Tuesday, November 29, 2011

Dialectics in Brief

Dialectics in Brief







Dear Readers,

I.Ideo-Taxonomies.



Fundamentally, dialectics is ideo-taxonomy.



The afore-stated proposition is true both in terms of the present, synchronic conceptual core of even the most developed, advanced forms of dialectics [however widely unnoticed this fact may be], and in terms of the diachronic, historical beginnings of dialectics, under that name, «dialektike'», in the work of Platon of Athens –


  • Whether or not the ideas, concepts, or categories so “taxonomized” are “things of the mind only”, that are remote from external, physical experience, or are ideas about external, sensuous things, things outside of the mind – i.e., “things of human, internal nature”, or “things of the mind”, that were constructed so as to “model” “things of external nature”,
and;
  • Whether or not these ideas represent categories, or mathematical systems -- e.g., arithmetical or geometrical axioms-systems -- or pre-human/extra-human natural systems.


Ideo-systematics means ideo-taxonomy, or 'ideas class-ification'.



Systematic dialectics is a “[recti-]linear” [sequential] method of presentation of an ideo-taxonomy.





The «artithmoi eide-tikoi» – the Assemblages of Idea[s-as]-Units, the “numbers of ideas”, or “ideas-numbers”, at the heart of Platon’s original dialectics -- constitute, precisely, an ideo-taxonomy, organized, “vertically”, as a idea-content regress, with «aufheben» relations of elevation, «cum» abstraction/"«gene»-ralization"-negation, or de-concretion-negation, «cum» conservation-in-implicitude connecting each layer / level / grade of this "class-ification" with the one "above" it --

...an «eide»-, or «idea»-super-super-«Gene» level/scale, atop an «idea»-super-«Gene» level/scale, atop an «idea»-«Gene» level/scale, atop an «idea»-sub-«Gene» level/scale, i.e., an «idea»-«Species» level/scale, atop an «idea»-sub-«Species» level/scale, atop an «idea»-sub-sub-«Species» level/scale ...

-- “gradating”, or “graduating”, from more abstract, more determinations-sparse "higher" levels, to "lower" levels of ever-more concrete, ever-more-determinations-rich contents, that, together, form an iterated-«aufheben» “ideo-meta-fractal”: a finite, scaled self-similarity “content-structure” of ideas.





Those classic Kantian/Fichtean/Hegelian evolutedialectical progressions/presentations, those of the form –

thesis ---> thesis & antithesis ---> thesis & antithesis & synthesis

-- instantiate a generic sequence [progression] – a progressive [self-]presentation -- of a generic ideo-taxonomy: the cumulative, progressive unfolding of a [dynamical, hence trans-Platonian] «artithmos eidetikos».


Thus, a natural medium for the presentation of the total dialectic of a given, "«speci»-alized", sub-totality universe-of-discourse, or for the full totality, the total [known] universe-of-discourse, is an Encyclopedia, such as Hegel's "Encyclopedia of the Philosophical Sciences" attempted to be, or which the F.E.D. "Encyclopedia Dialectica" aims to be.

Such an should be presented, not in the alphabetical order of the names of the categories / concepts / classes / «arithmoi» that it expounds -- although an alphabetical index is a needed aid --but in their order of dialectical evocation, their "genetic" order, the dialectical "order of genesis" of these categories / concepts / classes / «arithmoi», from their predecessor categories / concepts / classes / «arithmoi», with all of the post-«arche'» categories / concepts / classes / «arithmoi» ultimately "descending from" their «arche'»-category / concept / class / «arithmos»: the "ever-present origin" of all of its successor categories /concepts / classes / «arithmoi».

But such trans-Platonic, trans-Hegelian -- i.e., Marxian -- Encyclopedias need to be updated continually, both for the metafinite-singularity-bourne, revolutionary irruption of new emergent properties / new emergent qualities / new emergent ontologies from their predecessor such, and for the clarification / correction of the human comprehension for those such already irrupted recently, and even for such already irrupted long ago.





