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

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


‘Seldon Functions, Dyadic & Triadic’.







Dear Reader,

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. 

 

 Regards,

 

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  =  q_a

-- 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 that ‘connotogram’, 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-thesis’ category, ahead of, in advance of, that “synthesis” category, higher in ‘qualo-fractal’ scale, 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-thesis’ category/«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-thesis’ category, in which the essential ‘‘‘dialectical [self-]contradiction’’’ of the Domain being ‘meta-modeled’, and of its «arché», a  =  q_a [---)> q₁,

breaks out again, anew, but at a yet higher level, at a higher ‘qualo-fractal’ scale, 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-fractal’ scale ‘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 on ‘tetradicity’, 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” is “measure”, 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.]. ... .”