I have reproduced, below, F.E.D. Vignette #14, by F.E.D. Chief Public Liaison Officer Aoristos Dyosphainthos.
The link to the F.E.D. website version of this vignette is given below --
http://www.dialectics.info/dialectics/Vignettes.html
http://www.dialectics.info/dialectics/Welcome_files/Aoristos_Dyosphainthos,v.1.0,F.E.D._Vignette_14,Dialectic_as_Self-Progression_of_Self-Activity_and_Resulting_Self-Change,30JUL2013.pdf
Enjoy!
Regards,
Miguel
F.E.D. Vignette #14 --
Dialectic as Self-Progression of Self-Activity and of Resulting Self-Change
by
Aoristos Dyosphainthos
Author’s Preface. The purpose of F.E.D. Vignette #14 is to illustrate
the ways in which F.E.D.’s ‘Dyadic Seldon Function’
captures characteristics that have, at various moments, from antiquity all the way through
to modern times,
been insightfully ascribed to the
universal dialectical
process,
including especially the characteristics of “self-activity”, of “self-change”,
or «auto-kinesis»
[Plato], and of [e.g., ‘‘‘dyadic’’’, or “second degree”]
nonlinearity.
A Note about the On-Line
Availability of Definitions of F.E.D. Key Technical Terms. Definitions
of Encyclopedia Dialectica technical terms, including of E.D. ‘neologia’, are available on-line via the following URLs --
-- by clicking on the links associated with each
such term, listed, in alphabetic order, on the web-pages linked-to above.
Links to definitions of the Encyclopedia Dialectica special terms most fundamental to this vignette are as follows --
«arché»
‘Meta-«Physis»’
«Physis»
-- and we plan to expand these definitions resources
as the Encyclopedia Dialectica Dictionary Project unfolds.
[Note: ‘‘‘Arithmetical
Quantifiers’’’ vs.
‘Arithmetical Qualifiers’. In the phrase “3 apples”, we
term “3” the “arithmetical [“pure”-]quantifier”, and “apples”
the ‘‘‘ontological’’’ -- or kind of thing -- ‘‘‘qualifier’’’. In the phrase “3 pounds of apples”, we term “pounds” the ‘metrical[-unit] qualifier’
-- or ‘‘‘unit of measure qualifier’’’
-- quantified by
the 3, which, together, ‘quanto-qualify’ the ‘ontological qualifier’, “apples”.
A key use-value of the dialectical arithmetics is to provide
algorithmic, ideographical-symbolic systems for the various kinds of
‘arithmetical qualifiers’,
both with and without the co-presence of ‘‘‘arithmetical quantifiers’’’.].
I. Introduction: The Marxian Provenance of Concepts of “Self-Activity” and “Self-Change”. The key terms
for this vignette -- “self-activity” and “self-change” -- first emerged, in Marx’s
writing, very close to the original irruption of the ‘psychohistorical materialist’ theory that is now called
“Marxian theory”, in what Engels called “the first document in which is
deposited the brilliant germ of a new world outlook”, namely, in Marx’s “Theses
of Feuerbach”, in the third of his eleven theses, written by Marx in early
1845, on the eve of the continent-wide republican revolutions of 1848 in which
both Marx and Engels were to later participate --
“The materialistic doctrine
concerning the change of circumstances and education forgets that circumstances
are changes by men and that the educator must himself be educated.”
“Hence this doctrine must
divide society into two parts -- one of which towers above [Engels: “as in
Robert Owens”].”
“The coincidence of the
change of circumstances and of human activity or self-change can be comprehended and rationally
understood only as revolutionary practice.”
[Loyd D. Easton and Kurt H.
Guddat, editors and translators, Writings of the Young Marx on Philosophy and Society, Doubleday & Company, Inc.
[NY: 1967], p. 401, emphasis added by
A.D.].
During 1845-1846, Marx and
Engels co-authored an extensively-articulated presentation of their new, ‘psychohistorical materialist’ world outlook, which,
however, was not published until 1932, and in which they summarized that new, ‘psychohistorical materialist’ world outlook as follows --
“...reality is only the
product of the preceding intercourse of individuals themselves. ...
The difference between the individual as a person and what is accidental to him is not a conceptual difference but a historical fact. ...
It is not a distinction that we have to make for each age, but one which each age makes itself from among the different elements which it finds in existence, and indeed not according to any theory, but compelled by material collisions in life.