In those writings of Platon which have survived the last Dark Ages – at least those up to the «auto-kinesis» [or self-change] revolution in Platon’s thought, late in his life – i.e., up to the dialogue entitled The Parmenides, Platon ideologized his «artithmoi eidetikoi» as an undynamical eternal stasis.

In later human history, dialectics -- especially with Marx and Engels, but also, to a degree, already with Hegel -- has come to be grasped as modeling changing and self-changing, or auto-kinesic, ideo-ontologies – i.e., dynamical ideo-ontologies -- by means of dynamical ideo-taxonomies.






II. Universal Algorithm.


The general rationale for the generic triad of the F.E.D. universal algorithm for dialectic is the following:





Something begins / opens any progression.


The «auto-kinesis» [self-change, “self-interaction”, “self-reflexion”, “self-squaring”, or “intra-action”] of that something then increases its quantity [increases the population of its individual units], i.e., that something expandedly reproduces itself.

As a consequence of increasing its own quantity beyond a determinate threshold, that first something gives birth to something new, to a second something, to a something qualitatively, ontologically different-- different in kind, not just different in quantity -- from itself, from that first something – i.e., gives birth to a second something whose own ensuing «auto-kinesis» then also increases its own quantity.

That second something typically arises out of the self-«aufheben» "self-containment" / "self-internalization" / "self-subsumption" / "self-re-entry" of the first something:  more specifically, by the "self-meta-«monad»-ization" / "self-meta-unit-ization" of the units, or «monads», of the first something.


Once both the first something and the second something [to which the first something gave rise] are in existence together, the two can begin to interact, and they do begin to interact.


Out of their interaction is born, at length, another new something, a third something -- something qualitatively, ontologically different -- different in kind, not just different in quantity – with respect to both the first something and the second something, albeit combining some features from each of them, its predecessors, as a result of their “inter-action” with each other -- i.e., as a result of each’s projection of its own nature upon the nature of the other.



[Up to this point, the Triadic and Dyadic Seldon Function algorithms agree].





I submit that this “general rationale” is the general story of our universe, both as a whole, and at all of the “levels”, or “meta-fractal scales”, within it.






Regards,


Miguel

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>>.


Triad:

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


Movement:

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


Definitions:

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.




TO BE CONTINUED


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

A “Purely-Quantitative" Movement of “Meta-Monadization"?

A "Purely-Quantitative" Movement of "Meta-Monadization"?



Dear Readers,

The purely-qualitative[self-]movements, and the qualo-quantitative” [self-]movements, of “[self-]meta-unit-ization, or of “[self-]meta-<<monad>>-ization, that we have recounted in this blog are, as we have seen, key to grasping both the mental and the physical [self-]movements, or [self-]progressions of our experience -- from predecessor <<arithmos>>/category to successor [meta-]<<arithmos>>/category -- as [self-]<<aufheben>> -- i.e., as dialectical -- [self-]movements; as dialectical [self-]progressions.

Out of curiosity – even if out of nothing else – let us ask the question: 

Is there a purely-quantitative movement of “meta-unit-ization, or of “meta-<<monad>>-ization?



My answer:  Yes!

And this movement is key to the notations of all of the ancient arithmetics, as well as to that of our modern, Hindu-Arabic – place-value/zero-as-empty-place-holder – arithmetical notation.

This movement is fundamental to all purely-quantitative arithmetics. 

It is the very ordinal/cardinal progression of arithmetical numerals itself!

I hold that this universal <<aufheben>> progression of numeration was adopted by our ancestors in response to both their goal of brevity of written expression, and to their goal of cognitive-advantage.

The only one of the ancient arithmetical notations for which we can readily illustrate this purely-quantitative progression of “meta-unit-ization, given the typographical resources ready-to-hand, is that of the “Roman numerals”.

