[This post is based upon the following F.E.D. source --
http://www.dialectics.info/dialectics/Primer.html
http://www.dialectics.info/dialectics/Primer_files/4_F.E.D.%20Intro.%20Letter,%20Supplement%20B-1,%20v.2_OCR.pdf
[pages B-24 through B-38] ].
We have been discussing, in recent posts to this thread, an NQ dialectical model of Marx's "Systematic-Dialectical" presentation, in volumes I. and II. of his Capital: A Critique of Political Economy.
We have modeled thereby the progression of human-social-relation-of-production categories that Marx presents -- but just those that fall under the exchange-value <<genos>> of social ontology [with one exception: the final category, connoted by E].
These are: (1) the Commodity-relation-of-production, (2) the Money-relation-of-production, (3) the hybrid, Money-Mediated Commodities-Circulations-relation, (4) the Kapital-relation, plus its two sub-categories of the "real subsumption" of previous social-relations ontology by the Kapital-relation ontology -- (5) Commodity Kapital and (6) Money-Kapital -- plus (7) the Kapital-relation's subsumption of the Money Mediated Circulations of Commodities relation -- the Circulation of the Aggregate Social Capital, as the circulation-sphere moment of the Self-Re-Production of the Total Social Capital and of Capitalist Society as a whole -- plus (8) a final category, that which we have termed here the Political-Economic Democracy-relation-of-production, superseding the Kapital-relation.
Re-expressing the above using the heuristic, "intension-al"/"intuitional" shorthand of the F.E.D. dialectical algebra, we obtain --
)-|-(s=3 = C + M + q/MC + K + q/KC + q/KM + q/KMC + E
-- for this specific interpretation -- specific to Marx's method of presentation of his critique of political economy -- of the generic stage 3 dialectical categorial progression --
|-|-|t=3 = q/1 + q/2 + q/3 + q/4 +q/5 + q/6 + q/7 + q/8
-- wherein [visible-]light-spectrum order [red, orange, yellow, green, blue, indigo, violet[, "ultraviolet", ...] ] is used to highlight dialectical, qualitative ordinality.
The first seven categories of this dialectical-presentation-model, as listed above, all represent content of our present experience in capitalist society.
Unlike those earlier seven categories, the eighth, final category of his progression, E, which, for this writer, connotes "Political-Economic Democracy", i.e., "Democratic Communism" [not Stalinist, bureaucratic state-capitalism], is not [yet] already extant in human experience.
The category denoted E is a category, not of the self-reproduction of capitalist society, but of its [self-]supersession.
The category denoted E is a prediction of Marx's systematic critique of capitalist political economy, about a future content of human experience.
It arises, in our model, via the "self-confrontation" of the Kapital-relation category.
If you see K in this model as connoting the dialectical determinate negation operation specific to the Kapital-relation, then you might notate this "self-confrontation of capital" as ~K = KK = K x K = K^2 = K-squared = K(K), connoting the determinate self-negation of the Kapital-relation.
If you see K in this model as connoting a specific dialectical aufheben function, then you might notate this "self-confrontation of capital" as --
"K of K"
-- as K(K), in K(K) = K + delta-K = K + E, i.e., as the "self-function of Kapital"; the "self-reflexive function of Kapital", the "self-application of the Kapital operation", the "Kapital function(argument)-identical", or "operator(operand)-identical", which self-confrontation irrupts the new social-relation-of-production ontology symbolized by delta-K or E.
This "self-action of the Kapital-relation" arises in stage s = 3 of the Systematic-Dialectic model, the stage which arises from the "self-confrontation" of the "categories-sum" of stage s = 2, representing all previous social-relations-of-production human-social ontology, including the Kapital-relation in its "formal subsumption" phase with respect to all previous social relations of production, but not yet in its "real subsumption" phase, which arises out of that self-confrontation of stage 2, which yields stage 3 --
)-|-(s=3 = )-|-(s=2 x )-|-(s=2 =
( C + M + q/MC + K ) x (C + M + q/MC + K) =
( ( C + M + q/MC + K ) + K x (C) + K x (M) + K x (q/MC)
+ K x (K) ) =
( C + M + q/MC + K ) + ( C + q/KC ) + ( M + q/KM ) +
(q/MC + q/KMC ) + ( K + q/KK ) =
C + M + q/MC + K + q/KC + q/KM + q/KMC + E
-- Given the "additive idempotency" rule, Axiom 7 of the NQ axioms stated in an earlier post to this thread, and given the "meristemal" non-distributive multiplication shortcut, for K as "meristem" ["growing edge"] of the )-|-(s=2 "cumulum".
