Full Title --
Part 8
of 9. Seldonian, Dialectical-Algebraic
Derivation of Fundamental Features
for the F.E.D.-predicted Global Successor System to [Self-]Global[ized]
Capitalism,
using the Dialectical ‘Meta-Equation’ that Models
the ‘Meta-Evolution’ of
the Human-Social
Relations of Production.
by [guest author] Hermes de Nemores.
Dear Reader,
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’. The ‘Meta-Equation’
of Human-Social Relations of
Production ‘Meta-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-Dialectical ‘Meta-Equation’ of Human-Social Relations of
Production
‘Meta-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 Equity’ socialized
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-Dialectical ‘Meta-Equation’ of Human-Social Relations of
Production
‘Meta-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_MU + NA_ + ... .
N_ + NQ_ + NU_ + NM_ + Nq_MN + Nq_MQ + Nq_MU + 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’’’.
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’.
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.
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.
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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