What appears accidental to the later age as opposed to the earlier -- and this applies also to the elements handed down by an earlier age -- is a form of intercourse [A.D.: later, Marx uses the term “social relations of production” in place of his original term, “forms of [human-social] intercourse”.], which corresponded to a definite stage of development of the productive forces.
The relation of the productive forces to the form of intercourse is the relation of the form of intercourse to the occupation or activity of the individuals.
(The fundamental form of this activity is, of course, material, on which depend all other forms -- mental, political, religious, etc. The various shaping of material life is, of course, in every case dependent on the needs which are already developed, and the production, as well as the satisfaction, of these needs is an historical process, which is not found in the case of a sheep or a dog..., although sheep and dogs in their present form certainly, but malgré eux, are products of an historical process.)
The conditions under which individuals have intercourse with each other ... are conditions appertaining to their individuality, in no way external to them; conditions under which these definite individuals, living under definite relationships, can alone produce their material life and what is connected with it, are thus the conditions of their self-activity and are produced by this self-activity.* [“*[marginal note by Marx:] Production of the form of intercourse itself.”].
The definite condition under which they produce, thus corresponds, as long as the contradiction has not yet appeared, to the reality of their conditioned nature, their one-sided existence, the one-sided-ness of which only becomes evident when the contradiction enters on the scene and thus exists for the later individuals.
Then this condition appears as an accidental fetter, and the consciousness that it is a fetter is imputed to the earlier age as well.”
The difference between the individual as a person and what is accidental to him is not a conceptual difference but a historical fact. ...
It is not a distinction that we have to make for each age, but one which each age makes itself from among the different elements which it finds in existence, and indeed not according to any theory, but compelled by material collisions in life.
What appears accidental to the later age as opposed to the earlier -- and this applies also to the elements handed down by an earlier age -- is a form of intercourse [A.D.: later, Marx uses the term “social relations of production” in place of his original term, “forms of [human-social] intercourse”.], which corresponded to a definite stage of development of the productive forces.
The relation of the productive forces to the form of intercourse is the relation of the form of intercourse to the occupation or activity of the individuals.
(The fundamental form of this activity is, of course, material, on which depend all other forms -- mental, political, religious, etc. The various shaping of material life is, of course, in every case dependent on the needs which are already developed, and the production, as well as the satisfaction, of these needs is an historical process, which is not found in the case of a sheep or a dog..., although sheep and dogs in their present form certainly, but malgré eux, are products of an historical process.)
The conditions under which individuals have intercourse with each other ... are conditions appertaining to their individuality, in no way external to them; conditions under which these definite individuals, living under definite relationships, can alone produce their material life and what is connected with it, are thus the conditions of their self-activity and are produced by this self-activity.* [“*[marginal note by Marx:] Production of the form of intercourse itself.”].
The definite condition under which they produce, thus corresponds, as long as the contradiction has not yet appeared, to the reality of their conditioned nature, their one-sided existence, the one-sided-ness of which only becomes evident when the contradiction enters on the scene and thus exists for the later individuals.
Then this condition appears as an accidental fetter, and the consciousness that it is a fetter is imputed to the earlier age as well.”
These various conditions,
which appear first as conditions of self-activity, later as fetters upon it, form in the whole
evolution of history a coherent series of forms of intercourse, the coherence
of which consists in this: in the place
of an earlier form of intercourse, which has become a fetter, a new one is put,
corresponding to the more developed productive forces, and, hence, to the
advanced mode of the self-activity of individuals -- a form which in turn
becomes a fetter and is then replaced by another.
Since these conditions correspond at every stage to the simultaneous development of the productive forces, their history is at the same time the history of the evolving productive forces taken over by each new generation, and is, therefore, a history of the development of the forces of the individuals themselves.”
Since these conditions correspond at every stage to the simultaneous development of the productive forces, their history is at the same time the history of the evolving productive forces taken over by each new generation, and is, therefore, a history of the development of the forces of the individuals themselves.”
Since this evolution takes
place naturally, i.e., is not subordinated to a general plan of freely combined
individuals, it proceeds from various localities, tribes, nations, branches of
labour, etc., each of which to start with develops independently of the others.
Furthermore, it takes place only very slowly; the various stages and interests are never completely overcome, but only subordinated to the prevailing interest and trail along beside the latter for centuries afterwards [A.D.: the latter phenomenon belongs to what F.E.D. terms ‘the evoluteness of meta-evolution’, and is captured by the “double-«aufheben» evolute product” rule of categorial multiplication, which undergirds the Seldon Functions, as we shall see below.].”
