Sunday, November 27, 2011

Part II. A.: An Intuitive Account of the Universality of the F.E.D. Generic Heuristic Algorithm for Dialectic

An Intuitive Account of the Universality of the F.E.D. Generic Heuristic Algorithm for Dialectic.

Part II. A.: Instances [<<Species>>] of Dialectical Progressions Viewed More Holistically, as "Progressions of '''Thesis / Anti-Thesis / Syn-Thesis''' Triads" --

Systematic-Dialectics Example 1. – The Opening Triad of Hegels Dialectical <<Logik>>.

Dear Readers,

This blog-entry, post # 79, contains Part II. A. of the planned multi-part posting for which blog-entry # 77 constituted Part I.

Transition to Part II. A.:   Instances [<<Species>>] of Dialectical Progressions Viewed More Holistically, as "Progressions of '''Thesis / Anti-Thesis / Syn-Thesis''' Triads" --

Systematic-Dialectics Example 1. – The Opening Triad of Hegels Dialectical <<Logik>>.

Hegel on the Dialectical Triad.  In his lectures on his dialectical <<Logik>>, Hegel spoke as follows on the dialectical triad --

The first determination [ i.e., «speci»-fication -- M.D.] is immediate, while the second one constitutes the sphere posited in its differentiation from the first.

Within every simple first determination, [e.g., ground,] what is determinately different from it [, e.g., the consequence of the ground] is at once also present, but it is at first present without being explicitly posited.

In the second determination, finitude [and with it contradiction] again enters.

The third determination is the unity of the first and the second, in which the contradiction is resolved. ...

The progression is as follows.

The beginning is simple, immediate. ...

Every newly emerging concept is more concretely determinate [i.e., is more-richly "<<
speci>>-fied" -- M.D.] than its predecessor.

We are always carrying everything that went before along with ourselves into what is new, but everything prior is, within what is new, put in its determinate place. [assertion by Hegel of the "«aufheben» evoluteness" of systematic dialectic -- M.D.]

Whereas, in what preceded, each [momentarily immediate] determination … passed as ultimate, it is now demoted into being only a moment . . ."

[G. W. F. Hegel, Lectures on Logic, Clark Butler, translator, Introduction to the Lectures on Logic, More Exact Concept and Division of the Science of Logic, [I. Being], Indiana U. Press [Indianapolis:2008], pp. 79-80, bold, italic underline shadow, and color emphasis added].

Examples of Dialectical Triads.

The Generic Example. In the examples to follow , we will start to “look into the ellipsis” that characterized the earlier, starting examples – into the “hybrids” or “syntheses” that were left-out, or left implicit, in those earlier examples – via the “explicitization” of the third term in each example below – that is, via the "explicitization" of their “C” terms – in place of the “ellipsis dots”, “”, employed previously.

Term C stands for the "real subsumption" of term A by term B, or the "mutual subsumption" of B and A -- for the "complex unity", or "hybridization", of "kind" A and/with "kind" B.

In the earlier examples presented at the start of this post, the progressions presented were all of the following generic form --

First Posit & First Op-Posit &...Second Op-Posit &...Third Op-Posit &...Fourth Op-Posit &... --->

-- or of the form --

First Posit & <<aufheben>> of First Posit &...<<aufheben>> of First Op-Posit &...<<aufheben>> of Second Op-Posit &...<<aufheben>> of Third Op-Posit &... --->

-- i.e., of the "algebraic" form --

A & B &...D &...H &...P &...--->. . . ..

All of the "hybrids", or [partial/total] "Syntheses", starting with the "First Com-Posit", were hidden in the "ellipsis dots" - ... .

The term C is "hidden" in the first group of ellipsis dots, E & F & G -- or, equivalently, E + F + G -- is "hidden" in the second group of ellipsis dots, I & J & K & L & M & N & O -- or, equivalently, I + J + K + L + M + N + O -- is "hidden" in the third group of ellipsis dots, and so on.

