**-**__Dialectical__**Algebraic***of Engels's Three*

**Expression***"*of

**Laws**"*'*

*The*__Dialectic__of Nature*'*in Their Seldonian Interpretation --

Dear Readers,

I have excepted, below, the latest entry to the blog by Aoristos Dyosphainthos, the Chief Public Liaison Officer for

**Foundation**[

*Encyclopedia**Dialectica***F**.

__.__

**E**__.].__

**D**The Engelsian three "Laws" of

__, in the words of Engels himself, are as follows --__

**Dialectics**For the full text, see --

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

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

http://www.dialectics.org/dialectics/Aoristoss_Blog/Entries/2013/3/2_Dialectical-Algebraic_Expression_of_Engelss_Three_Laws_of_Dialectics.html

Regards,

Miguel

**One additional way for we of**

*"***F**.

**.**

__E__**. to celebrate, and to celebrate by succinctly summarizing, . . . recent Vignette --**

__D__**F**.

**.**

__E__**. Vignette**

__D__**#10**

**--**on the unification of Engels’s three “

*” of*

**laws****, is to express those three “laws” in the**

__dialectics__

__dialectical__**of the Seldonian**

*ideography**‘*

*First*

__Dialectical__

*Algebra**’*, that of the

**arithmetic.**

__Q__The purpose of this blog entry is to share that celebration, as that summary, with our public.

The first task is to communicate the meaning(s) of the

__dialectical__*-*used for this formulation --

**ideographical symbols**The next task is to express Engels’s three

*“*of

**laws**”*‘*in terms of the symbols defined above, and in accordance with the Seldonian interpretation of those three

**The**’__Dialectic__of Nature*“*, as rendered . . . in

**laws**”**F**.

**.**

__E__**. Vignette**

__D__**#10**.

[Reception of the meanings of these

*of Engels's*

__-__**dialectical****algebraic expressions***"*-- and especially of

**laws**"*"*

**laws**"**2**and

**3**-- will be facilitated, for the reader, if it is kept in mind that the operation of the generic

*, represented by '*

__-__**dialectical****negation operator****~**' in the typography available herein, but by a more "angular" rendering in the JPEG images pasted-in to this blog-entry, can be characterized in a simple way.

Its operation can be characterized, syntactically, and informally, as that of an operation which acts like

*"*, that is, it replaces itself with an exact copy of the symbol immediately to its right, a copy that is thus placed immediately to the left of that symbol that was copied from immediately to the right of this

**a horizontal**,**leftward ditto mark**"*, and this*

__dialectical__negation sign*is thereby removed, eliminated, supplanted by that copy.]*

__dialectical__negation signAfter that task is accomplished, the final task for this blog-entry is to translate those ideographic renderings of Engel’s

*“*back into their exact prose counterparts, and to narrate some of the nuances of those ideographical formulations.

**laws**”We leave to a later presentation the exposition of the detailed

*“*

*inner interconnection of these laws with one another**”*[cf. Engels,

**], in part, by means of their derivation, as theorems, from the first order axioms of the**

__Dialectics of Nature__

__Q__**, from the definitions of the symbols used, as above, and from several additional**

__dialectical__arithmetics*‘*

*Principles of*

*Nature**-*

__Dialectic__*’*.

For now, let us simply say that

**and**

*unity**of these Engels’s*

**interconnectedness***“*is implicitly contained in the

**laws**”**itself, in its assertion that the vast**

*Dyadic Seldon Function**,*

__qual__itative*of our*

**ontological diversity****is**

*cosmos*

*seede***in the**

*d*

__self__*-*

*iterated*__self__*-*

**of a single,**

*movement**‘‘‘*

*singular**’’’*,

*/«*

**ontic category****» as «**

*arithmos***», with the term «**

*archÃ©***» meaning 'the**

*archÃ©**in a*

**ultimate ancestor***, e.g., in an*

**meta**-**genealogy**'*--*

**ontological categorial progression**namely, the

__>-|-<__**(0**

**)**'''

**seed**'''

*in:*

**ontological category**

>-|-<>-|-<

**(t**

**) =**

**[**

__>-|-<__**(0**

**) ]^(2^t)**.

Engels’s three

*“*of

**laws**”*‘*in terms of the symbols defined above, and in accordance with the Seldonian interpretation of those three

**The**’__Dialectic__of Nature*“*, as rendered by . . . in

**laws**”**F**.

**.**

__E__**.**

__D__**Vignette**

**#10**, look like this --

-- whose direct “prose” translations are the following --

**1**. "The

**t**-

*cumulum***is,**

*ontology*__increment__**plicitly,**

__ex__**contained in the**

__not__**t**

*ontology**-*, which, over time, turns itself into the full self-action of that

**cumulum****t**

*ontology**-*, which equals that

**cumulum****t**

*ontology**-*non-amalgamatively added to that

**cumulum****t**-

*cumulum***, which sum is equal to the**

*ontology*__increment__**t**

**+**

**1**

*ontology**-*, which

**cumulum**

__does__**plicitly contain the**

__ex__**t**-

*cumulum***, and that**

*ontology*__increment__**t**-

*cumulum***is qualitatively, ontologically unequal to the**

*ontology*__increment__**t**

*ontology**-*itself."

