Full Title: Systematic-Dialectical-Mathematical Model of the Value-Form Content of the Three Volumes of Marx's Capital, Translated into a "Q&A" Dialogue.
Below I have extracted, for your benefit in regard to '''knowledge
representation condensation''' in the domain of Marxian
social-revolutionary theory, the section from pages I-42 through I-46 of F.E.D. Vignette #4, The Goedelian Dialectic of the Standard Arithmetics.
"There is a much simpler, 8-term model of the ‘‘‘Value-Form Dialectic’’’ content of Marx’s Capital.
This simpler model averts the ‘homeomorphic defect cited above.
But it is also far less detailed in its coverage of that content, due to its issuing from a ‘‘‘shallower’’’ «arché».
The «arché» of this simpler model is the alternative «arché»/“cell-form” that Marx mentions in the passage from his Preface to Capital, quoted above: “...in bourgeois society the commodity-form of the product of labour -- or the value-form of the commodity -- is the economic cell-form.” [emphasis added by M.D.].
This simpler, 8-term model also averts the issues of ‘sub-tabular correspondences of terms’ raised by the more complex,16-term model, set forth above, which issues from Marx’s ‘‘‘deeper’’’, Elementary Value-Form «arché»/“cell-form” alternative.
In the model issuing from the ‘‘‘shallower’’’ «arché» of the ‘‘‘Commodity’’’ category as a whole, denoted in the equations above by C«K»,
each term maps to no ‘‘‘deeper’’’ than the Chapter level [albeit with
some '''straddling’’’ of pairs of Chapters] -- or even to the level of
an entire “Part”, in one case, the case of its final ‘full synthesis’
We “solve” this model’s ‘Dialectical Equation’ -- map its 8 terms to Marx’s Table(s) of Contents -- as set forth below.
First, let’s view the full ‘Dialectical Equation’, deployed in stages:
. . .
The solution-definition of each of the 7 terms, derived from the «arché», already defined above, are the following:
. . .
‘Dialogue-ic’ Translation of the 8-Category Dialectical-Algebraic Model of the Value-Form Dialectic of Marx’s Capital.
The eight-term dialectical-ideographical model of the ‘‘‘Value-Form Dialectic’’’ content of Marx’s Capital, rendered above, can be translated into a narrative, two-party, “Q&A”-format 'dialogue-model', one with the same essential content as the dialectical-ideographical model.
A transcript-excerpt of such a ‘dialogical narrative-model’ is exhibited below: the above model of Capital ‘re-presented’ as a prose dialogue.
This dialogue can usefully be read as a self-questioning and self-answering of a single, fictive/representative observer/participant in the presently-existing system of social economy.
A phrase used repeatedly in the dialogue below is “[the dialectical] analysis of a [category]”, whose Marxian usage has special features vis-à-vis its usual connotations.
The Marxian, dialectical analysis of a category
is the detailed ‘explicitization’ of its implicit content -- of all
that the category being analyzed ‘‘‘contains’’’; of all that is immanent
in that category as conceived -- prior to such analysis -- as a whole,
without explicit articulation of its parts.
The dialectical analysis of a category is thus the delineation of its detailed internal constitution; the ‘ideo-taxonomic’ delineation of its implied composition, in terms of the sub-categories of that category; of the «species» of that category, taken as «genos»; the formulation of its ‘sub-categories sum’, of which it, as a whole, is, implicitly, the ‘cumulum’.
Q1. ¿What is the simplest category that grasps the totality of our ‘untheorized’, ‘unsystematized’,
“chaotic” [Marx], “raw” experience of the present/capitalist system of
societal self-reproduction in which -- and as part of which -- we live?
A1. The “social relation of production” category of “Commodities”.
Indeed, “The wealth of those societies in which the capitalist mode of
production prevails, presents itself as “an immense accumulation of
commodities,” its unit being a single commodity. Our investigation
must therefore begin with the analysis of a commodity.” [K. Marx,
opening words of Capital, volume I.]. ...
This analysis of a representative unit of this category of “Commodities”,
an analysis that unpacks its implicit content, thus already leads to a
detailed grasp/explanation of much of our experience of the modern
social system in which, and as part of which, we live.