Note: Within the )-|-(s=3 "cumulum" as a whole, the sub-series q/KC + q/KM + q/KMC represents the "real subsumption", by the Capital-social-relation-of-production, of all previously-posited social relations of production.
Now, the F.E.D. writings usually interpret such a "self-function", here generically notated by X( X ), or by X< X >, in the context of a model of an Historical Dialectic, as distinct from a model of a Systematic Dialectic, as arising at that stage in the development of the X "arithmos" -- i.e., in that of the "population" of X-type "individuals" or "units" -- when the quantitatively expanding self-reproduction / growth of that "population" reaches its critical-density threshold for qualitative, ontological change / growth, as a result of the "self-envelopement", "self-surroundment", or "self-environment" of the X-type "units".
That is, earlier, before that "self-environmented" stage, the X-type "units" are fewer in number, and are therefore largely "other-environmented" / "predcecessor-environmented".
That is, they are "environmented" by previously-irrupted ontology, by the units of predecessor "arithmoi", especially by those of their immediate predecessor ontology / ontological category / "arithmos".
In that stage, the X-type units are busy "auto-catalytically" converting portions of their predecessor type units into more units of themselves, as connoted, for X = K, by the following terms of our Systematic Dialectic model of Capital, if we re-interpret it into Historical-Dialectical terms:
K(C) and K(M) and K(q/MC) [to be "read off as" K of C, and K of M, and K of q/MC, respectively], which my also be written K x C, K x M, and K x q/MC, respectively.
The term K(C) connotes the conversion of Commodities into Kapitals, the Kapitals-subsumption of Commodities, the appropriation [or [ex]propriation] of Commodities for Kapitals.
The term K(M) connotes the conversion of Monies into Kapitals, the Kapitals-subsumption of Monies, the appropriation [or [ex]propriation] of Monies for Kapitals.
The term K(q/MC) connotes the conversion of Money-Mediated Commodities-Circulations [MMCC] into Kapitals'[-Circulation], the Kapitals'-subsumption of MMCC, the appropriation [or [ex]propriation] of MMCC for and by Kapital(s).
However, when the population quantity and "density" of X-type "units" exceeds a certain limit, in the loci of such "densification", the interaction of X-type "units" with other X-type "units" -- the "self-environment" of the X-type "units" -- begins to become important, relative to the "environment" of X-type "units" by their predecessor type(s) of "units", and relative to the interaction of X-type "units" with their predecessor type(s) of "units".
At that stage, the "self-operation" X(X) irrupts, the process of the "self-conversion" of X into something that is "meta-" to X, e.g., X(X) = K(K) -- connoting the "self-subsumpion" of the Kapital-relation; the "self-conversion" of [part of] the units of the Kapital-relation into the units of a new "arithmos", of a new and unprecedented socio-ontological category of relations-of-production, connoted by E; the self-[ex]propriation of K.
For example, in their "Dialectic of Nature" / "Dialectic of Natural History" Historical-Dialectical model, the "self-confrontation of the sub-atomic particles", symbolized as --
s< s > = s + delta-s = s + q/ss = s + a
-- is interpreted as describing the quantitative expanded self-reproduction of sub-atomic "particles", at that stage of that quantitative growth and physical-spatial self-concentration/"self-densification" of the many local cosmological populations of sub-atomic particles, e.g., protons, whereby proton-proton interactions start to become more frequent and important, relative to, e.g., proton-quark interactions, which auto-catalytically convert proton-predecessor quarks into more protons.