Furthermore, it takes place only very slowly; the various stages and interests are never completely overcome, but only subordinated to the prevailing interest and trail along beside the latter for centuries afterwards [A.D.: the latter phenomenon belongs to what F.E.D. terms ‘the evoluteness of meta-evolution’, and is captured by the “double-«aufheben» evolute product” rule of categorial multiplication, which undergirds the Seldon Functions, as we shall see below.].”
[Karl Marx, Frederick Engels, The
German Ideology, Progress Publishers [Moscow:
1968], pp. 88-90, emphasis added
by A.D.]
In the voluminous 1857-1858
work by Marx, posthumously entitled “Foundations of the Critique of
Political Economy” [“«Grundrisse»”], and first published in 1939, in its section
entitled “Forms which precede capitalist production. (Concerning the
process which precedes the formation of the capital relation or of original
accumulation)”, Marx describes the “self-change” which results from this “self-activity” of human “social
individuals” in the self-development of the early agricultural village
communities of humankind -- all the way from gradual, “evolutionary”,
quantitatively-“dynamical” “self-change”, to “sudden”, “revolutionary self-change”, or, in F.E.D.’s version, to
‘meta-evolutionary, socio-onto-dynamical, meta-dynamical, meta-finite singularity’ “self-change”, in the following terms --
“...In so far as property is
merely a conscious attitude to the conditions of production as to one’s own
-- an attitude established by the community for the individual, proclaimed and
guaranteed as law; in so far as the existence of the producer therefore appears
as an existence within the objective conditions belonging to him, it is
realized only through production.
Actual appropriation takes place not through the relationship to these conditions as expressed in thought, but through active, real relationship to them; in the process of positing them as the conditions of man’s subjective activity.”
Actual appropriation takes place not through the relationship to these conditions as expressed in thought, but through active, real relationship to them; in the process of positing them as the conditions of man’s subjective activity.”
“But this also clearly means
that these conditions change.”
“What makes a region of the
earth into a hunting-ground, is being hunted over by tribes; what turns the
soil into a prolongation of the body of the individual is agriculture.
Once the city of Rome had been built and its surrounding land cultivated by its citizens, the conditions of the community were different from what they had been before.”
Once the city of Rome had been built and its surrounding land cultivated by its citizens, the conditions of the community were different from what they had been before.”
“The object of all these
communities is preservation, i.e., the production of the individuals which
constitute them as proprietors, i.e., in the same objective mode of existence,
which also forms the relationship of the members to each other, and therefore
forms the community itself.
But this reproduction is at the same time necessarily new production and the destruction of the old form.” ...
But this reproduction is at the same time necessarily new production and the destruction of the old form.” ...
... “The act of reproduction itself
changes not only the objective conditions -- e.g., transforming village into
town, the wilderness into agricultural clearings, etc. -- but the producers
change with it, by
the emergence of new qualities, by transforming and developing themselves in production, forming new powers and new conceptions, new modes of intercourse, and new speech.” ...
... “The
community itself appears as the first great force of production.” ...
“...In the last instance the
community and the property resting upon it can be reduced to a specific stage
in the development of the forces of production of the
labouring subjects -- to which correspond specific relations of these subjects with each
other and with nature.”
“Up to a certain point, reproduction. Thereafter, it turns into dissolution.” ...
“... All the forms in which
the community imputes to the subjects a specific objective unity with the
conditions of their production, or in which a specific subjective existence
imputes the community itself as condition of production, necessarily correspond
only to a development of the forces of production which is limited both in fact
and in principle. (These forms are of
course more or less [A.D.: pre-human-]naturally evolved, but at
the same time also the results of a [A.D.: human-]historic process.”
“The
evolution of the forces of production dissolves them, and their dissolution is itself an evolution of
the human forces of production.”
“Labour is initially undertaken on
a certain basis -- first primitive -- then historical. Later, however, this basis or presupposition
is itself cancelled [A.D.: i.e., becomes «aufheben»] ... as having become too narrow for the development of the progressive
human horde.”
[E. J. Hobsbawm, ed., Jack
Cohen, transl., Karl Marx: Pre-Capitalist
Economic Formations, Internat’l. Publishers [NY:
1969], pp. 92-97, emphasis added by A.D.].
Lastly, in volume one of
Marx’s «magnum opus» -- Capital: A Critique of Political Economy -- we find the following
account of human “self-activity” and “self-change” as human self-development in Marx’s definitional
description of his core category of “human
labor” --
“Labour is, in the first
place, a process in which both man and Nature participate, and in which man of
his own accord starts, regulates, and controls the material re-actions between himself and Nature.
