-conditions, necessary, but not at all "inevitable-izing" in themselves. They imply a certain fund of human social surplus product — of potential "human social free energy" or "human social negentropy", which can be applied to the production of such human social prosperity — spiritual and mental as well as "physical" prosperity.  Whether it will be so applied, however, is a matter of the actual story of human history, of the actualized individual and collective choices and actions; of the expressed collective will of concrete humanity, as mediated through the popular institutions of human social governance, which, during the class society phase of human history, have been ruling-class-dominated.

Wealth is the redintegrated differentiation of human activities and capacities — redintegrated from the point of view of contributing to human societal self-reproduction, to human social evolution, to the concrete manufacture of human history as the actual story of [wo]man, and to human social individual self-realization.  A certain level of human population and productivity are required to make possible a certain degree of this differentiation and elaboration of human activity. Too few people and there simply aren't enough people to fill the opportunities or "social openings" ['''human social niches'''] that arise for greater elaboration, and thus to become "exceptional" human social individuals. Or, the exceptional effort of specialization required, at low levels of 'human activity articulation',  is too narrowing, which results in another kind of loss. Too low a productivity and the population level itself is endangered, the people produced are too "strung-out" to maintain — let alone advance — the level of social creativity/productivity.  Or, the opportunities, the "social openings ['niches']" don't arise to be filled in the first place; the society can't afford to spare sufficient individuals from the predominant mode of social mere-subsistence activities.

Human social wealth is not a question of "fine" or refined objects of wealth isolated as objects. One fine piano, one great Stradivarius violin, is not the issue. The realization of a given refinement-level of activity and its products as social wealth presupposes a certain multiplicity of [re]production — otherwise it is but "the exception which proves the rule" of a lower level of social wealth actualization.  Were we to abandon our technology and our other cultural acquisitions, and revert to tribal ways, we could perhaps still, within that first generation, and maybe within a second generation, make high-quality steel, high-quality utensils, even wood frame homes, as curiosities, but in ever-diminishing quantity [as well as quality].

Quantity and quality are linked here too.  Until, for example, there are enough musicians, enough audiences, and a high enough level of musical activity and appreciation, certain levels of refinement in musical instruments, musical compositions, etc., are virtually unattainable.  There is not enough need, not enough demand, to support the development of the gifted, and of the rare, and of the so-inclined individuals in devoting/investing the time and facilities required to attain such levels of quality.

Quantity and quality do not form an antinomy, a radical dualism, but rather a profound and ongoing interpenetration.

The reverse is also true.  If you "quantitatively" reduce the human population and productivity of human society, shrink the World-Market — or, shrink what resides behind it, and is valuable from a socialist, sublating point of view — the world organization of human labor; the objective socialization of the means of human social [re-]production, and of the process of human social [re-]production — you thereby induce a lower quality of human society.  If you attack the productivity of human labor, you force a decline in human population through grisly mass death, via the resulting contraction in per capita output, because the resulting social product is insufficient to support the extant human population.

If you cut off part of the world from world trade, it withers, like an organ severed from the organic body which birthed it. One region of world society is enabled to specialize in certain forms and fields of human activity/production to the point of bringing them to the highest contemporary standards' quality of development, only because other regions contemporaneously do likewise in other fields — because other regions are performing other productive activities to a higher degree of specialization, of quality, and of productivity. Cut off the 'interflow' of these productions, and each region has to go back to providing "everything" for itself, spread thin, with less expertise, and at lower quality, thus lowering the quality of total social wealth, of human social synergy/negentropy, for all regions so cut-off: human social 'de-connexion'  reduced totality increased human social entropy / decreased human social organization, e.g., in the sense of Chardinian "complexity-consciousness".   

In a developed World-Market, the different continents and nations should be grasped as homologous to different geographical organs of a world geographical social-reproductive organism. Autarkic "local self-sufficiency" is analogous to a liver cell or an entire liver, spleen, etc., seceding from a human body and trying to go it alone. If it can survive at all — which is most unlikely — it could only do so more poorly than before, and as something other than and less than what it was before. It is a delusion of abstraction to think that an organic part can be separated from its organic whole and yet remain as it was.  In reality, its old characteristics and identity are destroyed by such severance.

The "World Market" global economy which comes into existence with — and as the fruition of — the capitalist stage of humanity's 'self-production' and "self-development", is no "set", no mechanical, linear, distributive superposition, or merely-aggregative sum of parts, but a dialectical totality, and is also the final totality of reference — short of cosmological Nature itself, as a whole — in all of Marx's works on his immanent critique of "political economy".

