This blog entry is sourced in the following F.E.D. writings --
http://www.dialectics.info/dialectics/Primer.html
http://www.dialectics.info/dialectics/Primer_files/8_Fract1-1_OCR.pdf
[especially page A-34].
http://www.dialectics.info/dialectics/Briefs.html
http://www.dialectics.info/dialectics/Briefs_files/_Brief2-29JUL2008_OCR.pdf
[especially pages II.-32 through II.-33].
There is a kind of generic "thesis --> anti-thesis --> synthesis" structure to the dialectical progression of the NQ "meta-numbers", or "Natural Dialectors", that base the F.E.D. "First Dialectical Arithmetic", and that also ground its "contra-Boolean algebra for dialectical logic".
[I used above, and will use throughout, colors in spectral order -- red, orange, yellow, green, blue, indigo, violet, ... -- to call attention to the "ordinalities" of dialectical categorial progressions].
However --
1. F.E.D.'s progression-model is more like this:
thesis --> thesis + anti-thesis --> thesis + anti-thesis + synthesis;
2. Their terminology is more general than that of "thesis", "anti-thesis", and "synthesis";
3. F.E.D.'s dialectical interpretations and progressions do not stop with the first triad, but extend to any needed extent [in a "potentially infinite" dialectical progression of categories].
I have put together a Chart, below, that surveys the generic dialectical interpretation of the first eight of these "generic Meta-Numbers", interpreted as "ontological category-qualifiers", or "ontological category symbols" ["categorograms"], to give you a feel for how these "meta-numbers" model dialectics.
This generic interpretation is also illustrated, in that chart, by its specific interpretation for the model of the [table of] contents of Marx's Capital, a model that was presented in this thread in an earlier post, and a model which covers the main "value-forms" of Marx's "circulations-process of capitals" thematics, but which does not yet cover Marx's "productions-process of capitals" thematics.
Background Preliminaries. Per F.E.D., the "dialectors" of their "First Dialectical Arithmetic" can be interpreted so as to model both "Systematic Dialectics" and "Historical Dialectics", though with some differences between the two modes of interpretation.
For "Systematic Dialectics", the successive sub-categories are named "arche'-thesis", or "contra-theses", or [partial or full] "uni-theses".
The word <<arche'>> is an ancient Greek word meaning "beginning", "starting point", "point of departure", "oldest ancestor", "ever-present [deep-past] origin", and the like.
For "Historical Dialectics", the successive sub-categories are, instead, named <<arche'-physis>>, or "meta-physes", or "uni-physes".
The word <<physis>> is an ancient Greek word referring to nature as a "self-growing" process-entity.
Dictionary definitions of <<physis>> generally run like this -- "the principle of growth or change in nature"; "nature as a source of growth or change"; "that which grows, becomes, or develops".
There is a tendency in the ancient Greek language to limit the meaning of <<physis>> to extra-human nature, and to name the "humanized" zones of nature <<anti-physis>>. However, I have observed that, in F.E.D. parlance, <<physis>> refers to the totality of nature, humanit(y)(ies) included.
The F.E.D. researchers, in their "dialectical-algebraic equations", use "categories sums" symbols like --
|-|-|, for generic dialectics;
)-|-(, for Systematic Dialectics, and;
>-|-<, for Historical Dialectics --
[best I can do with the typography available], i.e., to denote "cumula", that is, "mixtures", of the units, or <<monads>>, forming assemblages of units -- <<arithmoi>>-- of ontologically different kinds, that co-exist, without "amalgamating", or converting completely to any one kind, or <<species>>.
For example, not all "pre-nuclear particles", not all "nuclear sub-atomic particles", and not all "atoms" are converted into molecules when, or after, the molecular level of organization first irrupts in a given locus of our cosmos, e.g., in a "molecular cloud" surrounding/forming a "proto-star", and forming the seed of another stellar-planetary system, similar to Earth's solar system.
F.E.D. calls such complete conversion of all predecessor ontology "convolution", and holds that most universes[ of discourse] are not "convolute", but, instead, are <<aufheben>>, or "evolute", conserving earlier ontology outside of, as well as inside of, their most-recently irrupted ontology.