He opposes himself to Nature as one of her own forces, setting in motion arms and legs, head and hands, the natural forces of his own body, in order to appropriate Nature’s productions in a form adapted to his own wants.
By thus acting on the external world and changing it, he at the same time changes his own nature.
He develops his slumbering powers... .”
[Karl Marx, Capital, Volume I, International Publishers [New York: 1967], p. 177, emphasis added by A.D.].
He opposes himself to Nature as one of her own forces, setting in motion arms and legs, head and hands, the natural forces of his own body, in order to appropriate Nature’s productions in a form adapted to his own wants.
By thus acting on the external world and changing it, he at the same time changes his own nature.
He develops his slumbering powers... .”
[Karl Marx, Capital, Volume I, International Publishers [New York: 1967], p. 177, emphasis added by A.D.].
II. E.D. Interpretation of the Initial Generic Ordinal Qualifiers undergirding the Seldon Function NQ_ Arithmetic.
Perhaps
a bit surprisingly, upon first apprehension, the first four, first-order-logic,
Dedekind-Peano Postulates for the “Natural” Numbers focus on
their ordinality, not on their cardinality, viz. --
1. 1 is a “Natural Number”.
2. The successor of any “Natural Number” is also a
“Natural Number”.
3. No two, distinct “Natural Numbers” have the
same successor.
4. 1 is not the successor of any
“Natural Number”, i.e., 1 has no ancestor within
the “Natural Numbers”.
These postulates thus
identify the essence of the “Natural Numbers”, explicitly,
in terms of [apparently purely-]quantitative ordinality. In keeping with this focus on the ordinal, Seldon defines the system
of the NQ_ dialectical arithmetic -- the first ‘antithesis-system’, or ‘contra-system’, to the “Natural Numbers” as «arché»-system -- in terms of qualitative
ordinality. The NQ , which he also calls the ‘meta-Natural meta-Numbers’, are,
in their simplest, least-interpreted essence, a consecutive sequence of
‘meta-numeral’ ideograms representing the successive qualities, not the quantities, of ordinality -- the quality of ‘first-ness’, followed by the quality of ‘second-ness’, followed by the quality of ‘third-ness’, and so on... --
satisfying the four first-order-logic ‘contra-Peanic’, ‘Qualo-Peanic’ axioms:
1q. The ordinal qualifier for the quality of ‘first-ness’ is an element of the ‘consecuum’ of generic ordinal qualifiers.
2q. The successor of any element of the ‘consecuum’ of generic ordinal qualifiers is also an element of same.
3q. Any two, distinct ordinal
qualifiers have qualitatively unequal successors.
4q. The ordinal qualifier for the quality of ‘first-ness’ is «arché»: not the successor of any element of its ‘consecuum’.
The symbols, or ‘meta-numerals’, that stand for the ‘meta-numbers’ of the NQ ‘archéonic consecuum’ are derived, syntactically, in a way which represents
the semantic ‘self-subsumption’, ‘self-subordination’, or ‘self-demotion’ [dialectical, self-«aufheben» self-negation] of the “Natural Numbers”. That derivation is part of the positive
fruition of the dialectical, immanent self-critique of the “Natural Numbers”, which
divulges the NQ as the implicit, most extreme known opposite, “Non-Standard
Model” of the “Standard”, Peano “Natural Numbers”. It involves the turning of the ‘generic ordinal quantifiers’ of the “Natural Numbers” into the ‘generic ordinal qualifiers’ of the NQ ‘meta-Natural meta-Numbers’. The conceptual ‘self-subsumption’ of the quantitative
ordinality intended by the Dedekind-Peano Postulates surfaces the NQ as their hitherto hidden,
implicit ‘intra-dual’, based upon the generic quality
of ordinality, a ‘‘‘genericity’’’ which we represent by the ‘meta-numeralic’ ideogram ‘q’. That ‘meta-numeral component’ represents ‘qualitative ordinality’, or ‘ordinal quality’, in general: just ‘q’, or, more fully expressed,
just qN.
To fully express, ‘meta-numeral-y’, or ideographically, the ‘consecuum’ of specific ordinal qualities, namely --
NQ =
{‘first-ness’; ‘second-ness’; ‘third-ness’, etc.}
-- we must add a second ‘meta-numeral component’, via ‘‘‘subordinating’’’ specific “Natural
Numbers”, as specific ‘ordinal quantifiers’, to the generic ordinal
qualifier
symbol ‘q’,
by ‘subscripting’ those specific “Natural Numbers” to a ‘script-level’
‘q’, ‘‘‘above’’’ them, yielding --
NQ =
{ q1, q2, q3, ... } [in which each ‘meta-number’ is a minimal, «genos»/«species» «arithmos eidetikos»
in its own right],
vs.