Q2. ¿Did that analysis of the “Commodities”
category completely exhaust our experience and knowledge of the
existing system of societal self-reproduction, or are there other
categories whose content is not explicitly covered by that of the
category of “Commodities”,
whose analysis could expand our comprehension of this system of social
life, and of the range of its human, social phenomena that we have
A2. The “Commodities” category, taken alone, leaves out any explicit coverage of a key part of our experience, that has to do with money.
The category of “Monies” comprehends explicitly a vast portion of our experience of the present system that is not captured explicitly by the “Commodities” category.
The foregoing analysis of the content implicit in the “social relation of production” category of “Monies”
thus accomplishes a further advance in our detailed, scientific
grasp/explanation of our experience of life within the present system of
self-reproduction of human-social life.
Q3. ¿Are “Commodities” and “Monies” just two absolutely separate, and, in some ways, diametrically, qualitatively opposite categories of ‘human socio-economic ontology’?
¿Or do these two categories interrelate, and combine, in
descriptions of the human-society self-reproductive process that are
adequate to our experience and knowledge thereof?
A3. “Yes” they are different, even qualitatively opposite, categories.
But also “No”, they are not absolutely separate or separable means of grasping our experience of modern society.
Indeed, the two categories are inseparable in accurate-to-experience descriptions of the buying and selling [exchange, ‘<->’]
activities which form a core component of our “raw” experience and
fragmentary knowledge as to how the present system of human-social life
reproduces itself, continues itself, extends itself to fill the “space”
of advancing historical time. “Commodities” are sold for “Monies”.
Those “Monies” are then used to buy other “Commodities”.
These “Commodities” are used to produce other “Commodities”.
Those other “Commodities” are then sold for [other] “Monies”, and those “Monies” are then used, again, to buy other “Commodities”.
We have “Commodities”, whose place is taken by “Monies”, whose place is then taken again by “Commodities”, whose place is then taken by “Monies”, whose place is then taken again by “Commodities”, or:
... <-> C <-> M <-> C’ ... C’’ <-> M’ <-> C’’’....
The ‘‘‘complex unity’’’, or ‘‘‘dialectical synthesis’’’, of these opposite categories of “Commodities” and “Monies”
is the category which describes the ongoing society-reproductive
process of the money-facilitated commodity exchange, which we name “The Monies-Mediated Circulations of Commodities”.
Q4. ¿Do the three ‘social relations of social self-re-production’ categories of “Commodities” [‘«arché» thesis’], “Monies” [‘first contra-thesis’], and “Monies-Mediated Circulations of Commodities” [‘first uni-thesis’],
taken together, exhaust our “raw” experience and fragmentary knowledge
of the existing system of human-social life reproduction, capturing and
comprehending all that is going on inside this system -- inside our
socio-economic lives -- i.e., all of its recurrent human-social
¿Or, are there still other
categories, so far left out of our explicit account, that are needed to
provide a more complete picture/scientific explanation of this
human-social [sub-]totality in which, and as which, we live?
These three categories taken together and mutually super[im]posed,
and the analyses that unpack their implicit content, do further advance
our detailed, scientific explanation of our experience of present-day
However, they still leave out fundamental aspects of that experience,
the experience of what is going on inside the present system of our
social lives and of the daily social activity of those lives’
Indeed, they still leave out of explicit account the category of “Capitals” itself -- the category of those special “Monies” which are not
just consumed, to buy those kinds of commodities that are used up to
continue/reproduce the availability, and the ability to work, of
worker-consumers, but of “Monies” which are “invested” so that they may “turn a [money-]profit”; “Monies” that “make more” “Monies”.
Some of the “Monies” used to “Circulate Commodities” are ‘‘‘Monies-Capitals’’’, not subsistence “Monies” [e.g., are not workers' wages revenues].
Some of the “Commodities” that are “Circulated” by those ‘‘‘Monies-Capitals’’’ are not subsistence “Commodities”, but are ‘‘‘Commodities-Capitals’’’, “Commodities” that may be sold for “Money-Profits”, over and above what they cost to produce.
