Monday, October 07, 2013

Part 1 of 9. Seldonian, Dialectical-Algebraic Derivation of the Successor System to Capitalism.


Full Title --
 

Part 1 of 9.  Seldonian, Dialectical-Algebraic Derivation of the Fundamental Features 

for the Global Successor System to [Self-]Global[ized] Capitalism

using the Dialectical Meta-Equationthat Models the Meta-Evolution 

of the Human-Social Relations of Production. 


by [guest author] Hermes de Nemores.



Dear Readers,

Questions have recently been raised in ‘www’ dialogues in which I participated as to what Karl Seldon derived, and how he derived it, with regard to the global system of ‘Democratic Communism’, or of ‘Marxian democracy’ -- of ‘Political-Economic Democracy -- as the global successor system to global capitalism, using the dialectical algebra that he discovered in 1996.

Such questions deserve an answer, and, starting with this blog-entry, the next sub-series of blog-entries will address these questions. 

The first nine of these blog-entries are from the writings of a first-time guest author here, Hermes de Nemores, the Secretary-General of Foundation Encyclopedia Dialectica, and the chairperson of its General Council, extracted from his recent update to an introductory text, whose earlier version is available via --





[see, in particular, pages B-24 to B-37 in the latter].

-- which I have adapted to the locally-available typography.


Regards,

Miguel










Example 5: NQ_ [Psycho]Historical Dialectical Meta-Model -- Taxonomy Level 2. TheMeta-Equation of Human-Social Relations of ProductionMeta-Evolution.

Karl Seldon applied the ‘algorithmic heuristic’, the non-extensional, ‘intensional/intuitional’ algebra of the Seldonian NQ_ “First Dialectical Arithmetic”, to derive a solution to a longstanding, central problem of Marxian, dialectical science.  This central problem was, explicitly, left unsolved by Marx and Engels. Nor had not it been solved adequately either by their ostensible followers ever since, as of the time of Seldon’s solution.  This central problem is that of the ontological, dialectical definition of the principal, essential features of the ‘socio-ontological category’ that represents the core social relations of production of the global successor system to the global system of capitalism*.  

The aim here is to “digest” the Seldonian derivation of that solution.

The ‘meta-equation’, or ‘equation of equations’, to be narrated, and, partially, to be solved, herein is one of the seven such Seldonian ‘meta-equations’ that we term ‘The Psychohistorical-Dialectical Equations’.

In its full Seldonian rendering, this ‘[Psycho]Historical-Dialectical Equation’ would be solved progressively, ‘‘‘inductively’’’, for each term subsequent to its originating, or «arché», ultimate ancestor, category-term, in progressive order, term-by-term, i.e., category-by-category, epoch-by-epoch, for both the epochs that belong to the past, behind our historically present epoch, re-constructing” our past, and then for our present epoch, and then, finally, for our future, ahead of our historically present epoch, thus pre-constructing’ -- pre-dicting”, or ‘before-saying’ -- our future.

Moreover, this ‘meta-equation’ would be formulated, and solved, not only in the algebra of NQ_, the Seldonian “First Dialectical Arithmetic”, but also in the dialectical algebras of a selection of the higher, descriptively richer, more “determinate” Seldonian systems of Dialectical Arithmetic, in the order that they arise in the dialectical progression of the Seldonian Dialectical Arithmetics, as given by the Seldonian ‘meta-equation’ --

)-|-(s = ( N_ )^(2^s) =  

N_ + NQ_ + NU_ + NM_ + Nq_MN + Nq_MQ + Nq_MU + NA_ +...+ Nq_AMU 

...

-- wherein N_ stands for the «arché» system of arithmetic, the “first order” axiomatization of the “Natural” Numbers, N, the axiomatization which “quantifies over” [talks about] only individual “Natural” Numbers, and not about the qualities shared by groups of such numbers [“second order”], etc.