**cumulum****2**. "The

**t**-

*cumulum***is**

*ontology*__increment__**plicitly contained in the**

__im__**t**

*ontology**-*, as a not-yet-actualized

**cumulum****, and the**

*potentiality***t**

*ontology**-*, over time, turns itself into its own

**cumulum****,**

__dialectical__**,**

*determinate*

__self__*-*«

**»**

*aufheben*

__self__*-*of itself, which equals itself non-amalgamatively and

**negation***“*added to the

**antagonistically**”**t**-

*cumulum***, which together equal the**

*ontology*__increment__**t**

**+**

**1**

*ontology**-*, which does

**cumulum****plicitly contain the**

__ex__**t**-

*cumulum***, which is the**

*ontology*__increment__

*supplementary**“*to the

**other**”**t**

*ontology**-*itself."

**cumulum****3**. "As epoch

**t**turns itself into epoch

**t**

**+**

**1**, the

**t**

*ontology**-*turns itself into the full self-action of the

**cumulum****t**

*ontology**-*, which is equal to the

**cumulum****,**

__dialectical__**,**

*determinate*

__self__*-*«

**»**

*aufheben*

__self__*-*of the

**negation****t**

*ontology**-*; then, next, as epoch

**cumulum****t**

**+**

**1**turns itself into epoch

**t**

**+**

**2**, the

**t**

**+**

**1**

*ontology**-*turns itself into the full self-action of the

**cumulum****t**

**+**

**1**

*ontology**-*, which is equal to the

**cumulum****,**

__dialectical__**,**

*determinate*

__self__*-*«

**»**

*aufheben*

__self__*-*of the

**negation****t**

**+**

**1**

*ontology**-*, which is equal to the

**cumulum****,**

__dialectical__**,**

*determinate*

__self__*-*«

**»**

*aufheben*

__self__*-*of the

**negation****,**

__dialectical__**,**

*determinate*

__self__*-*«

**»**

*aufheben*

__self__*-*of the

**negation****t**

*ontology**-*."

**cumulum**

__Commentary on Engels____’__. The

**s First***“***Law**”**of Dialectics****of the**

__quant__itative nature**that passes into the**

*kind of change***,**

__qual__itative

*ontological***-- the latter represented by**

*kind of change*

__>-|-<__**(t**

**)**-- in the

__dialectical__*-*of

**algebraic expression***“*

**law**”**1**cannot be expressed,

__as__**, in the**

*such*

*purely**-*,

__qual__itative

*purely**-*of the

**ontological language**

__Q__**, and at this**

__dialectical__algebras

*cumula**-*scale of description.

**of**-**ontological**-**categories**It can be adumbrated only, by a kind of

*‘*, as the total

**’**__qual__itative shadow of the__quant__itative**of any**

*absence***plicit presence/containment of the**

__ex__**,**

__qual__itative increment of new ontology

__delta____-__

__>-|-<__**(t**

**)**, in

__>-|-<__**(t**

**)**, versus its full,

**plicit presence/containment in**

__ex__

__>-|-<__**(t**

**+1)**.

There is, at the

*ontological**-*scale of description, a

**categorial**

__dialectical__*-*of

**algebraic expression***“*

**law**”**1**that can be formulated in the seventh,

*‘*

**-**__quant__o**’**__qual__itative

__dialectical__*-*in the Seldonian

**algebra****, the '**

__dialectical__progression of__dialectical__algebras__' algebra, that we will present later, in another venue.__

**Mu**

__Commentary on Engels____’__. As . . .stated in

**s Second***“***Law**”**of Dialectics****F**.

**.**

__E__**.**

__D__**Vignette**

**#10**--

**The quality of**

“

“

**of the old vanguard ‘onto-type’, versus its successor, may not always be experientially and affectively accessible to its human observers, which is why**

*oppositeness***.**

__F__**.**

__E__**.calls**

__D__**2**nd terms in its

*‘*

__ideo__*-*

__dialectical__

*meta*

**-**

*models**’*

*‘*

__contra__*-*

*thesis**’*terms, whereas it calls

**2**nd terms in its

*‘*

**[**

__physi__**]**

__c__

__o__*-*

__dialectical__

*meta**-*

*models**’*

*‘*

__meta__*-*

*physis**’*terms.