We can describe this purely-quantitative <<aufheben>> progression thusly --

I ---> I, I & I = II ---> I, II, I & I & I = III --->

I, II, III, I & I & I & I = IIII = IV ---> I, II, III, IV, IIIII = IVI = V;


...V ---> ...V,...V & V = X ---> ...V,...X;


...X ---> X,...X & X = XX ---> ...X,...XX,...X & X & X = XXX --->

...X,...XX,...XXX,...X & X & X & X = XL --->

...X,...XX,...XXX,...XL,...XXXXX = XLX = L;   


...L ---> ...L,...L & L = LL = C;


...C ---> ...C,...C & C = CC ---> ...C,...CC,...C & C & C = CCC --->

...C,...CC,...CCC,...C & C & C & C = CCCC --->

...C,...CC,...CC,...CCC,...CCCC,... C & C & C & C & C = D;


...D ---> ...D,...D & D = M, = ...D,...M,

= I,...V,...X,...L,...C,...D,...M, ---> .....

-- wherein the new numeral – the new unitV is a five-fold meta-unit of the <<arche’>>-unit I [IIIII = V], wherein the meta-unit X is a two-fold second-degree meta-unit of the first-degree meta-unit V [VV = X], wherein the meta-unit L is a five-fold third-degree meta-unit of the second-degree meta-unit X [XXXXX = L], wherein C is a two-fold fourth-degree meta-unit of the third-degree meta-unit L [LL = C], wherein D is a two-fold fifth-degree meta-unit of the fourth-degree meta-unit C [CC = D], and wherein M is a two-fold sixth-degree meta-unit of the fifth-degree meta-unit D [DD = MV].


Our modern Hindu-Arabic numerals regularize this purely-quantitative, meta-fractal, meta-unit-ic, <<aufheben>>-progression thusly --

1&1&1&1&1&1&1&1&1&1 = 10;

10&10&10&10&10&10&10&10&10&10 = 100;

100&100&100&100&100&100&100&100&100&100 = 1,000, etc., etc.

-- with 10 as meta-1”, with 100 as meta-10”, and with 1,000 as meta-100”, etc., etc.




Regards,

Miguel

Monday, November 21, 2011

Part I.: Intuitive Account of the Universality of F.E.D.’s Generic Heuristic Algorithm for Dialectic

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

Part I
.: Instances [<<Species>>] of Dialectical Progressions Viewed One-Sidedly, as "Progressions of Antitheses"



Dear Readers,

Evolute Progressions and Diachronic Dialectics. Our experience and our cognition encounters – when it continues to attend over any substantial stretch of time, of temporality, of history – progressions of entities, in which the earlier-emerged entities for the most part persist – continue to be extant – together with the later-emerged, including the most-recently-emerged, entities.

For example, consider the “universe-of-discourse” of social entertainment media/infrastructure:

live theaters --->

live theaters & … recorded movie-theaters --->

live theaters & … movie theaters & … home radios --->

live theaters & … movie theaters & … home radios & … home televisions --->

live theaters & … movie theaters & … home radios & … home televisions &
home and mobile, recorded and live, audio and video entertainment-delivery computerized internet devices ---> . . .

That is, [live-play] theaters did not completely die out and disappear, though their population size and activity level were somewhat curtailed, and they were otherwise modified, by the emergence of [recorded-]movie theaters.

Likewise, live theaters and movie theaters did not become completely extinct, although their “socio-mass” was curtailed, in the case of movie theaters, and further curtailed, in the case of live-play theaters, and also otherwise modified, due to the emergence of home radios.

Again, live theaters and movie theaters and home radios did not completely go out of existence as a consequence of the emergence of home televisions, though their existences were somewhat [further] curtailed, and otherwise modified due to that emergence. And so on.