E.g., Seldon’s social relations of production ‘meta-equation’, after having been first formulated, and then solved, in the ideographical language of the Seldonian “First Dialectical Arithmetic”, would be progressively reformulated, and solved, in at least the dialectical algebras of the second, RU_, sixth, Rq_MU, fourteenth, Rq_AMU, thirtieth, Rq_BAMU, and sixty-second, Rq_GammaBAMU, dialectical arithmetics, for the version of the 'meta-equation' above which replaces N_ with R_, the first-order axiomatization of the "Real" Numbers.

The solution-procedure for ‘dialectical meta-equations’ formulated in the algebra of the Seldonian “First Dialectical Arithmetic”, for specifically diachronic, [Psycho]Historical-Dialectical ‘meta-equations’, has not yet been cleared for public dissemination by the F.E.D. General Council.  However, the partially parallel, partially corresponding solution procedure for specifically synchronic, Systematic-Dialectical ‘meta-equations’, named ‘The Organonic Algebraic Method’, has been released, and is publicly accessible via the following links --








The 'Dialectic of Human Nature', within cosmological Nature as Totality, from the viewpoint of the historical 'meta-evolution' of the 'human-social relations of [human society self-re-]production' is the focus of the 'meta-model' of human-social 'meta-evolution' explored in this section. 

Let us 'open up' the h [human species] component of the 'Taxonomy Level 1' universe ‘meta-model’ in a different way.  Let us do so in a way which focuses on the 'evolute' [as opposed to 'convolute'] progression of human social relationships of human-societal self-reproduction, or of human-social relations of production-incenting/-inducing circulation, as identified by Marx in his dialectical, immanent critique of classical, capitalist political economy.

Let us thereby construct a different '2nd-level' universe ‘meta-model’ for the relative 'meta-evolutions' going on 'inside' the h ontological category, locus Terra, with the following kind of 'meta-fractal' structure, or '[quanto-]qualitative scaling self-similarity structure', of the ‘multi-meta-ontic, multi-meta-monadic historical cumulum’ of 'social-relations-of-production / social-praxis ontology'.

We can do so via the following "interpretations" or "assignments" of the ‘meta-number’ unit-qualifiers, { qk }, the abstract, generic dialectical ontological categories, contained in NQ_ | k in N, to specific 'ontological categories' [ontos’], or «arithmoi», made up out of the 'ontic species' of '[meta-]monads', or '[meta-]units', of human social relations of production 'social ontology'.  The social relations units, or «monads», that constitute these categories, or «arithmoi», are described, herein, as active subjects. The real subjects, behind these, their social relations of production labels, are human agents, social individuals, who act as personifications of these, the social relations of their own social reproduction.

The following assignments [‘[--->’] of specific to generic category-symbols stipulate a solution to this section’s subject ‘meta-equation’ through its epoch t = 4, but not for its epochs t = 5+.  The purpose of this example is to narrate the stipulated solution to epoch t = 4, and to derive a solution for epoch t = 5.  The ‘stipulated solution’ up into epoch t = 4 is as follows --


A  denotes the human-social activity onto / «arithmos» which has, as its units / «monads» / connoted content, immediate Appropriations of the "raw" products of nature, without "improvement" for human use, by human labor, i.e., with little-to-no human 'use-value-added'.  This is the stipulated «arché», or originating ‘socio-ontological category’,  for the dialectic of the human social relations of production per this dialectical ‘meta-model’, i.e., for this modeled self-progression of [proto-]human[oid], or 'meta-[animal-]social', systems of social relations, such that A  = qA [---> q1;


G denotes the onto / «arithmos» of '2nd degree Appropriation', i.e., of 'serial-Appropriation' and / or 'cross-Appropriation', of ‘nature-products’, yielding a ‘second nature’, of by-humans-improved, for human use, products, that is, Goods / intra-tribal Gifts as '2nd degree' Appropriations, or 'meta-Appropriations' [made out ] of '1st degree' Appropriations [or 'containing' heterogeneous multiplicity of '1st degree'] Appropriations, as social-relations units / «monads», i.e., as the ‘‘‘elements’’’ of 'human social-relations ontology', with '1st degree Appropriations' as the sub-units / sub-«monads» of / “inside” these new, Goods/Gifts units; the 'self-«aufheben»' 'self-internalization' / 'self-subsumption' / 'self-conservation' of '''Raw Appropriations''' as human social-relations of [social-re-]production «monads», such that G  =  qG  =  qAA [---> q2;


