Dear Reader,
Key Proposition: Dialectical negation is «aufheben», determinate negation,
To describe the timing of that self-development, of its reaching its critical point, and of what develops thereafter, requires the richer languages of the [meta-]systematic-dialectical progression of the dialectical ideographies.
Minimally, it requires a language which incorporates at least a discrete-time, or step-count, Whole-number variable, s, such as do the Seldon Functions.
Below, I have posted excerpts from a vignette that I have just written for F.E.D., entitled --
Two Alternative Interpretations of "The Negation of the Negation"
-- the full text of which can be reached via the following URLs --
Happy reading!
Regards,
Miguel
F.E.D.
Vignette #9 --
Two Alternative Interpretations of
“The Negation of the Negation”.
by
Miguel Detonacciones
Author’s Preface. The purpose of Vignette #9 is to present two alternative
interpretations of the central dialectical “negation of the negation” process, which are
both ambiguously implicit in many discourses that invoke dialectics, but whose
differences can be readily ‘explicitized’ using the F.E.D.
First Dialectical Algebra.
A Note about the On-Line
Availability of Definitions of F.E.D. Technical Terms. Definitions
of Encyclopedia Dialectica technical terms and ‘neologia’ are available
on-line via the following URLs --
-- by clicking on the links associated with each
such term, listed, alphabetically, on the web-pages linked above.
The Encyclopedia Dialectica special terms
most fundamental to this vignette are indicated below, together with links to
their E.D. definitions
--
«aufheben»
Seldon Functions
-- definitions resources which will be expanded as
the F.E.D. Encyclopedia Project
unfolds.
I. Preliminary Note: “Negation of Negation” in the Context of the Boolean Algebra of
Formal Logic.
Boolean
Negation is Abstract Negation. If, in the
“Primary Interpretation” -- the ‘Existential Interpretation’ -- per Boole, of
Boole’s original arithmetic and algebra for formal logic, we select a case
in which x = 1,
asserting, by that equation, that the «arithmos» or assemblage of Xs, of the X-kind of “logical individuals”, i.e., that the category or
“class” x, exists, then the Boolean negation of that x, written 1 - x, produces absolute
nothingness, Boole’s “Nothing”, "0":
1 - x =
1 - 1
=
0
= “Nothing”, the ‘‘‘empty class’’’, the
‘‘‘empty category’’’, the “«arithmos»” devoid
of any «monads», or individuals.
II. Two Distinct Meanings for
the Phrase ‘‘‘The Dialectical Negation of the Negation’’’ .
Key Proposition: Dialectical negation is «aufheben», determinate negation,
not
“abstract negation” / “absolute negation”.
0. That about which both Interpretations Agree:
Key Assertion: ~x = xx,
i.e., the dialectical negator of an ontological category, x, is that ontological category, x, itself.
Dialectical negation is, primarily, self-negation, self-«aufheben», determinate self-transformation / self-development / self-change / «autokinesis».
The dialectical negation operation for an ontological category, x, is not an other operation than its operand, is not another “function” than its “argument”, is not other than the self-same ontological category, x, itself.
The ontological category symbol, x, is itself also a symbol for an operation, for an operator, for a function, for a process, for an ‘ideo-eventity’ -- specifically, for some special kind of «aufheben» operator.
The dialectical, «aufheben» negation operator for x is x itself.
That is, dialectical negation of x, ~x, is, in its primary instance, not negation by an external other, not by an alien operation, operator, or category, but is, on the contrary, self-negation, internal negation, immanent negation, a self-movement, a self-induced change, a self-driven process, expressing the dialectical internal contradiction, or self-contradiction -- the ‘self-duality’, or ‘intra-duality’ -- of the category/operation/process/eventity symbolized by x, which process expresses not a “propositional [self-]contradiction” of the kind encountered in formal logic, but an ‘intra-contra-kinesis’ of the kind codified by a contental, ontological, existential -- dialectical -- logic.