Instead of "convolution", we see, in actuality, they hold, "evolution": some "mass-energy" remains at no higher than the "pre-nuclear" [e.g., "quark"; "gluon"] level of organization, and some at no higher than the "nuclear sub-atomic" [e.g., proton] level of organization, and some at no higher than the "atomic" [e.g., Helium He, Nitrogen N, Oxygen O, etc.] level of organization, while some of it does <<aufheben>> itself from, e.g., the atomic level of organization, to the new, next-higher, more inclusive molecular level of organization [e.g., Water H2O, Methane CH4, diatomic Oxygen O2, etc., etc., etc.].
F.E.D., in its "algebra for dialectical logic", represents such "evolute" self-developments of nature -- i.e., of <<physis>> -- by a qualitatively heterogeneous -- and therefore "unaddable", "non-amalgamative" -- "sum", or "cumulum", of "categorograms", with each "categorogram" representing an "ontological category", or <<arithmos>>, "assemblage" of <<monads>>, or of "units", such as, if we take as given that --
n = "pre-nuclears",
s = "nuclear sub-atomics",
a = "atoms", and
m = "molecules"
-- and noting that we mean, by 3^2, "three squared", and, by 2^(3^2), "two to the power (three squared)", or "two to the 9th power" --
>-|-<3 = <n>^(2^3) = <n>^8 = n + s + ... + a + ... + m.
All of the "categorogram symbols" above are, in turn, "interpretations", or "assignments", of the "generic dialectical meta-numbers" that constitute the "set", or "space", that F.E.D. names NQ:
NQ = { q/1, q/2, q/3, q/4, . . . }.
For example, for the cosmological "cumulum" represented above, F.E.D. assigns ( symbolized by the relation-symbol '[--->' ) specific model qualifiers to generic qualifiers as follows --
n [---> q/1,
s [---> q/2,
a [---> q/4,
m [---> q/8.
The ancient Greek word <<arithmos>> -- often mis-translated into modern English as simply "number", connoting our -- modern -- "law-of-value"-unconsciously-inculcated concept of "purely-quantitative number" -- meant, for the less-law-of-value-permeated <<mentalite'>> of the ancient world, "an assemblage of" -- or "a number of" -- qualitative units, qualitative <<monads>>, or qualitative "holons", all of some "<<speci>>-fic" -- all of some <<species>> -- or all of some "<<gene>>-ric" -- all of some <<genos>> -- "kind": all of some one, determinate ontological category.
The operation that F.E.D. names "self-meta-<<monad>>-ization", or "self-meta-holon-ization", or "self-meta-unit-ization" is, per them, the very heart of dialectical process.
It is the concrete <<aufheben>> process whereby each next, new, successor [meta-]<<arithmos>> is formed by that kind of [self-]action which is the "[self-meta-]unit-ing" of some of the units, <<monads>>, or holons of the immediate-predecessor <<arithmos>>, uniting them into the new, higher [more inclusive] "meta-units" of that new "meta-<<arithmos>>"/meta-population, thus, concurrently (1) <<aufheben>>-determinately-negating, (2) <<aufheben>>-scale-elevating, and (3) <<aufheben>>-subsumedly-conserving those former units, now as the sub-units inside each of the new, [meta-]units of the new [meta-]<<arithmos>> thus [self-]created.
Example: the cosmological [self-]formation of a next, successor <<arithmos>>, or population, of "molecular units", or of "molecules", out of a part of the predecessor <<arithmos>>, or population, of "atomic units", or of "atoms".
If q/a or a connotes this predecessor <<arithmos>> of <<monads>>, then, in the F.E.D. "First Dialectical Algebra", as "interpreted" or "assigned" to model "cosmological self-meta-evolution", q/aa, or m, connotes its successor [meta-]<<arithmos>> of [meta-]<<monads>>.
CHART.
domain....Historical Dialectics: <<arche'-physis>>."meta-physes"."uni-physes"
domain.Systematic Dialectics: <<arche'>>-thesis."contra-theses"."uni-theses"
[ideo-]ontological "categorogram"
[qualifier] first irrupts in
historical-epoch,
t, or in
presentation-
stage,
s.qualifier.<<Das Kapital>> Model."arche'-thesis"."contra-theses"."uni-theses".
0...q/1......C: Commodities..........arche'............................................
1...q/2......q/CC = M: Monies........................1st-contra...................