N = { 1, 2, 3, ... }.
Note that this opposition of an arithmetical system of purely-quantitative ordinality, based upon the N, versus an arithmetical system of purely-qualitative ordinality, based on the NQ, is not a radical dualism, imagined as an absolute, irreconcilable diremption between an absolute quantitative and an absolute qualitative. This opposition is, on the contrary, a dialectical antithesis-sum. The N quantifiers are still there, as ‘specifiers’ -- still present -- in, or ‘‘‘under’’’,
the generic qs of the NQ qualifiers, though subsumed, subordinated, demoted -- demoted to being their mere subscripts or denominators: The N quantifiers are still “contained” in[side] [‘‘‘beneath’’’]
the NQ qualifiers. That is, each NQ qualifier is an «aufheben» determinate negation / conservation / elevation-into-one-step-higher-generality of an individual N quantifier.
The joint «aufheben» elevation of the quantitative
ordinals «species» yields the «genos» ‘q’, of the qualitative ordinals.
For this first layer of
interpretation of these “purely-qualitative” NQ ‘meta-numbers’ -- which does not yet make explicit their universal
interpretability for the modeling of dialectical progressions -- this is all that they
represent: abstract
temporality; [abstract chronological]
order; generic ‘ordered-ness’; the consecutive succession
of ‘qualitative ordinality’; the ‘consecuum’ of order quality or of order qualities.
But even here, at this
minimally-interpreted stage of the construction of the NQ dialectical arithmetic, there is already a kind of
generic ‘connotative entailment’ at work. True, it is but a shadow, and but a
‘pre-vestigial’ harbinger, of the richness of the kind of particularity of categorial followership that drives forward,
intuitively, the dialectical, purely-qualitative logic of the more concrete, more specific dialectical-algebraic interpretations thereof. A case in point is exemplified in the very NQ algebraic
model of
The Dialectic of Nature that is used for the
illustrations presented herein.
This generic ‘connotative entailment’ can be formulated as
follows: ‘second-ness’ follows -- and even
follows from --‘first-ness’; ‘third-ness’ follows [from] ‘second-ness’, and so on.
In the next section, the
construction, by iterated interpretations layering, of the Seldonian first dialectical arithmetic will advance from this
harbinger of ‘connotative entailment’ to the following, still generic, but at last also explicitly
dialectical, form of ‘connotative entailment’ ordinality: ‘ first full antithesis follows from the self-interaction of [«arché»-]thesis; first full synthesis follows from the mutual interaction of first full thesis and first full antithesis’, and
so on.
III. Dyadic Seldon Function Interpretation of the Initial Generic NQ Ontological Category Qualifiers.
‘dialectical model meta-equation’ form for the functions-family
of the Seldon Functions is that of a generic cumulum symbol [ ‘|-|-|’ ] on the LHS [Left-Hand
Side] of the ‘dialectical meta-equation’, equated to an RHS expression
representing ‘self-reflexive operation’ of an [«arché», ‘‘‘seed’’’, ‘‘‘cell-form’’’, or ‘ultimate ancestor’ ontological category symbol [represented, generically, by ‘q1’] -- indicating its recurring ‘self-reflexion’ via a ‘meta-exponentiated’, monotonically
increasing whole-number-valued ‘‘‘independent variable’’’ [‘h’ ] -- on the RHS of the generic Seldon
Function equation, viz. [with ‘generic-ness’ connoted by the
“rectangular” motif of the
symbols-set]:
If v = 2, the Generic Seldon Function above is said to belong
to the Dyadic Seldon Function
sub-family. If v = 3, the
Generic Seldon Function
above is said to belong to the Triadic Seldon Function sub-family. Our remarks herein are concentrated on the Dyadic Seldon Functions, because the main ‘dialectical-mathematical meta-equation’, modeling a historical dialectic, exposited herein, is of the v = 2 variety.
With
v = 2, and selecting that special generic
Dyadic Seldon
Function form
that we reserve for a historical dialectic, the form of the ‘meta-model
meta-equation’
to be used in the illustrations herein, becomes, more specifically --
-- wherein the symbol t, replacing the more generic
symbol h, represents the generic algebraic parameter-variable
for the historical epoch modeled, and wherein, in
general, the “angular” motif of
the entire symbols-set used is to connote the historical dialectic domain
of ‘dialectical
modeling’.