C denotes the onto / «arithmos» of pre-Money, 'bartered' Commodities, or of Goods+ -- having direct use-value
but having 'indirect, exchange-use-value' as well; of '2nd degree' or '[meta-]Goods' [made up out] of '1st degree', 
other Goods [or 'symbolically ['''socio-psychologically''', '''collectively-mentally'''] containing' [a heterogeneous 
multiplicity / list of '1st degree', other] Goods, as social-relations units / «monads», with Goods obtainable by them in 
customary barter-exchange as their sub-«monads»; the 'self-«aufheben»' 'self-internalization' / 'self-subsumption' / 
'self-conservation' of '''Goods''' as social-relations-of-production [meta1-]«monads», such that 
C  =  qC  =  qGG [---> q4;


M denotes the onto / «arithmos» of Monies as units / «monads», born when a single Money-Commodity singles-out as accepted, near-universal equivalent; a 'socio-ontological category' of '2nd degree', or 'meta-, Commodities' [made up] of '1st degree' Commodities [or 'symbolically ['''psychologically''', '''mentally'''] containing' a heterogeneous multiplicity / list of '1st degree'] Commodities, which these Monies can customarily “purchase”, as their sub-units / sub-«monads»; the 'self-«aufheben»' 'self-internalization' / 'self-subsumption' / 'self-conservation' of ‘‘‘Commodities’’’ as social-relations-of-production [meta2-]«monads», such that M  =  qM   =  qCC [---> q8;

K denotes the onto / «arithmos» of «Kapitals»; Money+ which makes more Money+; autocatalytic [exchange-]values as units / «monads»; a ‘socio-ontological category’ of 2nd degree’ or ‘[meta-]Monies[made up out] of [or symbolically [‘‘‘psychologically’’’, ‘‘‘mentally’’’] containing’ a size-heterogeneous multiplicity of ‘1st degree’] Monies, acquired as “[net] retained earnings”, i.e., the monetary profits [or losses] of previous-period capital circulations / realizations, or as “expected” [mentally imagined] monetary profits/losses of future capital investment ventures / “deals” -- of their projected circulations / realizations / monetary proceeds -- the ‘self-«aufheben»’ ‘self-internalization’ / ‘self-subsumption’ / ‘self-conservation’ of ‘‘‘Monies’’’ as social-relations [meta3-]«monads», such that 

K  =  qK  =  qMM [---> q16


-- with the following, stipulated-solution, human-social meta-genealogies, or ‘meta-social meta-phylogenies’ --

A --->  ~<A> = AxA = <A>2 = <A + D<A> > =  <A  + qAA> = <A + G >  ¬{<,=,>}   A;

G --->  ~<G> = GxG = <G>2 = <G + D<G> > =  <G  + qGG> = <G + C>  ¬{<,=,>}  G;

C --->  ~<C> = CxC = <C>2 = <C + D<C> > =  <C + qCC>  = <C + M>  ¬{<,=,>}  C;

M --->  ~<M> = MxM = <M>2 = <M + D<M> > = <M + qMM> = <M + K>  ¬{<,=,>}  M

-- wherein '--->' denotes the word "becomes", and wherein '~' denotes the operation / operator of dialectical, determinate, <<aufheben>> negation, and wherein the symbol '¬{<,=,>}' denotes the relation of ontological, heterogeneous, qualitative inequality, i.e., the relation of "non-quantitative inequality' -- of 'not less than and not equal to, and not greater than'.



Objective:  Solve the following ‘sub-equation’, and enter the result into the total ‘meta-equation’ solutions for t = 5+ --

K --->  ~<K> = KxK = <K>2 = <K + D<K> > =  <K + qKK> = <K + ?>  ¬{<,=,>}  K.



The operations above, are, in each case, special 'selfaufheben»' 'self-conversion'/'self-negation'/-
'self-conservation'/'self-elevation' operations.

The general NQ_ ‘Historical-Dialectical Meta-Equation’ to be solved in this section is --   

>-|-<t = <A>^(2^t).