The equation ~x = xx means that the eventity denoted by x becomes its own negator when its self-development reaches its critical point, its point of ‘self-meta-evolution’ or of ‘self-revolution’.
Key Assertion: ~x = xx,
i.e., the dialectical negator of an ontological category, x, is that ontological category, x, itself.
Dialectical negation is, primarily, self-negation, self-«aufheben», determinate self-transformation / self-development / self-change / «autokinesis».
The dialectical negation operation for an ontological category, x, is not an other operation than its operand, is not another “function” than its “argument”, is not other than the self-same ontological category, x, itself.
The ontological category symbol, x, is itself also a symbol for an operation, for an operator, for a function, for a process, for an ‘ideo-eventity’ -- specifically, for some special kind of «aufheben» operator.
The dialectical, «aufheben» negation operator for x is x itself.
That is, dialectical negation of x, ~x, is, in its primary instance, not negation by an external other, not by an alien operation, operator, or category, but is, on the contrary, self-negation, internal negation, immanent negation, a self-movement, a self-induced change, a self-driven process, expressing the dialectical internal contradiction, or self-contradiction -- the ‘self-duality’, or ‘intra-duality’ -- of the category/operation/process/eventity symbolized by x, which process expresses not a “propositional [self-]contradiction” of the kind encountered in formal logic, but an ‘intra-contra-kinesis’ of the kind codified by a contental, ontological, existential -- dialectical -- logic.
The equation ~x = xx means that the eventity denoted by x becomes its own negator when its self-development reaches its critical point, its point of ‘self-meta-evolution’ or of ‘self-revolution’.
To describe the timing of that self-development, of its reaching its critical point, and of what develops thereafter, requires the richer languages of the [meta-]systematic-dialectical progression of the dialectical ideographies.
Minimally, it requires a language which incorporates at least a discrete-time, or step-count, Whole-number variable, s, such as do the Seldon Functions.
. . .
https://www.point-of-departure.org/Point-Of-Departure/ClarificationsArchive/Arithmoi/Arithmoi.htm
In the Encyclopedia
Dialectica research, both of these two interpretations of
the core-dialectical, self-«aufheben» process of the ‘self-negation of the self-negation...’, have been
found to be useful -- both the Dyadic and the Triadic versions of the Seldon Function have
been found useful -- for the formulation of dialectical ‘meta-models’
of the ontological ‘self-revolutions’
of nature, of the ‘meta-dynamical’,
‘self-meta-evolutionary
transitions’ from
one epoch and regime of dynamical “evolution” to its expanded-ontology successor such epoch.
Links to definitions of additional Encyclopedia Dialectica special
terms deployed in the discourse above --
«arché»
https://www.point-of-departure.org/Point-Of-Departure/ClarificationsArchive/Arche/Arche.htm
«arithmos»
and «arithmoi»
http://point-of-departure.org/Point-Of-Departure/ClarificationsArchive/Arithmos/Arithmos.htmhttps://www.point-of-departure.org/Point-Of-Departure/ClarificationsArchive/Arithmoi/Arithmoi.htm
«autokinesis»
‘auto-negation’ or ‘self-negation’
http://point-of-departure.org/Point-Of-Departure/ClarificationsArchive/AutoNegation/AutoNegation.htm
Boole’s
Algebra
categorial
category
dialectical categorial
progression
‘‘‘dialectical contradiction’’’ versus ‘‘‘propositional contradiction’’’, etc.
http://point-of-departure.org/Point-Of-Departure/ClarificationsArchive/DialecticalContradictions/DialecticalContradictionsW.htm
http://point-of-departure.org/Point-Of-Departure/ClarificationsArchive/DialecticalContradictions/DialecticalContradictionsWG.htm
http://point-of-departure.org/Point-Of-Departure/ClarificationsArchive/DialecticalContradictions/DialecticalContradictionsWG.htm
dynamics versus ‘‘‘meta-dynamics’’’
‘‘‘eventity’’’
evolution versus ‘‘‘meta-evolution’’’
«monad»
ontological category
ontology
