Sunday, October 20, 2013

Part 8 of 9. Seldonian, Dialectical-Algebraic Derivation of the Successor System to Capitalism.


Full Title -- 

Part 8 of 9.  Seldonian, Dialectical-Algebraic Derivation of 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 have participated, as to what Karl Seldon derived, and also as to how he derived it, with regard to the global system of ‘Democratic Communism’, or of ‘Marxian Democracy’ -- of ‘Political-Economic Democracy -- as the possible global successor system to the global capitalist system, using the 'algorithmic-heuristic' algebra of dialectics that he discovered in 1996.

Such questions deserve an answer. 

This blog-entry summarizes the eighth part of Seldon’s answer. 

This blog-entry was extracted from writings of Hermes de Nemores, Secretary-General of Foundation Encyclopedia Dialectica, and chairperson of its General Council, from his recent update to an introductory text, whose earlier version is available via the following links --





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

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

Enjoy this eighth part of Hermes de Nemores’ re-telling of Seldon’s amazing saga of solution!



Regards,


Miguel











Example 5:  NQ_ Psychohistorical-Dialectical Meta-Model. TheMeta-Equation of Human-Social Relations of ProductionMeta-Evolution’ [Part 8 of 9].



SUMMARY:  The predicted «species» of the «genos» of 'Generalized Equity' -- a 'meta-dynamical disjunctive syllogism' for the epochal transition from K to E.  We discern the following 'socio-ontological' «species» of human-social relations [of production] as inhering within the «genos» of 'Generalized Equity', and as expected, by us, to be manifested by, and ingredient in, the emergence of E from K --


a. Internality Equity:  of private stockholders [«arché» 'onto' of 'Generalized Equity', seeded in K; thus K is partially «aufheben»-conserved -- i.e., under Publics' Boards'/other, containers/constraints -- within E];

b.  Citizen Externality Equity:  of public stakeholders [‘intra-dual contra-thesis’ to 'Internality-Equity']; «arché» social-relations-of-production 'onto' of 'meta-Capitalist', 'Equitarian Society'];

c.  Citizen Birthright Equity:  equal social resources grants to each new citizen, at conception or at birth; egalitarian social self-investment / self-endowment trust-funds, with legislated "moral hazard" mitigators;

d.  Citizen Stewardship Equity rights of each working adult, including to membership in, and 1-person/1-vote 'economic suffrage' within, the 'producers' councils', or 'stewards' councils', democratically managing the socially-/legally-/constitutionally-favored, socialized producer's cooperative enterprises, and including the right to share in the profits-of-enterprise of any such producers' cooperative in which that citizen works, with partial rights of use/disposition over the socially-owned means of social reproduction ceded, in stewardship, but not in local ownership, to these socialized producers' cooperatives/local producers' associations, under the collective/democratic control of their members/'stewards' councils', in continuous negotiation with these enterprises' own 'externality-equity'-holding 'publics' boards', as part of Equitarian Society's «aufheben»-negation/conservation/elevation of market-based economic-only checks-and-balances regarding the pricing and quality of the goods/services supplied to the citizen-consumers by these enterprises, into additional, Equitarian political-economic checks-and-balances, using Equitably-allocated, socially-owned means of social reproduction, such that this newly-emergent 'Stewardship-Equity-relation' of production increasingly supplants the likewise «aufheben»-conserved/constrained '''wage-labor'''/private-capital social-relationship-of-production [cf. the model of "Economic Democracy" constructed by David Schweickart in his Against Capitalism, Cambridge University Press [NY: 1993], as well as in his After Capitalism, Rowman & Littlefield Publishers, Inc. [NY:  2002], to which we are indebted, in part, for key aspects of this crucial sub-principle of 'Generalized Equity'.];

e. Citizen Allocational Equity: Equitable regional-geographical allocation of social property access -- of socially/publicly-owned means of social reproduction resources/funding -- on a «per capita», or per human person basis.  Truly Equitable distribution of, e.g., the public assets ceded in Stewardship to local and regional producers' associations, may involve, especially initially, from the point of view of the internationally base-elected A.I.D.P. [«Association Internationale des Directeurs Publiques»] -- or from the point of view of an international referendum, by all citizens, world-wide -- compensatory and reparative elements, until the injustices of past capitalist-imperialist social auto-cannibalization of the capital-hinterland, and of former "Second World" and "Third World" regions of the globe, has been adequately redressed.  Such allocative Equity, in any case, involves the solution of presently unsolved -- and hardly even posed -- problems of 'social-negentropy accounting' in the context of a 'meta-market' social system, in which mere monetary-valuations provide an even more inadequate metric of 'social-reproductive use-value' than they do now, still within the integument of capital.