The very value of objects, of human social artifacts, including their economic [exchange-]value as well as their use-value, is determined in a dialectical way, i.e., is a 'totality-relation', a relation of the particular object to the World-Market as a totality.  For example, surplus value exists only in relation to the total working class and to the state of the capital-relation-based World Market social-relationship-of-production. Thus, a transistor would be an object without value in the context of 19th Century capitalism, and a single, isolated factory producing transistors would produce no exchangeable value, and thus no surplus-value, regardless of the number of hours worked by its workers in relation to the labor-time-value of their subsistence-costs.  An object like a transistor can become an object of value, of profitability, only in the context of a world division of labor elaborate enough, and a human population sophisticated enough, to make personal utility [and social-reproductive use] of such an object.  The value produced at a given factory or by a given worker depends upon the state of the rest of the world social reproductive system/network as well as upon that factory's or worker's own state, and not just upon its own state alone.  Value is totality-determined.  [Note that the totality to which any '''self''' belongs, or in which any " 'self' " inheres, includes that self, and thus also includes the moment of self-referential determination, self-reflexive determination, karmic determination, non-linear determination, or self-determination]. This also works the other way around:  a factory producing a tremendous amount of exchangeable value — in the form, say, of vacuum tubes, or of [e.g., Swiss] mechanical watches, or of mechanical calculators — can find the value of its efforts suddenly, drastically fall, through no apparent causative change in its own operations or local situation. This fall in value can occur due to "non-local causes", e.g., by virtue of the development, installation, and utilization, of a new product, say of transistors, or of digital electronic watches, or of digital electronic hand calculators, at [initially] geographically remote localities in the world reproductive network [which global reproductive network presently takes the form of global Capital, or of the capital-based World Market].

Though we have yet to fully develop the conceptual tools, and the social-statistical, social-census infrastructure to measure it, this "lawful" pattern of interconnection of human social quantity and of human social quality, this principle of incipient human 'sociometry', is, so far, best placed under the rubric of 'human social negentropy', or ''human social negative entropy', as the human-societal form/level/quality of the universal phenomenon of negentropy — of "free energy", 'anti-entropy, or 'antentropy'.  Human social negentropy refers to the interconnectedness of the "size" [mass, population] and "complexity[-consciousness]" [level of organization or of self-interconnexion] of human-society-in-evolution, such as we have just attempted to describe. The dialectical-logical analysis of the whole-parts relation we have picked up in Marx is the kind of logic necessary for the comprehension of social reproduction. And until humanity understands its own social self-reproductive process, humanity will be unable to achieve practical, true-in-daily-life, concrete freedom, that is, a democratically 'self-planning society', an actualized and democratic political-economy, a political-economic democracy — and thus, the conscious, artful, aesthetic, collective, desirable, and democratic partial design of its own future history; not bureaucratic, totalitarian state-capitalism, but that higher level of human social negentropy known as truly "social[ist] society".

All this is not to say that all present — capital-profit-driven — industrial activities are negentropic, that [relative] pollution does not exist, that population should always grow or can never reach a size that is too large for the existing productive forces and other facilities. Much social "production" today is actually net 'un-production'; is actually devoted to the destruction of previously created human social negentropy or [human-social, holistic-]use-value, due to the enfetterment and perversion increasingly imposed by the Capital-relation upon the human societal-[self-re-]productive self-forces in late/decadent-phase capitalism.

Examples include most military production, although some of the technological development engendered by military spending can be partially recouped for human social-negentropic purposes [just as, on the other side of the human 'social-profitability ledger', earlier-produced objects [and '''laboring subjects'''] of human social negentropy can be «detourned» into activities which produce social entropy and waste, e.g., those of "overkill" military "production", "production" of life-destroying tobacco products, of side-effect-laden, lethal pharmaceutical 'pseudo-medicines', and of diabetes-, heart-disease-, and cancer-inducing 'pseudo-food'. Such is always the case «in potentia»]. No social activity is absolutely, but only relatively, "entropic" or "negentropic".  The burgeoning of such human-socially "entropic", or social-organization-depleting and -destroying — and human-socially malignant — social activities and industries, is a sign of the inner crisis of Capital, which has been festering and metastasizing since WWI; is a manifestation of the distortion, perversion, enfetterment and, finally, the dissipation and destruction [reversal] of the growth of the [human society-re-]productive forces enforced by the Capital-relation at this stage of the development of those [self-]productive [self-]forces, as foretold by Marx on the basis of the "law" of human social evolution he discovered, as noted above.