Indeed, the bulk of the present-day global human socio-economic process
of human-societal self-reproduction can be described as a
usually-profit-yielding ‘‘‘Circulation of Commodities-Capitals mediated by Monies-Capitals’’’, an alternation of “Commodities” and “Monies” in the form of an alternation of ‘“Commodities-Capitals’’’ and ‘“Monies-Capitals’’’.
. . . .
The foregoing analyses of these “Capitals” categories -- these categories named‘“Capitals-in-General’’’, & ‘“Commodities-Capitals’’’, & ‘“Monies-Capitals’’’ and their overall socio-economic process category, named ‘‘‘The Self-Circulations of the Total Social Capital’’’
-- have leaped our detailed grasp and scientific explanation of the
socio-economic phenomena that we have recurrently experienced in the
system of socio-economy that we live today, far ahead of where we began,
with the simple, abstract category of “Commodities”.
Q5. ¿OK? We have arrived at a ‘qualitative sum’, a ‘non-amalgamative cumulum’, a ‘non-reductive super[im]position’ of 7social relations categories -- “Commodities”, “Monies”, ‘‘‘Monies-Mediated-Circulations-of-Commodities’’’, ‘“Capitals-in-General’’’, ‘“Commodities-Capitals’’’, ‘“Monies-Capitals’’’, and ‘‘‘The Self-Circulations of the Total Social Capital’’’, the
latter as a categorial description of the socio-economic process of
contemporary global human societal self-re-production as a whole.
¿Do these seven categories
amount to an adequate, complete account of the system of
‘socio-[political-]economy’ in and as which we live?
¿Or are there other categories that are needed to contain/provide a fuller explanation?
The dialectical analysis of these seven categories comprehends a great
deal about the present system of human-societal self-reproduction.
But these categories are still deficient in many ways, falling far short
of a full theorization of a ‘‘‘synchronic slice’’’ or cross section cut
through the society of today.
For the present purpose, we will finish by focusing upon just one of
these deficiencies, but one that constitutes, in a very important way,
the final deficiency of a categorial progression that
constitutes a ‘‘‘systematic dialectical’’’ theory-presentation: the
transition from the self-reproduction to the ‘self-revolutionization’
and self-transcendence of such a system.
In the Platonian and Hegelian traditions of ‘“Systematic Dialectics’’’, such a transition has no place.
After all, unless the ‘‘‘synchronic slice’’’ in question, that is the
locus of systematic presentation, and our experience and knowledge of
life in that slice, happens to encompass the period of revolutionary
transition from system to successor system, that transition is outside
the locus of explanation and presentation, and the phenomena of that
transition are outside of our “raw” experience and fragmentary
However, for the Marxian tradition of ‘“Systematic Dialectics’’’,
which is founded upon a recognition of the transient, transitory, and
transitional character of all natural formations, including of all
human-social formations, and for which any ‘‘‘synchronic slice’’’, or
“cross-section cut from history” is recognized as merely a synchronic
abstraction from the essential ‘‘‘diachronicity’’’ and ‘‘‘historicity’’’
of reality, an account of the transition from the predecessor to the
successor system must form the final phase for its method of
This final phase does, however, still involve historical extrapolation
from present experience and experiential knowledge to a
dialectically-inferred, diachronic, historical future.
It involves transitioning the presentation from the ‘re-construction’ of
the past to its present form, to the ‘pre-construction’ and the
‘present[ize]-ation’ of the future’ -- prediction.
Marx described this ‘proto-historical-dialectical’,
‘quasi-diachronic’, final phase in his ‘systematic/synchronic dialectics
method of theory-presentation’ in the following terms:
“On the other side, much more important for
us is that our method indicates the points where historical
investigation must enter in, or where bourgeois economy as a merely
historical form of the production process points beyond itself to
earlier historical modes of production.
In order to develop the laws of bourgeois economy, therefore, it is not necessary to write the real history of the relations of production.
But the correct observation and deduction of these laws, as having
themselves become in history, always leads to primary equations -- like
the empirical numbers, e.g. in natural science -- which point towards
the past living behind this system.
These indications, together with a correct grasp of the present, then
also offer the key to the understanding of the past -- a work in its own
right which, it is to be hoped, we shall be able to undertake as well.
