Saturday, December 01, 2012

The Dialectic of Oppositions.

Full TitleThe [Systematic] Dialectic of  Oppositions -- Three <<Species>> of That <<Genos>>    

Dear Readers,

The Public Liaison Officer of the F.E.D. General Council, Aoristos Dyosphainthos, has just posted F.E.D. Vignette #6, entitled "The Dialectic of Oppositions", to the website --

-- excerpts of which are presented below, with adaptation to the typography available herein.




                                                                   F.E.D. Vignette #6 --

                       The Dialectic of Oppositions:

               Three «Species» of That «Genos»

                                                              by Aoristos Dyosphainthos

Authors Preface.  The purpose of Vignette #6 is to ‘‘‘locate’’’, for the guests of this site, that individual «species» of the  «genos» of opposite-ness that characterizes F.E.D.’s generic dialectical-process interpretation for the Seldon Function progressions based on its 1st Dialectical Arithmetic.

A Note about Notation.  The Encyclopedia Dialectica notation and notational conventions, employed throughout this Vignette, are described in the five ‘*.jpg’ images, reachable via the following link --

-- by clicking on the 09/30/2011 links marked “1st Module” and “2nd Module”, on the 10/01/2011 link marked “1st Module”, and on the 07/14/2012 links marked “1st Module” and “2nd Module”, in the Prefatories Series section on that Home Page.

The dialectical systematics’/‘dialectical taxonomicsof the category of Oppositions --  

a Trans-Platonian «Arithmos Eidetikos»: 

Both the ‘‘‘Systematic Dialectics’’’, and the Meta-Systematic Dialectics, of dialectical theory-presentation are about opposition, and its resolution.   

¿But about what kind of opposition?   

About this question, we observe that much confusion prevails in public discourse. 

The purpose of this Vignette is to assist the guests of this site, if afflicted with any part of this prevailing public confusion, to clear it up for and in themselves.

Public discourse seems to fix more emphasis upon a kind of “eternally” cyclical/synchronic, necessarily co-existent, ‘polar-complementary, mutually-completing’, and “symbiotic” opposite-ness, such as female-vs.-male, plant-vs.-animal, or North-Pole-vs.-South-Pole [i.e., of a bar magnet].   

Dr. Charles Musès, one of the early mentors of The Foundation, had called attention also to a conceptually-neglected, and, indeed, ‘“opposite’’’, second category of opposition, in these terms:    

...Whereas before, we have a multitude of natural and mutually complementing pairs like female/male, day/night, finite/infinite, white/black, et. al., now we have the additional possibility of pathological, host/parasite pairs like good/evil, honesty/deception, health/sickness, in which we have no longer two self-completing entities, both of which are needed in the scheme of things. 

Rather, we now have pairs of which only one is needed for well-being, the other being parasitic (not symbiotic) and actually inimical to it. 

The Pythagoreans, misunderstanding their Egyptian teachers, placed the host/parasite duality of good and evil (hence also sickness) on the same footing as the quite different class of benign, self-complementary duals of finite/infinite, male/female, et al. 

And later philosophers, both oriental and occidental (e.g., Carl Jung), have repeated that fundamental error, stemming from inaccurate perception that failed to make the distinction between two radically different kinds of opposites:  those which are wave-like and mutually complementary; and the later, pathological variety. . . where one of the pair parasitizes on the other and, attacking it, attempts to destroy it permanently. 

The grip of the ancient error in the human mind is evidenced by the fact that this fundamental distinction was taught in no university philosophy course of the twentieth century as of 1983. 

Indeed, Jung’s confused “coincidence of opposites” continues to be parroted.

[Charles Musès, Destiny and Control in Human Systems:  Studies in the Interactive Connectedness of Time (Chronotopology), Kluwer-Nijhoff Publishing [Boston:  1985], pp. 136-137].

The examples of matter vs. anti-matter, and of opposing armies joining battle, provide further example cases of this second «species», this contra-thesis contra-category, of opposition -- contra to the first «species», the one called complementary opposition:  the second «species» that Dr. Seldon came to name annihilatory opposition.

In early dialogues with Dr. Musès, Dr. Seldon insisted upon the salient existence of yet a third basic «species» of the «genos» of oppositenesses, a dialectical synthesis of the previous two, which Dr. Seldon named both supplementary opposition, and progressive opposition.   

