Dear Readers,

Below, I have posted excerpts from a vignette that I have just written for

**F**.__.__**E**__., entitled --__**D****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__*. The purpose of*

__’__**s Preface****Vignette**

**#9**is to present two alternative interpretations of the central

__dialectical__*“*process, which are both ambiguously implicit in many discourses that invoke

**negation of the negation**”**, but whose differences can be readily ‘explicitized’ using the**

__dialectics__**F**.

**.**

__E__**.**

__D__**.**

*First*__Dialectical__Algebra

__A Note about the On__

__-__

__Line Availability of Definitions of__

__F____.__

__E____.__

__D____.__

**. Definitions of**

__Technical Terms__**technical terms and ‘neologia’ are available on-line via the following URLs --**

__Encyclopedia Dialectica__
-- by clicking on the links associated with each
such term, listed, alphabetically, on the web-pages linked above.

The

**special terms most fundamental to this vignette are indicated below, together with links to their**__Encyclopedia Dialectica__**.**__E__**. definitions --**__D__
«

**»***aufheben*

*Seldon Functions*

-- definitions resources which will be expanded as
the

**.**__F__**.**__E__**.**__D__**Project unfolds.**__Encyclopedia__

__I____.__

__Preliminary Note____:__

*“*

__Negation of Negation__

__”__**.**

__in the Context of the Boolean Algebra of Formal Logic__**Boolean Negation is**. 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

*Abstract*Negation**x**

**=**

**1**, asserting, by that equation, that the «

**» or**

*arithmos***of**

*assemblage***X**s, of the

**X**-kind of

*“*

*logical individuals**”*, i.e., that the category or “class”

**x**,

**, then the Boolean negation of that**

__exists__**x**, written

**1**

**-**

**x**, produces

**, Boole’s “Nothing”, "**

*absolute nothingness***0**":

**1**

**-**

**x**

**=**

**1**

**-**

**1**

**=**

**0**

**=**“Nothing”, the ‘‘‘empty class’’’, the ‘‘‘empty category’’’, the “«

**»” devoid of any «**

*arithmos***», or**

*monads***.**

*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__**=**

__x__**,**

__x__i.e., the

__dialectical__**of an ontological category,**

*negator***, is that ontological category,**

__x__**, itself.**

__x__

__Dialectical__**is,**

*negation***,**

*primarily*

__self__*-*

**,**

*negation*

__self__*-*«

**»,**

*aufheben*

*determinate*

__self__*-*

**/**

*transformation*

__self__*-*

**/**

*development*

__self__*-*

**/ «**

*change***».**

*autokinesis*The

__dialectical__

*negation***for an ontological category,**

*operation***, is**

__x____an__

**not***operation than its operand, is*

**other***an*

**not**__“function” than its “argument”, is__

**other***than the self-same ontological category,*

__not____other__**, itself.**

__x__The ontological category symbol,

**, 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 «**

__x__**»**

*aufheben***.**

*operator*The

**, «**

__dialectical__**»**

*aufheben*

*negation***for**

*operator***is**

__x__**itself.**

__x__That is,

__dialectical__**of**

*negation***,**

__x__**~**, is, in its

__x__**instance,**

*primary*

__not__**by**

*negation***, not by an**

*an*__external____other__**operation, operator, or category, but is, on the contrary,**

*alien*

__self__*-*

**,**

*negation*

__internal__

**,**

*negation*

__immanent__

**, a**

*negation*

__self__*-*

**, a**

*movement*

__self__*-*

*induced***, a**

*change*

__self__*-*

**, expressing the**

*driven*__process__

__dialectical__

*internal***, or**

*contradiction*

__self__*-*

**-- the**

*contradiction**‘*

__self__*-*

*duality**’*, or

*‘*

*in*__tra__*-*

*duality**’*-- of the category/operation/process/eventity symbolized by

**, which**

__x__**expresses**

__process__**a “propositional [self-]contradiction” of the kind encountered in formal logic, but an**

__not__*‘*

*in*__tra__*-*

*contra**-*

*kinesis**’*of the kind codified by a contental, ontological, existential --

**-- logic.**

__dialectical__The equation

**~**

__x__**=**

__x__**means that the eventity denoted by**

__x__**becomes its own**

__x__**when its**

*negator*

__self__*-*

**reaches its critical point, its point of**

*development**‘*

__self__*-*

__meta__*-*

*evolution**’*or of

*‘*

__self__*-*

*revolution**’*.

To describe the timing of that

__self__*-*

**, of its reaching its critical point, and of what develops thereafter, requires the richer languages of the [**

*development*

__meta__*-*]

*systematic**-*

__dialectical__**of the**

*progression*

__dialectical__**.**

*ideographies*Minimally, it requires a language which incorporates at least a discrete-time, or

**tep-count, Whole-number variable,**

__s__**s**, such as do the

**.**

*Seldon Functions***. . .**

In the

**research, both of these two interpretations of the**__Encyclopedia Dialectica__**core-****,**__dialectical____self__*-*«**» process of the***aufheben**‘*__self__*-***negation of the**__self__*-***versions of the***...’, have been found to be useful -- both the***negation***Dyad**ic*and the*Triadic***have been found useful -- for the formulation of***Seldon Function*__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 --**

«

**»***archÃ©***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*

*‘*or__auto__-negation’*‘*__self__-negation’

**
**

http://point-of-departure.org/Point-Of-Departure/ClarificationsArchive/AutoNegation/AutoNegation.htm

**
**

**’s**

**Boole****Algebra**

*categorial*

*category*

__dialectical__

*categorial progression***
**

*‘‘‘*versus

**’’’**__dialectical__contradiction*‘‘‘*

**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

**versus**

*dynamics*

*‘‘‘meta-*

**dynamics**’’’**
**

**
**

*‘‘‘*

**eventity**’’’

**
**

**versus**

*evolution**‘‘‘meta-*

**evolution**’’’**
**

«

**»***monad*

**
**

**ontological category**

**ontology**