Specifically, it is true, because of the finite nature of all material resources, that the problem of social reproduction is never finally solved. That problem is, rather, constantly reproduced to a higher degree, and on a higher level/scale, and, in the normal course, resolved anew in a continuing, upward-turning helical spiral. The technology-specific natural resources which any technology of human social reproduction both calls into consciousness and draws upon to sustain human social life and growth are always inherently finite in extent, and eventually approach exhaustion. A new innovation or system of innovations is episodically [and continually!] required to then supersede the old natural resource base of human society with a fresh natural basis for human social self-production. Therefore, human faculties must be ever cultivated to higher degrees and into higher, emergent qualities — even from the point of view of "bare, material survival" — which cultivation depends upon the health of the total human social reproductive process [at least for so long as humanity remains humanity, constrained by its extant physical vehicles].

To the extent that the arts, including music, contribute to the elevation of human consciousness, and to the "triggering" of "creative bursts" and sustained cognitive and technological advances, as well as to the maintenance and upkeep of human creative faculties, to the widening of the internal mental and emotional horizons of their experiencers and audiences, as well as of their producers, then these arts are also quite vital from a human social reproductive standpoint. This is so even apart from their contribution to the higher dimensions of human realization which, while not necessarily antagonistic or 'uncontributory' to human social reproduction in the least, are experiences which appear as ends-in-themselves, self-ends. In that self-justifying characteristic, they are unlike most of the rest of human social reproductive activity, which is not consciously an end-in-itself; not its own self-justifying purpose. That is, these "aesthetic" experiences are experiences without which mere societal sustenance and material wealth, and human life itself, may lose their charm, their relish, and their meaning, and may thus encourage in part, 'resultingly' desperate individuals, however well-fed, to escape life, through drug addiction, or through even more direct and immediate forms of suicide, or through the pursuit of sadistic and parasitic forms of tyrannical, unchecked political power, mass torture, and mass murder, etc., etc.

The foregoing argument only points up the general realization that the deeper basis of human social wealth, the real core of the '''human productive forces''', is neither "raw", "unimproved" natural resources, as the more '''bestial''' versions of economic ideology, such as 'Zeroism'/'Negativism', would have it, nor humanity-sub-created/humanity-improved nature, in the form of instrumental, technological facilities, heavy-industrial "fixed assets", and massive public-works infrastructure, as Stalinism would have it. The deeper basis of human social wealth is, on the contrary, the attained and sustained level/quality of development of the general human social individual, of the self-powers and developed creative, cognitive faculties, and manual, skill-faculties and capacities of the working and creating human population.

Such a perspective on culture, on "the arts and sciences", has been largely lost and hard to attain even a glimpse of, let alone sustain, in the ideological environment of the last nine decades, wherein "art", including music, has increasingly taken the form of a degenerative reflection of a degenerating interregnum of partially blocked or failed human social evolution.  This perspective nonetheless remains true to the experience of those who have dwelt — however briefly or 'sustainedly' — at the outer limits of contemporary knowledge. They regularly report finding both stimulus and sustenance for their creative powers and processes in the preserved high points of ascendant phase capitalist artistic and scientific productions.

By means of the foregoing arguments I have asserted a special case of, and hope also, thereby, to have made clear, by illustrating, what is meant in general by that formulation of the principle of "holonomic" '''fractality''' / "recursivity" / 'self-reflexivity' which holds that a true whole dwells implicitly within each of its parts as their inner premise and support, as well as being constituted by them — in short, which holds that there exists a relationship of 'inter-presupposition' between dialectical, historical, concrete totalities and their constitutive parts.

Unsupported by the results of the existence of other parts of the world human social reproductive organism — by those of other human social individuals worldwide — a formation like contemporary Japan or West Germany would rapidly become impossible, unsupportable, and would rapidly degenerate from its present social quality, and quickly die out — would vanish, if extracted as if a "separable part" from that organism.  Its existence is premised upon the existence of the rest of the world reproductive network, and changes locally as that network changes globally, or changes in others of its localities. Remote, "non-local" actions within the World Market [sub-]totality can have local consequences for such a locality. The existence of such localities is not simply locally constituted:  that existence is globally constituted. That local existence changes or disappears with changes or disappearances in that global "rest-of-the totality".