The formerly-latent, unmanifest

*of the ‘‘‘self-interaction’’’ of the up-until-then newest ‘onto-type’ constitute an*

**potentials***‘*

*immanent*

*other**-*

**ness**

*’*

*, an*

*‘*

*intra**-*duality’, or

*‘*

*self**-*duality’, an

*‘*

*internal**-*

**/**

*self**-*

*opposition**’*, of that up-until-then newest ‘onto-type’, one which becomes

*‘*,

**outered**’*, once the intensity of population ‘‘‘self-interaction’’’, or ‘intra-action’, breaches the threshold whereafter the next newest ‘onto-type’ becomes ‘irruptively*

**externally manifested***,*

**actualized**’*as the*

**actualized***'*

*supplementary other**of the dominant, external-face/-manifestation of its predecessor vanguard ‘onto-type’.*

**’****”**

__Commentary on Engels____’__. Relative to the scale of

**s Third***“***Law**”**of Dialectics****presented in the algebraical rendering above, at a more intensive scale of ‘**

*negation of negation***ime’, ‘**

__t__**emporality’, or ‘**

__t__**t**-epochality’,

**value of**

*every*

__>-|-<__**(t**

**)**, for

**t >**

**0**, can be grasped as the product of a

**.**

__dialectical__negation of negationThat is, if each

**of**

__value__

__>-|-<__**(t**

**)**is understood to

**, already, in itself, in**

__be__**ral, an**

__gene__*‘‘‘*, and, in

**eventity**’’’**, a**

*particular***,**

*particular*

__speci__fic

*negation***-- a**

__operation__**,**

*particular*

*specific***,**

__dialectical__**, «**

*determinate***»-**

*aufheben***-- then every**

*negation*__operator__

__specific__**of**

__value__

__>-|-<__**(t**

**)**falls under the

**symbol**

__general__**~**:

__>-|-<__**(t**

**)**

**IS CONTAINED IN**

**~**.

Therefore, for

__all__**t+**

**1**, we have that

__>-|-<__**(t**

**+1)**

**IS CONTAINED IN**

**~**

**~**, each

**of**

__value__

__>-|-<__**(t**

**+1)**thus instancing

**, viz. --**

*negation negation*

__>-|-<__**(1)**

**=**

__>-|-<__**(0)**

__>-|-<__**(0)**

**=****~**

__>-|-<__**(0)**

**IS CONTAINED IN**

**~**

**~**;

__>-|-<__**(2)**

**=**

__>-|-<__**(1)**

__>-|-<__**(1)**

**=****~**

__>-|-<__**(1)**

**IS CONTAINED IN**

**~**

**~**;

__>-|-<__**(3)**

**=**

__>-|-<__**(2)**

__>-|-<__**(2)**

**=****~**

__>-|-<__**(2)**

**IS CONTAINED IN**

**~**

**~**, and, in

**ral --**

*gene*

__>-|-<__**(t+1)**

**=**

__>-|-<__**(t)**

__>-|-<__**(t)**

**=****~**

__>-|-<__**(t)**

**IS CONTAINED IN**

**~**

**~**.

It is only

__>-|-<__**(0)**, the ‘‘‘«

**»’’’,**

*archÃ©**‘*

*the*

*ultimate ancestor**’*, the opening,

__non__*-*singleton/‘‘‘singularity’’’ of an historical

**cumulum****, or**

*progression of cumula**‘*, of

**consecuum of cumula**’**, e.g. of**

*ontological categories***, etc., i.e., it is only the**

*system categories**“*,

**founding term**”

>-|-<>-|-<

**(0)**[--->

__q__1**,**

**IN**W__Q____=__{ q0**,**

__q__1**,**

__q__2**,**

__q__3**... },**

that

**be expressed as a product of**

__cannot__

__dialectical__negation*-*, and that

**negation****be expressed as being, itself, an**

__cannot__**, at least not in that same particular**

*ontic cumulum***and**

*language**‘*

**meta**-**model**’of

**{**

__>-|-<__**(t)**

**}**--

__>-|-<__**(0)**

**IS**the meaning of

__CONTAINED IN__*NOT***~**

**~**;

__>-|-<__**(0) ~=**

__>-|-<__**(t)**

__>-|-<__**(t)**for

__any__*value*of

__>-|-<__**(t)**, i.e.,

__>-|-<__**(0)**has

**in**

*no*__predecessor__**{**

__>-|-<__**(t)****|**

**t**

**is IN****W**

**}**.

But in

**ral, for**

*gene*

__any__**fic**

*speci**value*of

**t**,

**t =**

**0**included, we have

**--**

**...**

~

**(t****)**~**(t**

**)**

**=****--->**

**~****(t+1****)**

~

~

**(t**

**+1****)**~**(t**

**+1****)**

**=**

**--->****~****(t+2****)**

~~

**(t****+**

**2****)**

**~****(t**

**+**

**2****)**

**=**

**--->****~****(t+3****)****~****(t****+**

**3****)**

**~****(t**

**+**

**3****)**

**=**

**--->****~****(t+4****)****...**.

**Links to definitions of additional**

__Encyclopedia Dialectica__**special terms deployed in the discourse above --**

**«**

*archÃ©***»**

*‘*-__auto__**negation**’

**or**

*‘*-__self__**negation**’

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

*categorial*

*category*

__dialectical__*categorial progression*

**
***‘‘‘*

**eventity**’’’**
**

**ontological category**

**ontology**

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