These sub-atomic-"particle" / sub-atomic-"particle" interactions then give rise to qualitative change, to qualitative growth -- to the irruption of the next new cosmological ontology, that of atoms.
This abstract process --
s< s > = s + a
-- in the specifically-interpreted, specifically-"connotized", "specificized", or "specific"[to the Dialectic of Nature as a whole, in this case] dialectical arithmetic, which corresponds, in the generic dialectical arithmetic, to --
[q/2] x [q/2] = [q/2] squared = the self-operation of [q/2] = [q/2]^2 = [q/2] + [q/(2+2)] = [q/2] + [q/4]
-- connotes, e.g., the concrete process of the first-generation stars, in which ionized Hydrogen "atoms" -- really, naked protons -- are "fused" together, via star-self-gravitationally-confined thermo-nuclear "fusion" reactions, to form [together with neutrons], initially, mainly Helium atomic nuclei, consisting typically of two protons fused together with two neutrons.
Given all of the above, it is interesting to see how Marx himself describes such a "self-confrontation of the Capital-relation", in two key passages of his writings about the transition to the successor system of the "Kapitals-System". The second passage is famously well-known. The first passage, unfortunately, far less well-known.
Here is how Marx described what is connoted by --
K< K >
-- in a Historical-Dialectical model of the Dialectic of Capital[ism]:
1. In this passage, Marx describes that aspect of the Kapital-relation whereby it functions as an operation of "bursting-asunder" of all [previous] social relations of production, once they come to enfetter the growth of the social forces of production [including, as a fetter upon the growth of the social forces of production, at last, itself]:
"... capital has pushed beyond national boundaries and prejudices, beyond the deification of nature and the inherited, self-sufficient satisfaction of existing needs confined within well-defined bounds, and the reproduction of the traditional way of life.
It is destructive of all this, and permanently revolutionary, tearing down all obstacles that impede the development of the productive forces, the expansion of needs, the diversity of production and the exploitation and exchange of natural and intellectual forces.
But because capital sets up any such boundary as a limitation and is thus ideally over and beyond it, it does not in any way follow that it has really surmounted it, and since any such limitation contradicts its vocation, capitalist production moves in contradictions, which are constantly overcome, only to be, again, constantly re-established [and, reproduced each time on an ever-larger 'meta-fractal' scale -- M.D.].
Still more so.
The universality towards which it is perpetually driving finds limitations in its own nature, which, at a certain stage of its development will make it appear as itself the greatest barrier to this tendency, leading thus to its own self-destruction."
[David McLellan, ed., The Grundrisse [by Karl Marx], Harper & Row [NY: 1971], pages 94-95, emphases added by M.D.].
2. In this passage, Marx describes that aspect of the Kapital-relation whereby it functions as an operation of "ex-propriation" of all [previous] forms of property, or of "propriation" [including, in its end, of its own form of property, or of "propriation"]:
"What does the primitive accumulation of capital, i.e., its historical genesis, resolve itself into?
In so far as it is not immediate transformation of slaves and serfs into wage-labourers, and therefore a mere change of form, it only means the expropriation of the immediate producers, i.e., the dissolution of private property based on the labour of its owner.
... as soon as the capitalist mode of production stands on its own feet... the further expropriation of private proprietors takes a new form.
That which is now to be expropriated is no longer the labourer working for himself, but the capitalist exploiting many labourers.
This expropriation is accomplished by the action of the immanent laws of capitalistic production itself, by the centralisation of capital.
One capitalist always kills many.
Hand in hand with this centralisation, or this expropriation of many capitalists by few, develops, on an ever-increasing scale, the cooperative form of the labour-process, the conscious technical application of science, the methodical cultivation of the soil, the transformation of the instruments of labour into instruments of labour only usable in common [the 'objective socialization' of the means of production, still pending their '[inter-]subjective socialization', in the form of the conscious creation, by the human species-for-itself, of a truly human, truly social, "social-ist", "associationist" society; the global, and global-market-subsuming, society of the democratically "associated producers" — M.D.], the economising of all means of production by their use as the means of production of combined, socialised labour, the entanglement of all peoples in the net of the world-market, and, with this, the international character of the capitalist régime. ...
