I have reproduced, below, part of a recent dialogue on dialectics.
"Q: Can you ... explain what dialectics.org is talking about?
A: What dialectics.org is talking about is a "Unified Theory of Universal Dialectics".
They start from/with Plato's dialectic, and note [see, for example, Plato's Dialogue "the Sophist"] that, in Plato's original concept, dialectic was about the right "ontological sorting" of things into their kinds, taking into account that things could be divided into different "species" categories, some of which shared the same "genus" categories, like as the more specific categories of "apples", "oranges" and "pears", all share/are "in" the more general category of "fruits".
Thus Plato's original dialectic was about "ideo-taxonomy", or "ideo-systematics" -- the "genus" and "species" relations of "assemblages of idea-units", or of "idea-monads", i.e., of "eide", which translates into ancient Greek as "arithmoi eide-tikoi" -- "numbers of idea units".
Plato initially conceived these "species" of ideas as the static and immutable backdrop of the changing flux of experience: an eternal "fixity" of the ideas/species, the "Eide", though he later reached toward a different view, based upon "auto-kinesis", "self-change".
Crucially, the dialectics.org folks note that the relation of a plurality of "species" idea-units to their singular "genus" idea-unit is one of "meta-unit-ization", or "meta-monad-ization", a term they coined to describe how a heterogeneous multiplicity of units at one level form a new level by combining into a single, new unit, that then self-reproduces to form a new "multitude", a qualitatively new KIND of "arithmos", representing "new ontology" -- the units of a NEW KIND of being.
So, a "genus" idea-unit is a "meta-monad" or "meta-unit" of its [usually several] "species" units, whose mutual differences "disappear into it", at its level of generality, and such that it differentiates or divides back into those "species-units" at their level of specificity.
They also point out that such "meta-monad-ization" is a specific form of the general -- often vaguely described -- dialectical process of "aufheben" [in Hegel's German], which means a process that simultaneously specifically changes something ["dialectically, determinately negates" it], "elevates" it [to a higher qualitative scale/level], and conserves it in its core reality [e.g., the different "species" are still "there", implicitly, "inside" their "genus", when attention shifts from them to their "genus"; the "apples" and "oranges" category-units are still "there", "inside" the "fruits" category-unit, implicitly though no longer explicitly].
With Hegel, and later, especially, with Marx, such "ONTOLOGICAL categories" -- or "KIND-of-thing categories" -- become much more dynamic.
The dialectics.org folks discovered a new arithmetic and algebra -- already predicted, but not constructed, by some of the deepest theorems of modern mathematical logic -- an "algebra of dialectical logic" which can be interpreted to describe such dialectical, "aufheben" processes of "self-meta-monadization" -- in Plato's work, in Hegel's work, in Marx's work, and in natural reality as a totality.
This leads them to a single 'dialectical meta-equation' which describes the genesis of the units all of the general categories of every known kind of thing that presently exists, or that is known to have once existed, in the actual, natural-historical, temporal order in which those things actually arose in cosmological history -- i.e., leads to a dialectical "theory of everything" -- and to similar "dialectical meta-equations", describing the "meta-evolution" of the sub-categories of those universal categories of kinds: to a "dialectical encyclopedia" of Nature as totality, including of human Nature, the human part of Nature.
For example, pre-nuclear "particles" [e.g., quarks and gluons] "self-meta-monadize" into "sub-atomic particles" [e.g., protons and neutrons], which, in turn, "self-meta-monadize" into atomic nuclei and atoms, which, in turn, "self-meta-monadize" into molecules, which, in turn, "self-meta-monadize" into prokaryotic cells, which, in turn, "self-meta-monadize" into eukaryotic cells, which, in turn, "self-meta-monadize" into multicellular organisms ["meta-phyta" and "meta-zoa"], which, in turn, "self-meta-monadize"' into "animal societies" [dogs, horses, cattle, meerkats, etc.] and "plant communities" [wild rices, wild wheats, wild barleys, wild ryes, wild corns], which then "self-meta-monadize" into human[oid]s-led "meta-societies", which then [they predict] eventually "self-meta-monadize" into "meta-humans-led meta-meta-societies".