Unsupported by the results of the existence of other parts of the world human social reproductive organism — by those of other human social individuals worldwide — a formation like your contemporary very personal self would rapidly become impossible, unsupportable, and would rapidly degenerate from its present social quality, and quickly die out — would vanish — if extracted as if a "separable part" from that organism, or if deprived of its current connections to those others. The 'Zeroist'/'Negativist' ideology, engineered, funded, and propagated by the ruling capitalist plutocracy, encourages you to consider all of those others as expendable as far as your own life and being are concerned; to consider all of those others as mere "over-population"; mere "pollution-people", whose extermination, purportedly, will actually improve your own standard of living. This pro-genocide sub-text of the '''People are Pollution''' pseudo-ecology movement inculcates a 'Meta-Nazi' delusion, aided and abetted by the illusions of the contemporary human social unconscious mind which the capitalist money-economy also reinforces.

If each part "contains" the whole, it thus also "contains" the other parts, of which that whole is constituted.  If each part truly "contains" the whole, it therefore also "contains" all  of the parts of that whole, and thus "contains" itself as well, as one part among those parts, implying a regress, though not an infinite one.  Let us therefore try defining "dialectics" — as the 'genericity' or generalization of the [existential] dialectic of an[y] [ev]entity — as the 'metry' of the total, dynamical relationship between that [ev]entity as part and its whole, i.e., and the totality in which it inheres [with respect to the universe of discourse appropriate for a given analysis in question].

This includes not only the relation of that [ev]entity to its "externity", to its "environment", but also its self-relation — its "internity" or "internal environment" as a relation.  It is "environed", or surrounded, not only by that which is external to it. It is also surrounded from within by its own past self [or selves], stored "as if" inside it, as well.  Thus this definition seems capable of encompassing both the "external forces", 'alien determination', or "external-determination" of the dynamics of that [ev]entity, and its internal-determination or self-determination, its internal-forces/self-forces — its "freedom" — as well.

Both (1) an [ev]entity's "independent-of-self" shaping/deflection/'other-determination' by its environment, by its "other-ness", and (2) its "self-production" or "self-action" "self-determination" — including those portions of the latter which are the "echoes" and "returns" of/upon it of its own past actions, mediated back to it through its "otherness"/external environment — are encompassed by this definition. Thus grasped, we hypothesize, the totality-determination/total determination of the being/becoming of each [ev]entity, containing within it two distinct moments — 'other-determination' + 'self-determination' — is encompassed by this definition [caveat:  most of content that these twin and intertwined categories should encompass for a typical [ev]entity may be beyond the knowledge/science, to date, of humankind.  I.e., for but one example:  we only "recently" became aware of the — invisible to our naked eyes — 'trans-violet' and 'sub-scarlet' ranges of the spectrum of the galactically- and trans-galactically-sourced electromagnetic radiation that pervades and bathes the galaxies, including our own bodies, from moment to moment].

Therefore, that Totality is only 'self-producing' and only 'self-developing'; only "[self-]reflexive.  If it changes, if it is a dynamical and not a statical Totality, then its change(s) can only be self-induced — the result of "self-action"; of self-interaction, or, at least, of the 'intra-actions' of [some of] the parts composing it, e.g., of the internal processes of its — inherent in its — existence.  For this Totality has no 'out-side'. No material agency or environment exists outside it — no external physical forces — that could act from without it to induce change in it.  If it "moves", it must be self-moving; self-propelled [in terms of physical [manifest] causes]. Thus, 'self-dynamical' Totality itself is the supreme model for "self-development". Therefore, to concentrate upon this self-reflexive aspect of the 'totality-relation' — to concentrate upon the dialectic of any [ev]entity contained within that Totality — is to concentrate upon that eventity's aspect as a concrete [sub-]totality, as a [partial] wholeness, as a [partial] universe[-unto-itself], as a "being-for-itself", that is, as a 'self-beholding'/'self-interacting' being, as opposed to its aspect as a mere part of any "larger" [sub-]totality. True, that larger [but perhaps still sub-]totality partially determines this eventity's existence externally, or as an external cause of that existence. Hence, with respect to that [sub-]totality, this [ev]entity may exist as "being-in-itself" "being-for-another", and, specifically, as "being-for-the-rest-of-that larger [sub-]totality that contains it — as well as existing as part of the full material Totality, the Universe as a whole.