The monopoly of capital becomes a fetter upon the mode of production, which has sprung up and flourished along with, and under it.
Centralisation of the means of production and socialisation of labour at last reach a point where they become incompatible with their capitalist integument.
This integument is burst asunder.
The knell of capitalist private property sounds.
The expropriators are expropriated."
[Karl Marx, Capital, Vol. I, Chapter 32, "Historical Tendency of Capitalist Accumulation", International Publishers, [NY: 1967], pages 761-764, emphases added by M.D.].
We might imagine the "[self-]expropriation" of capital [and of its personifications], predicted in the passage immediately above, as the uprising, within productive capital, of variable capital -- of alienated [= sold, for wages] labor-power -- negating constant capital, including fixed-capital, as capital, and thereby also negating itself as variable capital.
All of the above serves to "explicitize" the implicit, connotative richness of the meaning of the "simple", four-symbol, dialectical, "self-function" formula --
K< K > = K + E
-- in the specifically-interpreted, specifically-"connotized", "specificized", or "specific"[-to-Capital, in this case] dialectical arithmetic, which corresponds, in the generic dialectical arithmetic, to --
[q/4][q/4] = [q/4]^2 = [q/4] squared = [q/4] + [q/(4+4)] = [q/4] + [q/8] --
-- or, if we use the deeper <<arche'>> for the Historical Dialectic of the "Meta-Evolution" of the Social Relations of Production than the Commodities category of human-social-relations ontology as corresponding to q/1, which F.E.D. actually uses [the "Predation"-relation, or the Appropriation of the "Raw" Products of Nature, without their improvement for human consumption by human labor], to --
[q/16]^2 = [q/16] + [q/(16+16)] = [q/16] + [q/32].
For more on the possible detailed meaning and workings of a society founded upon the new social relation of production connoted by E, see the thread in the RevLeft Theory Forum entitled "Dialectical, 'Intra-Dual' Design of Democratic-Communist Constitutions".
Regards,
Miguel
F.E.D. definitions of special terms utilized in the texts above --
<<arithmos>>
http://point-of-departure.org/Point-Of-Departure/ClarificationsArchive/Arithmos/Arithmos.htm
<<aufheben>>
http://point-of-departure.org/Point-Of-Departure/ClarificationsArchive/Aufheben/Aufheben.htm
[the] capital-relation
http://www.dialectics.org/dialectics/Glossary_files/D.I.,Post,Phono-Neograms,%5BC%5D.w3_OCR.pdf
categorial progressions
no definition as yet available in Archive
categories-sum
http://point-of-departure.org/Point-Of-Departure/ClarificationsArchive/Cumulum/Cumulum.htm
[the] commodity-relation
no definition as yet available in Archive
critical density threshold
http://point-of-departure.org/Point-Of-Departure/ClarificationsArchive/SeldonFunctions/SeldonFunctions.htm
cumulum, pl. cumula
http://point-of-departure.org/Point-Of-Departure/ClarificationsArchive/Cumulum/Cumulum.htm
democratic communism
http://www.equitism.org/Equitism/Theory/PoliticalEconomicDemocracy/PoliticalEconomicDemocracy.htm
http://www.equitism.org/Equitism/AmendmentXXVIII/AmendmentXXVIII.pdf
determinate negation
http://point-of-departure.org/Point-Of-Departure/ClarificationsArchive/SeldonFunctions/SeldonFunctions.htm
dialectical algebra
http://point-of-departure.org/Point-Of-Departure/ClarificationsArchive/Mathematics/Mathematics.htm
dialectical arithmetic
http://point-of-departure.org/Point-Of-Departure/ClarificationsArchive/Mathematics/Mathematics.htm
dialectical negation
http://point-of-departure.org/Point-Of-Departure/ClarificationsArchive/SeldonFunctions/SeldonFunctions.htm
dialectical presentations [models]
