Thursday, August 20, 2015

'Seldon in Session' #3: 'Seldon Functions, Dyadic & Triadic'.

[My] Full Title:  ‘Seldon in Session Series, blog-entry #3 --

Seldon Functions, Dyadic & Triadic.

Dear Readers,

This blog-entry continues a new series, here, of excerpts from Karl Seldon’s “introduction to dialectics sessions, for new recruits. 


In this new series, I will share with you some of the delectable morsels of creative mentation that fly forth from these sessions, once their transcripts have been edited, by the E. D. editors, and cleared, by the Foundation’s General Council, for public sharing.

I have entered, below, an excerpt of Karl Seldon’s remarks from the edited transcript of a recent such session. 




Miguel Detonacciones,

Member, Foundation Encyclopedia Dialectica [F.E.D.],
Officer, F.E.D. Office of Public Liaison.








[Karl Seldon] --


Note that, in this presentation, by a category we also mean, like the ancients, the representation of an «arithmos», of an assemblage of qualitative units, e.g., of a population of individuals [individuals which/who may be active agents of evolutionary, and of meta-evolutionary, change, though not necessarily being human agents/subjects] -- of a concrete ‘‘‘number’’’ of concrete «monads».




Our NQ_-based family of dialectical functions -- principally the dyadic dialectic-function and the triadic dialectic-function -- are, generically, functions of an NQ_ CONSTANT:  they are functions, namely, of the known value q1.

However, specifically, with q1 interpreted, i.e., assigned [‘<(---]’] to a specific «arché» category --  

q1 <(---] a  =  qa

-- so as to form a specific dialectical meta-model, our dialectical functions become functions of an NQ_ VARIABLE.

This variable -- e.g., a -- is also a partial algebraic unknown.

It is so in the sense that the total implicit/potential content of that intension, of thatconnotogram, a, is never fully known, and becomes partially known only gradually, with the extension/divulgence of its dialectical categories-progression, as the hidden intra-multiality of that «arché» is progressively revealed/-‘explicitized/actualized in the expanding cumulum of that categories-progression, that issues forth from that «arché», as generated, in terms of its ideographic-symbolic representation, by the escalation in the “Natural” Number value of the ‘self-iteration parameter’ independent variable of these dialectic-functions.

For our dyadic dialectic-function meta-equation meta-models of dialectical process/progression, it is the most recent past contra-thesis category that is the source of the next, new, higher contra-thesis category.

For any stage of such a progression -- for any value of the ‘self-iteration parameter’ beyond s = 1 [for synchronic dialectics], or t = 1 [for diachronic dialectics] -- it is the most recent contra-thesis category [-- the category that had just reconciled with all of the preceding categories, that it op-poses, in the form of the most recent synthesis category, the category that had just superseded that contra-thesis category --] that, next, supersedes that synthesis in turn, “turning the flank” of that synthesis category, making an end-run around, and thereby escaping, that synthesis category, thus placing the self-hybrid category of that contra-thesis category, i.e., its new contra-thesiscategory, ahead of, in advance of, that synthesis category, higher in qualo-fractalscale, and in complexity/determinateness, than that synthesis category. 

The internal contradiction -- the intra-duality or intra-multiality -- of the «arché» category, which resides at the root of the entire dialectical categorial progression,  recurringly re-asserts itself, bursts forth again, each time at a specifically new, higher level/scale, from out of the intra-duality, or of the intra-multiality, of each most recent contra-thesis category, when that contra-thesis category operates upon itself, as a specific «aufheben» operation, e.g., as an «arithmos»-self-meta-«monad»-izing operation, yielding itself again, its own simple reproduction [cf. Marx], but together with the new contra-thesiscategory/«arithmos» [ net result of a qualitatively, ontologically expanded self-reproduction of and by that «arithmos»-of-«monads»], which was born[e] by/from/out of the old --

old contra-thesis x old contra-thesis = old contra-thesis2 = old contra-thesis + new contra-thesis, e.g., generically --

q2 x q2  =  q22  =  q2 + q2+2  =  q2 + q4.

Each new contra-thesis, born[e] of that intra-duality, irrupts into explicitude, or into actuality, through the self-reflexion, the self-reflexive action, or the ‘‘‘self-activity’’’ [cf. Marx], i.e., through the ontological ‘‘‘self-multiplication’’’ [‘“self-squaring”’, cf. Mandelbrot], of that formerly most recent contra-thesis category.

That ‘‘‘self-squaring’’’ of the old contra-thesis category net-yields a new contra-thesiscategory, in which the essential ‘‘‘dialectical [self-]contradiction’’’ of the Domain being meta-modeled, and of its «arché», a  =  qa [---)> q1,

breaks out again, anew, but at a yet higher level, at a higher qualo-fractalscale, than that of its preceding, ancestor contra-category.

For our triadic dialectic-function meta-equation meta-models of dialectical process/progression, it is the most recent past uni-thesis, or synthesis, category, that is the source of the next, new, higher contra-thesis category, due to the specific new intra-duality of that most recent past synthesis category itself, that is, of the very category that resolved in itself the preceding specific intra-duality.

Each synthesis category, by its self-reflexion, by its self-reflexive action, by its ‘‘‘self-activity’’’, i.e., by its ontological ‘‘‘self-multiplication’’’ [‘“self-squaring”’], amplifies its own specific endo-duality, until that endo-duality bursts forth into a new exo-duality, in the form of a new, higher qualo-fractalscale contra-category --

old uni-thesis x old uni-thesis = old uni-thesis2 = old uni-thesis + new contra-thesis, e.g., generically --

q3 x q3  =  q32  =  q3 + q3+3  =  q3 + q6.”

In the light of the foregoing considerations on triadicity and dyadicity in our dialectical-functions-based meta-models of dialectical process/progression, it is of value to evaluate the following two passages from Hegel’s remarks, on triplicity, and ontetradicity, in the generic numberology of dialectic --

“...Kant did not apply the infinitely important form of triplicity -- with him it manifested itself at first only as a formal spark of light -- to the genera of his categories (quantity, quality, etc.), but only to their species which, too, alone he called categories.  Consequently he was unable to hit on the third to quality and quantity.” [Note:  Per Hegel’s «Logik», that third ismeasure, an «arithmos» of quantifiable qualitative «monads», or units, of measurement; of quantifiable dimensional qualifiers -- F.E.D.]

[Hegel, Science of Logic, Prometheus [NY: 1969], p. 327, emphases added by F.E.D.].

“Any division is to be considered genuine when it is determined by the Concept.  So genuine division is, first of all, tripartite; and then, because particularity presents itself as doubled, the division moves on to fourfoldness as well.  In the sphere of spirit trichotomy predominates, and it is one of Kant’s merits to have drawn attention to this.”

[Hegel, The Encyclopedia Logic, Hacket [NY: 1991], p. 298, emphases added by F.E.D.]. ... .