-- and wherein a^b denotes "a raised to the power b", e.g., 2^3   =   2 "cubed"   =   8.




This 'meta-model' addresses the 'meta-dynamical meta-evolution' of 'meristemal' human-social relations of human-society self-production [including of the [transitory] reproduction of these very human-social relations of society self-production themselves, as their epoch’s 'meristemal', subsuming relations of production].

This ‘meta-model’ of that '''historical dialectic''' of '''the social relations of production''' is expressed compactly by the symbol-complex '<A>^(2^t)' in the ideographical language of the NQ_dialectical ideography’.

Note that this 'meta-model' abstracts completely from the '''other side''' of the historical development of the human social individual, namely, from the growth of the '''social forces of production''' [i.e., from the growth of the human-social 'self-force' -- of the 'self-reflexive force', or, equally, the 'self-refluxive force' -- of human society’s 'self-production'; of human, 'meta-social' society's human 'socio-onto-mass' 'self-productivity', or 'self-reproductivity'].  The '''[psycho]historical dialectic''' of the growth of these "forces" is merely implicit in this 'meta-model meta-equation', whereas the social relations of production form its explicit focus.  Among the Seldonian ‘Psychohistorical-Dialectical Equations’, there is another ‘meta-equation’, whose ingredient equations have the epochs of the growth of the social forces of production as their explicit focus, and for which the ‘meta-evolution’ of the social relations of production is merely implicit.

Nonetheless, the growth of the 'society-reproductive forces' remains the implicit driver of the entire movement posited by this model, from A to G to C, to M to K, and beyond. 

For example, the transition from G dominance to the emergence and dominance of C ‘human socio-ontology’, and of the Commodity barter-exchange praxis among tribal communities, requires a level of human social Goods-productivity, which can sustain a sufficient level of human population, and sufficiently dense, surfeit '''populations''' of human-made Goods-artefacts, to the point that opportunities for one tribal community to encounter and to barter its surplus, to-it-use[value]less Goods to neighboring tribal communities, in exchange for their, complementary, Goods-surpluses, becomes probable enough and frequent enough to be reliable/practicable/sustainable.

For another example:  it is clear that the most essential species of Capital, Industrial Capital, i.e., not qMM = K [which connotes, directly, only the "antediluvian" species of Capital, chiefly merchant's Capital and usurers' Capital, originating within the Money[-&-Commodity] circulation process, and arising before the Capital-relation has seized control of, and reshaped, the society-[re-]production process, i.e., before the advent of 'Capital-ist' society proper], but rather qKMCGA, which signifies the '''real subsumption''', by the Capital-relation, of all of its predecessor social relations of production ‘socio-ontology’ -- i.e., of M, C, G, and A -- requires the social permeation of the wage labor relation, and therefore also of the wage labor revenue, supporting the proletarian working class, which in turn requires that the human society hosting/characterized-by the Capital-relation has attained a level of productivity/productive force such that each individual worker is, on average, able to produce more than the value-equivalent of that worker's daily subsistence-requirements during each day of work, so as to produce the “surplus-value” basis for the other-classes-supporting revenues:  profit of enterprise, rent of land, interest on money-capital, governmental tax, etc.

Otherwise, there would be no potential surplus product to serve as an objective basis for the very possibility of profit of enterprise, hence of any 'epochally-sustainable' possibility of existence for Industrial Capital, or for a '''Capitalist society''' -- meaning a society whose 'meristemal'/predominant social relation of production is the Capital-relation.

Marx, in the Grundrisse, or '''Foundation''', of his dialectical, immanent critique of capitalist political economy, clarified the natures of, and the interrelationship of, the social forces of production and the social relations of production, in connexion with the total "pre-history" of the truly human species, as follows:  "Productive forces and social relationships -- the two different sides of the development of the social individual -- appear to be, and are, only a means for capital, to enable it to produce from its own cramped base. But in fact they are the material conditions that will shatter this foundation." [David McLellan, editor, The Grundrisse, Karl Marx, Harper & Row [NY:  1971], p. 143, emphases added by F.E.D.].