Decoding the "algebra" above,
C stands for the "first full synthesis", E, F, and G stand for the "first partial synthesis", the "second partial synthesis", and the "second full synthesis", respectively -- i.e., for the "real subsumptions" of A by D, of B by D, and of C by D, respectively -- and I, J, K, L, M, N, and O stand for the "third partial synthesis", the "fourth partial synthesis", the "fifth partial synthesis", the "sixth partial synthesis", the "seventh partial synthesis", the "eighth partial synthesis", and the "third full synthesis", respectively -- i.e., for the "real subsumptions" of A by H, of B by H, of C by H, of D by H, of E by H, of F by H, and of G by H.

Systematic-Dialectics Example 1. – Opening Triad of Hegels Dialectical <<Logik>>.


A & B & C = Being & Nothing & Becoming.


Being ---> Being & Nothing ---> Being & Nothing & Becoming.


Being = Abstract, indeterminate, immediate being; the most general & unmediated concept of being.

Nothing = Abstract, indeterminate, immediate nothing; the most general & unmediated concept of nothing.

Becoming = Unity of intra-duals: moving from Nothing to Being, coming-to-be[ing], or arising, [from Nothing], &/vs. passing-out-of-being / passing-away / passing or moving from Being to Nothing.

Commentary: The category Being is the <<arche’>> category – or founding category – of Hegel’s entire philosophical system – the single category from which all of the total of ~273 categories, fundamental, per Hegel, to modern human language, and, thus, to modern human thought, and which he divides among his <<Logik>>, his <<Natur>>, and his <<Geist>> [i.e., his Human Spirit] sub-systems -- are to be dialectically derived.

But the second category in that stream of ~273 categories is the category Nothing, into which the category Being “immediately passes over”.

That is, when the human mind “forms itself into”, and simulates – or mentally “embodies” – the category Being, it instantly finds that this category is so deficient in specific, determinate content that it is equivalent to the category Nothing.

There is a set-theoretical way of clarifying this “ideo-phenomeonological” finding of Hegel’s. However, this way could not have been Hegel’s way, in detail, because set theory as such was not yet extant during Hegel’s lifetime. Yet this way is apt nonetheless.

Consider the “universal set” for any of the many sufficiently rich “universes-of-discourse” that human cognition constructs. That “universal set” will be the set of all “objects” – the set of all “logical individuals” – that are part of that “universe-of-discourse”.

That universal set will represent, set-theoretically, in the form of an “extension”, the common quality, or single “intension”, shared by all of those “individuals” -- the elements, or members of that universal set, or “universe-of-discourse” set.

Consider, for example, the set of all celestial objects in the Solar System, including the Sun, all of its planets, all of their moons, the constituents of the rings of Saturn and of Uranus, the dwarf planets, planetoids, and planetesimals, the asteroids, the comets, the interplanetary dust grains of our intra-solar-systemic medium, etc.

Now, try to mentally grasp, and to name, the single quality that they all share in common, but that they do not share in common with all other solar systems, or with all other objects in the known universe. That will be the singular quality common to all of the “being” of the “celestial objects of our Solar System” universe-of-discourse.

Now take an ancient Greek view of any of these diverse “universes-of-discourse”. Each such “universal set” is an <<arithmos>> of <<monads>>, i.e., is an assemblage of qualitative units, each of whose diverse qualitative units – “elements” or “members” – is a qualitatively distinct <<monad>>, yet one qualitatively similar to all of the others in that it must share the quality that is common to them all, the “essence-ial” quality that defines their “universe”.

When you – mentally – “look” at your mentally-constructed image of such a set “from the inside”, you “see” a rich plenitude of diverse being, a qualitative heterogeneity and multiplicity. When you mentally “look” at your mental image of such a universal set “from the outside”, you see a unity, the single unit that is this set itself, as a whole, which represents the “intension” – the common quality – of all of the diverse qualities inside that unit, that set, that universe.

Now, as best you can, form within your mind, and consider, the set of all universes-of-discourse -- the set of all universal sets – that is, the set which takes every one of those universes-of-discourse – every one of all possible universal sets – as its elements, as its members, as its units, i.e., as its <<monads>>.