F.E.D. qualifies such progressions as evolute progressions, as opposed to convolute progressions --

http://point-of-departure.org/Point-Of-Departure/ClarificationsArchive/Evolute/Evolute.htm

http://www.dialectics.org/dialectics/Glossary_files/F.E.D.,%20A%20Dialectical%20%27%27Theory%20of%20Everything%27%27,%20Volume%200,%20FOUNDATIONS,%20Edition%201.00,%20last%20updated%2024AUG2011,%20Definition,%20%27%27%27CONVOLUTE%27%27%27,%20JPEG,%20for%2003SEP2011.jpg



Hegel on the ''Evolute-ness'' of Dialectical Progressions. While it is true that the philosophical, dialectical ideology developed by G. W. F. Hegel suffers from the defects identified by Karl Marx, Hegel's work also contains -- at least in the sphere of systematic dialectics, i.e., in the sphere of the dialectical "method of presentation" of theories of dialectical [sub-]totalities -- a rich and systematic "cumulum" of resources for the development of scientific dialectics, and one which is readily accessible to dialectical-scientific immanent critique, as Marx also noted, and instantiated. For Example:

"
. . .the progress from that which forms the beginning is to be regarded as only a further determination [<<speci>>-fication -- M.D.] of it, hence that which forms the starting point of the development remains at the base of all that follows and does not vanish from it.

The progress does not consist merely in the derivation of an other, or in the effected transition into a genuine other; and in so far as this transition does occur it is equally sublated
[i.e., it is equally «aufheben»-ated -- M.D.] again.

Thus the beginning of philosophy is the foundation which is present and preserved throughout the entire subsequent development, remaining completely immanent in its further determinations [i.e., the beginning of the «Logik» is the «arché» of «Logik»; its ‘‘‘governing source’’’; its ‘‘‘ever-present origin’’’ -- M.D.
]."


[
Georg Wilhelm Friedrich Hegel, Science of Logic, With What Must Science Begin? [Introductory Essay], translated by S. Houlgate, in S. Houlgate, The Opening of Hegel’s Logic, Purdue University Press [West Lafayette, Indiana: 2006], pp.175-179, italic bold-face and underline emphasis added. NOTE: All of the F.E.D. Dialectical Meta-Models that I have recounted/re-presented in this thread exhibit the characteristics described by Hegel in the emphasized passages above.].



Again, Hegel --

"...the determinateness
[‘«speci»-ficity-- M.D.] which was a result is itself, by virtue of the form of simplicity into which it has withdrawn, a fresh beginning; as this beginning is distinguished from its predecessor precisely by that determinateness, cognition rolls onward from content to content.

First of all, this advance is determined as beginning from simple determinatenesses, the succeeding ones becoming ever richer and more concrete.

For the result contains its beginning and its course has enriched it by a fresh determinateness.

The universal constitutes the foundation; the advance is therefore not to be taken as a flowing from one other to the next other.

In the absolute method the Notion maintains itself in its otherness, the universal in its particularization, in judgment and reality; at each stage of its further determination [i.e., of its further
‘«speci»-fication -- M.D.] it raises the entire mass of its preceding content, and by its dialectical advance it not only does not lose anything or leave anything behind, but carries along with it all it has gained, and inwardly enriches and consolidates itself.".

[G. W. F. Hegel,
Science of Logic, Translated by A. V. Miller, Humanity Books [NY: 1969], Volume II., Section 3., Chapter 3., The Absolute Idea (1812), p. 840, bold-italic-underline-shadow-color emphasis added].



Truly-Empirical Science: Following Nature = Following [Natural] History. The history of our cosmos as a whole, in terms of the “kinds of being(s)”, or the “ontology”, that has successively appeared/emerged in its history, exhibits this evolute progression form/content.

[ Note: The term <<aufheben>> here means an operation that concurrently qualitatively changes, and also contains/conserves, and also elevates the entity upon which it operates.

The "elevation" moment of the <<aufheben>> operation is an escalation of the entity thus operated upon in terms of its "qualo-quantitative" scale [thus evoking the hitherto unrecognized "fractal" aspect of dialectic].