Supplementary-opposite pairs are, initially at least, diachronically-related, with one both pre-existing, and giving birth to, the other, even if they become, later, after that birth, and after some maturation, mutually symbiotic and co-existent.  They are typically also connected by a[n] ‘[self-]«aufheben» process’. 

Example cases of supplementary opposition include those of the kind of opposition that exists between temporal, historical predecessor and successor systems, and between other kinds of predecessor/successor pairs, e.g., between a 'self-hybrid' «arithmos» made up out of «monads», and its successor 'self-hybrid' meta-«arithmos»’, made up out of the meta-«monads»’ of those «monads», and other successions in which the successor typically quanto-qualitativelyexceeds and supersedes its predecessor -- parents vs. children, atom units vs. multi-atom molecule units; city-state units vs. multi-city-state empire units; ancient and medieval, pre-capitalist, “antediluvian” [Marx] forms of Monies, vs. Money-Capitals, and the human-social system of capitalism vs. its F.E.D.-predicted successor-system, that of political-economic democracy, etc. 

The ‘micro-temporal’, ‘ordinally-sequentially-related’, Qualo-Peanically-related’, «aufheben»-related consecua of the presentational progressions of ‘‘‘Systematic Dialectics’’’, and of Meta-Systematic Dialectics, also inhere in this third category of opposition. 

Supplementary opposition is the «genos» for meta-monadologically’-related consecutive 'self-hybrid' «arithmoi», i.e., for meta-fractally’-related, similarity-linked consecutive 'self-hybrid'quanto-qualitative scales of ‘ideo-ontology’, and of ‘physio-ontology’.

Perhaps needless to say, after the definitional descriptions and exemplifications set forth immediately above, all of the aporial oppositions encountered in Miguel’s recent F.E.D. Vignette #4 meta-systematic dialecticalexposition of  The Gödelian Dialectic of the Standard Arithmeticsare cases of this third «species»; of supplementary opposition. 

Thus, the sub-system W# is a supplementary opposite [ ‘~’ ] of N#,  Z# a supplementary opposite [ ‘~’ ] of W#,  Q# a supplementary opposite [ ‘~’ ] of Z#, R# ~Q#, C# ~ R#, and H# ~ C#, ... .

Note, in Vignette #4, that the axioms-systems given explicitly for these successive/progressive Standard Arithmetics are mostly «aufheben»-conserved in the transition from predecessor to successor axioms-system, also with ‘ideo-ontologically’ new, ‘‘‘supplementary’’’  axioms being added, to create the successor system.   
But note, also, that some of the predecessor system’s axioms are “crossed out” in these representations, because they no longer exist or apply at the new ‘ideo-ontological level’ of the supplementary system.

Likewise, in the human-social domain, one would expect a progressive capitalist system to «aufheben»-carry-forward/subsume many features of its predecessor human-social system, such as the mercantile capital and usurers’ capital ‘antediluvian’ forms of capital, and also such as the “monies” socio-ontology, and the “commodities” -- even some of the barter -- human ‘socio-ontology’, etc., but not serf labor, and/or slave labor, stabilized in perpetuity alongside of wage-labor, capital’s ‘essence-ial’ labor-form, at least not all the way into its ascendant phase.

This latter observation, together with the former, will afford you a sense of the ‘‘‘complex unity’’’ of annihilatory opposition and complementary, non-annihilatory opposition, that constitutes supplementary opposition.

The diagram below is set forth to summarize the above-narrated, four-«eide»-«monads» assemblagearithmos»] -- or ‘trans-Platonian’, four-fold «arithmos eide-tikos» -- that summarizes F.E.D.’s systematic dialectic of oppositions, both ‘formulaically’, using the Triadic Seldon Function, as of so = 1, and ‘[picto]graphically’, as yet a further example of F.E.D.dialectical [ideo-]systematics, or dialectical ideo-taxonomics.

Three ‘‘‘extra credit’’’ questions --

¿In what «species» of the «genos» of  oppositions does the ‘‘‘opposition’’’ of annihilatory opposition vs. complementary opposition inhere? 

¿In what «species» of the «genos» of oppositions does the ‘‘‘opposition’’’ of annihilatory opposition vs. supplementary opposition inhere? 

¿In what «species» of the «genos» of oppositions does the ‘‘‘opposition’’’ of supplementary opposition vs. complementary opposition inhere?

Our solution:  rectification of the «arche'»  --

For an earlier F.E.D. presentation of this issue, see the final two pages of the document linked-to below.,%20Supplement%20B-1,%20v.2_OCR.pdf

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