The Seldon Functions bring with them a
further, second
layer of interpretation of the NQ qualifiers,
{ q1, q2, q3, ... },
by which they are interpreted as qualifiers that stand for generic dialectical physio-ontological categories, e.g., for ‘‘‘physis’’’ categories, or for full or partial ‘meta-physis’ categories, or for full or partial ‘uni-physis’ categories.
{ q1, q2, q3, ... },
by which they are interpreted as qualifiers that stand for generic dialectical physio-ontological categories, e.g., for ‘‘‘physis’’’ categories, or for full or partial ‘meta-physis’ categories, or for full or partial ‘uni-physis’ categories.
If we assign
[ ‘[--->’ ] the «arché»-physis category, qa, to the generic NQ qualifier ‘meta-number’, q1, as signed by ‘qa [--->
q1’, and if we can discern that qa, and all of its successor-categories, and their cumula, as generated by
its successive, cumulative,
‘Seldon-functional self-operations’, connote «aufheben» operators, that is, dialectical negation operators,
then the Dyadic Seldon
Function is seen to
signify, under the axioms of the system of arithmetic of the NQ ‘meta-numbers’
[
http://www.dialectics.info/dialectics/Correspondence_files/Letter17-06JUN2009.pdf
], a ‘self-iterated’, cumulative recurrence of dialectical “negations of [the]
negations”.
With every [unit] increase in t, the Dyadic Seldon Function ‘formulaic recipe’ calls for
the dyadic self-operation of the result of the
previous dyadic self-operation, i.e., for a negation of the negation
of the result of the previous negation
of the negation. Only for
t = 0 -- only for the case in which no self-operation occurs -- is the
“result” a singleton [physio-] ontological category symbol, the symbol for the «arché» [physio-]ontological category alone, instead of that
“result” taking the form of a cumulum
of [powers-of-]two
[or more] such symbols, i.e., a “non-amalgamative sum” [cf. Musès], or an «a-sumbletoi»
sum [cf. Plato], of ‘[physio-]ontological category’ symbols, since 20 = 1, and since qa1 = qa.
For example, if we take epoch t = 1, and denote the «arché» ontological category simply by a, for syntactical convenience, then the Dyadic Seldon Function calls for the following, as per the NQ_ axioms, since 21 = 2 --
-- wherein a [---> q1 connotes the «arché» category,
or ‘‘‘«arché»-physis’’’,
and where
b [---> q2
connotes the first ‘meta-physis category’, with ‘+’ here standing for a generalized addition operation, that encompasses the addition of qualitatively distinct terms, and with ‘´’ here standing for a generalized multiplication operation, that encompasses the multiplication operation specific to the NQ qualifiers.
b [---> q2
connotes the first ‘meta-physis category’, with ‘+’ here standing for a generalized addition operation, that encompasses the addition of qualitatively distinct terms, and with ‘´’ here standing for a generalized multiplication operation, that encompasses the multiplication operation specific to the NQ qualifiers.
If we take
‘< a > x < a >’
with
< a >
connoting the category to be dialectically negated, and with
‘< a >’
connoting the category doing that dialectical [self-]negating, with
‘< a >’
as the dialectical, determinate ‘negation-sign’ specific to
< a >
as the object of the so-indicated dialectical, determinate negation operation, then we have
‘< a > x < a >’,
as a whole, as connoting the first dialectical negation, by the negation-operation
< a >
of the self-same negation operation,
< a >,
that is also the operand of the negation-operator
< a >,
forming what Seldon calls an -- ideographically signed --
‘subject [< a >]-verb[< a >]-object[< a >] identical’,
yielding a first dyad: ‘‘‘physis + meta-physis’’’, or
‘< a > x < a >’
with
< a >
connoting the category to be dialectically negated, and with
‘< a >’
connoting the category doing that dialectical [self-]negating, with
‘< a >’
as the dialectical, determinate ‘negation-sign’ specific to
< a >
as the object of the so-indicated dialectical, determinate negation operation, then we have
‘< a > x < a >’,
as a whole, as connoting the first dialectical negation, by the negation-operation
< a >
of the self-same negation operation,
< a >,
that is also the operand of the negation-operator
< a >,
forming what Seldon calls an -- ideographically signed --
‘subject [< a >]-verb[< a >]-object[< a >] identical’,
yielding a first dyad: ‘‘‘physis + meta-physis’’’, or
‘«arché» category + first meta-category’, viz. --
< a > x < a > = qa x qaa =
qa x qb =
a + b
qa x qb =
a + b
-- which, in terms of the generic, minimally-interpreted NQ arithmetic, is a dialectical interpretation of the generic --
The second iteration of this dialectical negation of the negation, corresponding to the consecutively next value of t namely, t = 2, for the NQ_ arithmetic interpreted for [psycho]historical dialectics, yields the following, ontologically-expanded cumulum of ontological categories -- a ‘dyad of dyads’, consisting of 4 consecutive ontological categories:
= < a +
b > x < a +
b >
= a + b + c + d.