Dialectical progressions are diachronic, finitary [meta-]fractals -- self-accelerating self-similarity regresses of continually escalating "qualo-quantitative" scale.

For example, it is obvious that a molecule, which <<aufheben>>-"contains" atoms -- which is a "self-internalization" of atoms, i.e., which is a "meta-atom", typically made up out of a heterogeneous multiplicity of atoms, wherein a molecule as unit is a "meta-unit" relative to its constituent atoms as units -- resides at a higher quantitative scale than do atoms, given that a molecule is typically larger as measured in linear size units [e.g., in radius], in mass units, and in volume units, than any of the atoms that are internal to it.

It is also not hard to see that a molecule resides at a higher qualitative scale than do its constituent atoms, and than do atoms external to it, that are not yet organized up to the molecular scale or higher, because by virtue of its <<aufheben>>-"containing" atoms, a molecule represents a higher qualitative unit, exhibiting new emergent qualities, qualities, and actions/behaviors, that are not yet possible/manifest at the atomic-and-no-higher level/scale of organization and of units.

Yet it is also clear that a molecule unit[y], in <<aufheben>>-"containing" atom unit[ie]s, and thereby in rising to, and constituting, a higher "qualo-quantitative" scale than that at which pre-molecular atom unit[ie]s reside, is also "similar" to an atom unit[y], in being also a qualitative [meta-]unit[y].

This <aufheben>>, "fractal-ogenic" operation is the operation that resides at the core of all dialectic ].


pre-nuclearparticles--->

self-<<aufheben>> of pre-nuclearparticles=

pre-nuclearparticles& multi-pre-nuclearparticle nuclearparticles--->

self-<<aufheben>> of pre-nuclearparticles& nuclearparticles=

pre-nuclearparticles& nuclearparticles&…multi-nuclearparticle atomic nuclei --->

self-<<aufheben>> of all of that =

pre-nuclearparticles& nuclearparticles&…atomic nuclei &…multi-atom molecules --->

self-<<aufheben>> of all of that =

pre-nuclearparticles& nuclearparticles&…atomic nuclei &…molecules &…multi-molecule prokaryotic cells --->

self-<<aufheben>> of all of the preceding =

pre-nuclearparticles& nuclearparticles&…atomic nuclei &…molecules &…prokaryotes &…multi-prokaryotic-cell eukaryotic cells --->

self-<<aufheben>> of all of the preceding =

pre-nuclears & nuclears &…nuclei &…molecules &…prokaryotes &eukaryotes &…multi-[eukaryotic-]cellular organisms --->

self-<<aufheben>> of all of the preceding =

pre-nuclears & nuclears &…nuclei &…molecules &…prokaryotes &…eukaryotes &…multicellulars &…multi-multi-cellular-organism animal societies --->

self-<<aufheben>> of all of the preceding =

pre-nuclears & nuclears &…nuclei &…molecules &…prokaryotes &…eukaryotes &…multicellulars &… animal societies &… multi-animal-society, humans-led [meta-]societies --->

self-<<aufheben>> of all of the preceding =

pre-nuclears & nuclears &…nuclei &…molecules &…prokaryotes &…eukaryotes &…meta-biota &… animal societies &… human societies &…multi-planetary-society “meta-humanity [F.E.D.-predicted next emergence, not yet [fully] actualized / only “fractionally”-actualized to-date] ---> . . . ..


Truly-Empirical Human-Social Science: Following [Human] History. The social history of Terran humanity also exhibits this evolute progressivepattern –

mutually-warring tribal societies --->

mutually-warring tribal societies &…prisoner-of-war slave-labor-based empires --->

mutually-warring tribal societies &…prisoner-of-war slave-labor-based empires &… serf-labor-based kingdoms --->

tribal societies &…slave-labor-based empires &…serf-labor-based kingdoms &…wage-labor-based republics ---> . . . ..