This is the "self-aufheben Dialectic of Nature" -- singular, not plural.
However plurality re-enters for them in that each "genus" in the main model has a "sub-dialectic" for the historical genesis of the units of its own "sub-categories", e.g., within the "molecules" "sub-universe", "monomer" molecules "aufheben self-meta-monadize", i.e., "polymerize", to form higher molecular units, "polymers" -- sugar units "aufheben self-meta-monadize" ["polymerize"] to form the higher "polysaccharide chain" units of starch molecules, e.g., cellulose units, amino acid "peptide" units 'self-meta-monadize' ["polymerize"] to form higher, "poly-peptide chain" protein molecule units, nucleic acid "nucleotide" units "self-meta-monadize" ["polymerize"] to form higher, "poly-nucleotide chain" RNA and DNA "macro-molecule" units, etc. The so-called "quaternary structure" of some proteins designates a yet higher level of 'meta-meta-monadization', and so on.
Using their new dialectical arithmetics/algebras, and such "dialectical meta-equations" [a "meta-equation" is a dialectical-mathematical formula that has a qualitatively different, individual equation as the "value" corresponding to each distinct "value" of that "meta-equation's" "epoch" parameter, t, i.e., a "meta-equation" is an "aufheben meta-unit" of those "equation-units" -- "made up out of a heterogeneous multiplicity of equation units"], the dialectics.org folks have constructed and published seven "simultaneous" such "dialectical meta-equations", each one reconstructing a different aspect of the history of humanity, which they call "The F.E.D. Psychohistorical-Dialectical Meta-Equations" --
Q: Does this Unified Theory of Universal Dialectics have predictive power or explanatory power, and if predictive as well as explanatory, could you give an example please?
A: Yes, both explanatory and predictive power.
In the taxonomy level 1 and level 2, the explanatory power is still very general, as it must be, because it must capture only the shared, generic features among many specifically different cases, but that power gets more specific as one "ascends" [Marx] into the models of the more specific taxonomy levels, and using the "more complex, more thought-concrete" dialectical algebras that arise in the F.E.D. "dialectic of the dialectical algebras".
For example, in their third "psychohistorical meta-equation", called "the [Meta-]Equation of Human Social Relations of Production Meta-Evolution", the equation for t = 4 predicts that the expansion of the quantity of, and of the spatial concentration of, the units of the capital/wage-labor social-relation-of-production category, symbolized K, will at length irrupt a qualitatively new, "meta-Kapital", social relation of production, by the end of that fourth historical epoch of social relations of production.
Clearly a falsifiable prediction.
This process of quantitative expanded reproduction of Kapital units, leading to irruption of the units of a qualitatively new category of social relations of production ontology, is built-in to that "meta-equation", but, as a separate[d] dialectical process, it looks like this:
K ---> K squared = K + delta_K = K + E.
[the "delta" is underscored as "delta", because it denotes a qualitative, ontological incrementation, not a purely-quantitative incrementation, as does just "delta"].
They identify the new social relations ontology, delta_K above, with the category of the units of a new, higher social relation of production, which they name "Generalized Equity", leading to "Political-ECONOMIC DEMOCRACY".
A rather detailed specification as to what the predicted "Generalized Equity" social relation of production, and as to what the predicted "Political-ECONOMIC DEMOCRACY" social formation will look like has been supplied.
With respect to past human history, there are "retro-dictive"/explanatory aspects, or "re-constructive"/explanatory aspects, to this "meta-model", as well as "pre-constructive"/explanatory, or predictive/explanatory aspects per se.