The additional 2 ontological category-symbols above are dialectically interpreted, per the E.D. standard, as follows:
c = third ontological
category,
first full uni-physis category;
d = fourth ontological
category,
second meta-physis category.
We will not here pursue this E.D. standard dialectical interpretation of the ontological categories generated by the
generic Dyadic Seldon Function beyond epoch t = 2, as
they are not required for the purposes of this vignette.
The ‘purely-qualitative calculations’ illustrated above
describe our expectations as to the meaning of this vignette’s illustrative ‘meta-model’ in terms of generic characterizations of its successive,
consecutive dialectical categories.
The next section addresses the heart of this ‘meta-model’ -- the specific meanings of the generic dialectical categories as applied to
the ‘‘‘special case’’’
of The Dialectic of Nature in
general.
IV. ‘‘‘Self-Activity’’’ and ‘‘‘Self-Change’’’ as Captured in the Dyadic Seldon Functions of the NQ_ Arithmetic.
If we would extend the theory left to us by Marx and
Engels, of the dialectic
of human history -- the dialectic of human Nature, i.e., the dialectic of just the human part of Nature -- explicitly into a theory
of The Dialectic of
Nature as a whole -- as begun by Engels, in his posthumously
published, incomplete, and fragmentary manuscript, given the title posthumous “Dialectics
of Nature” -- then we must extend the Marxian concepts of “self-activity” and of “self-change”, as set forth by Marx and Engels
in the passages quoted in section I., above, to encompass “selves”, i.e., “subjects”, or “causal agents”,
other than individual human “subjects”
/ “agents”,
or human-social, collective “subjects”
/ “agents”
-- whole human societies as collective “subjects” / “agents” -- alone. In framing a Marxian theory of The Dialectic of Nature
as a whole, we must get beyond limiting our discourse of ‘subject-ivity’, of ‘subject-ness’,
of ‘subject-hood’ -- i.e., of the «genos» of causal agency in general -- of an agent that operates
upon natural objects, including upon the objective aspects of its own self, to just one of
the «species»
of that «genos»;
indeed, beyond limiting our discourse to just the most recent and most
developed, self-conscious
«species» of
that «genos»
known to us: human ‘subject-ivity’.
Causal agency, in this cosmos, is not limited to human agency
-- far from it!
Therefore, the quality of ‘subject-ivity’, ‘subject-ness’,
‘subject-hood’ is not
limited to human individuals or to whole human societies, although human ‘subject-ivity’ or agency is the highest degree of ‘subject-ivity’ known
to humans.
Any natural
causal agent whose name can aptly -- i.e., with empirical
truthfulness -- be cast into the “subject” role and position / “slot” of a well-formed
English sentence is a “subject”
of some degree. A special case of such sentences involves the
same name occurring, aptly, in both
the subject
and the object
“slots” of such a sentence -- forming a ‘‘‘subject / object identical’’’, or, in our cases, a ‘subject / verb / object identical’, since the entity whose
name is both subject and object of such a sentence also has its
[self-]activity, its “verb”, absorbed into itself, absorbed into that entity,
and one with that entity. That is, such
an entity is thereby being represented as an ‘event-entity’, an ‘‘‘eventity’’’,
or, in mathematical terms, as an ‘‘‘operator’’’, unifying both “operation” and “operand”
-- and thus also as a ‘noun / verb identical’; as an ‘operation / operand
identical’, or as a ‘function / argument identical’.
We illustrate, below, the ways in which a ‘Dyadic Seldon Function Historical-Dialectical Meta-Equation Meta-Model’ describes a given history
as ‘a self-progression of self-activity for a thereby self-growing [via [past] self-activity]] ‘cumulum’ of
self-actors
/ ‘‘‘eventities’’’, yielding an ontologically different, self-«aufheben» self-expanded self-acting
‘cumulum’, for each of its
successive historical
epochs -- i.e., for each
successive value of the discrete time parameter, t. We so illustrate by means of the special case of the
most general Dyadic Seldon Function ‘Meta-Model’ available -- the ‘Dialectical Theory of Everything’, Dialectic of Nature as Totality ‘Meta-Equation’ --
-- with n denoting the «arché-physis»
‘physio-ontological’ category of ‘sub-nuclear particles”, e.g., quarks and leptons.