Beyond NQ_-Algebra Versions of this Meta-Model.  The Socio-Ontological Category E as Rendered in Versions of the Psychohistorical-DialecticalMeta-Equation of Human-Social Relations of ProductionMeta-Evolution as Expressed in the Algebras of the 24th and 56th Seldonian Dialectical Arithmetics. 

There is a dialectic within the taxonomy, also within the synchronic systematics, of the predicted next, E, 'Generalized Equity' «Genos» category of human-social relations of production ‘socio-ontology’, even beyond apart from the oppositeness of the capital equity seed-form of 'Generalized Equity' and the «arché» «species» of that new «Genos», the new -- at last to be recognized -- fundamental Human Right of Citizen Externality Equity’, that lends itself to a systematic-dialectical Marxian method of presentation.


The first, «arché-species», the thesis-«species», of this new «Genos» of 'Generalized Equity', Citizen Externality Equity’, is a category of purely-collective, social property-right, a universal, all-citizens property right, an individually-owned and -owed generalized equity voting right that can only be exercised collectively, publicly, as we have seen in previous parts of this presentation.


The second, anti-thesis-«species», of this new «Genos» of 'Generalized Equity', Citizen Birthright Equity’, is a category of essentially personal property-right, a transfer of wealth, of social property, of social equity, from society collectively, as a whole, to each individual member thereof, as a universalized personal inheritance, albeit as a personal right constrained socially, publicly, by social law, by political legislation, in the interests of society as a whole, so as to mitigate the moral hazard immanent to this new -- newly recognized and at last to be implemented -- Human Right, as we have also seen in previous parts of this presentation.


The third, synthesis-«species», of this new «Genos» of 'Generalized Equity', Citizen Stewardship Equity’, is a category of individual social property-right,  and of social individual property-right.


It combines ‘‘‘momenta’’’ of collective property right, characterizing the first, thesis-«species», of Citizen Externality Equity, with ‘‘‘momenta’’’ of personal property right, characterizing the second, anti-thesis-«species», of Citizen Birthright Equity.
 

The Fundamental Human Right of Citizen Stewardship Equity’ is personal right of each citizen to participate in a qualified ‘‘‘Association of Producers’’’ -- in a Citizen Stewardship Equitysocialized producers’ cooperative, with a qualifying business plan, in market competition with other such cooperatives, and thus to have access to means of production social property -- in ‘‘‘stewardship’’’ and in collective entrepreneurship, not in private ownership of those means of production, and including the right to a 1-person/1-vote electoral power in the election of mandated and recallable enterprise management, and in all other whole-enterprise decisions as well, as a deliberating and voting member of the assembly of the enterprise membership, and the right to an equal share in the profits of enterprise of that enterprise, as well as to a potentially unequal compensation for skills exercised, and for weekly personal life-time devoted, to the collectively-decided work of that enterprise. 


This personal voting right is a voting right exercised collectively, within the collective of the Citizen Stewardship Equity enterprise, and exercisable only within that collective.


This third «species», of 'Generalized Equity', 'Citizen Stewardship Equity’, is a ‘‘‘complex unity’’’ of the collective property right characteristics of the first «species», Citizen eXternality Equity’, with the personal property right characteristics of the second «species», of Citizen Birthright Equity’, a unity which fulfills Marx’s vision of an individual property right at and as the basis of the successor system to the Capitalist system even more than do the earlier-presented two.


That is, in particular, this third newly-recognized «species» of Fundamental Human Right fulfills, even more than the earlier-presented two, that characterization of the social relations of production, of the property rights, immanent to the successor system to the Capitalist system which Marx expressed so powerfully in the climactic chapter of Capital, volume I, as follows --

“The capitalist mode of appropriation, the result of the capitalist mode of production, produces capitalist private property.  This is the first negation of individual private property, as founded in the labour of the proprietor.  But capitalist production begets, with the inexorability of a law of Nature, its own negation.  It is the negation of the negation.  This does not re-establish private property for the producer, but gives him individual property based on the acquisitions of the capitalist era:  i.e., on co-operation and the possession in common of the land and of the means of production.” [Karl Marx, Capital, volume I, Chapter XXXII, Historical Tendency of Capitalist Accumulation, International Publishers [New York:  1967], p. 763, emphases and textual ordinal color-coding added by HdeN].