http://point-of-departure.org/Point-Of-Departure/ClarificationsArchive/SystematicDialectics/SystematicDialectics.htm
explicitize, explicitization
no definition as yet available in Archive
<<genos>>, dialectical
http://point-of-departure.org/Point-Of-Departure/ClarificationsArchive/Genos/Genos.htm
historical dialectics
http://point-of-departure.org/Point-Of-Departure/ClarificationsArchive/HistoricalDialectics/HistoricalDialectics.htm
human-social forces of production ontology
no definition as yet available in Archive
human-social relations of production ontology
no definition as yet available in Archive
[logical] individuals [<<monads>>]
http://point-of-departure.org/Point-Of-Departure/ClarificationsArchive/Monad/Monad.htm
intension, intensional [w.r.t. dialectical-ideographical symbols]
no definition as yet available in Archive
intra-dual, intra-duality
http://point-of-departure.org/Point-Of-Departure/ClarificationsArchive/SeldonFunctions/SeldonFunctions.htm
intuition, intuitional [w.r.t. dialectical-ideographical symbols]
no definition as yet available in Archive
meristem, meristemal
no definition as yet available in Archive
method of discovery, Marxian
no definition as yet available in Archive
method of presentation, Marxian
http://point-of-departure.org/Point-Of-Departure/ClarificationsArchive/SystematicDialectics/SystematicDialectics.htm
[the] money-relation
no definition as yet available in Archive
ordinality, dialectical
no definition as yet available in Archive
ordinality, qualitative
no definition as yet available in Archive
ordinality, quantitative
no definition as yet available in Archive
political-economic democracy
http://www.equitism.org/Equitism/Theory/PoliticalEconomicDemocracy/PoliticalEconomicDemocracy.htm
http://www.equitism.org/Equitism/AmendmentXXVIII/AmendmentXXVIII.pdf
self-confrontation [of an <<arithmos>>]
http://point-of-departure.org/Point-Of-Departure/ClarificationsArchive/SeldonFunctions/SeldonFunctions.htm
self-densification, critical, singularity
http://point-of-departure.org/Point-Of-Departure/ClarificationsArchive/SeldonFunctions/SeldonFunctions.htm
self-envelopment [of an <<arithmos>>]
http://point-of-departure.org/Point-Of-Departure/ClarificationsArchive/SeldonFunctions/SeldonFunctions.htm
self-environment [of an <<arithmos>>]
http://point-of-departure.org/Point-Of-Departure/ClarificationsArchive/SeldonFunctions/SeldonFunctions.htm
self-function(s)
http://point-of-departure.org/Point-Of-Departure/ClarificationsArchive/SeldonFunctions/SeldonFunctions.htm
self-negation, dialectical
http://point-of-departure.org/Point-Of-Departure/ClarificationsArchive/SeldonFunctions/SeldonFunctions.htm
self-operation(s)
http://point-of-departure.org/Point-Of-Departure/ClarificationsArchive/SeldonFunctions/SeldonFunctions.htm
self-subsumption
http://point-of-departure.org/Point-Of-Departure/ClarificationsArchive/SeldonFunctions/SeldonFunctions.htm
self-surroundment [of an <<arithmos>>]
http://point-of-departure.org/Point-Of-Departure/ClarificationsArchive/SeldonFunctions/SeldonFunctions.htm
social ontology; socio-ontology
no definition as yet available in Archive
state-capitalism [fully-conglomerated national supercorporation, in competition with other national state-capitals in the world-market]
http://www.equitism.org/Equitism/Theory/PoliticalEconomicLawOfMotion/PoliticalEconomicLawOfMotion.htm
subsumption, formal
no definition as yet available in Archive
subsumption, real
no definition as yet available in Archive
systematic dialectics
http://point-of-departure.org/Point-Of-Departure/ClarificationsArchive/SystematicDialectics/SystematicDialectics.htm
units [<<monads>>]
http://point-of-departure.org/Point-Of-Departure/ClarificationsArchive/Monad/Monad.htm
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