2...q/3......q/MC: MMCC...............................................1st-full-uni..
"...q/4......q/MM = K: Kapitals.......................2nd-contra..................
3...q/5......q/KC: Commodity-Kapitals............................1st-partial-uni..
"...q/6......q/KM: Money-Kapitals.................................2nd-partial-uni..
"...q/7......q/KMC: COTASC........................................2nd-full-uni.....
"...q/8.......q/KK = E: Pol.-Econ. Democracies..3rd-contra....................
.
.
.
MMCC = Money Mediated Commodities Circulations;
COTASC = Circulations Of The Aggregate Social Capital.
The pattern of <<arche'>>-thesis, contra-theses, and partial and full uni-theses, exhibited in the chart above, continues -- in an expanding, but predictable, fashion [predictable from the logic of the pattern of the first 8 dialectical sub-categorizations] -- for t > 3 and for s > 3.
The Generic "Dyadic Seldon Function" categorial progression Model of Dialectics-in-General -- for both Systematic and Historical Dialectics -- runs as follows:
|-|-|k = [q/1]^(2^k) --
|-|-|0 = [q/1]^(2^0) = [q/1]^1 = [q/1];
|-|-|1 = [q/1]^(2^1) = [q/1]^2 = [q/1] + [q/2];
|-|-|2 = [q/1]^(2^2) = [q/1]^4 = [q/1] + [q/2] + [q/3] + [q/4];
|-|-|3 = [q/1]^(2^3) = [q/1]^8 =
[q/1] + [q/2] + [q/3] + [q/4] + [q/5] + [q/6] + [q/7] + [q/8].
The Specific "Dyadic Seldon Function" categorial progression Model of the "Presentational", "Method of Presentation", or "Order of [Category/Concept] Presentation" Systematic Dialectic of Marx's <<Das Kapital>> [circulation-value-forms only], which Model is a Specific "Interpretation" or "Assignment" of the Generic Model just given above, runs as follows:
)-|-(s = [ C]^(2^s) --
)-|-(0 = [ C]^(2^0) = [ C]^1 = [ C];
)-|-(1 = [ C]^(2^1) = [ C]^2 = [ C] + [ M ];
)-|-(2 = [ C]^(2^2) = [ C]^4 = [ C] + [ M ] + [ q/MC] + [ K ];
)-|-(3 = [ C]^(2^3) = [ C]^8 =
[ C ] + [ M ] + [ q/MC] + [ K ] + [ q/KC ] + [q/KM ] + [ q/KMC ] + [ E ].
Thus, we are stating, via the CHART above, that the "<<speci>>-fic", systematically-ordered, systematically-staged, presentational, critique-of-political-economy "[sub-]categories cumulum" --
)-|-(s=3 = Commodities-in-general + Monies-in-general + MMCC + Kapitals-in-general + Commodity-Kapitals + Money-Kapitals + COTASC
+ Political-Economic-Democracies-in-general
-- is a "<<species>>" instance of, or is a "<<speci>>-fic" instance of, the systematically-ordered, "<<genos>>", or "<<gene>>-ric", "[sub-]categories cumulum" --
|-|-|k=3 = arche'-thesis + 1st-contra-thesis + 1st-full-uni-thesis + 2nd-contra-thesis + 1st-partial-uni-thesis + 2nd-partial-uni-thesis + 2nd-full-uni-thesis
+ 3rd-contra-thesis.