The «Genos» of the 'Generalized Equity' social relation of production alone is explicitly expressible in that most primitive version of the Psychohistorical-DialecticalMeta-Equation of Human-Social Relations of ProductionMeta-Evolution that is expressible via the ‘intuitional-intensional’, heuristic algebraic language of the NQ_ arithmetic of dialectics.

But the NQ_ system of dialectical arithmetic is only the second, anti-thesis system of such arithmetics, in the Seldonian, step-by-step, systematic, dialectical method of presentation of the systems of dialectical arithmetic, as given by the Dyadic Seldon Function Meta-Equation --


 )-|-(s   =  (N_)^(2^s)   =   

N_ + NQ_ + NU_ + NM_ + Nq_MN + Nq_MQ + Nq_M+ NA_ + ... .



The first, thesis system, or «arché», of such arithmetics is denoted by -- 

N_, [----) q1 

-- which represents the first-order-only axiomatization of the system of arithmetic of the “Natural” Numbers, for which “non-standard models” have long been known to be ‘‘‘co-implicated’’’.  

The thesis system, N_, is one whose numerals are “pure”, unqualified quantifiers, e.g., one which can express only the quantifier “two” out of the phrase “two apples”, or out of the phrase “two pounds of apples”, via the generic ideogram 2 in both, and in all such, cases. 


The first-anti-thesis system, NQ_, which has N, denoting the higher-order axiomatization of the “Natural” Numbers system of arithmetic, as its ‘pre-subscript’, is one whose ‘meta-numerals’ are “pure”, unquantifiable ontological qualifiers, representing ontological categories, e.g.,  only the category “apples” from out of the phrase “two pounds of apples”, via the generic ideogram qn, wherein n denotes a specific “Natural Number”, used as a ‘post-subscript’ ordinal quantifier.


The NQ_, [----) q2 system is the first such ‘‘‘non-standard model of the Natural Numbers system of arithmetic’’’ in that Seldonian progression of systems of dialectical arithmetic.


The third, first-synthesis system of such arithmetics is denoted by --

NU_ = Nq_QN, [----) q3 

-- which also has N, denoting at least a second-order axiomatization of the “Natural” Numbers system, as ‘pre-subscript’.  


It is one whose ‘meta-numerals’ represent a ‘‘‘complex unity’’’, or ‘dialectical uni-thesis system’, ‘‘‘hybridizing’’’ the [meta-]numerals of its two predecessor systems, N_ and NQ_, so that the ‘meta-numerals’ native to NU_  can express both ‘‘‘[ontological] quantification’’’ and ‘‘‘ontological qualification’’’, together, in a single, compound symbol. 


I.e., ‘meta-numerals’ of the NU_ system of dialectical arithmetic are quantifiable ontological qualifiers, or, equally/symmetrically, are qualified ontological quantifiers, representing a specific quantity of the qualitative units, ‘‘‘logical individuals’’’, ‘‘‘elements’’’, ‘’’members’’’, or «monads» that “make up” ontological categories, e.g., both the here-quantified, and, thus, quantifiable, ontological category, apples, and its quantifier, two, from out of the phrase two pounds apples, by means of the compound ‘meta-numeral’ ideogram 2u°n, where n denotes a specific “Natural Number”, used here as a ‘post-subscript’ ordinal quantifier, and where ‘°’ signifies the quantifiability of the monadic qualifier, u°n.

In this example, u°n stands for the quantifiable ontological category of "apples", i.e., for a quantification of how many individual "apples" presently "populate" the category of "apples" in or for the context being described by the compound symbol 2u°n.  In this case, that "local" population of "apples" is just 2.    

Metrical unit qualifiers, e.g., lbs., do not begin to be ‘explicitized’ until system 4

NM_, [----) q4.

 

Using, instead, the 24th axioms-system of dialectical arithmetic in that Seldonian, presentational dialectical progression of systems of dialectical arithmetic, the Nq_BA [----) q24 system, we can represent, explicitly, both the three «species», and the one «Genos», of the 'Generalized Equity' social relation of production, as below.  

Herein, B stands for the Greek capital letter Beta, and A for capital Alpha.


The generic, uninterpreted” -- or, more accurately, minimally-interpreted’ -- ‘meta-numeral’ of the Nq_BA system of dialectical arithmetic needed to model this dialectic is --


................................................................................................................................b
.........................................................................................................--------------------------------
...........................................................................................................a1....+....a2....+....a3....+ ...


-- where b stands for the lower case letter beta, and a for the lower case alpha, and where both represent unquantifiable ontological-category qualifiers. 

