Tuesday, January 29, 2013

Two Interpretations of "The Negation of the Negation", F.E.D. Vignette #9


Dear Readers,

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



Authors 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. 


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.

 . . .





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 ontologicalself-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.htm
https://www.point-of-departure.org/Point-Of-Departure/ClarificationsArchive/Arithmoi/Arithmoi.htm



«autokinesis»



auto-negation or self-negation

Booles Algebra

categorial

category

dialectical categorial progression

‘‘‘dialectical contradiction’’’  versus ‘‘‘propositional contradiction’’’, etc.

dynamics versus ‘‘‘meta-dynamics’’’

‘‘‘eventity’’’

evolution versus ‘‘‘meta-evolution’’’

«monad»

ontological category

ontology




 

Tuesday, January 22, 2013

Dialectic -- A Compact Definition: F.E.D. Vignette #8








Dear Readers,

I have excerpted below, the opening section of F.E.D. Vignette #8, entitled "Dialectic -- A Compact Definition."

Enjoy!


Regards,

Miguel



P.S.  The full text of F.E.D. Vignette #8 is available to you for free-of-charge download via the following links --

http://www.dialectics.org/dialectics/Welcome.html

http://www.dialectics.org/dialectics/Vignettes.html

http://www.dialectics.org/dialectics/Welcome_files/Miguel%20Detonacciones,v.2.0,F.E.D._Vignette_%238,Dialectic_--_A_Compact_Definition,this_version_posted_28JAN2013.pdf






                                                                   F.E.D. Vignette #8 --

 Dialectic:   A Compact Definition.


                                                                      by Miguel Detonacciones



Authors Preface.  The purpose of Vignette #8 is to present a compact definition of our fundamental term, ‘‘‘dialectic’’’, plus an “extended” version of that compact definition -- extended into greater explicitude -- as well as to suggest how that definition entails several possible algebraic interpretations.


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»


«arché»



-- definitions resources which will be expanded as the F.E.D. Encyclopedia Project unfolds.


Simplest Definition. 

Dialectic is «aufheben».


Extended Definition. 

A ‘‘‘dialectic’’’ is the progression of new ontology -- of new kinds of “existence”, or of new kinds of “being”, including of new kinds of “physical” being, as in historical dialectics, e.g., that of pre-human nature, or of new kinds of “idea” being [e.g., new categories/concepts], as in systematic dialectics, or of new kinds of both types of ‘‘‘material’’’ together, as in the [psycho-socio-politico-economico-]historical dialectic of human social nature  -- that issues from the recurring self-application of an originating, or «arché», «aufheben» process/operation/operator, & which forms ever richer new «aufheben» processes/operations/operators with every recurrence, or self-iteration, of its self-application.