For present purposes, for this section, we will not solve this Seldonian, social relations  ‘meta-equation’ --

>-|-<t = <A>^(2^t)


-- in bootstrap fashion, from A onward, as all ‘‘‘following from’’’ this «arché»/ultimate ancestor social relations category, A, by ‘connotational entailment’ from the connotations of that «arché» social relations category/term itself, alone.  Instead, we will narrate and describe, rather than derive, the “stipulated solution” of this ‘meta-equation’, as stated above, for all of its epochs that belong to our historical past, for ‘meta-model’ epochs 0 through 4.  Only then will we derive a solution, here, for epoch t = 5, the ‘meta-model’ epoch which represents our present and our incipient future, the epoch in which the ‘‘‘real subsumption’’’ of all priorly-arisen-and-still-extant social relations of production, by the Capital-relation, has already arisen, and in which the radically new social relation of production herein named the Generalized Equity-relation is predicted to arise.  We will also, for the most part, omit narrations, and solutions, for the ‘partial synthesis’ or ‘‘‘hybrid’’’ categories/terms of this ‘meta-equation’, e.g., for qGA, or qKMCGA, etc., instead concentrating mainly on narrating the stipulated solutions for the 1st, qAA = G, the 2nd, qGG = C, the 3rd, qCC = M, and the 4th, qMM = K, self-hybrid’, ‘dialectical antithesis’ terms/categories, and on solving for the 5th “dialectical antithesis” term/social-relations category, which will remain, until that solution, in the status of a dialectical-algebraic “unknown”:  qKK  =  ?  = X, wherein the symbol '=' denotes the relationship "is equal to by definition".



The [pre-]historical process of human social formation; the historical self-progression of human-social formations; the 'meta-dynamical self-meta-evolution' of human society; the historical succession of qualitatively/‘socio-ontologically’ distinct, '''historically-specific''', 'merely-dynamical' human-social dynamical systems of social relations of production that form, together, what we term the 'diachronic meta-system' of human societies, and of their net-expanding sequence of ‘human-social ontologies, in terms of the NQ_ model of human-social 'non-ontostasis' described above -- i.e., of human-social 'onto-dynamasis' -- '''looks''' to us as follows, per the self-iteration of its «arché», A, through its epoch t = 4 [≈ 1 epoch-unit ‘behind’ our present] --

t   >-|-<t   Interpreted Arithmetic [‘Socio-Ontological’, Intensional-Intuitional, Connotational, Categorial Symbols]                                                


>-|-<0 = <A>^(2^0) = A = 

Stipulated origin / «arché»:  Predation / direct or immediate Appropriation of the raw or "not-humanly-refined" products of [principally extra-human/pre-humannature; the foraging/scavenging/hunting/gathering human-social relations of production only, near the '''vanishing point''' of 'human-social' or 'meta-animal-social' economy back into its predecessor, 'animal-social' ecology, i.e., near the 'emergence point' from l into h;


 >-|-<1 = <A>^2^1 = <A>^2 = Ax<A> = ~<A> = <A ~+~ G> = 

Predations + Productions;

 >-|-<2 = <A>^2^2 = <A + G>^2  = <A + G>x<A + G>  = <<A + G + qGA>  ~+~ C>;

 >-|-<3 = <A>^2^3 = <A G qGC>^2

<<A G qGC qCqCqCGA> ~+~ M>;

 >-|-<4 = <A>^2^4 = <<A + G + qGA + C + qCA + qCG + qCGA> ~+~ M>^2 =

  
<<A + G + qGA + C + qCA + qCG + qCGA + M +
                                                                                                                                                  qMA + qMG + qMGA + qMC + qMCA + qMCG + qMCGA ~+~ K >

-- wherein '~+~', formally, denotationally equivalent to just '+', emphasizes, 'connotationally', the qualitative, heterogeneous, and supplementary-oppositional addition here involved.




Commentary on the Reconstructive Stipulated Solution Expressed Ideographically Above.