-- or, in terms of what Marx and Engels called the social relations of production, or ‘“the forms of [human-]social intercourse”’ [in, e.g., The German Ideology] --

predatory Appropriations of the “raw” products of pre-human/extra-human nature --->

<<aufheben>> of that =

rawAppropriations & human-labor-improved/refined [by multi-/cross-Appropriation of natural properties]Goods”/“Use-Values--->

<<aufheben>> of that =

rawAppropriations &Goods &…Exchange-Use Value of Goods: Bartered Commodities --->

<<aufheben>> of all of the preceding =

rawAppropriations &Goods &…Commodities &…Monies --->

<<aufheben>> of all of the preceding =

rawAppropriations &Goods &…Commodities &…Monies &…Capitals --->

<<aufheben>> of all of the preceding =

rawAppropriations &Goods &…Commodities &…Monies &…Capitals &… Generalized Equities [F.E.D.-predicted next emergence, not yet actualized] ---> . . . ..



[Note: The "meta-unit-ic" -- or "meta-<<monad>>-ic" -- concretization of the core-dialectical <<aufheben>> operation, is not so directly manifest in the case of the dialectical progression of the Marxian "human-social relations of production" as it is in the cases of the other dialectical progressions invoked in this blog entry.

This observation points-up the difference between historical dialectics, the first "contra-category, and psychohistorical dialectics, the second "contra-category", in the F.E.D. [psychohistorical] dialectical progression of their "dialectic of the dialectic itself".

This is because the "meta-<<monad>>-izations" in the case of the "human-social relations of production" dialectic -- i.e., of the "forms of human-social intercourse" dialectic -- are not as "physical" as they are in most of the other cases invoked herein.

The <<aufheben>> "internalizations"/"containments" & qualitative negations & conservations & scale-elevations in the case of the Marxian "human-social relations of production" dialectic are mind-mediated, inter-subjective, collective-psychological, "meme-etic", "human-phenomic" changes in the psychohistorical material[ity] of humanity, rather than "purely" physical <<aufheben>> [self-]operations.

For a detailed rendition of the "meta-<<monad>>-ization" content of the <<aufheben>> processes in the historical progression of the Marxian "human-social relations of production", see --

http://www.dialectics.org/dialectics/Primer_files/4_F.E.D.%20Intro.%20Letter,%20Supplement%20B-1,%20v.2_OCR.pdf

-- pages B-24 through B-32 ].



-- or, in terms of the human-social geography/"meta-geology" of human-social formations --

bands of proto-human hunter-gatherer-foragers/scavengers --->

self-<<aufheben>> of that =

bands & initially multi-band encampments --->

self-<<aufheben>> of that =

bands & camps &…initially multi-camp villages --->

self-<<aufheben>> of all of the preceding =

bands & camps &…villages &…initially multi-village tribal chiefdoms --->

self-<<aufheben>> of all of the preceding =

bands & camps &…villages &…chiefdoms &…initially multi-chiefdom/multi-tribe-alliance city-states --->

self-<<aufheben>> of all of the preceding =

bands & camps &…villages &…chiefdoms &…city-states &… multi-city-state empires --->

self-<<aufheben>> of all of the preceding =

bands & camps &…villages &…chiefdoms &…city-states &…ancient empires &…multi-empire-remnant/-fragment modern nation-states --->

self-<<aufheben>> of all of the preceding = . . . =

bands & camps &…villages &…chiefdoms &…city-states &…empires &…nation-states

&…
multi-
nation-state poli [e.g., the EU]

&…planetary poli
[F.E.D.-predicted future emergence, not yet actualized] --->. . . ..

-- although Terran human-social formations-history does appear to have somewhat more in the way of convolute tendencies than do some other such progressions, along with its also evident evolute tendencies.