Only in the case of that maximal Totality do "self-determination" and "other-determination"; "other-/external-causation" and "self-/internal-causation"; "other-relation" and "self-relation" — "being-in-self" and "being-for-self" — coincide.  In the case of that ultimate material Totality, we may say that the moment of 'other-determination' simply vanishes, or, perhaps more fruitfully, that this moment becomes one of a "self-otherness". In this concept of 'self-otherization', we may discover the general philosophical concept of 'self-alien-ation', the concept of a "subject", or "agent", or "self", making itself alien to itself; foreign to itself; a stranger to itself [cf. the ancient "law-of-karma" concept of 'self-duplication' as an 'echoic', action-self-mirroring "meeting self", or 'meeting of/encounter with past self-as-action by later self-as-action', i.e., as a delayed, time-lagged, time-offset symmetry — the later "meeting" or confrontation of a human personal self with the consequences of [a] past state(s) of its own action(s), committed by it upon the world, upon the totality, or, mainly, upon a portion thereof; upon [an]other('s) of that human personal sel(f)(ves), whether or not those consequences return later to that 'committor' as personified in the form of the actions of another single human individual, or of a group of such individuals, as later similar actions of that rest-of-the-totality, or, mainly, of a portion thereof, back upon the human personal self of the committor who had initiated those earlier similar actions upon that rest-of-the-totality, or, mainly, upon a portion thereof; upon [an]other sel(f)(ves)].

Marx applied this philosophical concept of "self-alienation" to the critique of political economy, wherein human self-alienation = self-selling — e.g., starting from (1) in its most implicit, rudimentary, indirect historical form, self-selling = barter exchange, exchange of products of the self, products produced by a specific human social individual — objectifications of the self of that individual — all the way out to (2) in its most direct, most naked, most elaborated form, self-selling = wage-labour. This latter species of self-selling — the selling away of control of the use of the majority of the human population's own life-[lives-]time to personified Capital; the making alien to itself, foreign to itself, estranged from itself of the majority of the hours of the very life[-time] of each so proletarianized, so prostituted human individual self — is the action which causes [and elaborates] the 'world inversion'; the practical inversion/[counter-]revolution of historical subject/historical agent versus historical object; the reification of Capital; the making into a 'pseudo-object' of the collective subject-ivity of [the ever-greater majority of] proletarianized and progressively proletarianizing humanity, and the making into a human life-/society-/history-shaping 'pseudo-subject', 'pseudo-agent' — 'pseudo-«Geist», and 'pseudo-God' — of Capital-value and thus of its [unintended, un-legislated, un-consented-to] "law-of-value"; the loss [or never-gain] of conscious human control of human social hi-story. The latter is but a special, historically-specific case — as well as, perhaps, the 'insighting' and inciting origin — of this general philosophical concept of self-alienation.
 
Thus, we have come to see that the theme of dialectic as ["laws" of[ self-development or of self-reflexive action — the self-reflexivity paradigm of dialectics — arises out of the dialectical whole-parts relation theme itself. The whole-parts interaction concept — and the concept that the existence of each part is determined by its totality, itself included — includes, as we have seen, above, and as we shall see further, below, both the moment of inherent, immanent, 'essence-ial, or internal determination / self-interaction / self-determination, and the moment of external determination / other-interaction / other-determination, of the existential elaboration or total development [life-course] of each such part of the whole-of-reference, or totality-of-reference, for that part.

3.    The Reflexivity Paradigm of Dialectics

4.    Dialectical Contradiction as Existential/Ontological Self-Contradiction

5.    Dialectics = The Dynamics of Autopoiesis

6.    ‘Self-Reflexion’ and Self-Negation

7.    Heraclitean versus Cumulative Continuity

8.    Definition of the Symbol ‘#’ for the Calculus of Dialectics

9.    The Helical Course of Development as a Model of “Negation of Negation”

10.    The “State-Space” Concept and Dialectics

11.    The “Dialectic of Nature” Controversy:  ‘Proto-Subjectivity’ and ‘Pre-Dialectic’

12.    What is “Mathematics”?

Part III – Significance:
Dialectics and Non-Linearity
[text to be included in the v3.0 release]

Part IV – Partial Fruition:
Towards a Calculus of Dialectics
[text to be included in the v3.0 release]

Reader's Key
[text to be included in the v3.0 release]