That set of sets will be a meta-<<arithmos>>” of/to each of the <<arithmoi>> that we considered before – an [meta-]<<arithmos>> which has all of those previously-considered <<arithmoi>> as its [meta-]units, or [meta-]<<monads>>. And that set of sets -- or <<arithmos>> of <<arithmoi>> -- will, set-theoretically, stand for the quality – will be the extension of the intension – of the all of the qualities of “being” common to all of the possible “universes-of-discourse”.

The resulting [meta-]quality will be so rarefied, so distilled of all specific content, so diluted due to the diversity of its constituent, included qualities, so subtle, so evanescent, so diaphanous to our mental perception, as to be equivalent to – as to be indistinguishable from -- that of the empty content of the set of all empty sets, the category Nothing.

The mentally-perceivable difference between the two “intensions”, the two qualities, will be ineffable.

In this way, we may view the category Being as being modeled by any given rich universe-of-discourse’s “universal set” as an <<arithmos>>, with the “members” or “elements” of that set as the units or <<monads>> of that <<arithmos>>.

The meta-unit-ization, or meta-<<monad>>-ization of that <<arithmos>> is then a meta-<<arithmos>>, the set of all universal sets, whose units, or <<monads>>, are each a single universe-of-discourse set, a “universal set”, the common quality of being shared by all of these diverse universes-of-discourse being equivalent to the singular quality of the category named Nothing.

Alternatively, we can view the first, Being, set as the total universal set – as the set of all objects capable of belonging to any possible universe(s)-of-discourse – and the second, Nothing, set as the result of the division of the contents of the first set into sub-sets, each representing a possible universe-of-discourse universal set.

By either approach, we encounter a perplexing and recurrent alternation in our perspective regarding Being.

When we mentally “look at” the set of all universal sets from its “out-side”, i.e., “seeing” it as a unit[y] in its own right, we encounter the equivalent of Nothing as the only quality that we can conceive and name as the commonality of such a vast diversity of constituent qualities.

When we mentally “look at” this set of all universal sets from its “in-side”, seeing the rich diversity of qualitatively distinct universes of discourses that it “contains”, we encounter our concept of the maximal qualitative plenitude of all Being.

This very movement of our minds, this spontaneous oscillation back-and-forth between our mental perception of Being and of Nothing, from Being to Nothing, then back to Being again, and then back to Nothing again..., as we shift our attention back and forth from the “in-side” of that set, to its “out-side”, then back to its “in-side” once again..., in a potentially unending, Sisyphosian alternation -- once we self-reflect, and become aware of this, our own mind’s self-movement -- spontaneously constitutes in[to] our consciousness a new, third category, Becoming.

Becoming describes this self-observed action/activity of our minds, by virtue of being a category not of conceptual stasis, or of “equilibrium”, or of “fixity”, but, on the contrary, one of potentially ceaseless mental self-movement, i.e., of “ideo-dynamasis”.

This Becoming, our spontaneous mental self-movement when our minds form and contemplate the categories of Being and Nothing, consists of two sub-movements.

The first of these two mental sub-movements is the movement of our minds from Being to Nothing – the movement of “coming to Nothing”, or “going [back] to Nothing” -- which Hegel calls passing away or ceasing to be.

The second of these two mental sub-movements is the movement of our minds from Nothing to Being – the movement of “coming to Being”, or “going [back] to Being” -- which Hegel calls coming to be, or arising.

Together, these two, alternating sub-movements constitute a single, “circular” movement, a movement of circulation from Being to Nothing to Being to Nothing to Being ..., to which Hegel gives a new category, which he names Becoming.

In dialectical-ideographicqualifiers” shorthand -- using the algebra of the F.E.D.First Dialectical Arithmetic”, with B or qB denoting the <<arche’>> category, Being -- the whole opening movement of human thought per Hegel’s first dialectical triad can be summarized as follows --

qB ---> qB & qBB = B & N ---> qB & qN & qNB = B & N & C

-- wherein it is understood that Becoming, connoted by C or, equivalently, by qNB, “contains” two intra-dualsB--->N, and N--->B – thus together constituting Becoming as B<--->N.


Part II. B.:  Systematic-Dialectics Example 2. – The Opening Triad of Marxs <<Kapital>>.

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