Synchronic Dialectics:   Method of Presentation of Dialectical Theories that Explain the Self-Reproduction of Systems. There are also “contemporaneous”, “synchronic”, “all-at-once” dialectical progressions, or dialectically-progressively-presented taxonomies – usually in the form of short-duration, or “micro-historical”, pedagogical/educational presentations [e.g., lectures, textbooks, slide decks, etc.] – which comprise the category of systematic dialectics, such as --


Universe-of-discourse: the system of contemporary phonetic written language.

letters of the alphabet --->

<<aufheben>> of that =

letters & multi-letter syllables --->

<<aufheben>> of that =

letters & syllables &…multi-syllable words --->

<<aufheben>> of all of the preceding =

letters & syllables &…words &…multi-word phrases --->

<<aufheben>> of all of the preceding =

letters & syllables &…words &…phrases &…multi-phrase sentences --->

<<aufheben>> of all of the preceding =

letters & syllables &…words &…phrases &…sentences &… multi-sentence paragraphs --->

<<aufheben>> of all of the preceding =

letters & syllables &…words &…phrases &…sentences &… paragraphs &…multi-paragraph texts --->

<<aufheben>> of all of the preceding =

letters & syllables &…words &…phrases &…sentences &… paragraphs &…texts &…multi-text/multi-chapter books --->

<<aufheben>> of all of the preceding =

letters & syllables &…words &…phrases &…sentences &… paragraphs &…texts &…books &…multi-book libraries --->. . . ..


-- or --

Universe-of-discourse: the system of contemporary computerware” [hardware & software].

bits --->

<<aufheben>> of that =

bits & multi-bit bytes --->

<<aufheben>> of that =

bits & bytes &…multi-byte computer-words --->

<<aufheben>> of all of the preceding =

bits & bytes &…words &…multi-word commands --->

<<aufheben>> of all of the preceding =

bits & bytes &…words &…commands &…multi-command programs --->

<<aufheben>> of all of the preceding =

bits & bytes &…words &…commands &…programs &… multi-program software systems ---> . . . ..


-- or --

Universe-of-discourse: the system of units of contemporary time metrology.

seconds --->

<<aufheben>> of that =

seconds & multi-second minutes --->

<<aufheben>> of that =

seconds & minutes &…multi-minute hours --->

<<aufheben>> of all of the preceding =

seconds & minutes &…hours &…multi-hour days --->

<<aufheben>> of all of the preceding =

seconds & minutes &…hours &…days &…multi-day weeks --->

<<aufheben>> of all of the preceding =

seconds & minutes &…hours &…days &…weeks &… multi-week months --->

<<aufheben>> of all of the preceding =

seconds & minutes &…hours &…days &…weeks &… months &…multi-month quarters --->

<<aufheben>> of all of the preceding =

seconds & minutes &…hours &…days &…weeks &… months &…quarters &…multi-quarter years --->

<<aufheben>> of all of the preceding =

seconds & minutes &…hours &…days &…weeks &… months &…quarters &years &…multi-year decades --->


<<aufheben>> of all of the preceding =

seconds & minutes&…hours &…days &…weeks &… months &…quarters &…years &…decades &…multi-decade centuries --->


<<aufheben>> of all of the preceding =

seconds & minutes &…hours &…days &…weeks &… months &…quarters &…years &…decades &…centuries &…multi-century millennia --->. . . ..


In all of the evolute progression examples above, I have used “ellipsis dots” -- -- to avoid detailing the “combinations” – the “hybrids”, or [full and partial] “syntheses” – that often arise in such evolute progressions.

These “combined forms” are related to a universal generalization of the “uneven and combined development” theory proposed by Leon Trotsky.

The final examples in this blog entry will be beginning to bring the “combined forms”, “complex unities”, “hybrids”, or “syntheses” back into "explicitude".



Dialectics Generalized. Let us consider a generic version of such evolute progressions, abstracting from all of the evolute-cumulative progressions cited above, and from many others as well, all of which have common features that we wish to preserve in this abstraction/generalization/generic version.