For example, this same "dialectical meta-equation", in its equation for the t = 2 epoch, is standardly interpreted as asserting that the "exchange-use" of Goods, the [pre-money] Commodity Barter social relation-of-production, will irrupt once the quantitative "population" level, and local spatial concentration, of the units of the Goods/obligatory-Gifts social relation of production crosses a threshold, i.e., once the social forces of production grow to a level which can sustain the reproduction of such a quantitative scale/concentration of Goods/Gifts units:
G ---> G squared = G + delta_G = G + C.
With respect to the overall "Dialectic of Nature" Meta-Model, it predicts that, with the quantitative growth/spatial-concentration of "human socio-mass" units, h, will come the irruption into existence of "delta_h", i.e., of a new, "meta-humanity" ontological category --
h ---> h of h = h times h = h + delta_h = h + y
-- a new <<genos>> which, they infer, will be characterized by three constituent <<species>>:
- a "thesis" species-category, which they name that of "human-genomic self-re-engineerings", g;
- a "contra-thesis" species contra-category, which they name "android robotics", g-squared, or g times g, minus g = delta_g = r, and;
- a "uni-thesis" species "uni-category" of the hybridization/dialectical synthesis/"complex unity" of the two, of r and g, which they name "cyborg prosthetics", or "cyborg bionics", c, such that r times g, minus g, = c.
Q: ...could you explain what they mean by "solution-epoch t = 4"?
Where do they get the "4" from?
A: Yes --for the "Dyadic Seldon Function" -- the one they typically use to formulate HISTORICAL dialectics, hisdtorical-dialectical processes/progressions -- you have an <<arche'>>-category symbol, i.e., an earliest ontological category symbol, or "ultimate ancestor" category symbol, raised to a variable power of "two to the t", where "t" counts the historical epochs of the progression.
Or, in the case of SYSTEMATIC dialectics, where you are presenting a categorial progression as a theory or explanation of some domain of human experience, the starting category symbol is raised to a variable power "two to the s", where "s" counts the "steps" or "stages" of your presentation.
For example, suppose that you dialectically model the Tables of Contents of the three volumes of Marx's "Capital", as a dialectical categorial progression presentation of a theory of capitalism, using their dialectical algebra.
By presentation-stage s = 4, you will have a power of 2^4 = 16, and a 4-fold "self-reflexion", of the starting category, e.g., of "The Elementary Form of Value" category.
The way that their dialectical algebra works, the "ancestor" category, raised to a power of 2 raised to the power 4 ["2^4"], = 16, will generate a sum of 16 category symbols, which have then to be "interpreted", or "solved" as to their best categorial meaning in the context of the [sub-]totality of human experience to be modeled/explained.
If you take Marx's "elementary form of [commodity] value" as the "ultimate ancestor category", "<<arche'>>-category", or "starting point category", of his treatise, and then raise its symbol to the power 16 -- e.g., e^2^4 = e^16 -- you get a solution for all of the "value-form" categories content of the three volumes.
If you take the category of the "Commodity" overall, not differentiated into its "Elementary", "Extended", and "General" Value-Forms, then, already by t = 3, i.e., with a power of 2^3 = 8 -- i.e., from C^2^3 or just C^8 -- you get a sum of eight categories that summarize the "Value-Form" content of Marx's treatise, but at a more general, less specific, summary level only, relative to what you get if you start from e, and go up to e^16.
If you want to generate the "production" categories as well as the "circulation"/"value-form" categories of Marx's treatise, using their dialectical algebra, then you have to choose as your starting category a deeper category than even e, "the elementary form of [commodity-]value", let alone than just C for the category of the "Commodity-in-General".
So, t = 0 [or s = 0] gives you a 2^0 = 1 category story,
t = 1 [or s = 1] gives you a 2^1 = 2 category story,
t = 2 [or s = 2] gives you a 2^2 = 4 category story,
t = 3 [or s = 3] gives you a 2^3 = 8 category story,
t = 4 [or s = 4] gives you a 2^4 = 16 category story,
and so on.