Saturday, March 02, 2013

'Dialectical-Algebraic' Expression of Engels's Three "Laws" of Dialectics

Dialectical-Algebraic Expression of Engels's Three "Laws" of '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 Dialectics, in the words of Engels himself, are as follows --






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.D. to celebrate, and to celebrate by succinctly summarizing, . . . recent Vignette -- F.E.D. Vignette #10 -- on the unification of Engels’s three “laws” of dialectics, is to express those three “laws” in the dialectical ideography of the Seldonian First Dialectical Algebra, that of the Q arithmetic.

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-ideographical symbols used for this formulation --








The next task is to express Engels’s three laws of The Dialectic of Nature in terms of the symbols defined above, and in accordance with the Seldonian interpretation of those three laws, as rendered . . . in F.E.D. Vignette #10.

[Reception of the meanings of these dialectical-algebraic expressions of Engels's "laws" -- and especially of "laws" 2 and 3 -- will be facilitated, for the reader, if it is kept in mind that the operation of the generic dialectical-negation operator, represented by '~' 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 "a horizontal, leftward ditto mark", 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 dialectical negation sign, and this dialectical negation sign is thereby removed, eliminated, supplanted by that copy.]


After that task is accomplished, the final task for this blog-entry is to translate those ideographic renderings of Engel’s laws back into their exact prose counterparts, and to narrate some of the nuances of those ideographical formulations.


We leave to a later presentation the exposition of the detailed inner interconnection of these laws with one another [cf. Engels, Dialectics of Nature], in part, by means of their derivation, as theorems, from the first order axioms of the Q dialectical arithmetics, from the definitions of the symbols used, as above, and from several additional Principles of Nature-Dialectic.


For now, let us simply say that unity and interconnectedness of these Engels’s laws is implicitly contained in the Dyadic Seldon Function itself, in its assertion that the vast qualitative, ontological diversity of our cosmos is seeded in the self-iterated self-movement of a single, ‘‘‘singular’’’, ontic categoryarithmos» as «arché», with the term «arché» meaning 'the ultimate ancestor in a meta-genealogy', e.g., in an ontological categorial progression --

namely, the >-|-<(0) '''seed''' ontological category in:

>-|-<
(t) = [ >-|-<(0) ]^(2^t).



Engels’s three laws of The Dialectic of Nature in terms of the symbols defined above, and in accordance with the Seldonian interpretation of those three laws, as rendered by . . . in F.E.D. Vignette #10, look like this --





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


1. "The t-cumulum ontology increment is, explicitly, not contained in the t ontology-cumulum, which, over time, turns itself into the full self-action of that t ontology-cumulum, which equals that t ontology-cumulum non-amalgamatively added to that t-cumulum ontology increment, which sum is equal to the t+1 ontology-cumulum, which does explicitly contain the t-cumulum ontology increment, and that t-cumulum ontology increment is qualitatively, ontologically unequal to the t ontology-cumulum itself."


2. "The t-cumulum ontology increment is implicitly contained in the t ontology-cumulum, as a not-yet-actualized potentiality, and the t ontology-cumulum, over time, turns itself into its own dialectical, determinate, self-«aufheben» self-negation of itself, which equals itself non-amalgamatively and antagonistically added to the t-cumulum ontology increment, which together equal the t+1 ontology-cumulum, which does explicitly contain the t-cumulum ontology increment, which is the supplementary other to the t ontology-cumulum itself."


3. "As epoch t turns itself into epoch t+1, the t ontology-cumulum turns itself into the full self-action of the t ontology-cumulum, which is equal to the dialectical, determinate, self-«aufheben» self-negation of the t ontology-cumulum; then, next, as epoch t+1 turns itself into epoch t+2, the t+1 ontology-cumulum turns itself into the full self-action of the t+1 ontology-cumulum, which is equal to the dialectical, determinate, self-«aufheben» self-negation of the t+1 ontology-cumulum, which is equal to the dialectical, determinate, self-«aufheben» self-negation of the dialectical, determinate, self-«aufheben» self-negation of the t ontology-cumulum."