Note: A truly empirical science – and, therefore, any true science in the essential sense of that word – must follow nature, which means, in part, that it must follow [natural] history.

That is, A truly empirical science must put forth models – or “meta-models” – which do not just represent all of the entities that are ever known to have appeared in empirical reality, but which must also generate these representations in the empirically-reconstructed historical order, and timings, in which these entities actually arose in the temporal, chronological, historical continuity of nature.

Per the generic version of such progressions --

First, human cognition, seeking to comprehend a given experienced/reconstructed progression, must “work-up” its data, information, evidence, and knowledge about the given progression-phenomena, until it can identify the temporal, historical origin, or beginning, of that progression: the very first entity in that empirically-reconstructed, historical progression of entities: the <<arche’>>-entity, call it A.

Next, human cognition must grasp the fundamentallawof dialectical logic, or the fundamentallawof dialectical thought, which generalizes to the fundamentallawof dialectical historical process, as it applies to the specific progression it seeks to model and master, namely --

A ---> A of A = [self-]<<aufheben>> of A = A + delta_A

-- where delta_A stands for a qualitative increment of new ontology – a new kind of being – a kind qualitatively different from that of A, but a new kind which results from the [self-]<< aufheben >> of the “old” kind, A – by means of the concurrent containment/conservation, and qualitative change/determinate negation, and elevation, of A, by A, itself.

The usual concrete form of this [self-]<<aufheben>> operation of the <<arche’>> is what F.E.D. refers to as meta-unit-ization, or meta-<<monad>>-ization

http://www.dialectics.org/dialectics/Glossary_files/F.E.D.,%20A%20Dialectical%20%27%27Theory%20of%20Everything%27%27,%20Volume%200.,%20FOUNDATIONS,%20Edition%201.00,%20first%20published%2010DEC2011,%20last%20updated%2020AUG2011,%20Definition,%20%27META-%27,%20for%2022AUG2011.jpg

http://www.dialectics.org/dialectics/Glossary_files/F.E.D.,%20A%20Dialectical%20%27%27Theory%20of%20Everything%27%27,%20Volume%200.,%20FOUNDATIONS,%20Edition%201.00,%20first%20published%2010DEC2011,%20last%20updated%2017AUG2011,%20Definition,%20ARCHE%27,%20JPEG_2.jpg

Once A is posited as [having-been / still-being] actual, or even as just being possible, the actualization of the initially-hidden potential of A, call it delta_A, or B, also becomes possible, beginning at some moment of time after the positing of the actuality, or possibility, of A, as a derivative of the prior actuality, or possibility, of A.

The possibility of B “descends” from, or is “inherited” from, the prior possibility, or actuality, of A.

Next, after both A and B have become, and remained, possible, or actual, their “unification”, “combination”, “hybridization”, or “synthesis”, call it –

B of A [minus A]”, or delta_[B; A], or C

-- also becomes possible, as a derivative of – as an “inheritance” from – the prior co-possibility, or co-actuality, of A and B together.


In summary, then, F.E.D.’s generic version of dialectical evolute progression holds that, over “micro-historical”, “meso-historical”, or “macro-historical” scales/intervals of historical time --

Ontology-state A goes to A & B, goes to A & B & C . . .

-- or --

Ontology-state A becomes A + B, becomes A + B + C . . .

-- or --

Posit goes to Posit + Op-Posit, goes to Posit + Op-Posit + Com-Posit. . ..

In that sub-sphere of historical dialectics "meta-modeling" of the pre-human/extra-human dialectic of nature, where the aspect of opposition, or "antagonism", between Posit and Op-Posit may not be so plain, it may be better to characterize the triadic sub-progressions as --

Posit goes to Posit + Meta-Posit, goes to Posit + Meta-Posit + Com-Posit. . ..





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



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. In the following examples, 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 blog entry, 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.









TO BE CONTINUED




Next:


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>>.