Historically Generic Commentary.  A Story of the Historical Labor of the Self-Birthing, 'Self-Delivery', and Self-«Bildung» / Self-Formation of Humanity. The '''story''' that this 'meta-model' is telling is one of the self-expansion of the social-relations-ontology, and thus of the very activities-ontology/praxis-ontology, of human society.

It encompasses, connotatively, key aspects of the extra-social, «anti-physis»/«physis» exchange/interchange, as well as of the intra-«anti-physis», i.e., the intra-social exchange aspects of the total history of human praxis.

This 'socio-onto-dynamasis' process involves the quantitative self-expansion and 'self-densification' of the '[meta-]monadic populations' of the leading 'socio-onto', or 'socio-ontological category' of human social praxis, within each given epoch of that ‘social ontology’.

This quantitative self-expansion and 'self-densification' eventually bring about a critical 'socio-ontic density'.

As each such '''critical-onto-mass-density''' threshold of such 'self-densification' is crossed, this crossing brings about the ‘self-densified’ 'self-surroundment', 'self-environment', 'self-confrontation', and 'self-interaction' or 'monadic intra-action'/mutual interaction of the «monads» of the leading-edge 'ontic population' of such social relations / social activities, up to its moment of 'self-reflexion' and 'self-involution' [cf. Chardin].

The resulting crisis creates new emergent such 'socio-ontos', or ‘socio-ontological categories’, triggering a change-in-social-relations-of-production 'social revolution', due to this irruption of new kinds of social relations of production, i.e., a 'social meta-evolution', or 'meta-system transition' [cf. Turchin], and a 'self-transcendence' [cf. Jantsch] of the extant human social system of human-social relations of human-societal [including of human-social relations of production] self-reproduction.

This story models that sequence of historical species of human society -- of historically specific modes of human-social reproduction; of human-social 'meta-evolutionary epochs' -- as the 'onto-meta-dynamics' of a singular historical/diachronic 'meta-system' -- that is, of a progressive-cumulative [«aufheben»] self-driven progression of human-social systems -- of human-social reproduction; of human-society-self-reproduction.

It models that self-progression as a human 'socio-onto-dynamasis'; as a net-expanding historical accumulation/'cumulum' of ever-richer, ever-more-elevated/«aufheben»-involuted ‘social relations of production ontology’, that Marx adumbrated in his famous Preface to his debut book on the dialectical, immanent critique of ideology in the “science” of economics, A Contribution to the Critique of Political Economy.



Historically Specific Commentary, Epoch t = 0.  Asserting Ontological Possibility for the «arché» category of social relations of production ontology. We begin our ideographical story of the ‘meta-evolution’ of the human-social relations of production, or of the “forms of [human-social] intercourse” [cf. Marx, Engels, The German Ideology], at its historical beginning, or ‘pre-beginning’, with the mode of “production” known as predation, as foraging and scavenging, or as “hunting and gathering” --

The historically specific, Epoch t = 0 equation that is contained in the historically generic meta-equation’, is: 

>-|-<0 = <A>^(2^0) = <A>^1 = A.


This long 0th epoch, epoch t = 0, per the historically generic ‘meta-equation’ of social relations of production ‘meta-evolution’ that is to be narrated herein, is described simply by its constituent historically specific equation >-|-<0 = A. 

This equation is simply the sole and singular assertion of the ontological possibility of the «arché», dialectical thesis category of the historical progression of ‘socio-ontological’ categories of social relations of production described by our ‘meta-equation’.  

It is, not the existential, but the ‘possibilial’ assertion of category A, which connotes the category of the non-production or pre-production prehistory of humanity, the category of the vanishing point of human-social production, the category of mere, “raw”, Appropriation of the productions of pre-human / extra-human Nature, by the actions of primitive proto-humanoids, continuing for millennia before the irruption, into possibility, of the next, historical-dialectical antithesis category, in this dialectical progression of possible categories of the human-social relations of production. 

From the connotations of this, dialectical thesis, category, all subsequent progressions of categories follow. 

That is, they “follow” in our ‘contra-Boolean’, ‘connotational entailment’, intensional, ‘algorithmic-heuristic’, intuitive, dialectical-logical sense.





TO BE CONTINUED

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