Regards,
Miguel
F.E.D. definitions of special terms utilized in the narrative above --
<<arche'>>
http://point-of-departure.org/Point-Of-Departure/ClarificationsArchive/Arche/Arche.htm
<<arithmos>> [plural: <<arithmoi>>]
http://point-of-departure.org/Point-Of-Departure/ClarificationsArchive/Arithmos/Arithmos.htm
<<aufheben>>
http://point-of-departure.org/Point-Of-Departure/ClarificationsArchive/Aufheben/Aufheben.htm
categories-sums
no definition for this term is available, as yet, in the Clarifications Archive
categorograms
no definition for this term is available, as yet, in the Clarifications Archive
contra-Boolean algebra [of dialectical logic]
no definition for this term is available, as yet, in the Clarifications Archive
convolute, convolution
http://point-of-departure.org/Point-Of-Departure/ClarificationsArchive/Convolute/Convolute.htm
cumulum [plural: cumula]
http://point-of-departure.org/Point-Of-Departure/ClarificationsArchive/Cumulum/Cumulum.htm
dialectical antithesis
no definition for this term is available, as yet, in the Clarifications Archive
dialectical <<arche'>>-<<physis>>
no definition for this term is available, as yet, in the Clarifications Archive
dialectical <<arche'>>-thesis
no definition for this term is available, as yet, in the Clarifications Archive
dialectical algebra
http://point-of-departure.org/Point-Of-Departure/ClarificationsArchive/Mathematics/Mathematics.htm
dialectical arithmetic
http://point-of-departure.org/Point-Of-Departure/ClarificationsArchive/Mathematics/Mathematics.htm
dialectical [categorial] progression
no definition for this term is available, as yet, in the Clarifications Archive
dialectical contra-thesis
no definition for this term is available, as yet, in the Clarifications Archive
dialectical logic
http://point-of-departure.org/Point-Of-Departure/ClarificationsArchive/DialecticalLogics/DialecticalLogics.htm
dialectical meta-numbers
no definition for this term is available, as yet, in the Clarifications Archive
dialectical meta-<<physis>>
http://point-of-departure.org/Point-Of-Departure/ClarificationsArchive/Physis/Physis.htm
dialectical synthesis
no definition for this term is available, as yet, in the Clarifications Archive
dialectical uni-<<physis>>
no definition for this term is available, as yet, in the Clarifications Archive
dialectical uni-thesis
no definition for this term is available, as yet, in the Clarifications Archive
dialectics, <<gene>>-ric
http://point-of-departure.org/Point-Of-Departure/ClarificationsArchive/DialecticsInGeneral/DialecticsInGeneral.htm
dialectics, historical
http://point-of-departure.org/Point-Of-Departure/ClarificationsArchive/HistoricalDialectics/HistoricalDialectics.htm
dialectics, <<speci>>-fic
no definition for this term is available, as yet, in the Clarifications Archive
dialectics, systematic
http://point-of-departure.org/Point-Of-Departure/ClarificationsArchive/SystematicDialectics/SystematicDialectics.htm
dialectors, "Natural"
no definition for this term is available, as yet, in the Clarifications Archive
evolute, evolution
http://point-of-departure.org/Point-Of-Departure/ClarificationsArchive/Evolute/Evolute.htm
<<genos>>, dialectical
http://point-of-departure.org/Point-Of-Departure/ClarificationsArchive/Genos/Genos.htm
holons
no definition for this term is available, as yet, in the Clarifications Archive, but see --
http://point-of-departure.org/Point-Of-Departure/ClarificationsArchive/Monad/Monad.htm
logic
http://point-of-departure.org/Point-Of-Departure/ClarificationsArchive/Logics/Logics.htm
<<mentalite'>>
no definition for this term is available, as yet, in the Clarifications Archive
method of discovery, Marxian
no definition for this term is available, as yet, in the Clarifications Archive
method of presentation, Marxian
no definition for this term is available, as yet, in the Clarifications Archive
<<monads>>
http://point-of-departure.org/Point-Of-Departure/ClarificationsArchive/Monad/Monad.htm
ordinality, qualitative, dialectical
http://point-of-departure.org/Point-Of-Departure/ClarificationsArchive/QualoPeanicity/QualoPeanicity.htm
<<physis>>
http://point-of-departure.org/Point-Of-Departure/ClarificationsArchive/Physis/Physis.htm
potentially infinite; potential infinity [as opposed to "actual infinity"]
no definition for this term is available, as yet, in the Clarifications Archive
qualifiers, ontological category
no definition for this term is available, as yet, in the Clarifications Archive
<<species>>, dialectical
http://point-of-departure.org/Point-Of-Departure/ClarificationsArchive/Species/Species.htm
Seldon Function, Dyadic
http://point-of-departure.org/Point-Of-Departure/ClarificationsArchive/SeldonFunctions/SeldonFunctions.htm
units, purely-qualitative
http://point-of-departure.org/Point-Of-Departure/ClarificationsArchive/Monad/Monad.htm
units, purely-quantitative
no definition for this term is available, as yet, in the Clarifications Archive.
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