Commentary on Engelss First Law of Dialectics. The quantitative nature of the kind of change that passes into the qualitative, ontological kind of change -- the latter represented by >-|-<(t) -- in the dialectical-algebraic expression of law 1 cannot be expressed, as such, in the purely-qualitative, purely-ontological language of the Q dialectical algebras, and at this cumula-of-ontological-categories scale of description.


It can be adumbrated only, by a kind of qualitative shadow of the quantitative, as the total absence of any explicit presence/containment of the qualitative increment of new ontology, delta->-|-<(t), in >-|-<(t), versus its full, explicit presence/containment in >-|-<(t+1).


There is, at the ontological-categorial scale of description, a dialectical-algebraic expression of law 1 that can be formulated in the seventh, quanto-qualitative dialectical-algebra in the Seldonian dialectical progression of dialectical algebras, the 'Mu' algebra, that we will present later, in another venue. 



Commentary on Engelss Second Law of Dialectics. As . . .stated in F.E.D. Vignette #10 --

The quality of oppositeness of the old vanguard ‘onto-type’, versus its successor, may not always be experientially and affectively accessible to its human observers, which is why F.E.D.calls 2nd terms in its ideo-dialectical meta-models contra-thesisterms, whereas it calls 2nd  terms in its physi[c]o-dialectical meta-models meta-physisterms.

The formerly-latent, unmanifest potentials of the ‘‘‘self-interaction’’’ of the up-until-then newest ‘onto-type’ constitute an 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, externally manifested, once the intensity of population ‘‘‘self-interaction’’’, or ‘intra-action’, breaches the threshold whereafter the next newest ‘onto-type’ becomes ‘irruptively actualized, actualized as the 'supplementary other of the dominant, external-face/-manifestation of its predecessor vanguard ‘onto-type’.




Commentary on Engelss Third Law of Dialectics. Relative to the scale of negation of negation presented in the algebraical rendering above, at a more intensive scale of ‘time’, ‘temporality’, or ‘t-epochality’, every value of >-|-<(t), for t > 0, can be grasped as the product of a dialectical negation of negation.

That is, if each value of >-|-<(t) is understood to be, already, in itself, in general, an ‘‘‘eventity’’’, and, in particular, a particular, specific negation operation -- a particular, specific dialectical, determinate, «aufheben»-negation operator -- then every specific value of >-|-<(t) falls under the general symbol ~:   >-|-<(t) IS CONTAINED IN ~.

Therefore, for all t+1, we have that >-|-<(t+1) IS CONTAINED IN ~~, each value of >-|-<(t+1) thus instancing negation negation, viz. --

>-|-<(1)      =    >-|-<(0)>-|-<(0)   =   ~>-|-<(0) IS CONTAINED IN ~~;

>-|-<(2)      =   >-|-<(1)>-|-<(1)    =   ~>-|-<(1) IS CONTAINED IN ~~;

>-|-<(3)      =   >-|-<(2)>-|-<(2)    =   ~>-|-<(2) IS CONTAINED IN ~~, and, in general --

>-|-<(t+1)   =   >-|-<(t)>-|-<(t)      =   ~>-|-<(t) IS CONTAINED IN ~~.

It is only >-|-<(0), the ‘‘‘«arché»’’’, theultimate ancestor, the opening, non-cumulum singleton/‘‘‘singularity’’’ of an historical progression of cumula, or consecuum of cumula, of ontological categories, e.g. of system categories, etc., i.e., it is only the founding term,

>-|-<
(0)   [--->   q1   IN    WQ  =   { q0, q1, q2, q3, ... },

that cannot be expressed as a product of dialectical negation-negation, and that cannot be expressed as being, itself, an ontic cumulum, at least not in that same particular language and meta-model
of { >-|-<(t) } --

>-|-<(0)  IS  NOT   CONTAINED IN the meaning of ~~;

>-|-<(0)   ~=   >-|-<(t)>-|-<(t) for any value of >-|-<(t), i.e.,

>-|-<(0) has no predecessor in {>-|-<(t) | t is IN W}.


But in general, for any specific 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 --



«arché»




auto-negation or self-negation




categorial




category




dialectical categorial progression


‘‘‘eventity’’’

ontological category

ontology



 






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