Spelled-out, the above,  purely qualitative fraction/fractal’ means --



.........................................................................................................................«Genos»
..............................................................................------------------------------------------------------------------------
...................................................................................«species»1.....+.....«species»2.....+.....«species»3.....+ ...


-- which thus captures, ideographically, the content-structure of the original dialectic, that of Platonian, «arithmoi eidetikoi» dialectical «arithmêtikê», and which we assign to, or interpret as, specifically --


.......................................................................................................................................................E
......................................................................................................................................-----------------------
.........................................................................................................................................X....+....B....+....S


-- given that E denotes the «Genos» named 'Generalized Equity', that X denotes its «species» named Citizen eXternality Equity’, that B denotes its «species» named  Citizen Birthright Equity’, and that S denotes its «species» named Citizen Stewardship Equity’, with the full ontological [“non-amalgamative”] division representing the third stage of the following three-stage dialectical progression [wherein  ----)’ means “goes to”] --



.................E................................................................E...............................................................E
................-----.......................----)......................------------...............----)...............----------------------.
..................X.........................................................X....+....B.........................................X....+....B....+....S


If we hold that the category Citizen Allocational Equity is not a full «species» category of 'Generalized Equity', but that it is, rather, a sub-«species» category, a sub-category, specifically, of the Citizen Stewardship Equity «species» of the 'Generalized Equity' «Genos», then we can draw upon the 56th axioms-system of dialectical arithmetic in that Seldonian, presentational dialectical progression of systems of dialectical arithmetic, the Nq_GBA [----) q56 system, as follows below.  

Herein, G stands for the Greek capital letter Gamma, and g for the same Greek letter, but in the lower case:  gamma.



The generic, uninterpreted” -- or, more accurately, minimally-interpreted’ -- ‘meta-numeral’ of the Nq_GBA system of dialectical arithmetic needed to model this dialectic is --


..........................................................................................................................g
........................................................................-------------------------------------------------------------------
..........................................................................____b1____....+....____b2____....+....____b3____...+ ...
....................................................................................a11...+.........................a21...+.........................a31...+...


-- where, again, b stands for the lower case letter beta, a for the lower case alpha, and such that all represent unquantifiable ontological-category qualifiers. 


Spelled-out, the above,  purely qualitative fraction/fractal’ means --


..................................................................................................................«Genos»
.........................................--------------------------------------------------------------------------------------------------------
..........................................____«species»1____.....+.....____«species»2____.....+.....____«species»3____.....+
...................................................sub-«species»11........................sub-«species»21........................sub-«species»31.....


-- and, given that A denotes the sub-«species» named Citizen Allocational Equity’, of the «species» named Citizen Stewardship Equity’, of the «Genos» named 'Generalized Equity', the third stage of the following three-stage dialectical progression becomes --


..................E..............................................................E...............................................................E
................-----.......................----).....................--------------...............----)...............-------------------------.
................_X_...................................................._X_...+..._B_...................................._X_...+..._B_...+..._S_
..................·........................................................·.....+.....·........................................·.....+.....·.....+.....A


-- wherein · is the generic non-existent, non-extant, ‘‘‘empty’’’, or unknown ontological category placeholder.



The foregoing presentation addresses the richer representation of Equitism only in two of the later, richer, more determinate purely-qualitative dialectical algebras, namely, in the algebra of Nq_BA [----) q24 and in that of Nq_GBA [----) q56.  


It does not address the much richer still representation of Equitism in the later, richer, more determinate quanto-qualitative dialectical algebras of the Seldonian, presentational dialectical progression of the Seldonian systems of dialectical arithmetic.


E.g., this discussion does not address the interpretation of Equitism in


Rq_BAMU [----) q31


let alone in 

Rq_GBAMU [----) q63


both of which involve solutions of nested “total differential equations”, or even of nested [and discretized] “partial differential equations”, via ‘metrically qualified’, and also ‘state-variable qualified’ or ‘control-parameter-qualified’ [thereby also ontologically-qualified], closed-form, time-varying, or spacetime-varying, independent variable solution-function-quantifiers, which are thus-qualified quantitative functions whose arguments are Real time, or the Real time coordinate/“independent variable”, t, together with Real “independent variables” for the x, y, and z coordinates of physical space, etc., representing, e.g., dynamical sub-sub-systems nested within dynamical sub-systems nested within dynamical systems, and wherein R_ denotes the first-order-logic axiomatization of the arithmetic of the so-called “Real” Numbers.




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