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”,
- 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 “evolute” dialectical 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.