Epoch t Cumulum-form ‘Power-form’ tth ‘Subject-[Verb[ x ]-]Object-Identical’ ‘Product- / Result-form’
< n + s + qsn + a + qan + qas + qasn + m >
. . .
In the table above, the symbol s stands for the first meta-«physis» ‘physio-ontological’ category of ‘sub-atomic particles”, that is, of ‘meta-quarks’, e.g., protons and mesons. The symbol a stands for the second meta-«physis» ‘physio-ontological’ category, of ‘atomic nuclei”, that is, of ‘meta-sub-atomic
particles’, e.g., Helium nuclei, He++. The symbol m stands for the third meta-«physis» category
of ‘physio-ontology’, that of ‘molecules”, i.e., of ‘meta-atoms’, e.g., H2O, water. The foregoing list covers the ‘self-hybrid’ categories of ‘physio-ontology’ expressed in the table above. We need not address the symbols for the ‘merely hybrid’ categories of ‘physio-ontology’, such as qsn and qasn, or their meanings, within the purposes of this vignette.
For all epochs t > 1, each of the entries under the ‘tth ‘Subject-[Verb[ ´ ]-]Object-Identical’’ column in the table above can be characterized in all of the following ways --
1. A ‘‘‘self-activity’’’; an activity of / by a [pre-human] ‘‘‘self’’’ / “subject” / causal agency [back-]upon
that same ‘‘‘self’’’
/ “subject” / causal agency, thus also
functioning as “object”
thereof -- as also object
of / to itself.
2. A ‘‘‘self-activity’’’; a ‘‘‘self-action’’’,
causing ‘‘‘self-change’’’--
here, not merely quantitative
change, but qualitative
change, ontological change [expansion
of the cumulum of possible ontology]
-- self-induced change;
change-in-self, induced by self.
3. A ‘self-labor’ [in a pre-human sense of the word “labor”]; a labor
upon self by self; a work upon
self by self; a ‘self-working-up’.
4. A ‘self-re-flex-ive function’ [cf. Russell,; Wittgenstein]; a ‘function’ which can be characterized [‘-ive’]
as, bending [‘flex’] back [‘re-’] upon, or to impact,
the very source [‘self-’] which generated / generates that ‘function’.
5. A ‘self-re-flux-ive function’ [cf. Ancient Eastern Philosophies / Religions]; a ‘‘‘karmic’’’ ‘action’ which is characterized [‘-ive’]
as, flowing [‘flux’] back [‘re-’] upon, and thus impacting,
the very source [‘self-’] which generated / generates that ‘action’ [cf. “the
karma-yoga performed by all things”].
6. An «autokinesis» [cf. Plato, Ancient Western Philosophy];
a self-motion;
a self-movement;
a self-change;
a change-in-self, induced by self.
7. A concrete, material self-mirroring / ‘‘‘self-reflection’’’ / ‘self-beholding’ that irrupts new ontology -- that surges-up a new,
expanded ‘cumulum of ontology possibility’ as expanded cosmological ‘self’[cf. Hegel, ‘‘‘Being-for-self’’’].
8. [from t = 2 on]: A ‘re-squaring of the already squared’; a ‘re-self-negating / determinate-negating / self-changing of the already self-negated / determinate-negated / self-changed’.
9. A
[quadratically]“nonlinear term” [as long as any of the terms in the ‘cumulum’ sum-representations
being ‘‘‘multiplied’’’ together are ‘‘‘unsolved-for’’’ / ‘unsemantified’,
‘dialectical-algebraic’ unknowns].
Links to definitions of additional Encyclopedia Dialectica special
terms deployed in the discourse above --
«arithmos aisthetos»
«arithmos eidetikos»
categorial
category
‘consecuum’
‘cumulum’
dialectical categorial
progressions
homeomorphic defects of
models
[The] Human Phenome
immanent
immanent critique
«monad»
ontological category
ontology
psychohistory
qualo-fractal
http://point-of-departure.org/Point-Of-Departure/ClarificationsArchive/QualoFractal/QualoFractal.htm
qualo-Peanic
‘self-meta-monad-ization’ or ‘self-meta-individual-ization’
or ‘self-meta-holon-ization’