This correct view likewise leads at the same time to the points at which the suspension [M.D.: i.e., the ‘self-«aufheben»’] of the present form of the production-relations gives signs of its becoming -- foreshadowings of the future.
Just as, on the one side the pre-bourgeois phases appear as merely historical, i.e. suspended [M.D.: ‘self-«aufheben»-ated’] presuppositions, so do contemporary conditions of production likewise appear as engaged in suspending themselves [M.D.: ‘«aufheben»-ating’ themselves] and hence in positing the historic presuppositions for a new state of society.”
[Karl Marx, Grundrisse, translated by Martin Nicolaus, Pelican [London: 1972], pp. 460-461, emphasis as per original].
There are ways in which our experience of the existing system of
socio-politico-economics points beyond itself, beyond the existence of
this existing system; foreshadows the possible self-induced breakdown of
this system, its internal, immanent ‘self-transitioning’ from a
‘self-organizing system’ to a ‘self-dis-organizing system’, and a ‘self-re-organizing system’.
Such foreshadowings include the recurring global economic crises, of
ever-increasing amplitude -- such as the global crisis that began in ~1907, the global “Great Depression” crisis that began in ~1929, the Global Wars -- WWI and WWII -- that followed the ~1907 and ~1929 crises, and the “Great Recession” crisis that began in ~2008
-- and also the quiet global expansion of producers’ cooperatives,
i.e., of worker-owned industrial capital; of ‘workers’ capitalism’, that
may all point beyond the self-reproduction of the capital-based system
of socio-political economy, to its gradual, and then sudden, self-non-reproduction;
to the production, from out of it, of a new system, e.g., of a higher
system, one that solves some of the problems of self-devastating global
crises, global wars, and global de facto genocides, with which the present system plagues itself.
Or, which may point to a self-induced breakdown of the existing global
system that eventuates in a new global war and/or a collapse into a New,
Final Dark Age: ‘‘‘the mutual ruin of the contending classes’’’ [see
Karl Marx and Frederick Engels, The Communist Manifesto].
Thus we need to consider, finally, a category of “Transition”, of the
‘self-transitioning’ of the present system into something else; a
category of the practical self-critique of the category of the presently predominant social relation of production; of the self-critique in practice of “the Capital-relation” [Marx].
Caveat. This dialogic model of the content of Marx’s three volumes of «Das Kapital» is, like all models, a ‘‘‘homeomorphism’’, a ‘‘‘many-to-one’’’ abbreviation, or mapping, of the object that it models.
In particular, this model addresses, explicitly, only the ‘‘‘value-forms’’’ content of Marx’s work, which includes Chapters I., III., and IV. of volume I, most of volume II, and only a little of volume III. It omits especially the production-centered parts of volumes I, II, and III, which would require a deeper «arché» -- one deeper than the “Elementary or Accidental Form of Value” «arché» addressed in the first model of «Das Kapital» exposited herein, above.
The present, dialogic model covers most of volume I up to Chapter V., entitled by Marx “Contradictions in the General Formula of Capital”, which addresses the primary «aporia»
of all modern political-economics, the paradox of the sustaining source
of the profit on [industrial] capital, and Marx’s solution to that «aporia», his theory of surplus-value.
This model does not address, in particular, in volume I,
the part on the production of absolute surplus-value, the part on the
production of relative surplus-value, the part on the production of
absolute and of relative surplus-value, or, in volume III,
the parts on the “lawful” fate of capital-profit, given its source in
surplus-value, i.e., the parts entitled “The Conversion of Surplus-Value
into Profit...”, “The Conversion of Profit Into Average Profit”, “The
Law of the Tendency of the Rate of Profit to Fall”, “The Division of
Profit into Interest and Profit of Enterprise”, and “Transformation of
Surplus-Value into Ground-Rent”.
This abbreviated model of «Das Kapital», because of
its very ‘abbreviated-ness’, is useful, given the familiarity of its
categories, for illustrative purposes regarding this essay’s main
‘meta-model’, given its similarities to, as well as its contrasts with,
The derivation-presentation of a fuller dialectical model of Marx’s Capital, flowing from a far deeper «arché» than either of those utilized in this essay, is planned to be the focus of a forthcoming separate work."